hydraulic study of a labyrinth weir integrated in a
TRANSCRIPT
Mathieu Everaert, Andreas Van hulle
Common Meuse
culvert - Application to a spillway in a levee of the
Hydraulic study of a labyrinth weir integrated in a
Academic year 2014-2015
Faculty of Engineering and Architecture
Chairman: Prof. dr. ir. Peter Troch
Department of Civil Engineering
Master of Science in Civil Engineering
Master's dissertation submitted in order to obtain the academic degree of
Laboratorium), Ir. Herman Gielen (nv de Scheepvaart)
Counsellors: Ir. Stéphan Creëlle, dhr. Jeroen Vercruysse (Waterbouwkundig
Supervisor: Prof. dr. ir. Tom De Mulder
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Mathieu Everaert, Andreas Van hulle
Common Meuse
culvert - Application to a spillway in a levee of the
Hydraulic study of a labyrinth weir integrated in a
Academic year 2014-2015
Faculty of Engineering and Architecture
Chairman: Prof. dr. ir. Peter Troch
Department of Civil Engineering
Master of Science in Civil Engineering
Master's dissertation submitted in order to obtain the academic degree of
Laboratorium), Ir. Herman Gielen (nv de Scheepvaart)
Counsellors: Ir. Stéphan Creëlle, dhr. Jeroen Vercruysse (Waterbouwkundig
Supervisor: Prof. dr. ir. Tom De Mulder
Foreword
A master dissertation is our final step before obtaining the degree of Master of Science in Civil
Engineering. During the past five years, we have been formed by Ghent University into the persons we
are today: reaching and striving for higher goals, increasing our mind-set and scientific background,
with this master dissertation as the icing on the cake.
Since we are both passionate about hydraulic engineering, we started this master dissertation full of
good-will and brimming with motivation. Although it was at times very challenging, pushing us to our
limits, we never lost faith in a good termination.
It is the right time to thank some people who significantly contributed to this thesis. We would like to
express our gratitude to prof. dr. ir. Tom De Mulder for his guidance, enthusiasm and corrections. PhD-
student ir. Stéphan Creëlle was always available to answer our questions straight away and to help us
out with our numerous problems. Thank you, Stéphan! Our thanks go out to PhD-student ir. Laurent
Schindfessel as well. Although he was not a supervisor of this dissertation, he could always be bothered
with questions and was always willing to help. Furthermore the technicians of the Hydraulics
laboratory , Stefaan Bliki and Davy Haerens, have contributed significantly to this thesis by constructing
and adapting our scale models for which we thank them.
Finally, we would like to thank some people, who have no direct link to this dissertation. Our parents,
for the opportunities they have given us. Furthermore, Mathieu would like to thank Charlotte Delhoux,
for supporting him whenever necessary.
Andreas & Mathieu
June 2015
Hydraulic study of a labyrinth weir integrated in a culvert - Application to a
spillway in a levee of the Common Meuse
By Mathieu Everaert and Andreas Van hulle
Master�s dissertation submitted in order to obtain the academic degree of Master of Science in Civil
Engineering
Academic year: 2014-2015
Supervisor: prof. dr. ir. Tom De Mulder
Counsellors: ir. Stéphan Creëlle, ir. Herman Gielen, ing. Jeroen Vercruysse
Faculty of Engineering and Architecture, Ghent University
Department of Civil Engineering
Chairman: prof. dr. ir. Peter Troch
Summary
To remove one of the remaining bottlenecks on the Common Meuse, a hydraulic structure needs to
be built in a levee near Heerenlaak. This document is a dissertation on the subject of this hydraulic
structure, consisting of a labyrinth weir integrated in a culvert. A tentative Qh-relation was derived by
Flanders Hydraulic Research during a desktop study. Due to the uncertainties of this study, additional
research is required.
To estimate the stage-discharge relation of the hydraulic structure, experimental measurements have
been performed on a scale model of the proposed design and a variety of other configurations.
Conclusions can be made regarding the different regimes which occur in the stage-discharge relations
by comparing the results of the different configurations. Where possible, theoretical formulas are
compared to the experimental data.
Based on the results obtained from the scale model tests and using the conclusions drawn from a
literature review, an estimation of the discharge capacity of the design is given and recommendations
for possible improvements and additional research are made.
Keywords
Labyrinth weir, culvert, stage-discharge relation, submergence effects, vortex-formation, scale model
1
Hydraulic study of a labyrinth weir integrated in a culvert �
Application to a spillway in a levee of the Common Meuse
Mathieu Everaert and Andreas Van hulle
Supervisor: prof. dr. ir. Tom De Mulder Councellors: ir. S. Creëlle, ing. J. Vercruysse, ir. H. Gielen, dr. ir. N. Van Steenbergen
Abstract
To remove one of the remaining bottlenecks on the Common Meuse in case of large floods, a hydraulic structure needs to be built in a levee near Heerenlaak. The proposed design of this structure, consisting of a labyrinth weir integrated in a culvert, requires additional research.
The main objectives of this research are to determine the stage-discharge relation of the structure and the maximum discharge capacity, and to suggest possible improvements of the design. Based upon the results retrieved from scale model testing this structure, as well as a set of variant hydraulic structures, and the knowledge acquired during a literature survey, recommendations for possible optimizations are given. Finally, an indication of the estimated increase in maximum discharge capacity of an optimized structure is given.
Keywords: labyrinth weir, culvert, stage-discharge relation, submergence effects, scale model
I. INTRODUCTION
To cope with an expected increase in discharge on the Common Meuse, a hydraulic structure needs to be constructed in the levee at Heerenlaak, Belgium. A conceptual design of this hydraulic structure has been made by nv De Scheepvaart and consists of a labyrinth weir integrated in a culvert. The construction will allow to divert part of the high discharges from the Meuse towards Heerenlaak, i.e. a pond with a downstream connection to the Common Meuse. Flanders Hydraulics Research performed a desk-top study to derive the stage-discharge relation of the proposed design. Due to the uncertainties of this tentative stage-discharge relation, it was recommended to carry out a scale model study. This is the topic of this master thesis.
II. HEERENLAAK
The proposed design for the hydraulic structure consists of a labyrinth weir with 2 cycles (further referred to as one unit) integrated in a culvert. A plan view of this design can be seen in Figure 1.
A number of these units should allow the passage of a target discharge of 300 m³/s through the Heerenlaak pond. This will lower the water level immediately downstream of the river bend in which the hydraulic structure is situated.
A. Specifics of the design
The top of the bottom slab is at 23.7 m T.A.W. (T.A.W. is the chart datum in use in Belgium). The height of the labyrinth wall (P) is 3 m, hence the crest of the weir is at 26.7 m T.A.W.. The distance between the crest of the weir and the roof of the culvert is 1 m. The roof of the culvert is supported by 3
(horizontal) beams aligned with the axis of the service road on the levee, i.e. perpendicular to the direction of the flow through the culvert. There are twelve (vertical) columns supporting the beams and the roof of the culvert. These columns and beams imply head losses and a reduction in available crest length of the weir.
The angle of the labyrinth walls with the flow direction is 8°. The total length of the crest is 58.8 m, hence an available area above the weir of 58.8 m². The inlet of the structure consists of two openings with a width of 5 m and height of 3m, thus the total inlet section is 30 m². The outlet section of the structure has an area of 30 m² as well.
Note that on both the upstream and downstream side of the structure, a U-shaped beam, with the soffit at a level of 26.7 m T.A.W. (i.e. the crest level of the weir), is present. This is shown in Figure 2. The purpose of this soffit is to prevent the ingress of floating debris in the Heerenlaak pond. This also implies that in order for water to pass through the structure, it has to dive first under the U-beam, before going up again to overtop the crest of the labyrinth weir. Hence, water only starts flowing over the weir when the water level upstream of the construction reaches the soffit of the U-beam.
Figure 2: Cross-sectional view of the labyrinth weir in a culvert
Figure 1: Plan view of the labyrinth weir in a culvert
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B. Boundary conditions
The up- and downstream water level are major factors influencing the discharge through the structure. They both depend on the discharge through the Meuse. Based on available data, it turns out that the difference between the upstream and downstream water level near Heerenlaak remains more or less constant around a value of 2 m, though it increases somewhat for higher discharges. For the optimization of the structure, several aspects have to be taken into account. The main constraint is that the optimized design should still fit within the body of the existing levee.
III. LABYRINTH WEIR
A. General concept
A labyrinth weir is a linear weir folded in plan view. As such, a longer total crest length is obtained for the same fixed width of a channel. Tullis et al. (1995) adopted the same formula as for a linear weir to calculate the discharge over a labyrinth weir.
where Q is the discharge [m³/s] Cd is the discharge coefficient [-] Lc is the total crest length of the structure [m] g is the gravitational constant [m/s²] HT is the total upstream head [m]
As can be seen from this formula, using a labyrinth weir allows the passage of a higher discharge for the same upstream head or the passage of an equal discharge for a lower head, when compared to a linear weir.
B. Variables
The main variables influencing the discharge relation of a labyrinth weir are the discharge coefficient and the crest length. In several ways, the discharge coefficient may be increased. This can be achieved by rounding the crest shape, decreasing the angle of the walls with the flow direction (although this implies a decrease in crest length), improving the approach flow conditions � However, the influence of many of these
adaptations diminishes for increasing values of HT/P.
C. Filled alveoli
The alveolus is the volume located between the walls of a labyrinth weir.
Filling the alveoli might be an effective way of reducing the construction costs of the structure. These are diminished by reducing the height of the walls, while maintaining the same level of the crest (Ben Saïd and Ouamane, 2011). This implies that hydrostatic forces are only acting on the upper portion of the wall, allowing for a smaller wall thickness and less reinforcement.
The discharge capacity of the structure is not affected by filling a limited volume of the alveolus (Ben Saïd and Ouamane, 2011). For heads HT/P > 2.5 no difference in hydraulic performance occurred for the weir with or without filling of the alveoli (Ouamane, 2013).
Filling the alveoli has the additional advantage of energy dissipation when the apron of the downstream alveoli is
designed as a stair step and may as well facilitate the construction process for the application at Heerenlaak.
IV. CULVERT
A culvert is a short channel or conduit placed through an embankment, dike, dam � Flow phenomena through culverts
are rather complex. Different flow regimes can be discerned based upon the upstream and downstream flow conditions. Only the regimes relevant to this work will be discussed.
Carter (1957) defined 6 types of flow regimes through culverts, 2 defined by inlet control and 4 by outlet control. The main parameter in the definition of these different types, is the submergence of the inlet. According to Carter, the inlet is submerged when the difference between the upstream water level and the culvert invert is smaller than 1.5 times the height/diameter of the inlet. Later on, Chow (1959) stated this to be a range of 1.2 to 1.5 times the height of the culvert. According to Henderson (1966), submergence occurs when the ratio of upstream specific energy to the barrel diameter (or barrel height) is higher than 1.2. The outlet becomes submerged when the tail water is higher than the culvert diameter/height (Carter, 1957).
The first three flow types, defined by Carter (1957), are not representative for the flow through the structure discussed, since the influence of the labyrinth determines the discharge. Type IV, V and VI, on the other hand, might be of interest.
Type IV is characterized by both ends of the culvert being completely submerged and the discharge can then be calculated by:
where Ai is the area of the inlet of the culvert [m²] Cd is the discharge coefficient [-] h1 is the piezo-metric head upstream of the culvert [m] h4 is the piezo-metric head downstream of the culvert [m] n is the roughness coefficient of Manning [s/m1/3]
L is the culvert length [m] R0 is the hydraulic radius of the culvert barrel [m]
Type V occurs when the inlet is submerged and the outlet is not. The culvert barrel flows partly full. The discharge can then be calculated by:
Type VI is similar to type V, except the barrel flows full and with free outfall.
V. TESTING
The scale model study is performed at the Hydraulics Laboratory of Ghent University. Each of the investigated scale models (scale factor 1/18) is installed in a current flume. By varying the downstream water level and increasing the discharge, the Qh-relations of the tested configurations are obtained. The water levels up- and downstream of the scale model are measured using ultrasonic water level sensors.
All data shown in this work correspond to a difference !h in upstream and downstream water level of about 2 m, unless explicitly stated otherwise. Some data in the graphs are
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obtained by interpolating between two measured data points in order to obtain the values corresponding to a !h of 2 m.
As mentioned previously, a number of variant hydraulic structures has been tested. Several abbreviations will be used throughout this work to refer to the different configurations. These abbreviations are explained in Table 1.
Table 1: Explanation of the used abbreviations
Abbreviation Explanation
LW_U_B&C
Labyrinth weir in a culvert with U-beams, internal beams and columns in the
structure. LW_U Labyrinth weir in a culvert with U-beams W_U Weir in a culvert with U-beams
LW_U_C Labyrinth weir in a culvert with U-beams,
Columns in the structure W_noU Weir in a culvert without U-beams
VI. DISCUSSION
A. LW_U_B&C
The obtained results on the scale model of the proposed design (i.e. configuration LW_U_B&C) can be seen in Figure 3.
Figure 3: Measured data and flow regimes for LW_U_B&C
Based on these results, three different flow regimes can be discerned, as indicated in Figure 3. The first flow regime is characterized by free flow over a labyrinth weir. The water flows freely over the labyrinth weir, with almost no influence of the weir being integrated in a culvert. The discharge is not dependent on the downstream water level for this regime.
At an upstream level of 28.0 m T.A.W., the inlet of the structure becomes internally drowned. This corresponds to the theoretical height at which the inlet of a culvert becomes submerged, namely when the headwater is at 1.2 to 1.5 times the height of the inlet (Chow, 1959). This second regime is comparable to Type V flow in a culvert.
A transition to a third regime occurs when the water level immediately downstream of the U-beam is at 26.7 m T.A.W. (i.e. the soffit of the downstream U-beam). For this water level the outlet becomes submerged. During this third regime, the discharge slightly declines to reach a more or less constant value for higher upstream water levels, which is consistent with Type IV flow from the culvert literature. The discharge is now depending on the difference between the water levels upstream and downstream of the construction.
B. Conclusions from other configurations
A wide variety of other configurations (linear weir, labyrinth weir, integrated in a culvert or not) were tested. Several design adaptations were made. This was done to gain insight in the Qh-relation of LW_U_B&C and to search for possible optimizations. The perceived regimes for LW_U_B&C (free flow over a weir, inlet under pressure, in- and outlet under pressure) were discerned for all tested geometries integrated in a culvert.
1) Constraining section for the discharge capacity
A comparison of a labyrinth weir and a linear weir in a
culvert (resp. LW_U and W_U) can be seen in Figure 4. In both configurations the crest is at the same level (i.e. 26.7 m T.A.W.) but W_U has a shorter crest length (11.5 m vs. 63 m) and an overflow area smaller than the inlet section of the structure (28.8 m² vs. 34.6m²).
Figure 4: Comparison between LW_U and W_U
When the overflow section above the crest of the labyrinth or linear weir is smaller than the inlet section, this overflow section of the culvert is the most restraining factor for the discharge capacity of the structure. This explains the lower discharge capacity of W_U. In case of LW_U, the most constraining factor is the inlet section. However, a higher capacity may still be reached by reducing the hydraulic losses in the structure (e.g. by removing the beams and columns supporting the roof of the culvert).
This is confirmed by comparing W_U and W_noU, for which the most constraining factor is the overflow section above the weir crest (Figure 5). These two configurations become submerged at the same moment, although the inlet section of W_noU is larger and has a larger inlet height than W_U.
Figure 5: Comparison between W_noU and W_U
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2) Removal of the beams and columns
The removal of the internal beams and columns, which support the roof of the culvert, reduces the losses and increases the overflow area between the weir crest and the roof. Also the eddies created by the beams, which reduce the capacity, disappear. Removing the beams leads to an increase in discharge of about 12 to 17 %, while the removal of both beams and columns resulted in an increase in discharge of about 15 to 20 % when compared to the LW_U_B&C configuration.
Figure 6: Comparison of LW_U_B&C, LW_U_C and LW_U
3) Removal of the U-shaped beams
Removing the U-beams of the structure causes the inlet of the structure to become drowned at higher water levels and leads to an increase in area of the inlet section. These factors explain the higher capacity of the structure without U-beams. This is illustrated in Figure 7.
Figure 7: Influence of the removal of the U-beams
4) Influence of !h over the structure
The overall head over the structure is about 2 m for most upstream water levels at the Meuse. However, this value may increase to up to 2.5 m for high upstream water levels. Testing has been performed on LW_U_B&C for different heads over the structure. The results are shown in Figure 8.
Figure 8: Results for LW_U_B&C for different !h
As can be seen from this figure, higher differences in up- and downstream water level leads to a higher capacity of the structure.
For the first regime, there is no discernible difference in capacity for different values of !h. As previously mentioned, the discharge during this regime is independent of the downstream water level.
When !h is higher, the second regime is present up to higher upstream water levels. This can be explained by recalling that the transition from the second to the third regime occurs when the outlet is drowned. Thus a higher head over the structure will result in a lower downstream water level for equal upstream water levels. Therefore, the transition occurs at higher water levels, compared to a situation with a lower head. Note that in case !h is 1 m, the second regime cannot be discerned. This is because the inlet and outlet become submerged at the same time (hupstream is 28 m T.A.W., hdownstream is 27 m T.A.W.).
During the third regime, the discharge depends on the water level difference between both sides of the structure. Hence, the higher capacity for higher values of !h.
C. Estimation of the discharge for the proposed design
There are two main reasons to assume that the maximum discharge capacity will be higher than the value of about 100 m³/s for one unit, as was shown in Figure 3.
A first reason is the minor geometrical discrepancy between the proposed design and the tested scale model LW_U_B&C. The discrepancy is caused by slightly smaller dimensions for the inlet section and slightly larger dimensions for the beams and columns, which imply a reduction in available overflow area in the structure. Therefore it is expected that the discharge of the proposed design will be 9 to 11% higher than measured on the scale model configuration LW_U_B&C.
A second reason to assume a higher discharge, in the final regime, is that for higher upstream water levels, the overall head will increase up to 2.5 m. This leads to a higher discharge capacity of the structure, as has been stated before (see Figure 8).
Taking into account these two aspects, it is assumed that a maximum discharge of 120 m³/s per unit can be reached. The influence of both factors leading to a higher discharge is shown in Figure 9.
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Figure 9: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors and a rising difference in
water level
D. Estimation of the discharge for an optimized design
A possible improvement of the proposed design is to integrate the beams supporting the roof in the ceiling of the culvert. By doing so, the hydraulic losses will decrease since there is a larger overflow area above the weir crest and less eddies will occur. Taking into account the aforementioned increase in capacity of 12 to 15% by removing the beams (see Figure 6), and considering that the capacity of the proposed design is more or less 120 m³/s (see Figure 9), a (conservative) value for the discharge capacity of 130 m³/s per unit is obtained for a design with the supporting beams integrated in the roof.
VII. CONCLUSIONS
Based upon the scale model study, three flow regimes have been discerned for the proposed design of the hydraulic structure. The first flow regime corresponds to free overflow over a labyrinth weir. The second regime starts when the upstream water level reaches a value of 28.0 m T.A.W. (i.e. when the inlet is internally drowned). This regime is comparable to the so-called Type V flow through a culvert. When the soffit of the outlet is also submerged (i.e. the water level immediately downstream of the downstream U-beam is at a level of 26.7 m), a third flow regime is perceived. Both inlet and outlet being drowned, this regime is comparable to the so-called Type IV flow through a culvert. During the third regime, however, the discharge capacity slightly decreases to reach a more or less constant value.
A peak discharge of 100 m³/s for one unit is reached at the transition of the second to the third regime. However, due to the minor geometrical discrepancies between the scale model and the proposed design, it is estimated that a discharge of 110 m³/s may be reached for the proposed design for a !h of 2 m
and up to 120 m³/s for !h equal to 2.5 m. These peak discharge values imply that 3 units of the proposed design have to be built in order to reach the target discharge for the structure of 300 m³/s.
Based upon the literature review, several aspects of the hydraulic structure may be improved (crest shape, rounded upstream abutments, rounded U-beams, filled alveoli �).
However, the impact of most of these improvements diminishes for large relative heads HT/P. The use of filled alveoli, however, seems promising since it might facilitate construction, reduce the cost and improve the dissipation of energy when the downstream apron is designed as a stair step.
Taking into account possible optimizations to the proposed design (e.g. integrating the supporting beams into or on top the roof) it is estimated that a peak discharge of 390 m³/s can be reached by constructing three units. This peak discharge is somewhat higher than the structure�s target discharge of 300
m³/s. Hence, it could be worth considering building an optimized structure with 5 labyrinth cycles instead of 6.
REFERENCES.
BEN SAÏD, M. & OUAMANE, A. (2011). Study of optimization of labyrinth weir. pp. 67-74 in: Erpicum, S., Laugier, F., Boillat, J.-L., Pirotton, M., Reverchon, B., & Schleiss, A. J. (Eds.). (2011). Labyrinth and Piano Key Weirs. CRC Press. Leiden: CRC Press/Balkema. CARTER, R.W. (1957). Computation of peak discharge at culverts US Geological Survey Circular, No. 376.
CHOW, V.T. (1959). Open Channel Hydraulics, New York: McGraw-Hill International HENDERSON, F.M. (1966). Open Channel Flow. New York: MacMillan Company OUAMANE, A. (2013). Improvement of Labyrinth Weirs Shape. pp. 15-22 in: Erpicum, S., Laugier, F., Pfister, M., Pirotton, M., Cicero, G. M., & Schleiss, A. J. (Eds.). (2013). Labyrinth and Piano Key Weirs II. CRC Press. Leiden: CRC Press/Balkema. TULLIS, P., AMANIAN, N. & WALDRON, D. (1995). Design of Labyrinth Weir Spillways. Journal of Hydraulic Engineering, ASCE, 121, nr. 3, pp. 247-255
Table of contents
CHAPTER 1: INTRODUCTION........................................................................................................ 1
1. Hydraulic structure at Heerenlaak ........................................................................................................... 1
1.1 Necessity of the structure ..................................................................................................................... 1
1.2 Heerenlaak ............................................................................................................................................. 1
2. Objectives ................................................................................................................................................ 3
CHAPTER 2: DISCUSSION OF THE DESIGN .................................................................................... 5
1. Conceptual design of the labyrinth weir in a culvert ................................................................................ 5
1.1 Bottom slab ........................................................................................................................................... 7
1.2 Inlet and outlet section.......................................................................................................................... 7
1.3 Position of the columns ......................................................................................................................... 7
1.4 Angle ...................................................................................................................................................... 8
2. Boundary conditions ................................................................................................................................ 8
2.1 Analysis of water levels ......................................................................................................................... 8
2.2 Design adaption constraints ................................................................................................................ 14
3. Q-h relation ........................................................................................................................................... 14
3.1 Weir ..................................................................................................................................................... 14
3.2 Inflow under pressure, free outflow.................................................................................................... 15
3.3 In- and outflow under pressure ........................................................................................................... 15
4. Important dimensions and levels ........................................................................................................... 16
CHAPTER 3: LITERATURE REVIEW .............................................................................................. 17
1. Scaling ................................................................................................................................................... 17
1.1 Types of similitude ............................................................................................................................... 17
1.2 Scale effects ......................................................................................................................................... 19
2. Linear Weirs ........................................................................................................................................... 22
3. Labyrinth Weirs ..................................................................................................................................... 23
3.1 General concept .................................................................................................................................. 23
3.2 Variables .............................................................................................................................................. 24
3.2.1 Crest Length Lc ................................................................................................................................. 24
3.2.2 Discharge coefficient Cd................................................................................................................... 25
3.2.3 Sidewall angle α .............................................................................................................................. 25
3.2.4 Cycle efficiency ε’ ............................................................................................................................ 26
3.2.5 Number of cycles N ......................................................................................................................... 27
3.2.6 Shape of the cycles .......................................................................................................................... 28
3.2.7 Headwater ratio HT/P ...................................................................................................................... 29
3.2.8 Vertical aspect ratio W/P ................................................................................................................ 29
3.2.9 Crest shape and wall thickness ....................................................................................................... 30
3.2.10 Ratio Wi/Wo ................................................................................................................................ 31
3.2.11 Labyrinth Weir Orientation, Placement and Cycle Configuration .............................................. 32
3.2.12 Aeration Conditions .................................................................................................................... 37
3.2.13 Filling the alveoli ......................................................................................................................... 38
3.3 Disadvantages ...................................................................................................................................... 40
3.4 Piano Key Weirs ................................................................................................................................... 40
3.5 Submergence effects ........................................................................................................................... 41
3.5.1 Influence of submergence ............................................................................................................... 41
3.5.2 Relationship by Villemonte ............................................................................................................. 42
3.5.3 Local submergence .......................................................................................................................... 43
4. Culverts .................................................................................................................................................. 44
4.1 Introduction ......................................................................................................................................... 44
4.2 Terminology ......................................................................................................................................... 44
4.3 Flow through a culvert ......................................................................................................................... 44
5. Vortices.................................................................................................................................................. 51
5.1 Introduction ......................................................................................................................................... 51
5.2 Formation and causes .......................................................................................................................... 52
5.3 Submergence ....................................................................................................................................... 54
5.4 Scale effects ......................................................................................................................................... 58
5.5 Problems .............................................................................................................................................. 60
5.6 Prevention ........................................................................................................................................... 60
6. Optimisation based on literature review and scale model testing ......................................................... 62
CHAPTER 4: EXPERIMENTAL SET-UP AND TEST PROCEDURE ..................................................... 65
1. Test facilities .......................................................................................................................................... 65
1.1 Current Flume ...................................................................................................................................... 65
1.2 Position of the scale model ................................................................................................................. 67
1.3 Honeycombs ........................................................................................................................................ 68
2. Measuring equipment............................................................................................................................ 69
2.1.1 Ultrasonic water level sensors ........................................................................................................ 69
2.1.2 Electromagnetic current meter ....................................................................................................... 70
2.2 Accuracy of surface measurements..................................................................................................... 71
3. Scale Model ........................................................................................................................................... 71
3.1 Full model ............................................................................................................................................ 71
3.2 Simple model ....................................................................................................................................... 74
3.3 Scaling .................................................................................................................................................. 75
4. Test procedure ....................................................................................................................................... 76
4.1 Stage-discharge relation ...................................................................................................................... 76
4.2 Velocity measurements ....................................................................................................................... 76
4.2.1 Testing procedure I ......................................................................................................................... 76
4.2.2 Testing procedure II ........................................................................................................................ 78
4.3 Visualization of the flow pattern using colouring dye ......................................................................... 78
5. Tested configurations of the Full and Simple models ............................................................................. 78
5.1 F_LWh_U_B&C .................................................................................................................................... 79
5.2 F_LWh_U_C ......................................................................................................................................... 80
5.3 F_LWh_U ............................................................................................................................................. 81
5.4 S_LWh_noCul ....................................................................................................................................... 82
5.5 S_LWh_U ............................................................................................................................................. 83
5.6 S_LWh_noU ......................................................................................................................................... 84
5.7 S_LWh_UMeuse .................................................................................................................................. 84
5.8 S_LWh_U_Raisedroof .......................................................................................................................... 85
5.9 S_Wh_U ............................................................................................................................................... 86
5.10 S_Wh/2_U ........................................................................................................................................... 87
5.11 S_Wh_noU ........................................................................................................................................... 88
5.12 Verification of the scale model dimensions ........................................................................................ 88
5.12.1 Full Model ................................................................................................................................... 88
5.12.2 Simple Model .............................................................................................................................. 88
CHAPTER 5: DATA PROCESSING ................................................................................................. 89
1. Remarks about the discussed data ......................................................................................................... 89
2. Data processing ..................................................................................................................................... 89
3. Accuracy of the results ........................................................................................................................... 92
CHAPTER 6: RESULTS AND DISCUSSION ..................................................................................... 95
1. Introduction ........................................................................................................................................... 95
2. Results ................................................................................................................................................... 96
2.1 S_Wh_U ............................................................................................................................................... 96
2.2 S_Wh_U and S_Wh/2_U .................................................................................................................... 103
2.3 S_Wh_U and S_Wh_noU ................................................................................................................... 106
2.4 S_LWh_noCul ..................................................................................................................................... 107
2.5 S_LWh_noU and S_LWh_noCul ......................................................................................................... 109
2.6 S_LWh_U, S_Wh_U and S_Wh/2_U .................................................................................................. 110
2.7 S_LWh_U and S_LWh_noU ................................................................................................................ 112
2.8 S_LWh_U and F_LWh_U .................................................................................................................... 114
2.9 Influence of the supporting beams and columns .............................................................................. 115
2.10 F_LWh_U_B&C for different Δh......................................................................................................... 117
2.11 Verification of the estimated stage discharge relation by FHR ......................................................... 118
2.12 Dip in the third regime ...................................................................................................................... 122
3. Optimisation ........................................................................................................................................ 123
3.1 Influence of raising the roof (S_LWh_U_Raisedroof) ........................................................................ 123
3.2 Removal of the downstream U-beam ............................................................................................... 124
4. Flow pattern and velocity measurements ............................................................................................ 126
4.1 Flow pattern ...................................................................................................................................... 126
4.2 Velocity measurements ..................................................................................................................... 128
4.2.1 Testing procedure II ...................................................................................................................... 128
4.2.2 Testing procedure I ....................................................................................................................... 131
4.3 Velocities downstream of the structure ............................................................................................ 138
4.4 Critical remarks .................................................................................................................................. 138
5. Quantification of vortices .................................................................................................................... 139
5.1 Presence of vortices .......................................................................................................................... 139
5.2 Critical submergence ......................................................................................................................... 140
5.3 Application to the future hydraulic structure .................................................................................... 144
CHAPTER 7: CONCLUSIONS ..................................................................................................... 147
CHAPTER 8: RECOMMENDATIONS FOR FURTHER RESEARCH .................................................. 150
BIBLIOGRAPHIC REFERENCES .................................................................................................. 151
APPENDIX A: PROPOSED DESIGN OF THE HYDRAULIC STRUCTURE .......................................... 157
APPENDIX B: VALEPORT MODEL 801 ELECTROMAGNETIC FLOW METER ................................ 159
List of figures
Figure 1: Indication of the Heerenlaak-area (adapted from Bing Maps) ................................................ 2
Figure 2: Plan view of the proposed hydraulic structure ........................................................................ 3
Figure 3: Front view of the labyrinth weir in a culvert (Side of the Meuse) ........................................... 5
Figure 4: Plan view of the labyrinth weir in a culvert .............................................................................. 6
Figure 5: Longitudinal section of the labyrinth weir in a culvert ............................................................ 6
Figure 6: Illustration of the labyrinth weir angle ..................................................................................... 8
Figure 7: Water level in the Meuse and the Heerenlaak pond in function of the discharge through the
Meuse near Maaseik (Vercruysse et al., 2013) ....................................................................................... 9
Figure 8: Water level in the Meuse upstream of the labyrinth weir in function of the discharge
through the Meuse near Maaseik (Vercruysse et al., 2013) ................................................................. 10
Figure 9: Water level in the Meuse downstream of the Heerenlaak pond in function of the discharge
through the Meuse near Maaseik (Vercruysse et al., 2013) ................................................................. 11
Figure 10: Water level upstream of the labyrinth weir in function of the discharge through the Meuse
near Maaseik (Vercruysse et al., 2013) ................................................................................................. 12
Figure 11: Over flow height in function of the occurrence in days per year (Vercruysse et al., 2013) 13
Figure 12: Qh-relation as mentioned in the FHR-report (Vercruysse et al., 2013) ............................... 15
Figure 13: Sharp crested weir (Berlamont, s.d.) .................................................................................... 22
Figure 14: A 4-cycle labyrinth weir with an indication of the geometric variables (adapted from Tullis,
Amanian and Waldron, 1995) ............................................................................................................... 24
Figure 15: Cycle efficiency vs. HT/P for half-round labyrinth weirs (Crookston,2010) .......................... 26
Figure 16: Cycle efficiency vs. HT/P for quarter round labyrinth weirs (Crookston,2010) .................... 26
Figure 17: Efficacy ε vs. sidewall angle α for quarter round trapezoidal weirs (Crookston,2010)........ 27
Figure 18: Nappe interference and cycle number for an aerated nappe at low HT/P (Crookston,2010)
............................................................................................................................................................... 28
Figure 19: General classifications of labyrinth weirs: triangular (A), trapezoidal (B) and rectangular (C)
(Crookston,2010) ................................................................................................................................... 29
Figure 20: Crest shapes (Crookston,2010) ............................................................................................ 30
Figure 21: Indication of the variables Wi and Wo (adapted from Ben Saïd and Ouamane,2011) ......... 31
Figure 22: Variation of the discharge coefficient for different ratios of Wi/Wo and Lc-cycle/W =4
(adapted from Ben Saïd and Ouamane,2011) ....................................................................................... 32
Figure 23: Orientations, placements and cycle configurations (Crookston and Tullis,2011) ................ 33
Figure 24: Labyrinth weir with a rounded front wall (left) and a flat wall (right) ( Ouamane, 2013) ... 34
Figure 25: Discharge coefficient according to the entrance shape of a labyrinth weir (adapted from
Ouamane,2013) ..................................................................................................................................... 34
Figure 26: Channel with and without lateral contraction ( Ben Saïd and Ouamane,2011) .................. 34
Figure 27: Variation of the discharge coefficient for a model with and without lateral contraction
(adapted from Ben Saïd and Ouamane,2011) ....................................................................................... 35
Figure 28: Geometry of an arced labyrinth weir (Crookston,2010) ...................................................... 35
Figure 29: Cd vs. HT/P for α =6° half-round trapezoidal labyrinth weir (Crookston, 2010) ................... 36
Figure 30: Cd vs. HT/P for α =12° half-round trapezoidal labyrinth weir (Crookston, 2010) ................. 36
Figure 31: Aeration conditions for a half-round crest (Christensen,2012) ........................................... 37
Figure 32: Filling of the alveoli (adapted from Ben Saïd and Ouamane,2011) ..................................... 39
Figure 33: Rectangular labyrinth weir with a shaped entrance, partially filled alveoli and a stepped
stair in the outlet key (Ouamane, 2013) .............................................................................................. 39
Figure 34: View of a PK weir spillway of the Gloriettes Dam in France during Construction (Électricité
de France) .............................................................................................................................................. 41
Figure 35: Dimensionless relationship describing submerged labyrinth weir performance (Tullis,
Young and Chandler,2006) .................................................................................................................... 43
Figure 36: Illustration of culvert flow, explaining the different parameters (Bodhaine, 1966) ............ 45
Figure 37: Type I flow, according to Carter (1957) ................................................................................ 46
Figure 38: Type II flow, according to Carter (1957) ............................................................................... 47
Figure 39: Type III flow, according to Carter (1957) .............................................................................. 47
Figure 40: Type IV flow, according to Carter (1957) ............................................................................. 48
Figure 41: Type V flow, according to Carter (1957) .............................................................................. 49
Figure 42: Type VI flow, according to Carter (1957) ............................................................................. 49
Figure 43: Directional and structural classification of vortices (Knauss, 1987) .................................... 51
Figure 44: Sources of rotational motion according to Knauss (1987) ................................................... 52
Figure 45: Three fundamental causes of vortex formation according to Durgin and Hecker, 1978..... 52
Figure 46: Free-surface vortex classification according to Alden Research Laboratory (Knauss, 1987)
............................................................................................................................................................... 54
Figure 47: Indication of the different parameters used by Gordon (ASCE, 1995) ................................ 56
Figure 48: Recommended submergence for intakes with proper approach flow conditions (Knauss,
1987) ...................................................................................................................................................... 57
Figure 49: Floating raft (Gulliver and Rindels, 1983) ............................................................................. 61
Figure 50: Submerged raft (Gulliver and Rindels, 1983) ....................................................................... 61
Figure 51: Illustration of the inclined corners between the U-beam and the culvert soffit ................. 64
Figure 52: Current flume used during the experiments ........................................................................ 65
Figure 53: Needle of the gage to measure the discharge ..................................................................... 66
Figure 54: Qh-relation of the calibrated weir ........................................................................................ 66
Figure 55: Stilling tube with hooked gage (left) and the device to adjust the height of the needle
(right) ..................................................................................................................................................... 67
Figure 56: Cogwheel to adjust the height of the downstream weir ..................................................... 67
Figure 57: Honeycombs ......................................................................................................................... 68
Figure 58: Comparison of the water surface on both sides of the honeycombs (right: highly
fluctuating levels at the upstream side; left: calmed down free surface at the downstream side) ..... 69
Figure 59: Ultrasonic distance sensor ................................................................................................... 69
Figure 60: Indication of the position of the ultrasonic water level sensors .......................................... 70
Figure 61: The Valeport model 801 electromagnetic current meter (source:
http://www.valeport.co.uk) .................................................................................................................. 71
Figure 62: Front view (left) and top view (right) of the hydraulic structure in the current flume ........ 72
Figure 63: Front view of the scale model .............................................................................................. 72
Figure 64: Rubber sealing to prevent seepage ...................................................................................... 73
Figure 65: Model before (left) and after (right) completion with a view through the PMMA-ceiling .. 74
Figure 66: Longitudinal cross-section of the Simple model .................................................................. 75
Figure 67: Indication of the removable U-beams.................................................................................. 75
Figure 68: Indication of the transverse locations of the velocity measurements (adapted from
Vercruysse et al., 2013) ......................................................................................................................... 77
Figure 69: Electromagnetic current meter on the metal bar during the measurements ..................... 77
Figure 70: catheter used for the colouring dye experiments ................................................................ 78
Figure 71: F_LWh_U_B&C ..................................................................................................................... 80
Figure 72: Indication of the removal of the supporting beams in F_LWh_U_C .................................... 80
Figure 73: View inside the labyrinth weir without supporting beams .................................................. 81
Figure 74: Indication of the removed parts in F_LWh_U ...................................................................... 81
Figure 75: Indication of the removal of columns and beams by comparing F_LWh_U_B&C (left) with
F_LWh_U (right) .................................................................................................................................... 82
Figure 76: Front view of S_LWh_noCul (upstream) .............................................................................. 82
Figure 77: Top view of S_LWh_noCul .................................................................................................... 83
Figure 78: Longitudinal cross-section of the Simple model (S_LWh_U) ............................................... 83
Figure 79: Front view of S_LWh_U ........................................................................................................ 83
Figure 80: Front view of S_LWh_noU from the side of Heerenlaak (downstream) .............................. 84
Figure 81: Indication of the Simple model with the removed U-beams (S_LWh_noU) ........................ 84
Figure 82: Indication of the removed U-beam in S_LWh_UMeuse ...................................................... 85
Figure 83: View on downstream side of S_LWh_UMeuse with removed U-beam ............................... 85
Figure 84: Front view of S_LWh_U_Raisedroof .................................................................................... 86
Figure 85: Longitudinal cross-section of S_LWh_U_Raisedroof, with indication of the heightened roof
............................................................................................................................................................... 86
Figure 86: Longitudinal cross-section of S_LWh_UMeuse, with a linear weir with a height of 3 m ..... 87
Figure 87: Longitudinal cross-section of S_Wh/2_U, with a linear weir with a height of 1.5 m ........... 87
Figure 88: Front view of S_Wh/2_U with sight on the linear weir at half the height of the inlet ........ 87
Figure 89: Longitudinal cross-section of S_Wh_noU, without U-beams .............................................. 88
Figure 90: difference between one cycle and one unit ......................................................................... 89
Figure 91: An overview of all data measured on F_LWh_U_B&C ......................................................... 90
Figure 92: Measured data points and interpolated values (F_LWh_U_B&C) ....................................... 91
Figure 93: Measured data points with different differences in up/downstream (F_LWh_U_B&C) ..... 92
Figure 94: Comparison of data measured at different dates on the F_LWh_U_B&C ........................... 93
Figure 95: Comparison of S_Wh_U with the theoretical curves for flow over a weir .......................... 99
Figure 96: Theoretical fit of flow through a culvert on S_Wh_U ........................................................ 101
Figure 97: Schematical representation of a drowned outlet .............................................................. 101
Figure 98: Indication of the rising water level between the outlet and the downstream sensor ...... 102
Figure 99: Indication of the different regimes observed in the Qh-relation of S_Wh_U ................... 103
Figure 100: Influence of the overflow section of the weir (S_Wh_U vs. S_Wh/2_U) ......................... 104
Figure 101: Theoretical fit on S_Wh/2_U ............................................................................................ 105
Figure 102: Schematical representation of the drowned inlet ........................................................... 105
Figure 103: Impact of U-beams on Qh-relation (S_Wh_U vs. S_Wh_noU) ......................................... 106
Figure 104: Theoretical curve compared to S_LWh_noCul ................................................................. 108
Figure 105: Submergence effects, red data points are calculated based on measurements, adapted
from Tullis et al. (2005) ....................................................................................................................... 109
Figure 106: S_LWh_noCul vs. S_LWh_noU ........................................................................................ 110
Figure 107: Comparison between S_LWh_U, S_Wh_U and S_Wh/2_U ............................................. 111
Figure 108: Impact of the U-beams on a labyrinth weir in a culvert (S_LWh_U vs. S_LWh_noU) ..... 113
Figure 109: Comparison between S_LWh_U and F_LWh_U ............................................................... 114
Figure 110: Demonstration of the difference in inlet geometry between the full model (left) and the
simple model (right) ............................................................................................................................ 115
Figure 111: Comparison of F_LWh_U_B&C, F_LWh_U_C and F_LWh_U ........................................... 116
Figure 112: Interpolated values for F_LWh_U_B&C for different Δh ................................................. 118
Figure 113: Estimation of the discharge through the proposed hydraulic structure based upon
geometrical errors, in comparison with the estimated Qh-relation proposed by FHR (Vercruysse et al.,
2013) .................................................................................................................................................... 120
Figure 114: Estimation of the discharge through the proposed hydraulic structure based upon
geometrical errors and a rising up/downstream difference , in comparison with the theoretical
estimation made by FHR (Vercruysse et al., 2013) ............................................................................. 121
Figure 115: Indication of the dip in the third regime .......................................................................... 122
Figure 116: Comparison of S_LWh_U and S_LWh_U_Raisedroof ....................................................... 124
Figure 117: Comparison of S_LWh_UMeuse and S_LWh_U ............................................................... 125
Figure 118: Maximal intensity of the injected dye, injection at about 29 m T.A.W. .......................... 127
Figure 119: Maximum intensity of the injected dye, injection at about 28 m T.A.W. ........................ 127
Figure 120: Maximum intensity of the injected dye, injection at about 26 m T.A.W. ........................ 127
Figure 121: Maximum intensity of the injected dye ........................................................................... 127
Figure 122: Indication of the measured data points on the experimentally derived Qh-relation for the
F_LWh_U_B&C-configuration ............................................................................................................. 129
Figure 123: Velocity measurements for data point 1 and data point 2 .............................................. 129
Figure 124: Stationary wave pattern on the side of the Meuse ......................................................... 130
Figure 125: Indication of the measured data points on the experimentally obtained Qh-relation of the
F_LWh_U_B&C-configuration ............................................................................................................. 131
Figure 126: Velocity measurements for data point 3 and a distance of 5 m upstream of the inlet ... 132
Figure 127: Velocity measurements for data point 3 at a distance of 10 m upstream of the inlet .... 132
Figure 128: Velocity measurements for data point 3 in the middle of the flume .............................. 133
Figure 129: Velocity measurements for data point 3 in the middle of the inlet section of a single cycle
............................................................................................................................................................. 133
Figure 130: Velocity measurements for data point 3 at the side of the flume ................................... 134
Figure 131: Indication of the gap between the side of the honeycombs and the wall of the flume .. 135
Figure 132: Velocity measurements for data point 4 at the middle of the inlet section .................... 135
Figure 133: Comparison of the velocity measurements for Q = 98.7 m³/s and Q = 95.15 m³/s at the
middle of the inlet section .................................................................................................................. 136
Figure 134: Conceptual drawing indicating the contraction of the velocity profiles for data point 3 137
Figure 135: Conceptual drawing indicating the contraction of the velocity profiles data point 4 ..... 138
Figure 136: Example of a full air core vortex at a discharge of 91 m³/s and an upstream water level of
28.24 m T.A.W. .................................................................................................................................... 139
Figure 137: Graphic representation of the measured submergence, compared to the calculated
critical submergences .......................................................................................................................... 142
Figure 138: Stimulation of vorticity caused by the geometry of the structure front, top view of
F_LWh_U_B&C .................................................................................................................................... 143
Figure 139: The front of S_LWh_U ...................................................................................................... 144
Figure 140: Cross-section of the hydraulic structure inside the body of the dike .............................. 145
Figure 141: Examples of the tentative trashtests ............................................................................... 145
List of tables
Table 1: Over flow heights with corresponding water level, discharge and occurrence (Vercruysse et
al., 2013) ................................................................................................................................................ 13
Table 2: Discharge through the Meuse near Maaseik in function of the water level in the Heerenlaak
pond (Vercruysse et al., 2013)............................................................................................................... 14
Table 3: Overview of important dimensions and T.A.W.-levels ............................................................ 16
Table 4: Limiting criteria to avoid significant scale effects in various hydraulic flow phenomena
(Heller, 2011) ......................................................................................................................................... 21
Table 5: Summary of the different flow types and characteristics according to Carter (1957) ............ 45
Table 6: Explanation of the used abbreviations .................................................................................... 79
Table 7: Used abbreviations and a description of the corresponding configuration ............................ 95
Table 8: Calculation of the Cd-coefficient based on S_Wh_noU ........................................................... 97
Table 9: Calculation of the Cd-coefficient based on S_Wh/2_U ............................................................ 97
Table 10: Calculation of the Cd-coefficient based on S_Wh_U ............................................................. 97
Table 11: Comparison between the experimentally and theoretically derived Cd-coefficients ........... 98
Table 12: Calculation of the Cd-coefficient .......................................................................................... 100
Table 13: Available area above the weir for different configurations ................................................ 116
Table 14: The measured data points, corresponding to the peak discharge and discharge at the dip
............................................................................................................................................................. 128
Table 15: Discharge and corresponding hupstream and Δh for which velocity measurements have been
executed .............................................................................................................................................. 131
Table 16: Critical submergence ........................................................................................................... 141
List of symbols
Symbol Description / Explanation Unit
A Inner apex width [m]
A3 Area of section of flow at the outlet [m²]
AC Flow area at the control section [m²]
Ai Cross-sectional area of the culvert inlet [m²]
am Acceleration in model scale [m/s²]
ap Acceleration in prototype scale [m/s²]
Bi Inlet cycle cantilever length [m]
Bo Outlet cycle cantilever length [m]
bs Distance of the side wall to the centre of intake in the formula of
Gürbüzdal [m]
Cd Discharge coefficient [-]
ck Circulation constant in Knauss's formula [1/s]
Cw Discharge coefficient per unit width of the labyrinth weir [-]
D Outer apex width [m]
dc Maximum depth of water in the critical-flow section [m]
Di Diameter or characteristic dimension of the intake [m]
e Distance from the bottom of the channel to the intake invert [m]
Fm Forces in model scale [N]
Fp Forces in prototype scale [N]
Fr Froude number [-]
g Gravitational constant [m/s²]
h Water depth [m]
H0 Total upstream head for a specific discharge under free flow conditions [m]
h1 Piezo-metric water level at in front of the culvert [m]
h3 Piezo-metric water level at outlet of the culvert [m]
h4 Piezo-metric water level downstream of the culvert [m]
Hd Downstream head [m]
hd Piezo-metric head downstream [m]
he Head loss due to contraction at the inlet [m]
hf1-2 Head loss due to friction between the approach section and the inlet [m]
hf2-3 Head loss due to friction in the culvert barrel [m]
hi Depth of water above centreline of intake at face of intake [m]
hnj Difference in upstream water level between data point n and data point j [m]
hR Effective head in the Rehbock formula of flow over a linear weir [m]
HT Total upstream head measured relative to the weir crest [m]
j Data point j [-]
k Constant representing the gradient of the linear relationship in Knauss's
formula [-]
L Length of the culvert [m]
L1 Actual length of the side leg [m]
L2 Effective length of the side leg [m]
Lc Crest length [m]
Lc-cycle Centre line length for a single labyrinth weir cycle [m]
Le Effective weir length, as defined by Tullis et al. (1995) [m]
Lm Length or dimensional denotation corresponding to the model [m]
Lp Length or dimensional denotation corresponding to the prototype [m]
m Total number of data points [-]
n Data point n [-]
n Roughness coefficient of Manning [s/m1/3]
N Number of labyrinth cycles [-]
Nc Swirl number [-]
P Height of the wall of the weir [m]
Q Discharge [m³/s]
Qf Free flow discharge related with a driving head HT [m³/s]
Qi Discharge of intake [m³/s]
Qj Measured discharge corresponding to data point j [-]
Qn, Measured discharge corresponding to data point n [-]
Qn, theoretical Theoretical, smoothened discharge corresponding to data point n [-]
Qs Submerged discharge related with a driving head HT [m³/s]
Qsw Specific discharge [m³/s/m
]
r Radius of the vortex [m]
R Hydraulic radius of the culvert barrel [m]
Rcrest Weir crest radius [m]
Re Reynolds number [-]
S Submergence factor (Hd/HT) [-]
Sc Submergence above the top of the intake [m]
Si Slope of the inlet cycle [-]
So Slope of the outlet cycle [-]
tm Time in model scale [s]
tp Time in prototype scale [s]
tw Wall thickness at the crest [m]
V1 Mean velocity in the approach section [m/s]
V3 Velocity at the outlet of the culvert [m/s]
V∞ Uniform approach flow velocity [m/s]
Va Approach speed [m/s]
Vi Average velocity through the inlet [m/s]
Vm Velocity in model scale [m/s]
Vp Velocity in prototype scale [m/s]
Vt Tangential velocity of approach flow [m/s]
W Width of one cycle [m]
WC Width of the approach channel [m]
We Weber number [-]
Wi Width of the inlet [m]
wnj Weigh factor for data point j to calculate the theoretical discharge for
data point n [-]
Wo Width of the outlet [m]
WT Width of the labyrinth weir [m]
z Height of the culvert inlet [m]
zi Submergence depth at intake [m]
α Sidewall angle [°]
α 1 Velocity-head coefficient at the approach section [m]
α a Scale factor with regard to acceleration [-]
α F Scale factor with regard to forces [-]
α L Scale factor with regard to length or in general a value of dimension [-]
α t Scale factor with regard to time [-]
α v Scale factor with regard to velocity [-]
β Approach flow angle [°]
ε Cycle efficacy [-]
ε' Cycle efficiency [-]
εmean Mean error on the measurements [-]
εn Relative error corresponding to data point n [-]
ν Kinematic viscosity [m²/s]
νm Kinematic viscosity in model scale [m²/s]
νp Kinematic viscosity in prototype scale [m²/s]
ρ Density [kg/m³]
σ Surface tension [N/m]
Abbreviations
Abbreviation Explanation
B&C The beams and columns in the internal structure are present.
C The columns supporting the roof are present in the internal structure. The
beams supporting the roof are not present.
F Full model
LWh Labyrinth weir with a wall height of 3 m
noCul The structure is not integrated in a culvert.
noU There are no U-beams.
Raisedroof In comparison to the other configurations, the roof is raised by 1 m. The height
of the U-beam changes from 1 m to 2 m.
S Simple model
U There are U-beams on both sides of the structure.
UMeuse There is a U-beam on the side of the Common Meuse. There is no U-beam on
the side of the Heerenlaak pond.
Wh Linear weir with a wall height of 3 m
Wh/2 Linear weir with a wall height of 1.5 m
1
Chapter 1: Introduction
The subject of this master dissertation is the hydraulic study of a labyrinth weir integrated in a culvert.
This dissertation is situated within the context of removing the remaining bottlenecks on the Common
Meuse, more specifically at Heerenlaak, Belgium. To attain this, a hydraulic structure has been
designed by nv De Scheepvaart. This hydraulic structure features a labyrinth weir integrated in a
culvert.
The necessity of the hydraulic structure will be explained and a brief overview of the specifics of the
design of the labyrinth weir in a culvert will be given, followed by the objectives of this master
dissertation.
1. Hydraulic structure at Heerenlaak
1.1 Necessity of the structure
The Common Meuse is a part of the river Meuse situated on the border between Belgium and the
Netherlands under the supervision of nv De Scheepvaart. Nv De Scheepvaart is an autonomous, public
agency responsible for the maintenance, operation, management and commercialization of the Albert
Canal, the Campine Canals, the Scheldt-Rhine River connection and the Common Meuse.
Nowadays the dikes and structures on the Common Meuse are designed for a discharge up to 3000
m³/s. The discharge is expected to increase to more than 4000 m³/s in the future. To cope with this
increased discharge, measures have to be taken. One of these measures concerns the area of
Heerenlaak, which is discussed below.
1.2 Heerenlaak
Heerenlaak is a recreational pond, situated between two consecutive bends of the Common Meuse
(see Figure 1). Heerenlaak is also the subject of a project concerning the removal of the bottlenecks on
the Common Meuse. This project consists of two modifications, among which the construction of a
hydraulic structure, which is the subject of this dissertation.
The first modification to the current situation is the relocation of the downstream connection between
the Heerenlaak area and the Common Meuse. The reason for this relocation is to avoid unwanted
sedimentation which takes place nowadays, since the current connection is located between two river
2
bends. By relocating the connection, the outflow will be directed more parallel to the Meuse, instead
of rather perpendicular to it. The repositioning of the connection is shown in Figure 1.
Figure 1: Indication of the Heerenlaak-area (adapted from Bing Maps)
The second modification, situated more upstream, is the construction of a structure which allows the
entrance of water from the Common Meuse to the Heerenlaak area. Through the hydraulic structure,
a flow of approximately 300 m³/s should be discharged from the Meuse into the Heerenlaak area and
from the Heerenlaak pond through the relocated connection back into the Meuse. This should result
in a lower discharge through the Common Meuse near the bend and therefore a lower water level.
The conceptual design of the hydraulic structure has been made by ir. H. Gielen (nv De Scheepvaart).
A plan view of the structure is shown in Figure 2. The design features a labyrinth weir integrated in a
culvert. A labyrinth weir can be seen as a linear weir folded in plan-view. By doing so, a higher discharge
can be dealt with for the same upstream water level or the same discharge for a lower upstream water
level, in comparison to a linear weir.
Further details of the proposed design can be found throughout this report or in Appendix A.
Heerenlaak
Position of the current
connection
Position of the relocated
connection
Position of the future hydraulic
structure
3
Figure 2: Plan view of the proposed hydraulic structure
2. Objectives
The main objective of this dissertation, is to verify by means of a scale model study how much discharge
can pass through the hydraulic structure proposed by ir. H. Gielen. This knowledge will allow nv De
Scheepvaart to make a well substantiated estimation of the required number of labyrinth weir cycles
in the hydraulic structure, in order to safeguard the Common Meuse and its river banks.
Besides the assessment of the maximal discharge, other objectives are pursued as well:
(1) Gain in-depth knowledge about labyrinth weirs, culverts and labyrinth weirs integrated in
culverts through a literature review.
(2) Verify the stage-discharge or Q-h-relation for the future hydraulic structure deduced from a
desk-top study by FHR (Flanders Hydraulic Research; Vercruysse et al., 2013). This verification
is done by performing a scale model study of the proposed design.
Axis of the road
Meuse
Heerenlaak
4
(3) Make a comparative scale model study of the performance of the proposed design with a
variety of other hydraulic structures in order to acquire insight into the stage-discharge
relation of the proposed design.
(4) Compare the abovementioned experimentally obtained results with theoretical formulas from
literature and try to explain the correspondence and differences between those.
(5) Try to optimize the geometry of the proposed design were possible and formulate
recommendations for further research.
5
Chapter 2: Discussion of the design
This chapter will elaborate on the specifics (dimensions and T.A.W.-levels1) of the proposed design.
How the relevant dimensions and levels have been obtained will be explained and the boundary
conditions of Heerenlaak will be discussed as well. The aim of this chapter is to increase the insight of
the reader in the future hydraulic structure and the Heerenlaak area. The theoretical regimes, which
have been discerned in the FHR report concerning the labyrinth weir in a culvert, are given as well. To
conclude, a table with an overview of important dimensions and T.A.W.-levels is given.
1. Conceptual design of the labyrinth weir in a culvert
As can be seen from Figure 3 and Figure 4, the proposed design consists of a labyrinth weir integrated
into a culvert. In the figures two cycles of a labyrinth weir are shown, but to reach the required flow
rate of 300 m³/s, more cycles may be needed. One can argue whether the cycles are triangular or
trapezoidal in plan shape, since the columns supporting the culvert roof have a certain width.
Figure 3: Front view of the labyrinth weir in a culvert (Side of the Meuse)
1 T.A.W. is the chart datum used in Belgium. It roughly corresponds to an average low water level at Ostend (situated along the Belgian North Sea shore).
6
Figure 4: Plan view of the labyrinth weir in a culvert
Figure 5: Longitudinal section of the labyrinth weir in a culvert
Axis of the road
Meuse
Heerenlaak
1 cycle
Meuse
Sheetpiles Spillway
Heerenlaak pond
7
1.1 Bottom slab
The bottom slab has a length of 22 m and a width of 16 m. The lowest point of the labyrinth weir will
be constructed at a height of 23.2 m T.A.W., which corresponds to a discharge of 10 m³/s in the river
Meuse at Maaseik, in order to avoid the need for drainage during the construction of the structure.
The thickness of the floor slab is 0.5 m. Since the walls of the weir have a height of 3 m, the crest of
the weir is at a level of 26.7 m T.A.W..
1.2 Inlet and outlet section
The inlet section at the side of the Common Meuse consists out of two rectangular openings, each
having a width of 5 m and a height of 3 m, making the total area of the inlet section 30 m².
Once the water has flown through the inlet section, it has to pass over the crest of the labyrinth weir.
The flow area above the crest of one cycle consists out of 2 rectangles having a length of 14.7 m and a
height of 1 m. Thus the available flow area above the crest of one cycle is 29.4 m² or almost double
the inlet section of one cycle. As a result, the velocities in the flow area above the labyrinth weir are
about half of the velocities in the inlet section.
The soffit of the inlet section and the crest of the labyrinth weir are at equal elevation (26.7 m T.A.W.).
This implies that, in order to pass through the structure, the water has to flow first under the soffit of
the inlet, which consists of a U-shaped beam, and then over the crest of the labyrinth weir. The purpose
of this is to prevent the ingress of floating debris from the Meuse into the Heerenlaak pond.
The outlet section consists out of 3 openings. One central opening, having a width of 5 m and a height
of 3 m and two openings on the side of the structure, each having a width of 2.5 m and a height of 3
m. Thus the area of the in- and outlet section is equal.
1.3 Position of the columns
The columns in the design, meant to support the roof of the culvert, have a square cross section with
the length of one side chosen equal to 0.4 m. They support three horizontal beams, having a square
cross section with a side of 0.4 m, placed perpendicular to the direction of flow. The position of the
columns is chosen in such a way that they are symmetrical with respect to the axis of the service road
on top of the dike. Their main purpose is to provide support for the service road on top of the hydraulic
structure. The twelve columns are indicated with blue circles in Figure 4.
8
A second aspect which has been taken into account for the positioning of the columns is the length of
the walls between each column. This distance should be limited to make sure that the heavy and long
prefabricated panels can still be transported by trucks towards the construction site. For the proposed
design this distance is maximum 5.2 m.
The columns are believed to act as breakers providing aeration of the nappe falling over the crest of
the weir.
1.4 Angle
The angle of the labyrinth walls with the longitudinal axis of the structure is 8°. This is illustrated in
Figure 6.
Figure 6: Illustration of the labyrinth weir angle
2. Boundary conditions
2.1 Analysis of water levels
The water level upstream of the labyrinth weir is one of the major factors influencing the discharge
through the structure. This upstream water level depends on the discharge flowing through the Meuse
upstream of the Heerenlaak area.
8 °
9
The water level downstream of the hydraulic structure can also have an impact when it exceeds the
level of the crest of the weir (i.e. 26.7 m T.A.W.) and is discussed further on. This downstream water
level equals the water level in the Heerenlaak pond.
The Hydrological Information Centre (HIC, a subdivision of Flanders Hydraulics Research, Antwerp,
Belgium) collects data on water levels of the navigable rivers. Based on these data and on a study
carried out by Arcadis, a brief analysis of the water levels upstream and downstream of the Heerenlaak
area is given in Vercruysse et al. (2013).
Figure 7: Water level in the Meuse and the Heerenlaak pond in function of the discharge
through the Meuse near Maaseik (Vercruysse et al., 2013)
Figure 7 consists of data compiled by the HIC during the period from 10/01/2008 to 01/07/2013 and it
shows the water level in the Meuse (at km 52.7), the water level in the Heerenlaak pond (in the centre
of the pond) and the difference between these two water levels.
From Figure 7 it follows that the difference between the water level upstream and downstream of the
(future) labyrinth weir remains more or less constant around a value of about 2 m, though it increases
somewhat for higher discharges. This will influence the discharge through the structure and is one of
the most important boundary conditions.
Water level Meuse
Water level Heerenlaak
Dif
fere
nce
up
/do
wn
stre
am
wa
ter
lev
el
[m]
Wa
ter
lev
el
[m
TA
W]
Discharge through the Meuse [m³/s]
Difference
10
Note that (for a given discharge through the Meuse) the scatter of the water level in the Meuse is less
than for the water level in the Heerenlaak pond. This is caused by the damping capacity of the pond of
100 ha which has to be filled or emptied every time the water level in the Meuse rises or lowers. The
maximum water level measured in Maaseik during this period is 31.2 m T.A.W..
Figure 8: Water level in the Meuse upstream of the labyrinth weir in function of the discharge
through the Meuse near Maaseik (Vercruysse et al., 2013)
The graph shown in Figure 8 is based on a study of Arcadis. Arcadis made a numerical modelling
analysis studying the impact of different modifications on the water level in the Common Meuse. The
graph shows the water level in the Meuse, upstream of the (future) hydraulic structure, as a function
of the discharge through the Meuse near Maaseik. The different curves represent:
- HIC 2008-2012: The water level in function of the discharge in Maaseik based on the data of
the HIC
- Arcadis – HS: The current situation based on the study of Arcadis
- Arcadis – AO: The current situation with autonomous development
- Arcadis – VKA_HS: The preferential situation: the water level with the labyrinth weir in a
culvert and relocated connection, based on the current situation
Wa
ter
lev
el
[m T
AW
]
Discharge through the Meuse [m³/s]
11
- Arcadis – VKA_AO: The preferential situation: the water level with the labyrinth weir in a
culvert and relocated connection, with autonomous development
The same graph has been made for the water level near the relocated connection of the Heerenlaak
area and the downstream part of the Common Meuse.
Figure 9: Water level in the Meuse downstream of the Heerenlaak pond in function of
the discharge through the Meuse near Maaseik (Vercruysse et al., 2013)
From Figure 8 and Figure 9 it can be concluded that the preferential situation, with the labyrinth weir
in place and the relocated connection, leads to lower water levels upstream of the weir and
downstream of the pond. However, the differences with the current situation are limited. Based upon
the relation between the water level in the Meuse near Maaseik ( km 52.7) and upstream of the
labyrinth weir (km 53.0), the data near Maaseik is converted into water levels upstream of the weir.
These are shown in Figure 10. Note that the difference of the water level just upstream of the weir and
the water level near Maaseik (km 52.7) is very limited with a maximal difference of 0.09 m.
Wa
ter
lev
el
[m T
AW
]
Discharge through the Meuse [m³/s]
12
Figure 10: Water level upstream of the labyrinth weir in function of the discharge
through the Meuse near Maaseik (Vercruysse et al., 2013)
Compiling the data from these graphs (HIC-data), the overflow height with reference to the crest height
of the weir (+ 26.7 m T.A.W.) can be found in function of the number of days. This is shown in Figure
11 and Table 1. From the graph and the table, it can be concluded that the labyrinth weir will work
during 19.2 days per year (water level higher than 26.7 m T.A.W.). During 63% of these 19.2 days (12.1
days), the water remains under the level of the ceiling of the weir (27.7 m T.A.W.). During 7.2 days, the
water level is higher than the level of the ceiling.
Discharge through the Meuse [m³/s]
Wa
ter
lev
el
[m T
AW
]
13
Figure 11: Over flow height in function of the occurrence in days per year (Vercruysse et al., 2013)
Table 1: Over flow heights with corresponding water level, discharge and occurrence (Vercruysse et al., 2013)
Over flow height [m] Water level [m TAW] Discharge [m³/s] Occurrence [days/year]
0.0-0.5 26.7 - 27.2 735 - 869 7.1
0.5-1.0 27.2 - 27.7 869 - 1012 5
1.0-1.5 27.7 - 28.2 1012 - 1167 2.6
1.5-2.0 28.2 - 28.7 1167 - 1310 1.9
2.0-2.5 28.7 - 29.2 1310 - 1470 0.8
2.5-3.0 29.2 - 29.7 1470 - 1660 0.9
3.0-3.5 29.7 - 30.2 1660 - 1850 0.4
3.5-4.0 30.2 - 30.7 1850 - 2040 0.2
4.0-4.3 30.7 - 31.0 2040 - 2180 0.4
The discharges corresponding to a water level of the Heerenlaak pond equal to the crest height and
the ceiling of the labyrinth weir in a culvert are given in Table 2. A minimal and maximal discharge are
given because of the water storage capacity of the pond which causes a certain lag when comparing
the water level of the Meuse and the Heerenlaak pond. Construction of the labyrinth weir will reduce
this lag, making the minimal discharges more representative.
Occ
urr
en
ce [
da
ys/
ye
ar
]
Over flow height [m]
14
Table 2: Discharge through the Meuse near Maaseik in function of the water level in the Heerenlaak pond (Vercruysse et al., 2013)
Height of water level in the Heerenlaak
pond
Minimal discharge
[m³/s]
Maximal discharge
[m³/s]
Crest height: 26.70 m TAW 1170 1400
Ceiling level: 27.70 m TAW 1610 1770
2.2 Design adaption constraints
Several requirements which have to be taken into account while making changes to the original design
are listed below.
- The length and width of the foundation slab may vary, as long as the structure still fits within
the body of the dike. The same is applicable to the height of the structure. Thus a structure
with a shorter length can have a larger opening above the wall, since it will still fit within the
boundaries of the dike.
- As mentioned before, the position of the columns has to be chosen in such a way that the
forces from the road above may be dealt with in a safe way.
- The length of the prefabricated panels has to stay limited, in order to avoid the need for special
transport.
3. Q-h relation
The discharge through the construction depends on the upstream- and downstream water levels.
Considering these levels, three different situations are being discerned in the FHR-report concerning
the hydraulic structure at Heerenlaak (Vercruysse et al., 2013). These different regimes are:
- free flow over a weir
- inflow under pressure, free outflow
- in- and outflow under pressure
The formulas and their theoretical background will not be repeated here. The reader is being referred
to Vercruysse et al., 2013.
3.1 Weir
When the water level in the construction stays below the level of the top plate (i.e. the ceiling of the
culvert), the construction will act as a weir.
15
3.2 Inflow under pressure, free outflow
This situation occurs when the piezometric head in the construction is higher than the level of the
ceiling (which implies that the inflow is under pressure; this occurs at a water level of 28.0 m T.A.W.)
but the downstream level in the area of Heerenlaak is still below the crest height of the spillway.
3.3 In- and outflow under pressure
This situation occurs when, compared to the situation described in 3.2, the downstream water level
rises above the crest of the spillway (i.e. at 26.7 m T.A.W.).
Figure 12: Qh-relation as mentioned in the FHR-report (Vercruysse et al., 2013)
0
20
40
60
80
100
120
140
160
180
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
h upstream [ m T.A.W.]
Based upon simulations of submerged in- and outlet
Weir regime
Submerged inlet
Submerged inlet and outlet
16
4. Important dimensions and levels
An overview of some important dimensions and T.A.W.-levels is given in Table 3.
Table 3: Overview of important dimensions and T.A.W.-levels
Floor of the culvert 23.7 m T.A.W.
Invert of the U-beam 26.7 m T.A.W.
Crest of the weir 26.7 m T.A.W.
Ceiling of the culvert 27.7 m T.A.W.
Area of culvert inlet section 30 m²
Area of culvert outlet section 30 m²
Crest length of labyrinth weir 58.8 m
Available area above the crest 58.8 m²
17
Chapter 3: Literature Review
To get a full understanding of the proposed design for the hydraulic structure and the parameters
which may impact the flow through the structure, a thorough literature review is performed. This
literature review focusses on the main aspects deemed useful such as scaling, the hydraulic
characteristics of labyrinth weirs and flow through culverts. The behaviour of weirs under submerged
conditions and the presence of vortices and their effect on the discharge capacity are briefly discussed
as well.
1. Scaling
The behaviour of labyrinth weirs is influenced by many variables, which makes it very difficult to make
an accurate prediction of the discharge capacity of a proposed design. This explains why for many
projects a scale model is tested in a laboratory preceding the start of the construction process. The
theory of similitude permits to scale the characteristics of flow from prototype to model.
1.1 Types of similitude
There exist three types of similitude, namely geometric similitude, kinematic and dynamic similitude.
Geometric similitude implies that the length ratios of the prototype and the model are equal. Also the
different angles in the model are equal to those of the prototype. A such, the model has the same
shape as the prototype, while the dimensions are scaled proportionally.
With
is a scale factor with regard to length or in general a value of dimension (subscript ‘L’) [-]
L is the length or a dimensional denotation, where subscript ‘m’ and ‘p’ stand for model and
prototype respectively [m]
When 2 models are kinematically similar, the ratio of the prototype and model velocities is equal.
Consequently, the time ratio and length ratio are equal:
and
18
Hence,
and
In other words, the flow conditions should be the same. Dynamic similitude indicates similitude of
forces. The ratio of forces at similar locations of the model and prototype should be a constant value
in dynamically similar systems. The following scale factors will determine a dynamically similar scale
model:
The forces acting on a hydraulic structure or scale model can be generated by pressure, gravity,
viscosity or surface tension. Giving the variety of these forces, perfect dynamic similitude is not
possible, for example because of the viscosity of the fluids. Therefore the dynamic similitude of the
dominant forces must be ensured. This is done by scaling based upon the laws of similarity (or
dimensionless numbers).
The most important dimensionless numbers regarding free-surface flow and applied to the structure
at Heerenlaak are the Froude number, the Reynolds number and the Weber number.
The Froude number is defined as the ratio of inertia forces to the gravitational forces:
Where
is the Froude number [-]
V is the velocity [m/s]
g is the gravitational acceleration, i.e. 9.81 m/s²
L is the characteristic length [m]
19
The law of Froude is most often used in systems with free-surface flow, when gravity is the
most dominant force. Scaling according to Froude’s law is done as follows:
à à
The Reynolds number is defined as the ratio of inertial forces to the viscous forces:
Where,
is the Reynolds number [-]
is the kinematic viscosity of the fluid [m²/s]
Reynolds law is most often used for flow under pressure or where the viscosity of the fluid has
a non-negligible influence. When scaling is done with respect to Reynolds law, the velocity can
be found:
à à
The Weber number is defined as the ratio between surface tension and velocity.
Where,
is the Weber number [-]
is the density of the fluid [kg/m³]
is the surface tension [N/m]
Weber’s law is to be applied when the surface tension is a significant factor in the hydraulic
process, which occurs when a water-air interface is present (e.g. vortices). However, in open
channel flow this is rarely the case (except for capillary waves).
1.2 Scale effects
In order to have similitude between two systems with a free surface, the Reynolds number and the
Froude number should be equal in both systems. Because the ratios of the viscosities and the densities
20
of the fluids in the two systems are usually equal to 1, it is impossible to have a model that is perfectly
dynamically similar. These ratios are usually 1 because the fluids are the same in the prototype as well
as in the model, namely water. Therefore, the most dominant mechanism is modelled, implying the
gravity effects of the free surface flow (Froude), while the Reynolds number will differ.
When the dimensionless parameters between the model and the prototype are not equal, the
performance of the scale model might be different than that of the prototype leading to discrepancies
in the results. These deviations are known as scale effects (Webber, 1979). Scale effects can be
negligible, depending on the relative values of the differing dimensionless numbers. However, thought
should be given to these distortions to keep them negligible.
Avoidance of significant scale effects is usually done by use of limiting criteria (Heller, 2011). These
criteria define a range of force ratios which a scale model must satisfy, so that the effects of scaling
are negligible with respect to the parameter or phenomenon being researched. In the same manner,
limiting scale size criteria can be applied to avoid significant scale effects. These limiting criteria and
limiting scale size criteria are the result of experimental tests or theoretical analysis.
For example, by considering a perfect fluid (viscous forces are zero), the equality of the Reynolds
number is not required anymore. The only parameter that has to be equal is the Froude number. This
consideration is only valid in case the viscosity forces are small, compared to the inertial forces, i.e.
when the Reynolds number is high enough. Hence, scale effects should be a minor influence when the
Reynolds number is above a certain limitation.
When air transport takes place in the model, scale effects will have a larger impact, because dynamic
similarity is impossible for geometrically similar models (Chanson, 2009). Chanson established that
since there are too many relevant dimensionless parameters when air transport takes place. Again,
keeping in mind certain limits considering the Weber and Reynolds number, these scale effects can be
minimized. Pfister and Chanson (2012) suggest that for high-speed air-water two-phase flows, scaled
by use of the Froude similitude, the necessary limitations are either or .
Heller (2011) assembled a table containing the limiting criteria and limiting scale size criteria leading
to moderate (not necessary negligible) scale effects, from which the criteria applicable to the structure
at Heerenlaak are shown in Table 4.
21
Table 4: Limiting criteria to avoid significant scale effects in various hydraulic flow phenomena (Heller, 2011)
Investigation Phenomenon Rule of thumb Reference
Air-entraining free vortex
at horizontal intake Flow conditions
and
Anwar el al.
(1978)
Broad-crested weir Discharge coefficient Overfall height ≥ 0.07 m Hager (1994)
Sharp-crested weir Lower nappe profile Overfall height ≥ 0.045
m
Ghetti and
D’Alpaos (1977)
Spillway
Amount of air
entrainment from
aerator
Rutschmann
(1988)
Stepped spillway Flow velocity profile air–
water mixture Scale ≥ 1 : 15 Boes (2000)
In the table above, following notations are used:
is the discharge of intake [m³/s]
is the submergence depth at intake [m]
is kinematic viscosity of water [m²/s]
is the density of water [kg/m³]
is the cross-sectional area of intake [m²]
is the surface tension between air and water [N/m]
h is the water depth [m]
22
2. Linear Weirs
A weir or spillway is a structure which allows the passage of water over it. Weirs are built for several
purposes such as measuring the discharge, increasing the water level, releasing the excess flood water
of storage basins… Based upon the shape of the weir, several types can be discerned ( sharp crested
weir, broad crested weir, overflow spillway) (Berlamont, 2003).
Figure 13: Sharp crested weir (Berlamont, s.d.)
The formula below gives the discharge over a sharp crested weir.
Where
Q is the discharge over the hydraulic structure [m³/s]
Cd is the discharge coefficient [-]
Lc is the crest length [m]
g is the gravitational constant [m/s²]
HT is the total upstream head [m]
This formula is derived from the formula proposed by Weissbach by assuming that the approach speed
Va of the flow is small and the velocity head becomes negligible when compared to HT. Other
assumptions made when deriving this formula are a uniform pressure distribution above the crest,
negligible head losses, the contraction of the flow above the weir crest ... (De Mulder, 2015). These
assumptions are not always fulfilled. Therefore a discharge coefficient is introduced.
The afore mentioned formula is often simplified by replacing HT by h, the upstream water level, leading
to Poleni’s formula:
23
3. Labyrinth Weirs
3.1 General concept
A labyrinth weir is a linear weir folded in plan view in a repetitive manner. By doing so, a higher total
crest length for a given overall spillway width is obtained. This allows the passage of a higher discharge
for a given total upstream head and total overall width or the passage of the same discharge for a
lower head. This can be seen from the equation giving the discharge of a linear weir, mentioned above.
Labyrinth weirs are particularly advantageous when the available width and the flood surcharge space
(i.e. the available space above the crest of the weir, which can be limited due to the presence of e.g. a
bridge) are limited and large discharges must be passed. (Lux and Hinchliff, 1985)
Another advantage of labyrinth weirs, besides the substantial increase in crest length, is the economic
cost of construction when compared to the standard weir. A disadvantage is the disturbed three-
dimensional flow at each discontinuity of the weir axis and the interference of the jets of adjacent
crests which reduce somewhat the performance of the labyrinth weir (Ouamane, 2013).
A common application of labyrinth weirs is the rehabilitation of an existing spillway when the capacity
has to be increased (Delleur, 2013). This increase in capacity can be required by an increase in
precipitation rate when compared to the precipitation rate anticipated during the design of the
structure or by a governmental desire for a design capable of dealing with floods with a higher return
period. Another application is the use of labyrinth weirs as energy dissipators, applied to control water
quality by aerating or de-aerating the flow (Falvey, 2003). Blanc and Lempérière (2001) advise the use
of a labyrinth weir for specific discharges less than 50 m³/(s·m). For higher specific discharges, the
labyrinth weir requires high walls, which imply a greater wall thickness and greater reinforcement.
The discharge of a labyrinth weir depends on many geometric variables, which are discussed below.
Also other, non-geometric variables play a role when determining the QH-relation of a labyrinth weir.
Tullis et al. (1995) adopted the afore mentioned equation for linear weirs to describe the QH-relation
of labyrinth weirs. This means that the capacity of a labyrinth weir is a function of the crest coefficient
Cd, the crest length Lc and the total head HT. Another equation which is also commonly used is given
below:
24
In this equation Cw stands for the discharge coefficient per unit width of the labyrinth weir. WT is the
overall width of the labyrinth weir, as can be seen in Figure 14. Sometimes the factor 2/3 is not included
in the formula and is taken into account in the value of Cw. Other formulae have been developed in the
past as well (Lux and Hinchliff (1985), Lux (1984)) but will not be mentioned here.
3.2 Variables
3.2.1 Crest Length Lc
As can be seen from Poleni’s formula, the discharge is proportional to the crest length. Thus, based on
this formula, an increase in crest length would lead to a proportional increase in discharge for a given
total upstream head. The total crest length can be calculated as follows (Delleur, 2003):
Where
L1 is the actual length of the side leg [m]
A is the inner apex width [m]
D is the outer apex width [m]
These variables are also explained in Figure 14.
Figure 14: A 4-cycle labyrinth weir with an indication of the geometric variables (adapted from Tullis, Amanian and
Waldron, 1995)
25
In the simplified design method, developed by Tullis et al. (1995), the total weir length is replaced by
an effective weir length Le. This is a more physical based approach to take into account for apex
influences on discharge efficiency rather than the “black box mixing” of all influences in the discharge
coefficient, which will be discussed below. The effective weir length is given by the following formula,
where L2 stands for the effective length of the side leg, as can be seen in Figure 14 (Schleiss, 2011).
Seamons (2014) reported that the effective weir length Le does not completely account for all
efficiency losses due to nappe interference and therefore recommends the use of the total crest length
Lc. This is consistent with the recommendation by Crookston and Tullis (2013). The losses due to nappe
interference are taken into account by the Cd-coefficient when using Lc.
3.2.2 Discharge coefficient Cd
Cd is a dimensionless discharge coefficient, influenced by weir geometry, flow conditions and aeration
conditions of the nappe. There are four different aeration conditions which can be discerned for the
nappe: clinging, aerated, partially aerated and drowned (Crookston and Tullis, 2011). These aeration
conditions will be discussed further on. The Cd value takes into account the effects of nappe collisions,
submergence and the assumptions mentioned when deriving the formula for Q. The values for Cd are
usually presented in terms of HT/P with P being the height of the wall of the weir. The value for Cd is
always smaller than 1.
3.2.3 Sidewall angle α
The sidewall angle α is 90° for a linear weir. When the sidewall angle is 0°, the walls are parallel with
the flow direction. The smaller the sidewall angle, the larger the developed crest length and the larger
the maximum discharge. However, the afore mentioned discharge coefficient Cd decreases with
decreasing sidewall angle, yet the increase in crest length compensates for the reduction in discharge
coefficient (Crookston and Tullis, 2011). According to Tullis et al. (1995) a labyrinth weir can increase
the discharge Q by 3 to 4 times.
For linear weirs the streamlines are perpendicular to the crest and two-dimensional. For labyrinth weir,
the streamlines in the nappe are almost perpendicular to the crest, whereas at the free water surface
the streamlines are directed in the downstream direction. For a decrease in angle between the crests,
there is an increase of the interference of the jets from adjacent crests (Khode and Tembhurkar, 2010).
26
3.2.4 Cycle efficiency ε’
A useful variable to combine the effects of the increase in crest length and the decrease in discharge
coefficient for decreasing sidewall angles, is the cycle efficiency. This concept was developed by
Willmore (2004). This variable is given by the following formula:
Where Lc-cycle stands for the centreline length for a single labyrinth weir cycle and W is the width of a
single labyrinth weir cycle, as can be seen in Figure 14.
The cycle efficiency is a useful design tool because it facilitates the comparison of hydraulic
performance of several acceptable spillway designs against other significant spillway factors, such as
construction costs associated with increasing or decreasing the weir length and apron size (Crookston
and Tullis, 2011).
Figure 15: Cycle efficiency vs. HT/P for half-round labyrinth weirs (Crookston,2010)
Figure 16: Cycle efficiency vs. HT/P for quarter round labyrinth weirs (Crookston,2010)
27
From Figure 15 and Figure 16 it can be seen that ε’ increases as α decreases and that the benefits of
smaller α angles decrease with increasing HT/P. When considering only discharge capacity, it seems
beneficial to select a small sidewall angle. No sidewall angles smaller than 6° are tested but probably
there is a limiting value below which the cycle efficiency begins to decrease.
Another variable, closely related to the cycle efficiency ε’ is the efficacy ε, given by the following
equation:
The efficacy is thus the cycle efficiency divided by the discharge coefficient of the linear weir. The
efficacy is a useful tool to compare the hydraulic performance of a labyrinth weir to that of a linear
weir. Results obtained by Crookston (2010), shown in Figure 17, exhibit an increasing trend in efficacy
ε with decreasing values of α. However, due to the requirement of linear weir data (Cd90°), which
complicates the procedure, it is advised to use the cycle efficiency rather than the efficacy when
optimizing labyrinth weirs.
Figure 17: Efficacy ε vs. sidewall angle α for quarter round trapezoidal weirs (Crookston,2010)
3.2.5 Number of cycles N
The larger the number of cycles, the more nappe interference will occur, which will reduce the
efficiency of the structure due to a relative decrease in the effective length of the weir crest. The nappe
collision also depends on the nappe aeration condition, which will be discussed further on. When
28
maintaining a constant length, the spillway footprint can be reduced by increasing the number of
cycles. However, a 4-cycle labyrinth will be more efficient than an 8-cycle labyrinth of equal length due
to the increase in the number of apexes and consequently a reduction in the length of weir crest due
to the higher amount of colliding nappes according to Crookston (2010). This is illustrated in Figure 18.
Figure 18: Nappe interference and cycle number for an aerated nappe at low HT/P (Crookston,2010)
However, Kozák and Sváb (1961) concluded that a larger number of small cycles is more efficient and
economical than a labyrinth weir of equivalent length composed of fewer cycles. It is important to note
that this study was conducted for small operating heads where discharge capacity is not significantly
reduced by sidewall angle and nappe interference. Waldron (1994) concluded that Cd is independent
of N, for the data tested (α = 12°).
3.2.6 Shape of the cycles
The cycles can have different shapes in plan view: rectangular, triangular or trapezoidal. A trapezoidal
or rectangular shape would be beneficial for ease of construction to provide a minimum required
workspace and would also minimize nappe interference and local submergence effects. A triangular
shape allows for larger crest lengths when comparing to a rectangular shaped labyrinth weir with the
same width (Schleiss, 2011).
Ouamane (2013) reported that the rectangular shape can be as effective as the trapezoidal shape and
is even more effective for relative heads lower than 0.5. Blancher, Montarros and Laugier (2010)
concluded the same with numerical models: the trapezoidal-shaped labyrinth is more efficient in terms
of specific discharge Qsw (i.e. discharge per unit width) for higher upstream heads thanks to its reduced
29
sensitivity to downstream submergence while the rectangular-shaped cycles are more efficient for
lower heads due to the longer total crest length.
Figure 19: General classifications of labyrinth weirs: triangular (A), trapezoidal (B) and rectangular (C) (Crookston,2010)
The proposed design for Heerenlaak consists out of trapezoidal cycles.
3.2.7 Headwater ratio HT/P
In general, an increasing driving head causes a decrease in discharge efficiency, quantified by the
discharge coefficient, with the exception of smaller HT/P values (Amanian, 1987). Both Hay & Taylor
(1970) and Lux (1989) recommend an upper limit for HT/P based upon the reduction in discharge
coefficient for increasing headwater ratios. Tullis et al. (1995) recommend an upper limit of 0.9, but
this was solely based upon the limit of the experimental results. Further research for higher headwater
ratios is required according to Crookston (2010). For the structure at Heerenlaak, headwater ratio will
exceed the recommended value of 0.9 when there is a high water level in the Meuse.
3.2.8 Vertical aspect ratio W/P
The vertical aspect ratio, also referred to as cycle width ratio, is the ratio of the width of one cycle of
the labyrinth (denoted by W) to the height of the walls, which is denoted by P. Lux (1984) and Tullis
(1995) both recommend a minimum aspect ratio of 2 to 3. Hay and Taylor (1970) showed that the
aspect ratio has no significant effect if it is greater than 2. For this value of the vertical aspect ratio the
negative effects of nappe interference on the discharge efficiency are avoided (Seamons, 2014).
Magalhães and Lorena (1989) recommended vertical aspect ratios greater than 2.5. Lux (1989) also
found from his experiments that the discharge coefficient decreased as W/P decreased. The proposed
30
design for the structure at Heerenlaak has an aspect ratio of 5/3, or 1.66 which is below the
recommended values.
3.2.9 Crest shape and wall thickness
A wide variety of crest shapes is available: sharp, flat, quarter-round, half-round, elliptical, truncated
ogee and WES crest shapes. Some of these crest shapes are presented in Figure 20.
Figure 20: Crest shapes (Crookston,2010)
Crookston and Tullis (2011) and Amanian (1987) noted higher Cd-values for the half-round (HR) crest-
shape when comparing to the quarter-round (QR) crest shape for HT/P < 0.4. The explanation given for
this is that a crest which is rounded on the downstream face helps the flow to stay attached (i.e.
clinging flow) to the weir wall, thus increasing discharge efficiency. For increasing values for HT/P the
difference between both crest shapes diminishes and becomes negligible when HT/P > 1. Willmore
(2004) concluded that the most hydraulically efficient crest shape from the ones depicted in Figure 20
was an ogee-type crest, with a leading radius of 1/3 tw and a trailing radius of 2/3 tw. The reason for
this is again that the geometry helps the nappe to cling to the downstream face of the weir at low
heads. He also stated that a half-round crest shape is more efficient than a quarter-round crest shape.
Blancher, Montarros and Laugier (2010) concluded, using numerical models, that an increase in wall
thickness leads to a decrease in specific discharge for Piano Key Weirs (PKW). Piano Key Weirs will be
briefly discussed further on.
Cicero and Delisle (2013) state, based on experimental testing that the efficiency of a PKW can be
increased by 10 to 20% using a QR or HR crest instead of a flat-topped shape.
31
Matthews (1963) studied the effects of curvature on weirs with a round-crest (i.e. QR, HR, ogee,…) and
concluded that weirs with a small radius of curvature would have a larger Cd than weirs with a large
radius of curvature, at a given head. An important ratio to take into account the effects of curvature is
the radius of curvature, given by HT/Rcrest, with Rcrest standing for the radius of the crest (i.e. tw/2, with
tw being the thickness of the weir wall). Most studies concerning the discharge coefficient for different
crest shapes include the effects of HT/Rcrest inherently on the physical models tested, i.e. the influence
of varying values for HT/Rcrest is taken into account in the Cd-coefficient (Crookston,2010).
For the future hydraulic structure at Heerenlaak, the proposed design consists of a flat crest.
3.2.10 Ratio Wi/Wo
The definition of the variables Wi and Wo can be seen from Figure 21. Wi stands for the width of the
inlet and Wo stands for the width of the outlet. Ben Saïd and Ouamane (2011) reported an increase in
labyrinth weir performance with an increase of the ratio Wi/Wo, although the number of tested
configurations was limited.
Figure 21: Indication of the variables Wi and Wo (adapted from Ben Saïd and Ouamane,2011)
32
The measured data can be seen in Figure 22. The difference between the models decreases with
increasing upstream head.
Figure 22: Variation of the discharge coefficient for different ratios of Wi/Wo and Lc-cycle/W =4 (adapted from Ben Saïd and
Ouamane,2011)
3.2.11 Labyrinth Weir Orientation, Placement and Cycle Configuration
Factors as the spillway orientation and placement, the inlet section and cycle configuration may
influence the flow capacity of a labyrinth spillway. Houston (1983) reported an increase in discharge
by 10.4 % for the Partially Projecting orientation when compared to the flush orientation for similar
entrance conditions and that the Normal orientation had a 3.5 % greater discharge than the Inverted
orientation. Crookston and Tullis (2011) compared a Normal and Inverse oriented labyrinth weir with
a sidewall angle of 6° and reported no change in hydraulic performance.
33
Figure 23: Orientations, placements and cycle configurations (Crookston and Tullis,2011)
In general, the discharge efficiency of the weir may be improved by orienting the cycles to the
approaching flow. Case studies by Babb (1976) and Houston (1983) reported that curved abutment
walls upstream of the labyrinth weir minimized the loss of efficiency caused by flow separation and
thus increase the capacity of the weir. Crookston (2010) stated that the relative increase in hydraulic
efficiency of the rounded abutment walls diminishes as N increases. The rounded inlet reduces flow
separation and turbulent flow over the crest when compared to projecting weirs. This leads to an
increase in nappe stability and an improved discharge efficiency (Christensen, 2012).
Ben Saïd and Ouamane (2011) reported a decrease in labyrinth weir performance (i.e. a decrease in
discharge coefficient) for a channel with contraction. This decrease in performance tends to increase
for increasing heads, as can be seen from Figure 27.
Blanc and Lempérière (2001) proposed a rounded front wall to improve the hydraulic performance of
the labyrinth weir. Ouamane (2013) reported an increase in performance of about 10 % when
comparing two models, one with a flat entrance and another with a profiled entrance. The explanation
for this is that the profiled shape facilitates the flow on each side of the front wall. The rounded shape
also eliminates the discontinuity points and thus reduces the disturbance effects at the top of the weir.
34
Figure 24: Labyrinth weir with a rounded front wall (left) and a flat wall (right) ( Ouamane, 2013)
Figure 25: Discharge coefficient according to the entrance shape of a labyrinth weir (adapted from Ouamane,2013)
Figure 26: Channel with and without lateral contraction ( Ben Saïd and Ouamane,2011)
35
Figure 27: Variation of the discharge coefficient for a model with and without lateral contraction (adapted from Ben Saïd
and Ouamane,2011)
A possible way of increasing the discharge capacity are arced labyrinth weir configurations. The cycles
of the labyrinth weir are now no longer following a straight axis, but are laying on a curved axis. They
are orienting the cycle to take advantage of the converging nature of the reservoir approach flow and
they further increase the weir crest length. The geometric layout of an arced labyrinth weir can be
seen in Figure 28.
Figure 28: Geometry of an arced labyrinth weir (Crookston,2010)
Figure 29 and Figure 30 clearly show an increase in discharge coefficient for the arced configuration.
36
Figure 29: Cd vs. HT/P for α =6° half-round trapezoidal labyrinth weir (Crookston, 2010)
Figure 30: Cd vs. HT/P for α =12° half-round trapezoidal labyrinth weir (Crookston, 2010)
This increased efficiency is attributed to the improved orientation of the cycles to the approaching
flow. However, local submergence limits the gains in discharge efficiency. Local submergence develops
sooner for arced labyrinth weirs because these geometries discharge more flow into the downstream
cycles and channel than a linear cycle configuration for a given HT (Crookston,2010). Local
submergence is discussed further on.
37
For most applications of a labyrinth weir, the approach flow is perpendicular to the weir axis. Dabling
(2014) conducted research on the discharge efficiency of a 4-cycle, 15° labyrinth weir with a
channelized approach flow and three different approach angles β (0°, 15° and 45°). He reported no
measurable loss in discharge efficiency for approach flow angles less than 15° and a decrease in
capacity of up to 10° for the 45° approach flow angle at the higher HT/P values. He also noted that at
low HT/P values there is little impact on hydraulic efficiency by the angled approach flow.
3.2.12 Aeration Conditions
As mentioned previously, there are four different aeration conditions: clinging, aerated, partially
aerated and drowned. However, different terms may be found in literature as well. Some labyrinth
weirs do not exhibit all aerations conditions. Aeration conditions are influenced by the crest shape, HT,
the momentum and trajectory of the flow passing over the crest, the depth and turbulence of flow
behind the nappe and the pressure behind the nappe (sub-atmospheric for non-vented or atmospheric
for vented nappes.) Some structures artificially aerate the nappe, creating a vented condition
(Crookston and Tullis, 2011). This is also the case for the proposed design: the columns act as breakers
and provide artificial aeration.
Figure 31: Aeration conditions for a half-round crest (Christensen,2012)
As HT increases, the nappe of a labyrinth weir will transition from clinging to aerated to partially
aerated and finally to a drowned condition. A clinging nappe refers to a nappe adhering to the
downstream face of the weir. An aerated nappe occurs when there is an air cavity behind the nappe.
An aerated nappe will transition to a partially aerated nappe when the air cavity behind the nappe
becomes unstable i.e. varies spatially and temporally. The behaviour of a partially aerated nappe can
be characterized as follows: the air cavity oscillates between labyrinth weir apexes, increasing or
decreasing the length of the sidewall that is aerated. An unstable air cavity causes fluctuating pressures
38
at the downstream face of the weir. A drowned nappe occurs for large values of HT/P and is
characterized by a large, thick nappe with no air cavity (Crookston, 2010).
Nappe interference occurs when two or more nappes collide. For labyrinth weirs this mainly happens
at the upstream apex and this may cause wakes downstream of the apex and standing waves. Nappe
interference reduces the local labyrinth weir discharge capacity (Crookston, 2010).
Increasing the upstream apex width by using trapezoidal or rectangular cycles instead of triangular
cycles may diminish the nappe interference and thus increase the discharge capacity. The downside of
increasing the apex width is a decrease of the overall crest length for a fixed channel width and a fixed
sidewall angle. Therefore increasing the apex width does not necessarily lead to an increase in
discharge capacity. Seamons (2014) reported that in general the reduction in nappe interference does
not outweigh the reduction in crest length. He states that the apex width should be as small as possible
while still maintaining the minimal space needed for construction.
Aeration conditions have a significant influence on the discharge capacity of a labyrinth weir.
Generally, a clinging nappe is more efficient than an aerated nappe. For increasing sidewall angles α
the inception of the drowned conditions begins at higher values of HT/P. Also the shape of the crest
has a large influence on the range of HT/P values for which a certain aeration conditions occurs
(Crookston, 2010).
3.2.13 Filling the alveoli
The alveolus is the volume located between the walls of a labyrinth weir. This is indicated in Figure 32.
A distinction is made between upstream or inlet alveoli and downstream or outlet alveoli. Filling of the
alveoli may be an effective way of reducing the construction costs of the weir. These are diminished
by reducing the height of the walls while maintaining the same height of the weir (Ben Saïd and
Ouamane, 2011). The reduction in free height of the walls allows to have hydrostatic pressure forces
only acting on the upper portion of the wall. This allows for a smaller wall thickness and less
reinforcement. However, the volume of concrete of the apron becomes larger (Ouamane, 2013).
Ben Saïd and Ouamane (2011) reported that filling ¼ of the length of the alveoli has no impact on the
discharge coefficient, regardless of the height of filling. When filling half the length of the alveoli and
for a filling height higher than P/3 the discharge starts to be affected, i.e. the discharge coefficient
starts to decrease.
39
Figure 32: Filling of the alveoli (adapted from Ben Saïd and Ouamane,2011)
Ouamane (2013) also reported that alveoli filling has no effect except for low heads. For heads HT/P >
2.5 no difference in hydraulic performance occurred for the weir with or without filling of the alveoli.
Another advantage of filling the alveoli is the dissipation of some energy, when the apron of the
downstream alveoli is designed as a stair step.
Willmore (2004) found the effects of an upstream ramp in trapezoidal labyrinth weirs to be negligible.
Figure 33: Rectangular labyrinth weir with a shaped entrance, partially filled alveoli and a stepped stair in the outlet key
(Ouamane, 2013)
40
3.3 Disadvantages
There are three main drawbacks for labyrinth weirs. A first disadvantage are the high reinforced
concrete quantities. A second downside is that the efficiency declines for high heads and high
discharges caused by the flow interference from the jets of adjacent crests. Labyrinth weirs also require
a massive basis. The recently developed Piano Key Weirs ( PKW, to be discussed further on) combine
the advantages of a traditional labyrinth weir with a reduced footprint (Lempérière, Vigny and
Ouamane, 2011).
Labyrinth weirs also cause a decrease in reservoir attenuation of flood waves and an increase in peak
outflows, caused by the increased hydraulic capacity. A solution for this problem is creating a staged
labyrinth weir. A staged weir is a weir for which different sections of the weir have different crest
levels.
3.4 Piano Key Weirs
Piano Key Weirs are a relatively new type of weir, which evolved from the traditional labyrinth weir. A
PKW is similar to a labyrinth weir since it consists out of a rectangular shape repeated in plan view. The
main difference is that the apexes are inclined, thus leading to a smaller footprint in comparison to a
traditional labyrinth weir. The discharge capacity of a PK weir depends on more variables than that of
a labyrinth weir. Some of the additional parameters are the slope of the inlet cycle Si, the slope of the
outlet cycle So, the inlet cycle cantilever length Bi, the outlet cycle cantilever length Bo and the height
of the parapet walls. These parapet walls are placed on the crest of the PK weir and transform the
upper part into a rectangular labyrinth weir. These walls help to increase the discharge capacity since
they improve the stream line pattern of the approaching flow and increase the outlet key volume
(Vermeulen et al., 2011).
41
Figure 34: View of a PK weir spillway of the Gloriettes Dam in France during Construction (Électricité de France)
3.5 Submergence effects
When the downstream water level is sufficiently low (i.e. lower than the crest of the weir, or more
precisely than the level positioned a critical water depth above the crest), the discharge over the weir
is independent of the downstream water level and the weir is said to operate in modular flow regime.
However, when the downstream water level exceeds the aforementioned level, the weir is said to be
submerged. For a submerged weir, the discharge is both a function of the upstream and the
downstream water level. This implies that the upstream water level (or head) increases for a given
discharge, or conversely that the discharge decreases for a given upstream head, relative to a free
discharge condition.
During the early days of the labyrinth weir, researchers assumed that the effect of submergence would
be much greater on labyrinth weirs than on linear weirs. Therefore labyrinth weirs were not designed
for submerged conditions (Tullis, Young and Chandler, 2006). Taylor (1968) disproved this assumption
and found that the effect of submergence on labyrinth weirs was less than for linear weirs. This was
later confirmed by Tullis, Young and Chandler (2006) and by Belaabed and Ouamane (2013).
3.5.1 Influence of submergence
Taylor (1968), Tullis et al. (2006) and Lopes et al. (2009) found that submersion has no impact on the
capacity of the structure until the downstream water level exceeds the weir crest. When the
42
downstream water level continues to increase and equals the upstream water level, the structure will
no longer work as a control structure.
3.5.2 Relationship by Villemonte
Villemonte (1947) developed a relationship describing the effects of submergence on the hydraulic
performance of rectangular weirs. He developed a flow reduction factor Qs/Qf for submerged sharp-
crested linear weirs as a function of a submergence ratio Hd/HT. Qs and Qf stand respectively for the
submerged and free-flow discharge rates associated with a driving head equal to HT. The equation
which Villemonte developed is as follows:
The exponent of 0.385 takes into account interaction effects and is determined by the method of
algebraic averages. Results of seven types of weirs tested by Villemonte have shown that the exponent
should be equal to 0.385 for a range of submergence practice from 0.00 to 0.90.
Taylor (1968) used the equation by Villemonte when comparing the performance of a submerged
linear weir to that of a submerged labyrinth weir. Falvey (2003) reported that Villemonte’s equation is
conservative in terms of capacity (head required to pass a given flow) for labyrinth weirs. Therefore he
recommended further research. Tullis, Young and Chandler (2005) conducted research on
submergence effects on three labyrinth weirs with differing geometries. They noted an average error
of 8.9 % and a maximum error of 22% in Villemonte’s equation for predicting submerged labyrinth weir
performance. They also reported a good agreement of Villemonte’s equation for linear weirs. A
dimensionless relationship between Hd/H0 and HT/H0 describing submerged labyrinth weir
performance was developed. H0 stands for the upstream head required for a fixed discharge in free-
flow conditions. This is shown in Figure 35. The submerged upstream head approaches the free-flow
head as the submergence level, Hd/H0, goes to zero and the tailwater depth approaches the head water
depth as the submergence levels increase. With a sufficient level of submergence, Hd will equal Hu and
the labyrinth weir will cease to function as a control.
43
Figure 35: Dimensionless relationship describing submerged labyrinth weir performance (Tullis, Young and Chandler,2006)
3.5.3 Local submergence
Local submergence occurs when the downstream water level locally exceeds the weir crest elevation.
Local submergence differs from the traditional submergence in that it does not necessarily encompass
the entire labyrinth weir. Local submergence is caused by the inflow exceeding the local outflow
capacity of the outlet cycle, resulting in a local increase in downstream water level. The local
submergence region develops downstream of the upstream apex and increases in size as the weir
discharge increases (Crookston, 2010). Local submergence occurs sooner (i.e. at lower HT/P values) for
smaller sidewall angles and can locally decrease the discharge efficiency (Belaabed and Ouamane,
2013).
44
4. Culverts
Flow through the hydraulic structure can be compared with flow through a culvert when either the
inlet or the in- and outlet of the structure is drowned. Because of the presence of a labyrinth weir in
the hydraulic structure, this comparison is not so straightforward. Nevertheless, a good knowledge of
culverts is required to try and understand the different characteristics of the hydraulic structure. Hence
part of the literature review is devoted to flow through culverts.
4.1 Introduction
A culvert is a short channel or conduit placed through an embankment, dike, dam … Culverts are built
for different reasons and consequently have many different definitions. The most common definition
found in literature is that culverts are designed to transport water underneath embankments or
roadways. A culvert can also be used to restrict flow for upstream detention and/or reduce the
influence of flood waves downstream of the culvert, which would be the main objective in case of the
proposal for the hydraulic structure at Heerenlaak.
4.2 Terminology
A culvert consists out of three mains parts, namely the entrance or inlet, the barrel and the outlet. The
most common cross-sectional shapes of the barrel are circular (i.e. pipe) or rectangular (i.e box
culvert). Considering the structure at Heerenlaak, the main focus will be on rectangular culverts.
The invert is defined as the bottom of the barrel while the barrel roof is called the soffit or obvert.
Further important notions to be considered are the upstream water level (i.e. the headwater) and the
downstream water level (i.e. the tailwater).
4.3 Flow through a culvert
Flow phenomena through culverts are complex. Different flow regimes can be discerned based upon
the upstream and downstream flow conditions. The control section of the flow or terminal section can
be at the inlet or at the outlet and the governing parameters can change unpredictably, causing
relatively sudden rises in headwater.
When the type of flow is known, the well-known equations for orifice, weir, or pipe flow and backwater
profiles can be applied to determine the relationship between head and discharge (Blaisdell, 1966).
45
Modern culvert design nomographs and computer programs which are based on the theory and
experiments are also available.
Carter (1957) defined a classification system of 6 types of flow through culverts based on the location
of the control section and the relative heights of the headwater and tailwater surfaces. The main
characteristics of each type are shown in Table 5. The different types are differentiated according to
type of barrel flow, the location of the control section (upstream or downstream) and the main factor
influencing the discharge and headwater level (i.e. kind of control). For each type, discharge equations
have been defined based upon the continuity and energy equations. The explanation of the different
parameters is given in Figure 36.
Figure 36: Illustration of culvert flow, explaining the different parameters (Bodhaine, 1966)
Table 5: Summary of the different flow types and characteristics according to Carter (1957)
Flow
type
Type of
barrel flow
Location of
control
section
Kind of control Culvert
slope
I Partly Full Inlet Critical Depth Steep < 1.5 < 1 1
II Partly Full Outlet Critical Depth Mild < 1.5 < 1 1
III Partly Full Outlet Tailwater Mild < 1.5 > 1 1
IV Full Outlet Tailwater Any > 1 > 1
V Partly Full Inlet Entrance
geometry Any 1.5 1
VI Full Outlet Entrance and
barrel geometry Any 1.5 1
46
Types I and II are defined by flow at critical depth, which in case of type I occurs at the upstream part
of the culvert and in case of type II at the downstream end of the culvert. The critical depth, dc , is the
depth at the point of minimum specific energy for a given discharge and cross section. The position of
the critical depth section depends on the headwater elevation, the slope of the invert, and the
tailwater elevation. For types I and II to occur, the headwater elevation above the upstream invert
must be less than 1.5 times the diameter or height of the culvert, .
Figure 37: Type I flow, according to Carter (1957)
TYPE I: Type I flow is characterized by a critical depth section near the culvert entrance and
the culvert barrel flows partly full. For type I to occur, the slope of the culvert barrel, S0, must
be greater than the critical slope, Sp , and the tailwater elevation, , must be less than the
elevation of the water surface at the control section, . The discharge equation is
Where
is the discharge coefficient [-]
is the flow area at the control section, defined as [m]
g is the gravitational constant, defined as 9.81 m/s²
is the piezo-metric water level at position 1 [m]
z is the height of the culvert [m]
V1 is the mean velocity in the approach section [m/s]
is the velocity-head coefficient at the approach section [-]
is the maximum depth of water in the critical-flow section [m]
is the head loss due to friction between the approach section and the inlet [m]
47
Figure 38: Type II flow, according to Carter (1957)
TYPE II: The second type is characterized by a partly full flowing barrel with a critical depth
section at the culvert outlet. The slope of the culvert S0 is less the critical slope Sc and the
tailwater elevation does not exceed the elevation of the water surface at the control section
. The discharge equation remains the same as type I with an adaptation considering
the barrel friction loss.
Where
is the head loss due to friction in the culvert barrel, from location 2 to 3 on Figure 38
[m]
For types III and IV, critical depth does not occur in the culvert and the tailwater elevation controls the
headwater level for a given discharge. The culvert can flow partly full, if , which is
defined as type III. Type IV on the other hand, is characterized by both ends of the culvert being
completely submerged which is denoted as full flow through the barrel.
Figure 39: Type III flow, according to Carter (1957)
48
TYPE III: For type III to occur, the headwater-diameter ratio should be less than 1.5 and the
tailwater should exceed the elevation of critical depth at the control section (either at the inlet
or at the outlet), but the outlet must not be submerged. The culvert barrel flows partly full. It
is further assumed that equals . The discharge equation for this type of flow is
Where
is the area of the section of flow at the outlet (position 3) [m²]
is the piezo-metric head at location 3 [m]
Figure 40: Type IV flow, according to Carter (1957)
TYPE IV: Type IV is characterized by both the entrance as well as the outlet being submerged
as is shown Figure 40. The culvert flows full and the discharge can be computed directly from
the energy equation between sections 1 and 4. Leading to the following discharge equation:
And
With
is the area of the inlet of the culvert [m²]
is the piezo-metric head at position 4, indicated at Figure 40 [m]
is the head loss due to the contraction at the inlet [m]
49
V3 is the velocity at position 3, indicated at Figure 40 [m/s]
n is the roughness coefficient of Manning [ s / m1/3]
L is the culvert length [m]
is the hydraulic radius of the culvert barrel [m]
Types V and VI are defined as flow under high head (Bodhaine, 1968) and will occur if the tailwater is
below the soffit of the culvert at the outlet and the headwater is equal or higher than 1.5 times the
diameter, .
Figure 41: Type V flow, according to Carter (1957)
TYPE 5: In type V the headwater elevation is higher than 1.5 times the inlet diameter. The
water flows rapidly at the inlet and the tailwater elevation is below the soffit at the outlet. The
culvert barrel flows partly full and at a depth less than critical. The discharge equation is
Figure 42: Type VI flow, according to Carter (1957)
TYPE 6: In type VI the barrel of the culvert flows full, under pressure and with free outfall. The
headwater-diameter ratio exceeds 1.5 and the tailwater does not submerge the culvert outlet.
The discharge equation between sections 1 and 3, neglecting and , is
50
The difficulty in applying this formula is the necessity of determining , varying from a point
below the centre of the outlet to its top, even though the water surface is at the top of the
culvert. This variation in piezometric head is a function of the Froude number.
Hee (1969, see Chanson, 1995) and Henderson (1966) established that for free surface flow in the
barrel, the ratio of upstream specific energy to the barrel diameter (or barrel height) should be less
than 1.2. This has been experimentally confirmed by Chanson (1995a). According to Chow (1959), the
entrance will be submerged when the headwater is less than a certain critical value, namely 1.2 to 1.5
times the height of the culvert, depending on the entrance geometry, barrel characteristics, and
approach condition.
51
5. Vortices
5.1 Introduction
During the measurements performed on the scale model, swirling motion of water and the formation
of vortices were noticed at the intake of the labyrinth weir in a culvert. These vortices can have a
negative impact on the flow through the structure and the structure itself.
Vortices can be divided in two classes, free surface vortices and sub-surface vortices (Hydraulic
Institute, 1998). Since the flow through the labyrinth weir in a culvert only triggers free surface
vortices, the main focus will be directed to free surface vortices.
Vortices can also by classified according to the direction and position of the intake. This classification
was made by Knauss (1987) and is shown in Figure 43. For the proposed design, only the horizontal
intake will be considered.
Figure 43: Directional and structural classification of vortices (Knauss, 1987)
52
5.2 Formation and causes
Swirls and vortices are formed by rotational motions of fluid regions. Hence they find their origins in
discontinuities in the flow pattern. These discontinuities cause swirling which can grow into vortices
when strong enough. Discontinuities leading to swirling are mostly found in the form of asymmetrical
flow areas. Knauss (1987) listed six different types of sources leading to rotational motion. These are
shown in Figure 44, where they are divided in rotational motion caused by symmetry (a) and caused
by a change in direction of the borderlines (b).
Figure 44: Sources of rotational motion according to Knauss (1987)
Durgin and Hecker (1978) defined the causes of vortices more generally in three fundamental types,
being:
- non-uniform approach flow to the intake due to geometric orientation
- the existence of velocity gradients
- obstructions near the intake
Figure 45: Three fundamental causes of vortex formation according to Durgin and Hecker, 1978
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The physical processes behind the formation of vortices are explained by Wu et al. (2006). They
attribute the compressing/expanding and the shearing process to be the two fundamental processes
behind fluid dynamics, such as vortex formation. Both processes are present when water flows through
an intake or in this case a submerged inlet.
The spinning motion is caused by shear stresses in the fluid. In ideal fluids with no viscosity, shear
stresses would force the different layers to slide over each other without any resistance. In real fluids,
viscosity is present which means that the fluid elements have some resistance against shearing stresses
putting the fluid elements into spinning motion.
The compression process is created by a sufficient amount of water above the intake, otherwise known
as submergence. This submergence provides enough pressure head to support the shearing process
and has thus a lower limit. However, higher submergence means the core length of the vortices is
extended, as a result the amount of circulation is larger and the amount of water required to be set in
a spinning motion to support the vortex structure is larger (Knauss, 1987). Hence, there exists a
submergence depth at which vortex formation starts and a submergence depth where the vortices
disappear.
The shape of the vortex is caused by the centripetal acceleration generating a drop of pressure in the
centre of the vortex. This pressure drop results in a local depression of the free surface. The magnitude
of the drop in the water surface depends on the equilibrium of gravity forces, centripetal acceleration
forces and surface tension, ranging from a dimple (strong circulation) to a vortex with a full air core
over the whole depth of submergence.
A dimple is a description of the appearance of the water surface, classified according to the Alden
Research Laboratory or ARL (Hecker, 1981). The ARL drafted a classification system of free surface
vortices to define the strength of different types of free surface vortices. The classification consists of
six stages which are shown in Figure 46.
This classification is based on visual observations. Classification of the intake vortices can also be
accomplished by measuring vortex related quantities, related to the strength of vorticity. Examples of
these quantities are the magnitude of swirl inside an inlet pipe, determination of the amount of
ingested air, changes in discharge coefficients and free surface velocities around the vortex core. Since
vortices are time dependent, fluctuate in strength and shift in position, the reliability of the
measurements can be low, the correlation between vortices and a selected parameter weak and the
selected parameters depend upon other parameters (Knauss, 1987).
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Figure 46: Free-surface vortex classification according to Alden Research Laboratory (Knauss, 1987)
5.3 Submergence
As explained before, there is a range of submergences in which vortices appear. This submergence is
one of the most determining factors in the creation of vortices. After the water rises above the intake,
vortices rapidly start to develop and they grow with increasing submergence until they reach a
maximum intensity. Afterwards, the intensity of the vorticity decreases again with increasing water
level. When the submergence increases even more, a critical submergence is reached.
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A considerable amount of research has been performed concerning this critical submergence. This
concept is defined by Jain et al. (1978) as the smallest depth at which strong and objectionable vortices
will not form anymore. Gordon (1970, cited from ASCE, 1995) defines it to be the submergence level
required to prevent air – entraining vortex formation. According to Yildirim and Kocabaş (1995) it is
“the value of submergence of the intake when air-entraining vortex just occurs”. For most research, it
is the threshold at which air-entraining vortices change into non air-entraining vortices. When studying
the critical submergence, attention must be paid to the definition of the different parameters, which
are determined by the researcher.
Several empirical and analytical formulas have been suggested to define the submergence at which
vortices appear. Only the main formulas will be discussed here. Gordon (1970, see Baykari, 2013)
explained the influencing aspects on the formation of vortices to be the geometry of the approach
flow to the intake, the velocity at the intake, the size of the intake and the submergence. He proposed
a formula which relates the submergence to the average velocity V through the inlet and the diameter
of the inlet. After transformation to SI-units, following formulas are obtained:
For symmetrical approach flow conditions:
For asymmetrical approach flow conditions:
In which
is the submergence above the top of the intake [m]
is the diameter of the intake [m]
is the average velocity through the inlet [m/s]
is the Froude number, defined as [-]
Gordon’s research was based on a study of 29 hydroelectric intakes. A disadvantage of Gordon’s
formula is that the parameters are not dimensionless thus it cannot be considered a universal
relationship for all intake designs (Rindels and Gulliver, 1983).
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Figure 47: Indication of the different parameters used by Gordon (ASCE, 1995)
The formula proposed by Knauss (1987, see ASCE, 1995) for the critical submergence is based on the
Froude number at the inlet and the direction of the intake (horizontal, vertical or inclined intake).
Where
k is a constant representing the gradient of the linear relationship [-]
is the depth of water above centerline of intake at face of intake [m]
is the diameter or characteristic dimension of the intake [m]
is the intake velocity [m/s]
Fr is the Froude number, defined as [-]
is the circulation constant, defined as [m²]
is the tangential velocity of approach flow [m/s]
r is the radius of vortex [m]
is the swirl number, defined as [-]
Knauss (1987) further recommended the minimum design submergences for well operating prototypes
with normal approach flow and proposed the curve shown in Figure 48. He recommends a
submergence depth of 1 up to 1.5 times the intake height/diameter for large size intakes, while for
medium and small size installations the following formula is proposed:
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With
is the depth of the water above the centre line of the intake [m]
is the Froude number, defined as [-]
Figure 48: Recommended submergence for intakes with proper approach flow conditions (Knauss, 1987)
More recent studies were done by Ahmad et al. (2008) concerning horizontal intakes. Ahmad et al.
performed an analytical and experimental study regarding critical submergence for a 90° horizontal
intake in an open channel flow. They found that the critical submergence depends on the (intake)
Froude number, ratio of intake velocity and channel velocity, Reynolds number and the Weber
number, with a more pronounced influence of the Froude number and the ratio of intake velocity and
channel velocity. Furthermore, they presented a predictor for the critical submergence when the
bottom clearance from intake to the bottom is equal to zero or half of the diameter, with satisfactory
results. The formulas for critical submergence are:
When the bottom clearance is zero (e = 0),
And when the bottom clearance is equal to half of the diameter (e = D/2),
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Where
e = the distance from the bottom of the channel to the intake invert [m]
= intake velocity [m/s]
= uniform approach flow velocity [m/s]
Gürbüzdal (2009) proposed a formula which included the Reynolds number based on experiments on
horizontal intakes to study the possible scale effects on the vortex formation. Another parameter of
influence incorporated in the proposed formula is the side wall clearance.
Where
= distance of the side wall to the centre of intake (symmetrical geometry) [m]
This formula is valid for
The bottom clearance in the experiments was zero (e = 0). Further observations concerning the side
wall clearance showed that the critical submergence becomes independent of the side wall clearance
when the ratio of the side wall clearance to the intake diameter ( / ) exceeds a value of 6.
5.4 Scale effects
Surface tension and the velocity and viscosity of the fluids are of importance for the research
concerning vortex formation. Consequently the Froude, Reynolds and Weber numbers come into play
when model studies are performed. Unfortunately, the laws of similitude cannot be satisfied
simultaneously, which can lead to discrepancies between the results of the scale model and the
prototype (see also paragraph 1, concerning scaling), also known as scale effects (Webber, 1979).
Hence, Froude and Reynolds similitude are impossible to fulfil simultaneously. The Froude number is
found to be the most influencing factor in all experiments conducted up to now and Froude similitude
is customary to be used as basis.
A lot of research has been done regarding the relative significance of the different parameters in the
vortex formation process. Surface tension and viscosity are parameters which are investigated
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extensively. From these studies, it was concluded that surface tension and viscosity effects are
negligible if the Reynolds and Weber number attain certain values.
Dagget and Keulegan (1974) demonstrated that surface tension does not influence the
formation of vortices when the Reynolds number is in the range from to
(no tests outside this region were performed). This conclusion was based upon a
comparison of different fluids (glycerine-water and oil mixtures) in a cylindrical tank.
Research done by Jain et al. (1978, cited in Yildirim and Kocabaş, 1995) showed that surface
tension has no influence on the formation of vortices when the Weber number is in the range
from to (with ). This research was based on vertical inlets.
For horizontal and vertical intakes in a long flume, surface tension does not affect the
formation of vortices when the Weber number is larger than (with ,
h being the submergence based upon the centre line of the intake), according to Anwar (1981,
cited in Rindels and Gulliver, 1983).
Further research done by Anwar (1978, cited in Rindels and Gulliver, 1983) on horizontal
intakes in a flume showed that viscous effects had no influence on the flow of a free surface,
if the Reynolds number is higher than (with and h defined as the
submergence from the centre line of the intake ).
According to Odgaard (1986), the criterion for neglecting the surface tension is a Weber
number exceeding 720. The criterion for neglecting the viscous effects is a Reynolds number
exceeding . Odgaard’s research is based on a free-surface, air-core vortex model.
Padmanabhan and Hecker (1984) found above a Weber number of 600 and a Reynolds number
of no significant scale effects when operating according to Froude similitude,
meaning that the surface tension and viscosity effects are negligible. These experiments were
conducted on a sump pump.
Summarizing the past research and experiments, surface tension can be neglected in case of the
Heerenlaak scale model when the Weber number is higher than 720 and the
viscosity can be neglected if the Reynolds number ( ) is higher than . This
prescribed Reynolds number increases with increasing Froude number. (Gürbüzdal, 2009)
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5.5 Problems
The formation of vortices is related with the risk of air entrainment at the inlet. This might be a source
of different problems which could impact the life time of the structure. According to Knauss (1987),
air-entraining vortices can be the cause of two hydraulic problems at intakes:
- Unfavourable vibrations
- Transport of trash through the closed channel
The most serious and relevant problems caused by vortices concerning the hydraulic structure at
Heerenlaak will be:
- Increase of head loss
- Reduction of intake discharge:
- Ingress of trash or debris
- Air entrainment
5.6 Prevention
The prevention of vortex formation is usually based upon providing enough submergence at the intake
and improvement of the approach flow conditions (avoid separation of flow, induced by abrupt
changes in the geometry of the boundaries, removal of obstacles …). Structural measures can be taken
such as lowering the Froude number by enlarging the inlet area. Unfortunately, these options are
difficult to apply in case of the Heerenlaak structure. Another solution to prevent the formation of
vortices is to use anti-vortex devices.
Gulliver and Rindels (1983) compiled a list of available anti-vortex devices, based upon the works of
Denny and Young (1957) and Ziegler (1976). The first anti-vortex device is a floating raft shown in
Figure 49. The intention of the raft is to disrupt the angular momentum at the water surface.
Experiments done by Ziegler (1976) found that the floating rafts disrupted the converging circular
water surface currents normally present in an organized vortex. In a developed vortex, the motion of
the water surface currents is a spiralling inflow toward the centre of the vortex. The raft prevented the
converging portion of this motion, but a very substantial circular motion still remained as swirl beneath
the raft.
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Figure 49: Floating raft (Gulliver and Rindels, 1983)
Ziegler (1976) performed tests on both floating as well as submerged rafts. He found that both rafts
prevented formation of air-entraining vortices. However, a raft submerged only by a small distance
below the water surface reacted on the upper portion of a vortex with a similar result to a floating raft,
while a raft submerged a substantial distance below the water surface reacted on the lower portion of
the vortex. The submerged rafts were perceived to be slightly better than the floating rafts. Ziegler
found that there was an optimum depth of submergence at which the rafts were most efficient.
Figure 50: Submerged raft (Gulliver and Rindels, 1983)
Trashracks can also be used to disrupt the angular momentum of the flow and can be used as anti-
vortex devices. According to Ziegler’s research, vortex formation is dependent on the size of the
trashrack. However, for the proposed hydraulic structure at Heerenlaak, thrashracks are not desirable
because of trash congestion at the inlet and the accompanying maintenance.
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6. Optimisation based on literature review and scale model testing
Based upon the literature, some recommendations and (possible) improvements of the proposed
design can be made. These improvements mainly aim at increasing the maximum discharge of the
hydraulic structure.
As mentioned in the literature review, rectangular-shaped labyrinth weirs are more effective for low
relative heads (HT/P<0.5) due to their longer total crest length, while trapezoidal-shaped labyrinth
weirs are more efficient for higher relative heads due to their reduced sensitivity to downstream
submergence (Ouamane, 2013, Schleiss, 2011 and Blancher, Montarros and Laugier, 2010). Assuming
an upstream water level of 32.0 m T.A.W., which corresponds to a discharge of ± 3000 m³/s through
the Meuse near Maaseik (see Figure 8), a relative head of 1.77, when neglecting the velocity head, is
obtained. Since the maximum discharge of the hydraulic structure is more essential to the design than
the Qh-relation, it is thus not deemed useful to adapt the design and replace the trapezoidal cycles by
rectangular cycles.
Increasing the inner and outer apex width of the current design will reduce the interference losses.
However, Seamons (2014) states that the reduction in interference losses does not outweigh the
reduction in crest length. Therefore no changes to the shape of the structure are recommended.
No consistent advice regarding the impact of a higher / smaller amount of cycles for an identical
spillway footprint can be given (Crookston, 2012, Waldron, 1994 and Kozák and Sváb, 1961).
Decreasing the amount of cycles while maintaining the same value for the overall crest length by
increasing the size of the cycles (by using the same scale factor for the direction perpendicular and
parallel to the axis of the road) is not an option at Heerenlaak, since the structure would then no longer
fit within the body of the existing levee.
Creating a larger amount of small cycles (while maintaining the same value for the overall crest length)
would increase the interference losses and would further decrease the vertical aspect ratio W/P, which
has a value of 1.66 in the proposed design whereas a value larger than 2 is recommended (Lux, 1984
and Tullis et al., 1995). However, this would offer the opportunity to increase the available area above
the weir. Due to the shorter length of the bottom slab, the height above the weir (which is limited by
the dimensions of the dike body) may be larger.
The crest of the labyrinth weir in the proposed design is of the flat crest type. Using a quarter-round,
half-round or an ogee type crest can increase the capacity significantly (Crookston and Tullis, 2011,
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Amanian, 1987, Willmore, 2004). However, the influence of the crest shapes manifests itself especially
at low heads, and disappears for higher heads. Therefore, replacing the flat crest of the proposed
design will lead to a better performance at low heads, but will most likely have little to no influence
for high heads during drowned conditions. Since the maximum discharge is the main interest for
making design adaptations, it is not beneficial to replace the crest in order to obtain a higher maximum
discharge.
Filling of the up- and downstream alveoli is a possible design adaptation worth considering. Filling the
alveoli up to a certain extent (i.e. limited height and length) has only an effect for low heads (Ben Saïd
and Ouamane, 2011) but, as has been mentioned before, this is not the main area of interest for the
discussion of the proposed design. Therefore, if filling the alveoli would lead to a cost reduction of the
hydraulic structure, this option is worth considering. For being an economical solution, the reduction
in cost of the walls should outweigh the cost for filling the alveoli. The cost for constructing the walls
declines since lower hydrostatic pressures act on the walls, allowing a smaller thickness. This implies
that at a certain location prefabricated panels with a smaller thickness can be used. A smaller thickness
of the walls will also lead to a higher capacity of the structure in comparison to structures with thicker
walls. Filling the alveoli also may facilitate the construction process. The prefabricated panels for the
walls may be attached to the alveoli.
Ir. H. Gielen has expressed the concern for the dissipation of energy of the discharge through the
hydraulic structure when it enters the area of Heerenlaak. Constructing the downstream alveoli as a
stair step, as shown in Figure 33Figure 32, might serve this purpose. This stair step reduces the cost of
constructing measures to dissipate energy downstream of the structure. Thus this saving in cost may
also be taken into account when considering to fill the alveoli or not.
Several measures can be taken to facilitate the flow towards the structure. Research showed that
rounding the upstream front wall may increase the performance of the structure with almost 10 %.
However, this increase diminishes and becomes negligible for higher heads. Rounding the external
edges of the upstream U-beam is another measure which may facilitate the flow. Facilitating the flow
may also imply that floating debris goes through the inlet section and enters the area of Heerenlaak.
Using an arced or projecting configuration is not an option at Heerenlaak, since these configurations
would then no longer fit within the body of the existing dike.
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Dabling (2014) mentioned that for increasing approach flow angles, the capacity of the structure
declines and that this decline is larger for higher values of HT/P. Considering that the future hydraulic
structure will be located in a bend of the Meuse and taking into account the results obtained by
Dabling, the change in hydraulic capacity of the approach conditions at Heerenlaak requires attention.
There are several possible design adaptations which will increase the discharge of the structure at a
given head. However, the influence of most of these adaptations diminishes for higher heads, and thus
the adaptations become useless. Nevertheless, the use of filled alveoli has quite some advantages,
being the dissipation of energy, a smaller wall thickness, a faster and more straightforward
construction process and possibly a cheaper cost of the hydraulic structure and the measures to
dissipate energy downstream.
From analysing the culvert regimes and corresponding formulas, enhancing the discharge through the
structure can be done by enlarging the inlet area, increasing the head over the structure and reducing
the hydraulic losses through the culvert. These losses can be reduced by rounding the edges of the U-
beams or the beams inside the structure, by preventing the formation of eddies (e.g. removing void
areas where eddies can form, by use of an inclined corner between the U-beam and culvert soffit, as
illustrated in Figure 51). Other possibilities in reducing hydraulic losses exist as well.
Figure 51: Illustration of the inclined corners between the U-beam and the culvert soffit
The formation of vortices at the inlet section is also a source of hydraulic losses, which has to be
avoided. These vortices can also lead to unwanted vibrations and ingress of trash through the
structure. Several possibilities exist to reduce the formation of vortices. The geometry and approach
conditions are of importance, because they can create rotational motion which enhances formation of
vortices. Furthermore the use of trashracks or submerged / floating rafts can be implemented to
reduce this formation of vortices. However, for the structure at Heerenlaak, this might not be an
option.
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Chapter 4: Experimental set-up and test procedure
In this chapter an overview will be given of the test facilities which were used to perform the
experimental measurements. Consequently, the measurement devices and testing procedure will be
discussed, followed by an overview and description of the configurations which were tested.
1. Test facilities
1.1 Current Flume
The scale model study is performed at the Hydraulics Laboratory of Ghent University, in a current flume
with a length of approximately 15 m, a width of ca. 0.70 m and a height of 0.68 m. A picture of the
current flume is shown in Figure 52. To provide the discharge through the flume, three different pumps
are available with a combined maximal flow rate of 500 l/s.
Figure 52: Current flume used during the experiments
The discharge through the flume is measured by means of a calibrated sharp-crested, rectangular weir.
The height of the water above the weir can be determined using a hooked gage submerged in a stilling
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tube connected to the reservoir. To do so, the needle of the gage needs to be positioned near the
water surface until the tip of the needle touches the free surface. Since the needle approaches the
water surface from underneath the free surface, a higher accuracy is reached because surface tension
is eliminated. The accuracy of the gage is about 0.3 mm. However, given the formula of the calibrated
weir, a measuring error of mm results in discharge error of only 1.1%.
Figure 53: Needle of the gage to measure the discharge
The calibration curve of the current flume is known and is depicted in Figure 54.
Figure 54: Qh-relation of the calibrated weir
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200 250
Q [
l/s]
h-h0 [mm]
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Figure 55: Stilling tube with hooked gage (left) and the device to adjust the height of the needle (right)
The water level downstream of the flume can be controlled by means of an inclined rectangular weir.
The crest level of this weir can be changed by adjusting the teeth of the cogwheel connected to the
weir.
Figure 56: Cogwheel to adjust the height of the downstream weir
1.2 Position of the scale model
The respective scale models are simply mounted in the (downstream half of) the flume, with the
longitudinal axis of the structure in-line with the flume axis. As a consequence, the scaled-down
structure is subjected to a relatively uniform approach flow. The rationale behind this approach is that
in the scale model only two cycles of the labyrinth weir are integrated in the culvert, whereas in the
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prototype a multiple of these cycles will be needed to attain the target discharge. Hence, the results
of this scale model study will be more representative for the inner cycles of the construction (which
have indeed an approach flow aligned with the structure) rather than for the outer cycles. The latter
might somewhat suffer from side effects, dependent on the detailed geometry of the diversion
between the river Meuse and the construction. Yet, nv de Scheepvaart is willing to shape this diversion
in order to have approach flow conditions which are as uniform as possible.
1.3 Honeycombs
Due to the presence of another scale model (related to another master thesis) in the upstream half of
the flume, honeycombs have been mounted at a certain distance upstream of the hydraulic structure,
in order to calm down the flow and the water level disturbances and to make the flow more uniform.
No flow streamliners are used on the downstream side of the structure since they might influence the
discharge capacity of the structure. The use of these streamliners is illustrated in Figure 57 and Figure
58. Streamliners are also used in the reservoir upstream of the calibrated weir, thus allowing to
determine the discharge more accurately.
Figure 57: Honeycombs
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Figure 58: Comparison of the water surface on both sides of the honeycombs
(right: highly fluctuating levels at the upstream side; left: calmed down free surface at the downstream side)
2. Measuring equipment
The equipment used to measure water levels and velocity profiles will be described below.
2.1.1 Ultrasonic water level sensors
By using ultrasonic water level sensors (Maxbotix LV-MaxSonar-EZ4) positioned above the water
surface, the distance of the latter relative to the sensor is registered. The sensor emits high frequency
sound waves which reflect when hitting a surface. This echo is then registered by the receiver of the
sensor. By measuring the time that it takes between emitting a signal and receiving, the ultrasonic
sensor can determine the distance between the sensor and the surface. The sensor then averages the
measured distances over a time period of 1 second and emits this signal wirelessly to a receiver
connected to a laptop.
Figure 59: Ultrasonic distance sensor
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There are two sensors used in the experiments: one located at the upstream side of the structure, at
a distance of 1.52 m with respect to the inlet section and one at the downstream side of the structure,
at a distance of 1.58 m with respect to the outlet section of the hydraulic structure.
Figure 60: Indication of the position of the ultrasonic water level sensors
2.1.2 Electromagnetic current meter
For the determination of velocity profiles, an electromagnetic current meter is used, more specific the
Valeport model 801 (see Appendix B). This device offers velocity measurements at a high precision
(±0.5% of reading plus 5 mm/s) over a velocity range from -5 m/s to 5 m/s.
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Figure 61: The Valeport model 801 electromagnetic current meter (source: http://www.valeport.co.uk)
2.2 Accuracy of surface measurements
Because of water surface fluctuations (+/- 5 mm), caused by ripples and waves, the accuracy of the
water level measurements is limited. The accuracy depends on the discharge, since for high discharges
the fluctuations of the surface are much larger than for low flow discharges. The ultrasonic sensors
allow determining the distance between the sensor and the water surface with an accuracy of 1 mm,
but because of the method of measuring the distance the real accuracy is 3 to 4 mm.
3. Scale Model
In the course of this scale model study experiments have been performed on two different scale
models, scaled with the same scale factor but having different features.
3.1 Full model
In the model that will be further referred to as the “Full model”, experimental measurements are
performed on an exact scale model of the design made by nv De Scheepvaart. Pictures of this model
and its position in the current flume can be seen in Figure 62 and Figure 63. A geometrical scale factor
of 18 is chosen such that the model will occupy almost the complete width of the current flume.
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Figure 62: Front view (left) and top view (right) of the hydraulic structure in the current flume
Figure 63: Front view of the scale model
73
The model is made out of Medium-Density Fibreboard (MDF). Poly Methyl Methacrylate (PMMA) is
used to create the ceiling of the structure. The PMMA-ceiling has the advantage that it is transparent,
allowing to observe the flow patterns through the ceiling of the hydraulic structure. The columns and
beams in the scale-model are made out of stainless steel (Figure 65). Under the bottom slab a rubber
sealing is applied to mitigate the flow of water under the structure as much as possible. Also between
the side walls of the model and the flume, there is a rubber sealing to prevent the seepage of water
(Figure 64). The model is finished with grey paint (Figures 12 to 14).
Figure 64: Rubber sealing to prevent seepage
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Figure 65: Model before (left) and after (right) completion with a view through the PMMA-ceiling
3.2 Simple model
A second model was made to allow testing on a wider variety of hydraulic structures, that were
deemed useful for comparison purposes. This second model, that will be further referred to as the
“Simple model”, offers the possibility of testing a linear weir and a labyrinth weir. Since the simple
model has a removable ceiling, these weirs can be tested as such or integrated in a culvert.
An additional advantage of the Simple model is that the U-shaped beams (U-beams), indicated in black
on Figure 66 and also shown in Figure 67, can be removed (contrary to what is the case in the Full scale
model). This allows investigating the possible effect of these U-beams on the discharge through the
hydraulic structure. Moreover, the ceiling of the culvert in the Simple model can be positioned at
different heights (contrary to what is the case in the Full scale model).
The hydraulic structure is again scaled with a factor 18. In this second model, no beams and columns
for supporting the roof of the culvert are present, which can be seen in Figure 66.
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Figure 66: Longitudinal cross-section of the Simple model
Figure 67: Indication of the removable U-beams
3.3 Scaling
As mentioned previously, the Froude number for the model and prototype remains the same (Froude
scaling). Considering this, the scaled velocities can be calculated.
The flow rate in the scale model can be calculated as:
Hence the flow rate in the scale model is a factor smaller than in the prototype at Heerenlaak.
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4. Test procedure
4.1 Stage-discharge relation
Before each testing session (i.e. once or twice a working day), the sensors are recalibrated when no
discharge flows through the flume. The water surface is then a level surface used as reference to
determine the position of the sensors relative to the base plate of the model. The height of the water
surface relative to the top of the base slab of the hydraulic structure is measured manually for both
the upstream and the downstream sensor and the distance between the sensor and the water surface
is denoted for the upstream and downstream sensor. In that way, the position of the sensor relative
to the top of the base slab is known. These values are then converted to an upstream and downstream
water level at prototype scale.
Subsequently a certain flow rate is set and once the water levels upstream and downstream of the
model are stabilized, the corresponding distances measured by the ultrasonic distance sensors are
denoted. Because of the fluctuating water level, the values given by the sensors fluctuate as well. An
average value is denoted. By use of the weir downstream of the flume, the downstream water level
can be raised in order to attempt to reach the target difference in water level between the river Meuse
and the Heerenlaak pond.
4.2 Velocity measurements
Velocity measurements have been executed during two separate testing sessions on the
F_LWh_U_B&C-configuration. Each session had some differences in testing procedure. The specifics
of each testing session will be explained further on. For all measurements, the Valeport Model 801
electromagnetic current meter has been used. A brief description of this device can be found in
paragraph 2.1.2 or in Appendix B. During a period of 1 minute, a velocity measurement was done every
second, after which the fixed average and the standard deviation are calculated by the electromagnetic
current meter.
4.2.1 Testing procedure I
Measurements upstream of the scale model were executed for two different data points (Q, hupstream,
Δh). For the first data point, velocity measurements are performed at three transverse locations (i.e.
perpendicular to the flow direction): in the middle of the current flume (indicated with A in Figure 68),
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close to the side of the current flume (C in Figure 68) and in the middle of the inlet section of a single
cycle (B in Figure 68), i.e. in between the two previous locations.
Figure 68: Indication of the transverse locations of the velocity measurements (adapted from Vercruysse et al., 2013)
For all locations, measurements are executed at different heights above the bottom of the current
flume in order to cover the complete section of the flume, both in height and width of the flume. The
height of the current meter is varied by stepwise moving it up or down on a steel bar. The final height
of the current meter is measured with a yardstick. The afore described testing method is executed for
two different longitudinal locations in front of the inlet section of the hydraulic structure (i.e. at 5 m
and 10 m upstream of the inlet of the hydraulic structure).
For the second data point, velocity measurements are only carried out at location B, i.e. in the middle
of the inlet section of a single cycle. The height of the device and its longitudinal position are again
being varied.
Figure 69: Electromagnetic current meter on the metal bar during the measurements
78
4.2.2 Testing procedure II
During the second testing session, measurements are carried out for a fixed height of the measuring
device, while the longitudinal position of the current meter is varied. The transverse position
corresponds to location B as indicated in Figure 68. Thus graphs showing the measured time-average
velocity for different distances relative to the inlet of the structure are obtained. This is done for two
separate data points, namely the peak discharge and the discharge at the dip of the third regime. The
fixed height of the device is at ± 1.2 m (prototype) below the upstream water level. This implies that
the height of the current meter depends on the data point being measured.
4.3 Visualization of the flow pattern using colouring dye
The colouring dye is injected at a certain distance below the water surface using a catheter. The
catheter has a length of 5 ¼ inches, i.e. 13.335 cm and an opening of 14 gauge, i.e. 1.98 mm. The
injection takes place in front of the middle of the inlet section at a distance of about 5 m upstream of
the structure. The colouring dye used in the experiments is Patent Blue V (also known as Food Blue 5
or Sulphan Blue). The injected volume of colouring dye is roughly between 5 and 10 mm³ for each test.
Figure 70: catheter used for the colouring dye experiments
During the injection of the dye, the flow pattern is being filmed. Using the image processing package
Fiji Is Just ImageJ these records are being processed to obtain a visualization of the flow pattern.
5. Tested configurations of the Full and Simple models
Besides the model of the design made by nv De Scheepvaart (i.e. the Full model), other configurations
were developed and tested in the Simple model. The latter configurations were tested in order to
elucidate the different factors influencing the Qh-relation of the hydraulic structure as well as to find
possible improvements of the designed structure. The results of these tests will be discussed further
79
on. All these configurations are obtained by modifying the two models (Full and Simple) which have
been discussed previously. Throughout this document, these configurations are referred to by well-
chosen abbreviations. These abbreviations are explained in Table 6 and the corresponding
configurations will be explained in this section.
Table 6: Explanation of the used abbreviations
Abbreviation Explanation
F Full model
S Simple model
LWh Labyrinth weir with a wall height of 3 m
Wh Linear weir with a wall height of 3 m
Wh/2 Linear weir with a wall height of 1.5 m
noCul The structure is not integrated in a culvert.
U There are U-beams on both sides of the structure.
noU There are no U-beams.
UMeuse There is a U-beam on the side of the Common Meuse. There is no U-beam on
the side of the Heerenlaak pond.
Raisedroof In comparison to the other configurations, the roof is raised by 1 m. The
height of the U-beam changes from 1 m to 2 m.
B&C The beams and columns in the internal structure are present.
C The columns supporting the roof are present in the internal structure. The
beams supporting the roof are not present.
5.1 F_LWh_U_B&C
This configuration concerns the Full model as designed by nv de Scheepvaart. This model features a
Labyrinth Weir in a culvert, the roof of which is supported by Beams and Columns and which has U-
beams both on the side of Heerenlaak and on the side of the Common Meuse.
80
Figure 71: F_LWh_U_B&C
5.2 F_LWh_U_C
In comparison to the previous model the beams supporting the roof are removed from the structure,
but the columns are still present. This implies enlarging the available area through which water can
flow inside the structure. The area increases with 3.27 %, in comparison to F_LWh_U_B&C (30.36 m²
vs. 29.4 m², both figures being on prototype scale). The removal of the three beams might also alter
the flow patterns in the structure.
Figure 72: Indication of the removal of the supporting beams in F_LWh_U_C
Meuse Heerenlaak pond
81
Figure 73: View inside the labyrinth weir without supporting beams
5.3 F_LWh_U
In comparison to F_LWH_U_B&C, both the beams and columns are removed from the structure. This
further increases the available area inside the structure in comparison with F_LWh_U_C. The available
area is now 31.8 m², i.e. an increase of 8 % compared to F_LWH_U_B&C. This configuration is tested
to investigate the influence of further enlarging the available section inside the structure. From a pure
practical point of view, this configuration is not relevant since columns are adopted in the proposed
design to support the roof, limit the length of the prefabricated wall elements and provide breaking of
the nappe.
Figure 74: Indication of the removed parts in F_LWh_U
Meuse Heerenlaak pond
82
Figure 75: Indication of the removal of columns and beams by comparing F_LWh_U_B&C (left) with F_LWh_U (right)
5.4 S_LWh_noCul
This configuration is tested on the Simple model. It is a labyrinth weir without a roof on top of it. The
labyrinth weir has the same wall height of 3 m as the labyrinth weir in the Full model. Pictures of this
configuration can be seen in Figure 76 and Figure 77.
Figure 76: Front view of S_LWh_noCul (upstream)
83
Figure 77: Top view of S_LWh_noCul
5.5 S_LWh_U
This configuration is tested on the Simple model. It features a labyrinth weir with a height of 3 m,
integrated in a culvert with U-beams. This configuration should be identical to F_LWh_U, although
there are some minor differences in dimensions between the Full and Simple models, which will be
discussed further on (see paragraph 5.12). This configuration is shown in Figure 79.
Figure 78: Longitudinal cross-section of the Simple model (S_LWh_U)
Figure 79: Front view of S_LWh_U
84
5.6 S_LWh_noU
This configuration is tested on the Simple model. It features a labyrinth weir with a height of 3 m,
integrated in a culvert without U-beams. This increases the inlet and outlet section from 30 m² to 41
m². This is an increase of 36.6 %.
Figure 80: Front view of S_LWh_noU from the side of Heerenlaak (downstream)
Figure 81: Indication of the Simple model with the removed U-beams (S_LWh_noU)
5.7 S_LWh_UMeuse
In comparison to S_LWh_U, the U-beam at the downstream side of the structure, i.e. at the side of
Heerenlaak pond, is removed. This implies that there is only a U-beam at the side of the Common
Meuse. This is indicated in Figure 82. The upstream U-beam needs to prevent the ingress of floating
debris from the Meuse into the Heerenlaak pond, but the downstream U-beam is believed to have no
such function.
85
Figure 82: Indication of the removed U-beam in S_LWh_UMeuse
Figure 83: View on downstream side of S_LWh_UMeuse with removed U-beam
5.8 S_LWh_U_Raisedroof
This configuration features a labyrinth weir with a height of 3 m in a culvert in the Simple model. The
roof of the structure (i.e. the culvert ceiling) is raised over a distance of 1 m. The soffit of the U-beams,
however, remains at the crest level of the weir, i.e. at + 26.7 m T.A.W.. Due to heightening the roof of
the structure, the height of the U-beam increases to 2 m. A cross section is shown in Figure 85. By
heightening the roof of the structure, the available area over which the water can flow in the structure
doubles to 134 m². However, the area of the inlet and outlet sections remains unchanged and is still
equal to 30 m².
Note that this configuration does not fit within the dike with its current dimensions. This can be solved
by reducing the length of the structure, which will lead to a different crest length over the weir, a
different angle between the walls of the labyrinth and the longitudinal axis, … However, to make a
well-based comparison, the length of this configuration remains the same as for the other
configurations. As a result, this configuration has no direct practical use for the hydraulic structure at
Upstream
(Meuse)
Downstream
(Heerenlaak)
86
Heerenlaak. Nevertheless, testing this configuration might provide additional insight with regard to
improvements.
Figure 84: Front view of S_LWh_U_Raisedroof
Figure 85: Longitudinal cross-section of S_LWh_U_Raisedroof, with indication of the heightened roof
5.9 S_Wh_U
This configuration of the Simple model features a linear weir with a height equal to 3 m in a culvert
with U-beams, i.e. the same height as the labyrinth weir in the Full model. This configuration implies
that the available area in the structure is the same as the area of the inlet and outlet section. The
location of the linear weir is in the middle of the culvert. This weir has a length of 11 m, in prototype
dimensions. Thus the available section above the weir is 11 m².
Upstream
(Meuse)
Downstream
(Heerenlaak)
87
Figure 86: Longitudinal cross-section of S_LWh_UMeuse, with a linear weir with a height of 3 m
5.10 S_Wh/2_U
In comparison to S_Wh_U, the height of the linear weir is divided by two, i.e. 1.5 m. The crest level of
the weir is then at + 25.2 m T.A.W. The available area in the structure then becomes 27.5 m², in theory.
This represents an increase of 150 % in comparison to S_Wh_U. Note that for this configuration the
water does not necessarily need to dive under the U-beam and then go over the crest of the weir. This
is indicated in Figure 87. For this model, the available section in the inside of the structure is 83.33%
of the inlet section, which is 33 m².
Figure 87: Longitudinal cross-section of S_Wh/2_U, with a linear weir with a height of 1.5 m
Figure 88: Front view of S_Wh/2_U with sight on the linear weir at half the height of the inlet
Upstream
(Meuse)
Downstream
(Heerenlaak)
Upstream
(Meuse)
Downstream
(Heerenlaak)
88
5.11 S_Wh_noU
In comparison to S_Wh_U, the U-beams are removed from the culvert, thus increasing the in- and
outlet section.
Figure 89: Longitudinal cross-section of S_Wh_noU, without U-beams
5.12 Verification of the scale model dimensions
5.12.1 Full Model
In order to manufacture the Full scale model at a limited cost, the technical staff of the laboratory has
made use of readily (commercially) available MDF-plates and stainless steel bars. This implies that the
geometry in the scale model is not exactly equal to the one in the design proposed by nv de
Scheepvaart. The MDF-plates used to construct the model have a thickness of approximately 1.85 cm,
which corresponds to a thickness of 33.3 cm in the prototype, whereas nv de Scheepvaart suggested
a value of 30 cm in the conceptual design. As a consequence, the inlet area of the Full model is 27.32
m² at the scale of the prototype, which is 9% smaller than the value of 30 m² suggested in the
conceptual design. The columns and beams in the scale model have a square cross-section with a side
of 2.5 cm, which corresponds to a side of 45 cm for the prototype, whereas the conceptual design
suggested a value of 40 cm. This means that there is a reduction in the available flow area over the
labyrinth weir with 2 %.
5.12.2 Simple Model
The area of the inlet section of the Simple Model is 27.81 m² at prototype scale, which is 9% smaller
than the value of 30 m² suggested in the design. The area of the outlet section is 28.83 m² at prototype
scale, which is 4% smaller than the suggested value of 30 m². The MDF-plates used to construct the
model have a thickness of 1.6 cm while for the Full model this was 1.85 cm. The thickness of 1.6 cm
corresponds to a thickness of 28.8 cm at prototype scale. The suggested value is 30 cm.
Upstream
(Meuse)
Downstream
(Heerenlaak)
89
Chapter 5: Data Processing
1. Remarks about the discussed data
An important remark concerning the data and the processing of it, is that the values used for
comparisons and explanations are already converted from model to prototype-scale. Hence all
discussed data will be based upon the values as they would appear in the real-life structure at
Heerenlaak.
Furthermore, all data discussed, corresponds to the discharge over a labyrinth weir of two cycles or a
structure with an equivalent width. This is indicated in Figure 90.
Figure 90: difference between one cycle and one unit
2. Data processing
During the experiments, a lot of data is gathered which is not relevant for the actual analysis of the
hydraulic structure or still has to be processed. Hence, a selection of the useful data is made. The
specific reason and method of selection and processing, will be explained in this chapter,
demonstrated on the data of the original model of the hydraulic structure (F_LWh_U_B&C).
1 cycle
1 unit
90
For the original model, the water heights upstream and downstream of the labyrinth weir in a culvert
are measured according to the method explained before. An overview of all data points measured for
the original configuration of the model, is shown in Figure 91. In this graph, the discharge Q is shown
in function of the upstream water height hupstream.
Figure 91: An overview of all data measured on F_LWh_U_B&C
After setting a certain target discharge and measuring the upstream and downstream water level, the
downstream water level is increased and the upstream and downstream levels are measured again.
This process of raising the downstream level is repeated several times. Afterwards, the discharge is
increased and this process is repeated.
Executing the measurements in this manner, makes that the different data points on this graph cannot
be compared with each other. The reason for this is that for the same upstream water level, several
discharges through the structure are possible, depending on the downstream water level. Hence the
data points can only be compared with each other when the difference between the up- and
downstream water level is the same.
The difference between the Meuse upstream and the Heerenlaak pond downstream of the hydraulic
structure is at a more or less constant value of 2 m, as explained in chapter 2, paragraph 2.1 (Figure 7).
Hence the data points selected to analyse the structure, will be the ones with a water level difference
of 2 m.
0
20
40
60
80
100
120
140
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
F_LWh_U_B&C
91
However, given the test facilities it is practically impossible to reach exactly the value of 2 m. Therefore,
the values measured having an up/downstream difference close to 2 m will be used to interpolate in
order to reach a constant up/downstream difference of 2 m which can be used for solid comparisons.
This is illustrated in Figure 92 were the data measured having an up/downstream difference of 2 m +/-
0.05m are interpolated to reach a constant difference of 2 m.
Figure 92: Measured data points and interpolated values (F_LWh_U_B&C)
Besides the practical difficulty in reaching the exact difference in up/downstream level of 2 m, also a
structural difficulty prevented reaching the 2 m difference. This is because the height of the
downstream water level is dependent on the discharge through the flume and the height of the weir
at the downstream end of the flume (see chapter 4, paragraph 1.1). When this weir is flat (at the level
of the flume base), the downstream water level for a given discharge cannot be lowered anymore.
When the upstream water level related to that given discharge is less than 2 m higher than the
mentioned downstream water level, reaching the target difference of 2 m is not possible. This problem
is often encountered in the first part of the Qh-relation of the tested models, when the water flows
freely over the labyrinth weir or rectangular weir. When parts of the structure start to work under
pressure, for example in case of a drowned inlet, the aforementioned problem disappears.
Since in this first part of the Qh-relationship the downward water level does not have an influence on
the upstream water level, it is not necessary to aim for a constant difference of 2 for comparison with
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
2 m +/- 0.05 m
Interpolation 2 m - curve
92
data from other models. This is illustrated in Figure 93, where the first part of the curve has the same
trend for various differences between up- and downstream water level, while for higher upstream
water levels the corresponding curves start to deviate. This transition will be further elaborated in the
results section.
Figure 93: Measured data points with different differences in up/downstream (F_LWh_U_B&C)
In conclusion, for the analysis and discussion of the data taken on different configurations, only the
interpolated data having a constant difference in up/downstream water level of 2 m will be displayed
together with the data from the first part of the curve where the downstream water level does not yet
influence the upstream water level.
3. Accuracy of the results
The accuracy of the results is demonstrated in Figure 94 by comparing data measured on
F_LWh_U_B&C on different occasions during the year. In between those different testing sessions, the
ultrasonic level sensors have been replaced or repositioned. Hence, a systematic measuring error
based on the location of the sensors, is excluded.
0.00
20.00
40.00
60.00
80.00
100.00
120.00
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
1 m +/- 0.05 m
1.5 m +/- 0.05 m
2 m +/- 0.05 m
2.5 m +/- 0.05 m
93
Figure 94: Comparison of data measured at different dates on the F_LWh_U_B&C
Figure 94 illustrates that over a period of time of 3 months, similar data values were measured. During
this period, the scale model was modified and moved, as well were the measuring sensors. This
indicates that the measurements were taken accurately and are reproducible, notwithstanding the
accuracy of the equipment.
To quantify the average error of the measurements, a kernel interpolation has been applied in order
to attain a smooth curve through this data. By applying this kernel, a theoretical, smoothened value
for the discharge, corresponding to each upstream height (in total 105 data points) for which
measurements have been performed, is calculated. This theoretical value is calculated by attributing a
weighing factor to each data point. This weighing factor depends on the square of the inverse of the
difference in upstream water level between two points: the point for which a theoretical discharge is
calculated and the point for which the weighing factor is calculated. After calculating the weighing
factor for each point, the weighing factors are scaled so the sum is 1. Thus the formula to calculate the
weighing factor is given by:
In which
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
9-11 februari 23 - 26 februari 15 - 16 april 23-27 april
94
n is the data point for which a theoretical discharge is calculated [-]
j is one of the other data points, i ranges from 1 to 105 and cannot be equal to n [-]
is the weigh factor for data point i to calculate the theoretical discharge for data point n [-]
m is the total number of data points, 105 in total [-]
hni is the difference in upstream water level between data point n and data point j [m]
The smoothened theoretical discharge corresponding to data point n is found by applying the weighing
factors on the discharges i:
is the smoothened value of the discharge, corresponding to data point n [m³/s]
is the measured discharge corresponding to data point j [m³/s]
These theoretical discharges are compared to the measured discharges, corresponding to a given n,
and the difference in discharges is expressed relative to the theoretical discharge. This is the relative
error of data point n. Since this value can either be negative or positive, the absolute value is taken:
is the relative error corresponding to data point n
Afterwards, the mean error is found by taking the mean of the relative errors of all data points.
The resulting mean error is 2.05 %, indicating that the tests have been performed with a good accuracy,
and were repeatable over the entire measurement period.
95
Chapter 6: Results and discussion
1. Introduction
The culvert with an integrated labyrinth weir is a complex structure and the presence of the U-shaped
beams even enhances the complexity of the proposed design. A simple understanding of this structure
is not evident when solely based upon the scale model tests of the proposed design (F_LWh_U_B&C).
Therefore, several more simple configurations have been defined and tested in order to meticulously
investigate the influence of the different aspects of the structure and to obtain, if possible, full insight
in the structure and its Qh-relation. Throughout this chapter, an overview of the tested configurations
and the obtained results will be given, followed by a discussion and comparison of the different
configurations.
The tested configurations have been described in detail in chapter 4, paragraph 5. In Table 7
underneath, a brief overview of the used abbreviations and a description of the corresponding
configurations is repeated for the sake of readability of this chapter.
Table 7: Used abbreviations and a description of the corresponding configuration
Abbreviation Description of the configuration
S_Wh_U Simple model, linear weir in a culvert with U-beams
S_Wh/2_U Simple model, linear weir in a culvert with a height equal to 1.5 m,
with U-beams
S_Wh_noU Simple model, linear weir in a culvert, no U-beams
S_LWh_noCul Simple model, labyrinth weir, not in a culvert
S_LWh_noU Simple model, labyrinth weir in a culvert, no U-beams
S_LWh_U Simple model, labyrinth weir in a culvert with U-beams
S_LWh_U_Raisedroof Simple model, labyrinth weir in a culvert with a raised roof.
S_LWh_UMeuse Simple model, labyrinth weir in a culvert with a U-beam on the side of the
Meuse
F_LWh_U_B&C Full model, labyrinth weir in a culvert with U-beams, with beams and
columns
F_LWh_U_C Full model, labyrinth weir in a culvert with U-beams, only columns
F_LWh_U Full model, labyrinth weir in a culvert with U-beams, no beams and
columns
96
As previously mentioned, the simple model is constructed without beams and columns in the internal
structure, in contrast to the full scale model F_LWh_U_B&C.
2. Results
2.1 S_Wh_U
One of the most basic and understandable hydraulic structures, is a simple, rectangular sharp-crested
weir. To investigate the influence of such a linear weir being in a culvert, tests are performed on the
S_Wh_U-configuration. By comparing the experimental data with the theoretical formula for a sharp-
crested weir, the impact of the culvert and the U-beams on the Qh-relation may be assessed. The Qh-
relation of such a weir is given by the following formula:
In this formula is the upstream head relative to the crest level of the weir. However, since the
velocity head is negligible compared to the total upstream head, it will be neglected. In that case the
formula is reduced to the formula of Poleni.
The crest length of the weir in the simple model is ± 0.64 m, which is ± 11.52 m on prototype scale. A
Cd-coefficient of the weir can be calculated by transforming the previous formula to the following form:
The Cd-coefficient of the linear weir will be calculated below not only for the S_Wh_U configuration
(Table 10) but for comparison purposes also for the S_Wh_noU (Table 8) and S_Wh/2_U (Table 9)
configuration.
For the S_Wh_noU configuration, water starts to flow over the structure before the upstream water
level reaches the soffit of the culvert at 27.7 m T.A.W.. Hence only data points for upstream water
levels below 27.7 m T.A.W. are taken into account when determining the Cd-coefficient.
97
Table 8: Calculation of the Cd-coefficient based on S_Wh_noU
S_Wh_noU
Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]
7.91 27.19 0.49 0.67
20.17 27.46 0.76 0.89
Average: 0.78
For the S_Wh/2_U-configuration, water flows freely over the weir for an upstream water level in the
range from 25.2 m T.A.W. (crest level of linear weir) to 26.7 m T.A.W. (the soffit of the U-beam).
Table 9: Calculation of the Cd-coefficient based on S_Wh/2_U
S_Wh/2_U
Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]
12.77 25.81 0.61 0.80
30.27 26.27 1.07 0.80
46.62 26.65 1.45 0.78
Average: 0.79
For the S_Wh_U configuration, water only starts flowing over the linear weir when the water level
reaches the soffit of the U-beam. This might influence the Cd-coefficient. For higher upstream water
levels, the internal structure becomes submerged and the flow pattern changes.
Table 10: Calculation of the Cd-coefficient based on S_Wh_U
S_Wh_U
Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]
5.10 27.07 0.37 0.68
7.41 27.17 0.47 0.67
12.28 27.30 0.60 0.78
21.45 27.59 0.89 0.75
Average: 0.72
The average Cd-coefficients corresponding to S_Wh/2_U and S_Wh_noU are very similar (0.79 and
0.78) whereas the Cd-coefficient of S_Wh_U is circa 10 % lower (0.72). According to the theory (see
below), the Cd-coefficient of S_Wh/2_U is supposed to have a higher value. However, no conclusions
will be made out of this, since a systematic increase of the linear weir height with 2 mm during the
experiments (e.g. caused by swelling of the wood or a calibration error), would imply a 10% increase
in the Cd-coefficient.
98
These experimentally obtained Cd-coefficients are compared with Cd-coefficients found in the
literature. Rehbock (1929) proposed a formula for the calculation of the discharge over a rectangular,
sharp-crested weir.
With hR being the effective head given by:
Since hR is used in this formula, the Cd-coefficients are also derived from the data (Table 11) using this
definition. For this formula, Rehbock proposes a theoretical determination of the Cd-coefficients:
In this formula, P is the height of the weir. This formula is valid for 0.003 < h < 0.75 m, h/P < 1, b > 0.3
and P>0.1. These criteria are fulfilled for the data shown in Table 11 on the S_Wh_U and the
S_Wh/2_U-configuration, whereas data for which these conditions are not fulfilled is left out. In this
table, a comparison between the theoretically and experimentally derived Cd-coefficients is given.
Table 11: Comparison between the experimentally and theoretically derived Cd-coefficients
S_Wh_U
Q [m³/s] h [m] Theoretical Cd [-] Experimental Cd [-]
5.10 0.37 0.61 0.67
7.41 0.47 0.62 0.66
12.28 0.60 0.62 0.77
S_Wh/2_U
Q [m³/s] h [m] Theoretical Cd [-] Experimental Cd [-]
12.77 25.81 0.72 0.79
The theoretical Cd-coefficients are underestimated by about 10 % compared to the experimental Cd-
coefficients. However, as is mentioned before, a systematic error of 1 or 2 mm would already imply an
increase in discharge coefficient of 5 to 10 %. Moreover, the weir inside the scale model cannot be
considered to be a sharp-crested weir, given the finite crest width of the weir (i.e. a MDF – plate of 16
mm).
99
The theoretical formulas of a sharp-crested weir are plotted on a graph with both a Cd-coefficient equal
to 0.72 and 0.79 and are compared with the experimental results of the S_Wh_U – configuration. This
graph is shown in Figure 95.
Figure 95: Comparison of S_Wh_U with the theoretical curves for flow over a weir
A good correspondence between the theoretical curves and the measured data can be seen for
upstream water levels smaller than about 27.7 m T.A.W., meaning that the structure acts as a simple
rectangular weir. The discharge only depends on the upstream level, more specifically on the upstream
head above the weir crest, and is independent of the difference between the up- and downstream
level. At higher upstream water levels, the influence of the U-beam is noticeable.
Starting from an upstream water level of 28.0 m T.A.W., the theoretical curve and measurements begin
to diverge. A second flow regime is perceived. In configuration S_Wh_U, the constraining flow section
is the overflow section between the weir crest and the culvert roof, as will be explained further on. As
such, it is considered to act as the inlet of the culvert (instead of the actual inlet) and becomes
submerged at an upstream level of 28.0 m T.A.W.. This is conform with the literature (e.g. Chow, 1959),
stating that the inlet of a culvert is submerged when the upstream water level is at 1.2 to 1.5 times the
inlet height (i.e. 26.7 m T.A.W. + 1.2 x 1 m = 27.9 m T.A.W. to 28.2 m T.A.W.). The structure acts
comparable to flow through a culvert in regime V.
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_Wh_U Theoretical formula, Cd=0.72 Theoretical formula, Cd=0.79
100
This can be verified by use of the theoretical formulas for flow through a culvert, regime V (see chapter
3, paragraph 4.3). The Cd-coefficient is derived from data on S_Wh_U.
- For flow through a culvert, regime V:
This leads to:
With being the height of the upstream water level and z the height of the culvert invert.
Since in configuration S_Wh_U, the constricting overflow area is the overflow area between the roof
of the culvert and the crest of the weir, this is considered to be the inlet of the culvert in this formula,
with section .
Table 12: Calculation of the Cd-coefficient
Flow through a culvert (Regime V)
Q [m³/s] hupstream [m T.A.W.] hdownstream [m T.A.W.] Cd [-]
47.99 28.31 26.31 0.74
50.03 28.56 26.56 0.72
Average: 0.73
The formula of flow through a culvert is valid from the moment the upstream water level is above
approximately 28.0 m T.A.W. and as long as the downstream water level does not exceed a height of
26.7 m T.A.W. (i.e. the level of the soffit of the U-beams).
When comparing these results (red curve in Figure 96) with the experimental results, again a good fit
is obtained.
101
Figure 96: Theoretical fit of flow through a culvert on S_Wh_U
S_Wh_U eventually reaches a maximum discharge of 52.6 m³/s at an upstream water height of 29.25
m T.A.W.. This maximum is reached when the outlet is not yet fully drowned. The water level still flows
underneath the downstream U-beam. Figure 97 shows what is meant by ‘a drowned outlet’.
Figure 97: Schematical representation of a drowned outlet
An important remark concerning the drowned outlet is that a downstream water level, measured
during the experiments, higher than 26.7 m T.A.W. does not necessarily imply a drowned outlet. When
high discharges pass through the structure, a high flow velocity is reached at the outlet of the hydraulic
structure, where also a contraction takes place caused by the downstream U-beam. The measured
downstream water level is thus usually higher than the water level at the outlet, since the downstream
level is measured in the flume approximately 1.5 m behind the outlet.
0.00
20.00
40.00
60.00
80.00
100.00
120.00
26.70 27.70 28.70 29.70 30.70 31.70 32.70 33.70
Q [
m³/
s]
hupstream [ m T.A.W.]
S_Wh_U Theoretical formula, Cd=0.87
Theoretical formula, Cd=0.79 Flow through a culvert
Upstream Downstream
26.7 m T.A.W.
27.7 m T.A.W.
23.7 m T.A.W.
Outlet drowned
102
This is the reason why for S_Wh_U, the outlet is drowned at a registered downstream water level of
27.25 m T.A.W. instead of 26.7 m T.A.W.. Therefore, the determination of whether the outlet is
drowned or not, is mainly visually.
Figure 98: Indication of the rising water level between the outlet and the downstream sensor
For upstream water levels higher than 29.25 m T.A.W., the outlet of S_Wh_U is fully drowned. The
water level just downstream of the hydraulic structure reaches or exceeds the soffit of the U-beam, as
illustrated in Figure 97. The discharge diminishes again and reaches a minimum of 43.6 m³/s for an
upstream water level of 31.41 m T.A.W.. This regime seems comparable to flow through a culvert, type
IV (see chapter 3, paragraph 4.3).
Beyond this water level, the discharge increases slightly and finally becomes constant. The reason for
this ‘dip’ in the curve is not yet understood. A possible explanation could be the presence of the U-
beams, or the formation of eddies inside the structure. More about this local minimum is explained in
section 2.12.
In conclusion, three different flow regimes can be discerned on the Qh-relation of the linear weir in a
culvert with U-beams. First, a regime where the water can flow freely over the weir. Secondly, a regime
in which the constraining inlet section is submerged. Finally, a regime in which both the constraining
inlet section and outlet are submerged. This third regime has a local minimum when the upstream
water level is at a height of 31.4 m T.A.W.. This is clearly illustrated in Figure 99.
103
Figure 99: Indication of the different regimes observed in the Qh-relation of S_Wh_U
2.2 S_Wh_U and S_Wh/2_U
To investigate which parameter is the most restricting on the discharge through the linear weir in a
culvert with U-beams (S_Wh_U), experiments have been performed on the same model but with a
weir crest which is lowered in the culvert (S_Wh_U/2). Lowering the height of the weir crest with 1.5
m increases the available area through which water can flow in the hydraulic structure with 150%,
while the in- and outlet section remain identical for both models.
Based upon the results, shown in Figure 100, a considerably higher discharge can be noticed for a
certain upstream water level for S_Wh/2_U in comparison to S_Wh_U. The maximum measured
discharge for S_Wh/2_U is 147.7 m³/s for an upstream water level of 29.22 m T.A.W.. For S_Wh_U this
is 52.6 m³/s for an upstream water level of 29.25 m T.A.W..
The peak discharge for both models seems to occur at similar upstream water levels, confirming that
the peak discharge is reached when the outlet becomes submerged. At the peak discharge, the
downstream water level is at a height of about 27.2 m T.A.W..
0
10
20
30
40
50
60
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_Wh_U
Regime 1:
Free overflow
over labyrinth
Regime 3:
Inlet and outlet submerged
Regime 2:
Inlet
submerged
Local minimum in regime 3
104
Figure 100: Influence of the overflow section of the weir (S_Wh_U vs. S_Wh/2_U)
For the data measured on the S_Wh/2_U-configuration, the peak is much sharper when compared to
S_Wh_U. This is because the target difference in up/downstream water level of 2 m could not be
reached. At 25.2 m T.A.W., the upstream level reaches the height of the low-crested weir and water
starts to flow over the weir. Because the height of the weir crest is very low compared to the bottom
of the current flume, the downstream water level already reaches the crest of the weir when the
upstream water level is approximately 26 m T.A.W.. From that moment on, the weir acts as a
submerged weir and the discharge over the weir is constrained by the downstream water level.
The theoretical formula for the discharge over a submerged weir (Villemonte, 1947) is used to verify
this:
The Cd-coefficient of the unsubmerged weir is required for this calculation (S_Wh/2_U), which was
determined previously and found equal to 0.79. However, since this Cd-coefficient is based on only 2
data points, a better match could be obtained with a Cd-coefficient of 0.83. These theoretical curves
are shown in Figure 101 with as input the values measured for hupstream and Δ h and as output, the
theoretical discharge based on the formula of Villemonte.
0
20
40
60
80
100
120
140
160
25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2 33.2
Q [
m³/
s]
hupstream [ m T.A.W.]S_Wh/2_U S_Wh_U
105
Figure 101: Theoretical fit on S_Wh/2_U
This curve is valid until an upstream water level of approximately 28 m T.A.W., i.e. when the inlet
becomes submerged. In this case, the inlet section of the culvert is the most constraining factor, since
the overflow area between the crest of the weir and the roof of the culvert is larger than the inlet of
the culvert. A description of the inlet of the culvert being submerged is shown in a conceptual drawing
in Figure 102. However, the inflexion point indicating a transition from the 1st to the 2nd regime, is
almost undiscernible.
Figure 102: Schematical representation of the drowned inlet
At upstream water levels higher than 29.2 m T.A.W., the outlet of the culvert is again fully drowned
and the discharge lowers until reaching a more or less constant value at an upstream height of 31.2 m
T.A.W..
0
20
40
60
80
100
120
140
160
25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2 33.2
Q [
m³/
s]
hupstream [ m T.A.W.]
S_Wh/2_U Flow over submerged weir, Cd=0.79 Flow over submerged weir, Cd=0.83
Upstream Downstream
26.7 m T.A.W.
27.7 m T.A.W.
23.7 m T.A.W.
± 28 m T.A.W. Inlet internally drowned
106
At approximately 31.2 m T.A.W., a dip in the curve is observed at a similar location as for S_Wh_U. The
average discharge after this dip is 46.69 m³/s for S_Wh_U and 119.63 m³/s for S_Wh/2_U. This is an
increase of 156%.
2.3 S_Wh_U and S_Wh_noU
By comparing S_Wh_U with S_Wh_noU, the influence of the removal of the U-shaped beams on the
flow over a linear weir in culvert may be analysed.
Figure 103: Impact of U-beams on Qh-relation (S_Wh_U vs. S_Wh_noU)
The same regimes as described previously are still present. During the first regime, no increase in
discharge is perceived by the removal of the U-shaped beams.
During the second, and definitely in the third regime, an increase in discharge occurs due to the
absence of the U-shaped beams. Removing the U-beams results in less losses and thus a higher
discharge for the same upstream head.
The change from the first to the second regime occurs again for an upstream water level of
approximately 28 m T.A.W.. The peak of the data occurs at higher upstream water levels for S_Wh_noU
(54.43 m³/s at 29.62 m T.A.W in comparison to 52.62 m³/s at 29.25 m T.A.W.)
0
10
20
30
40
50
60
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]S_Wh_noU S_Wh_U
107
The transition from the first to the second regime occurs at the same upstream water level for both
configurations. This indicates that the main restraining factor is the overflow area between the weir
crest and the soffit of the culvert. As such, the discharge is not significantly influenced by enlarging the
inlet of the culvert. This also confirms the assumption of this overflow area acting as the inlet of the
culvert. Otherwise the transition would occur at an upstream level of about 28.5 to 29.7 m T.A.W.. (i.e.
1.2 to 1.5 times the height of the culvert inlet according to Chow, 1959).
The third regime is again characterized by the presence of a local minimum as is also observed in the
Qh-relation of S_Wh_noU. Several tests confirm the presence of this dip in the curve. By comparing
S_Wh_U with S_Wh_noU, it can be concluded that the U-beams do not have an impact on this dip and
on the shape of the Qh-relation in general.
2.4 S_LWh_noCul
Since the proposed hydraulic structure consists of a labyrinth weir in a culvert, the theoretical specifics
of this labyrinth weir are also verified by use of a scale model, consisting of just a labyrinth weir
(S_LWh_noCul).
The theoretical curve, describing the Qh-relation of a labyrinth weir is compared to the data measured
on S_LWh_noCul. The theoretical Qh-relation is calculated as follows:
HT is again the upstream head, relative to the crest of the labyrinth weir (26.7 m T.A.W.). In the graph,
Hupstream will be used, which equals HT + 26.7 m. In this case, the upstream velocity head is not negligible
and will be used in the formulas.
Cd is calculated based on the trend lines composed by Tullis et al. (1995):
However, this formula is valid for an apex width t ≤ A ≤ 2t, HT / P < 0.9, t ≈ P/6 and a quarter-round
crest shape with radius R = P/12. These conditions are mostly not fulfilled, but for the sake of the
comparison, this formula has been applied anyhow.
The crest length is calculated as follows (see chapter 3, Figure 14):
108
N, the number of cycles, is two for this configuration. L1 is 89.4 cm, the inner apex width is 1.8 cm and
the outer apex width is 5.3 cm. These dimensions are measured on the scale model. Thus they need
to be multiplied with the scale factor of 18 to obtain the dimensions on the scale of the prototype. The
theoretical curve and the measured data can be seen in Figure 104.
Note that the data for S_LWh_noCul do not correspond to the target water level difference of 2 m,
since it was practically not possible to attain this difference in the current flume (see chapter 5,
paragraph 2). However, as has been mentioned in the literature review (chapter 3, paragraph 3.5) and
as can be seen from the formula giving the QH-relation of a labyrinth weir, it is only the upstream
water level which plays a role, as long as the weir is not submerged downstream.
Figure 104: Theoretical curve compared to S_LWh_noCul
The theoretical curve and the measured data only correspond for low discharges. As explained before,
the conditions for applying the formula of Tullis are not fulfilled, which might be the cause.
For fixed discharges (among others Q = 66.3 m³/s and Q = 149.4 m³/s) the downstream water level was
varied by increasing the height of the downstream weir to investigate the influence of increasing
downstream water levels on the discharge. As long as the downstream water level does not exceed
0
50
100
150
200
250
300
26.7 27.2 27.7 28.2 28.7 29.2
Q [
m³/
s]
Hupstream [ m T.A.W.]
S_LWh_noCulvert Theoretical formula for labyrinth weir
109
the crest of the weir, the upstream water level remains unaffected and submergence has no impact
on the capacity of the structure. This is consistent with the research conducted by Taylor (1968), Tullis
et al. (2006) and Lopes et al. (2009). Thus, by avoiding submergence of the hydraulic structure, a
significant increase in capacity can be obtained.
For several fixed discharges, both submerged and modular flow conditions have been tested. For these
discharges, a graph with Hd/H0 vs. HT/H0 is created to verify whether the measurements correspond to
the graph describing submergence effects on labyrinth weirs developed by Tullis, Young and Chandler
(2005). This graph can be seen in Figure 105. H0 is the head required for a fixed discharge under
modular flow conditions. H0 is not calculated by transforming the formula giving the discharge over a
labyrinth weir, but is known from the measured data corresponding to modular flow conditions.
Figure 105: Submergence effects, red data points are calculated based on measurements, adapted from Tullis et al. (2005)
2.5 S_LWh_noU and S_LWh_noCul
The labyrinth weir in a culvert without U-beams (S_LWh_noU) is tested to investigate the impact of
the culvert ceiling on the Qh-relation over a pure labyrinth weir (S_LWh_noCul). The absence of U-
beams implies that S_LWh_noU starts to be submerged when the upstream water level exceeds a
Submergence effects
110
value of approximately 28.5 to 29.7 m T.A.W. (i.e. 1.2 to 1.5 times D, according to Chow, 1959). Hence,
for lower upstream water levels, there should be no discernible difference in Qh-relation. This is indeed
confirmed by the measurements, as can be seen in Figure 106.
Figure 106: S_LWh_noCul vs. S_LWh_noU
The peak discharge of S_LWh_noU is assumed to be around 184 m³/s, based upon the surrounding
values and comparisons with other configurations. However, this discharge could not be reached
during the experiments due to logistic reasons. No further conclusions can be drawn from this graph.
2.6 S_LWh_U, S_Wh_U and S_Wh/2_U
The next step in understanding the future hydraulic structure, is the addition of the U-beams to the
labyrinth weir in a culvert (S_LWh_U) and to evaluate whether or not the same trends can be discerned
as for the linear weirs in a culvert (S_Wh_U and S_Wh/2_U). The obtained data are shown in Figure
107.
0
20
40
60
80
100
120
140
160
180
200
26.7 27.2 27.7 28.2 28.7 29.2 29.7 30.2 30.7 31.2 31.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_noCul S_LWh_noU
111
Figure 107: Comparison between S_LWh_U, S_Wh_U and S_Wh/2_U
From an upstream water level of 26.7 m T.A.W., i.e. when water starts to flow over the structure, until
an upstream water level of approximately 28 m T.A.W., the first regime can be discerned for S_LWh_U.
This regime is similar to the first regime observed in S_Wh_U and S_Wh/2_U. However, the slope of
the Qh-relation is much steeper for the labyrinth weir compared to the rectangular weir, hence allows
for a larger discharge for equal upstream water levels. A larger crest length, allowing more water to
flow over the labyrinth weir is the cause of this difference in slope between S_Wh_U and S_LWh_U.
S_Wh/2_U has a similar slope during the first regime as S_Wh_U, but starts to flow over at an upstream
height of 25.2 m T.A.W., whereas in case of S_Wh_U this is at 26.7 m T.A.W.; hence the difference in
discharge between S_Wh_U and S_Wh/2_U, as explained before.
The transition from the first to the second regime takes places at an upstream water level of
approximately 28 m T.A.W. for all three configurations. For S_LWh_U and S_Wh/2_U, this is the result
of the inlet of the culvert being drowned. For an inlet with U-beams, this is at an approximate upstream
water level of 28 m T.A.W. (i.e. 1.2 to 1.5 times the height of the inlet). For S_Wh_U, however, the
overflow area between the crest of the weir and the soffit of the culvert is the most constraining
section. The transition occurs at about 28 m T.A.W. as well, but in this case it is the result of the most
restraining flow section being submerged, as was indicated before.
0
20
40
60
80
100
120
140
160
25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_U S_Wh_U S_Wh/2_U
112
The transition point from the second to the third regime differs between S_LWh_U on the one hand
and S_Wh_U and S_Wh/2_U on the other hand. For S_LWh_U, this transition appears at an upstream
level of approximately 29.7 m T.A.W. and a downstream level of 27.7 m T.A.W., whereas for S_Wh_U
and S_Wh/2_U this upstream water level is 29.25 m T.A.W. and downstream level of 27.25 m T.A.W.
(the soffit of the downstream U-beam is at 26.7 m T.A.W.). However, in both cases this transition takes
place when the outlet is on the verge of drowning. Because of the high flow velocities and the presence
of the downstream U-beam, a contraction at the outlet was observed. This explains why the transition
from the second to the third regime occurs at different downstream water levels, while it was
determined visually that in all three configurations the outlet became submerged at that particular
moment.
In the third regime, the discharge of S_LWh_U remains more or less constant around a value of 130
m³/s, which is consistent with the formula of flow through culverts, regime IV (see chapter 3, paragraph
4.3). However, a local minimum is found, which is for all three different configurations at an
approximate upstream water level of 31.2-31.4 m T.A.W.. This local minimum is further discussed in
paragraph 2.12.
The maximal discharge through S_Wh/2_U is about 11% higher than the maximal discharge through
S_LWh_U. This can partially be caused by a larger inlet section of about 20%, considering that the
labyrinth weir reduces the inlet section partially (i.e. by the presence of the upstream apex). However,
since the overflow section between the weir and the culvert soffit is smaller for S_Wh/2_U (approx.
29 m²) compared to the overflow area in S_LWh_U (approx. 66.9 m²), higher energy losses will
decrease this maximal discharge.
In conclusion, the labyrinth weir in a culvert allows for a much higher discharge than a linear weir
during the first regime. In the second regime, the restraining factor is the smallest section through
which the flow needs to pass, in combination with the accompanying energy losses through the
structure.
2.7 S_LWh_U and S_LWh_noU
The impact of the U-beams on the labyrinth weir in a culvert can be assessed by comparing the data
of a labyrinth weir in a culvert with U-beams (S_LWh_U) to the data of the model without U-beams
(S_LWh_noU). This comparison is shown in Figure 108.
113
Figure 108: Impact of the U-beams on a labyrinth weir in a culvert (S_LWh_U vs. S_LWh_noU)
The peak discharge of the S_LWh_noU-configuration is assumed to be about 184 m³/s, based upon the
surrounding values. However, this discharge could not be reached during the experiments due to
logistic reasons.
Removing the U-beams (S_LWh_noU) leads to a higher discharge capacity in comparison to S_LWh_U,
which was also observed on the model with a rectangular weir (S_Wh_U vs. S_Wh_noU). The cause of
this increase in discharge is twofold.
On the one hand, the height of the inlet increases with 33 % by removing the U-beams. As a result, the
inlet in the S_LWh_noU-configuration becomes drowned at an upstream water level which is higher
than in the S_LWh_U-configuration (approx. 28.5 m T.A.W. vs. 28 m T.A.W.) and thus the second
regime starts at higher upstream water levels. This results in a much higher discharge going through
the S_LWh_noU-configuration.
On the other hand, removing the U-beams increases the area of the inlet section with 36%, as has been
mentioned in chapter 4. This also enhances the discharge through the structure. Assuming that the
second regime is comparable with flow through a culvert (regime V), this would result (based on the
formula for flow through a culvert, regime V, see chapter 3, paragraph 4.3) in a discharge which is also
36 % higher. By comparing the discharges of the second regime for both configurations, it was found
that the increase in discharge was about 35% to 40 %, which supports this theory.
0
20
40
60
80
100
120
140
160
180
200
26.7 27.7 28.7 29.7 30.7 31.7 32.7
Q [
m³/
s]
hupstream [m T.A.W.]
S_LWh_U S_LWh_noU
114
Due to a lack of data, no clear-cut remarks can be made concerning the third regime. For high upstream
water levels (> 31.0 m T.A.W.), the S_LWh_U-configuration gives a discharge which is 37 to 40 % higher
than for the S_LWh_noU configuration.
2.8 S_LWh_U and F_LWh_U
The Simple model gives the possibility to test a wide variety of hydraulic structures, as has been
illustrated in the previous sections. However, there are some features of the proposed design which
are not incorporated in the simple model. Therefore a comparison is made in this paragraph between
the S_LWh_U configuration of the Simple model and the F_LWh_U configuration of the Full model. A
comparison of the measurements on both configurations is shown in Figure 109.
Figure 109: Comparison between S_LWh_U and F_LWh_U
During the first regime, there are only small differences between both configurations, which could be
attributed to minor differences in geometry or to the accuracy of the measurements. However, during
the second, and definitely in the third regime, the S_LWh_U-configuration seems to have a higher
discharge capacity than the F_LWh_U configuration.
The main reason for this discrepancy is assumed to be the difference in the design of the inlet of both
models. The different geometries can be seen in Figure 110. For the F_LWh_U-configuration, the U-
0
20
40
60
80
100
120
140
160
26.7 27.7 28.7 29.7 30.7 31.7 32.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_U F_LWh_U, difference of 2 m +/- 0.08 m
115
shaped beam is fabricated according to the proposed design (i.e. as a U-shape), while for the S_LWh_U-
configuration, there is a straight vertical wall at the location of the U-beam. This leads to different flow
patterns in both models. The U-beam from the Full model, creates a dead zone of water above the
inlet, in which the water has almost no velocity and has a lot of swirling motion caused by this
geometry. In contrast, on the Simple model this dead zone of water and the swirling motion is reduced
significantly. This could (partially) explain the lower discharge capacity for the F_LWh_U-configuration.
Figure 110: Demonstration of the difference in inlet geometry between the full model (left) and the simple model (right)
Another difference in inlet geometry, is that for the S_LWh_U-configuration the U-beams have
rounded edges, which is not the case for the F_LWh_U-configuration. This leads to higher losses for
the latter and could explain the less steep curve for this configuration.
Visual observations in the model show that for the S_LWh_U-configuration the occurrence of vortices
is significantly lower than for the F_LWh_U-configuration. These vortices also imply a decrease in
discharge. The occurrence of these vortices is most likely related with the differences in inlet geometry,
enhancing the swirling motion and thus the formation of vortices in case of the Full model. This is
discussed further in paragraph 5.
A last explanation given for the higher capacity of the S_LWh_U-configuration is the larger size of the
inlet-section (2.6 %) and the outlet section (2.3 %) in comparison to the F_LWh_U-configuration.
2.9 Influence of the supporting beams and columns
The last step in the process of experimenting is the verification of the impact of the beams and
columns, supporting the roof of the culvert, on the discharge capacity of the structure. Therefore, the
F_LWh_U_B&C-configuration is being compared to the F_LWh_U_C and F_LWh_U configurations. The
removal of these structural elements will increase the available flow area over the labyrinth weir and
116
will decrease the aeration (in case the columns act as artificial breakers of the falling nappe). The
influence of the removal of the beams and columns on the available area over the weir can be seen in
Table 13.
Table 13: Available area above the weir for different configurations
Configuration Available area [m²] per cycle
F_LWh_U_B&C 29.4
F_LWh_U_C 30.4
F_LWh_U 31.8
Figure 111: Comparison of F_LWh_U_B&C, F_LWh_U_C and F_LWh_U
The previously described regimes also occur in the F_LWh_U_C and the F_LWh_U_B&C configurations,
around similar water levels as mentioned before.
In the first regime, a very small difference can be noticed in the discharge of the F_LWh_U_B&C-
configuration as compared to the F_LWh_U_C and F_LWh_U configurations, which can be attributed
to the small difference in overflow length.
In the second regime, the slope is steeper for the F_LWh_U_C and for the F_LWh_U configuration. The
explanation for this is the reduction of hydraulic losses when no supporting beams and columns are
present. The F_LWh_U configuration should be steeper than the F_LWh_U_C configuration, although
0
20
40
60
80
100
120
140
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
h upstream [ m T.A.W.]
F_LWh_U, 2 m +/- 0.08 m F_LWh_U_C F_LWh_U_B&C
117
the accuracy of the measurements and quantity of the data in the second regime, does not allow to
make any definite conclusions on the steepness of the curve.
The influence of the columns on the discharge is small, since the difference in discharge between the
configuration with and without columns (F_LWh_U vs. F_LWh_U_C) is limited. When the supporting
beams are present, a more significant decrease in discharge is noticed in comparison with F_LWh_U_C
and F_LWh_U. The presence of the beams causes much more hydraulic losses in the culvert, resulting
in a lower discharge through the structure for similar upstream water levels.
Another important conclusion is that the curves visibly start diverging at an upstream water level of
about + 27.5 m T.A.W., until the outlet becomes submerged. They stay more or less at a constant offset
(of about 14.5 m³/s) for higher upstream water levels.
In the third regime, again the presence of a local minimum is observed. This is discussed in 2.12.
2.10 F_LWh_U_B&C for different Δh
Besides testing with a target difference in upstream and downstream water levels Δh equal to ± 2 m
(as was the case in the previous paragraphs), the F_LWh_U_B&C-configuration has also been tested
with other target values: Δh = 1m, 1.5 m and 2.5 m. The reasons for this are twofold. Firstly to gain
additional insight in the stage-discharge relation of the hydraulic structure at Heerenlaak. A second
reason is to anticipate on the design of future, similar hydraulic structures at other locations in the
Common Meuse, which are characterized by other Δh values. The same hydraulic structure might have
a different Qh-relation and performance at different locations. The resulting graph is shown in Figure
112 below.
118
Figure 112: Interpolated values for F_LWh_U_B&C for different Δh
Several conclusions can be drawn based upon these measurements. A first main conclusion is that for
higher differences in water level Δh, the structure will have a higher discharge capacity. The outlet is
drowned at a higher upstream water level, allowing the discharge to increase during the second
regime.
A second conclusion is that for the first regime, the capacity is independent of the difference in water
level. The only influencing parameter is the upstream water level.
A third conclusion is that for the measurements corresponding to a difference in water level of Δh = 1
m, the second regime as defined previously for the case of Δh = 2 m does not occur. The explanation
for this is that, due to the limited difference in water level, the outlet starts to be submerged when the
inlet is drowned. Therefore the second regime, where the inlet is submerged with free outflow, is not
present.
2.11 Verification of the estimated stage discharge relation by FHR
The data measured on the F_LWh_U_B&C configuration can now be compared to the tentative Qh-
relation based on a desk-top study by FHR (Vercruysse et al., 2013) prior to the present scale model
study.
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
Δh = 2 m Δh = 2.5 m Δh = 1 m
119
As indicated in chapter 4, paragraph 5.12, the Full model has some small differences in geometry
compared to the proposed hydraulic structure. Prior to obtaining the best estimation of the discharge
of the proposed structure, the impact of these differences will be discussed.
Firstly, the inlet section of the Full model is 9% smaller than the suggested value of 30 m² in the design
of the hydraulic structure. As is concluded in the comparison between S_LWh_U and S_LWh_noU,
enlarging the inlet section should result in a discharge which is higher. The resulting discharge through
the proposed hydraulic structure is thus assumed to be about 9 % higher than for F_LWh_U_B&C,
based on the aforementioned conclusions.
Secondly, the columns and beams in the scale model have a square cross-section corresponding to a
side of 45 cm on prototype scale, whereas the conceptual design suggested a value of 40 cm. This
means that the scale model has a reduced flow area over the labyrinth weir. Moreover, the beams
create high hydraulic losses inside the structure. Based upon the comparison between F_LWh_U_C
and F_LWh_U_B&C, an estimation of the discharge through the prototype is made, given that the
discharge through F_LWh_U_C was about 15 % higher than through F_LWh_U_B&C. For a scale model
with more accurate dimensions of the beams, the stage-discharge relation should be in between that
of F_LWh_U_B&C and F_LWh_U_C. When evaluating the increase in overflow area of F_LWh_U_C
compared to F_LWh_U_B&C, an estimation of the increase in discharge capacity, for a model with
more accurate beam dimensions (i.e. reducing the beam dimensions in F_LWh_U_B&C), can be made.
This is done by taking the ratio of the absolute increase in overflow area of the more accurate model
to the absolute increase of the F_LWh_U_C when compared to F_LWh_U_B&C and multiplying this
with the afore mentioned increase of 15%. Thus the discharge through the prototype is assumed to be
about 1.5 to 2 % higher than the discharge through F_LWh_U_B&C.
Furthermore, the walls of the labyrinth are 3 cm thicker in F_LWh_U_B&C, than on the design of the
proposed structure. As is mentioned in the literature review about labyrinth weirs, an increase in wall
thickness leads to a decrease in specific discharge (Blancher, Montarros and Laugier, 2010). However,
this decrease is not quantified in the latter publication and the possible increase on the discharge
through the proposed structure is assumed to be negligible compared to the discharge through
F_LWh_U_B&C.
120
In conclusion, the discharge through the future hydraulic structure is assumed to be about 9 to 11 %
higher than is measured on the F_LWh_U_B&C-configuration. A comparison between the original and
the corrected (i.e. 9 to 11% higher) data measured on the F_LWh_U_B&C-configuration and the
estimated stage-discharge relation, based upon a desk-top study by FHR (Vercruysse et al., 2013) is
shown in Figure 113.
Figure 113: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors, in
comparison with the estimated Qh-relation proposed by FHR (Vercruysse et al., 2013)
For the first regime (i.e. the weir regime), the desktop-based curve somewhat underestimates the
discharge. This can be attributed to the fact that conservative assumptions have been made in the
desktop study, to account for the large uncertainties concerning the different influence factors on the
hydraulic structure.
When the second regimes starts (i.e. at 28.0 m T.A.W.), there agreement between the desktop-based
QH-relation and the measured one becomes very poor . Yet, the transition from the second to the third
0
20
40
60
80
100
120
140
160
180
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
h upstream [ m T.A.W.]
FHR: simulations of submerged in- and outlet FHR: Weir regimeFHR: Submerged inlet FHR: Submerged inlet and outletF_LWh_U_B&C Estimation based on geom. differences, 9 %Estimation based on geom. differences, 11 %
121
regime occurs at a similar upstream water level (i.e. at ± 29.2 m T.A.W., when the outlet is submerged
as well).
The desktop-based curve takes into account the rising of the head (i.e. the difference between the up-
and downstream level) from 2 m to approximately 2.5 m for high discharges at the Meuse, and
corresponding high upstream water levels, as shown in chapter 2, Figure 7. This is an additional
explanation for the poor agreement between the desktop-based and the measured Qh-relation. The
influence of the rising difference between the Meuse and the Heerenlaak pond, can be incorporated
in the result, by evaluating the curve with a Δh of 2.5 m (see 2.10). When considering that Δh changes
from 2 m at an upstream water level of 29.5 m T.A.W. to 2.5 m at an upstream water level of 31 m
T.A.W., an estimation can be made which incorporates the geometrical errors and the rising value of
Δh over the construction. This estimation is shown in Figure 114. It is obvious that the agreement with
the desktop-based values is somewhat better.
Figure 114: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors and a
rising up/downstream difference , in comparison with the theoretical estimation made by FHR (Vercruysse et al., 2013)
0
20
40
60
80
100
120
140
160
180
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
h upstream [ m T.A.W.]
FHR: simulations of submerged in- and outlet FHR: Weir regime
FHR: Submerged inlet FHR: Submerged inlet and outlet
F_LWh_U_B&C Final estimation, 11 %
Final estimation, 9 %
122
It should be mentioned that the report on the desktop-study (Vercruysse et al. 2013) clearly states that
the estimated Qh-relation is afflicted with a lot of uncertainties and therefore recommended that the
hydraulic structure would be tested in a scale model study, which is the subject of the present master
thesis. Thanks to this scale model testing it becomes clear that the maximum discharge through the
construction is less than what was estimated based upon the desktop-study.
2.12 Dip in the third regime
During the evaluation of the data, a local minimum in the third regime was consistently observed in
the tests concerning a labyrinth or linear weir integrated in a culvert. In some cases, this local minimum
is very pronounced, while in other cases it is but a peculiarity in the curve of the third regime.
Considering the hypothesis of flow through a culvert (regime IV) is valid in the third regime , the
discharge should remain more or less constant. However, the corresponding formula of flow through
a culvert (regime IV) incorporates a Cd-coefficient, hence hydraulic losses may influence the discharge.
The data for different configurations are shown in Figure 115. The fact that this dip was observed
consistently, signifies that it cannot be related to the accuracy of the measurements or errors during
measuring.
Figure 115: Indication of the dip in the third regime
0
20
40
60
80
100
120
140
160
180
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_U F_LWh_U_C F_LWh_U, 2 m +/- 0.08 mF_LWh_U_B&C S_Wh_U S_Wh_noUS_Wh_UMeuse S_LWh_U_Raisedroof
123
While testing, some possible theories about the origin of this phenomenon were tested. The first
theory was that this local minimum was due to the formation of eddies inside the labyrinth weir, close
to the apex. However, this theory could be discarded when comparing the experiments on the
labyrinth weir in a culvert with the experiments on a linear weir in a culvert. The presence of this dip
in the curves of these configurations (i.e. with a linear weir), counteracts this theory.
A second theory, was that the presence of the dip was related to the presence of the U-beams.
However, tests were performed on a linear and labyrinth weir inside a culvert with and without U-
beams. In both cases, the dip was observed in the results, discarding this theory.
A third theory is based on observations during testing. At high discharges, in the third regime, a zone
of water with a return current was perceived near the water level downstream of the outlet of the
scale models, indicating that the culvert might be lengthened hydraulically. This could explain the
decrease in discharge. These observations were done on the S_Wh_noU-configuration. However, this
was not investigated further, but might require additional research.
3. Optimisation
Two additional configurations, which may have practical use for the further optimisation of the design
of the structure at Heerenlaak, have been built and tested, i.e.. the S_LWh_U_Raisedroof configuration
and the S_LWh_UMeuse-configuration.
3.1 Influence of raising the roof (S_LWh_U_Raisedroof)
Raising the roof implies doubling the available area above the labyrinth weir, in comparison to
S_LWh_U. As was mentioned before, the removal of the beams and columns (F_LWh_U in comparison
to F_LWh_U_B&C) also causes an increase in available flow area above the weir and leads to a higher
discharge capacity. Based on these measurements and conclusions, one would expect an increase in
capacity of the structure due to raising the roof of the structure. A comparison of S_LWh_U and
S_LWh_U_Raisedroof is presented in Figure 116.
124
Figure 116: Comparison of S_LWh_U and S_LWh_U_Raisedroof
The measurements show a decrease in capacity of the structure by raising the roof, which is not in
accordance with the expectations. The afore described regimes do occur for the S_LWh_U_Raisedroof
configuration but the stage-discharge relations of S_LWh_U and S_LWh_U_Raisedroof begin to diverge
from an upstream water level of 28.7 m T.A.W. The maximum capacity of the S_LWh_U_Raisedroof
configuration is 117 m³/s. The surprising decrease in capacity might have several explanations. One
possible explanation is that the larger amount of available area in the structure facilitates the creation
of eddies, which in turn increases the head losses, hence a decrease of the overall capacity of the
structure.
3.2 Removal of the downstream U-beam
A second configuration, tested to obtain an improved discharge capacity with respect to the proposed
design, is the S_LWh_UMeuse-configuration. This model has only a U-shaped beam at the inlet (i.e.
the Meuse side) while the U-beam at the outlet (i.e. the Heerenlaak side) is removed.
The reason for removing the downstream U-beam is threefold. First, the costs of the future hydraulic
structure could be reduced. Secondly, the utility of the downstream U-beam is questioned. Given the
water level difference between the Meuse and the Heerenlaak pond, the flow through the structure
0
20
40
60
80
100
120
140
160
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_U S_LWh_U_Raisedroof
125
will always be directed from the Meuse to the Heerenlaak pond. Hence, no ingress of floating debris is
possible from the downstream side and if debris from the Meuse would have flown into the structure,
the presence of the downstream U-beam could make it more difficult to remove this debris. A third
reason, is that by removing the downstream U-beam, the flow at the outlet is not forced to contract
in the downward direction, improving the conditions for the bottom protection at the outlet.
The influence of the removal of the U-beam on the side of Heerenlaak (S_LWh_UMeuse) in comparison
to the proposed design (S_LWh_U) can be seen in Figure 117.
Figure 117: Comparison of S_LWh_UMeuse and S_LWh_U
The removal of the downstream U-beam leads to an increase in capacity when compared to the
S_LWh_U configuration. This increase occurs in the second regime, where the curve is much steeper
in case of S_LWh_UMeuse, because removing the downstream U-beam reduces the hydraulic losses
inside the structure.
The outlet is drowned at an upstream water level which is somewhat higher. Given the larger outlet
section, this is a logic result.
0
20
40
60
80
100
120
140
160
180
26.7 27.7 28.7 29.7 30.7 31.7 32.7
Q [
m³/
s]
hupstream [ m T.A.W.]
S_LWh_U S_Wh_UMeuse
126
The third regime has the same shape for both configurations, but the higher discharge of the
S_LWh_UMeuse configuration that was built up during the second regime remains present as a
constant offset throughout the third regime.
In conclusion, the S_LWh_UMeuse configuration is believed to have some (economic and practical)
advantages over the S_LWh_U-configuration and allows a larger maximum discharge through the
future hydraulic structure. This could mean a reduction in number of required units. Hence, this option
is worth considering in the presumption that this U-beam is not required for a retaining, bearing or
other function.
4. Flow pattern and velocity measurements
Velocity measurements are performed to gain insight in the flow pattern upstream of the structure
(mainly the contraction of the flow) and to be able to give an estimation of the specifics of the bottom
protection. The location of the contraction is of importance for nv De Scheepvaart in order to fine-tune
the approach flow conditions towards the hydraulic structure. Note that the velocity measurements
have been performed on the F_LWh_U_B&C – configuration, which is according to the design of nv De
Scheepvaart, and that the position of the bottom of the flume is at 22.3 m T.A.W. in prototype
dimensions. Thus the tested situation does not correspond to the boundary conditions of the future
hydraulic structure.
4.1 Flow pattern
To visualize the flow pattern towards the structure, experiments using colouring dye were performed
and recorded. These experiments were performed for the peak discharge of 99.8 m³/s and an
upstream water level of 29.24 m T.A.W.. The injections were done at varying depths. The maximum
intensity of the injected dye can be seen in Figure 118, Figure 119,Figure 120 and Figure 121. Two
figures are provided for the same flow pattern to be able to discern both the flow pattern and the
colouring dye.
127
Figure 118: Maximal intensity of the injected dye, injection at about 29 m T.A.W.
Figure 119: Maximum intensity of the injected dye, injection at about 28 m T.A.W.
Figure 120: Maximum intensity of the injected dye, injection at about 26 m T.A.W.
Figure 121: Maximum intensity of the injected dye
128
From these figures, it can be seen that for injection at higher levels, a vertical contraction of the flow
takes place towards the inlet section. For heights, in between 23.7 m T.A.W. and 26.7 m T.A.W. (i.e.
the level of the top of the bottom slab and the soffit of the U-beam), the contraction becomes less
noticeable.
4.2 Velocity measurements
4.2.1 Testing procedure II
By executing the experiments with colouring matter, a good insight in the location of the contraction
was obtained. This location is further concretized by performing velocity measurement at a constant
height underneath the water surface. These measurements were taken at different longitudinal
positions upstream of the hydraulic structure. About the test procedure, more explanation is given in
Two different data point were measured in the stage-discharge relation, having a given upstream
height and discharge. The corresponding values are given in Table 14, where hmeasurement is the height
at which the velocity is measured.
Table 14: The measured data points, corresponding to the peak discharge and discharge at the dip
Nr. Q [m³/s] hupstream [m T.A.W.] hmeasurement [ m T.A.W.]
1 99.89 29.298 28.074
2 91.33 30.972 29.874
In the table above, h measurement stands for the height at which the velocity is being measured. This is at
a level roughly 1.2 m below the upstream water level. The data points mentioned in Table 14, are
indicated on the experimentally obtained Qh-relation in Figure 122.
129
Figure 122: Indication of the measured data points on the experimentally derived Qh-relation for the F_LWh_U_B&C-
configuration
The resulting graph is shown in Figure 123.
Figure 123: Velocity measurements for data point 1 and data point 2
0.8
0.9
1
1.1
1.2
1.3
0 5 10 15 20 25
velo
city
[m
/s]
distance relative to inlet section [m]
Data point 2 (hupstream = 30.97 m T.A.W. and Q = 91.3 m³/s)
Data point 1 (hupstream = 29.3 m T.A.W., Q = 99.9 m³/s)
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream[ m T.A.W.]
F_LWh_U_B&C
1 2
130
From Figure 123 can be seen that for data point 1 (corresponding to a peak discharge of 99.9 m³/s and
an upstream water level of 29.3 m T.A.W.), higher velocities occur in comparison to the discharge at
the dip (91.3 m³/s). Note that both measurements are taken at different heights relative to the bottom
of the flume, but at the same height below the upstream water level. The cause of these lower
velocities is because of a higher upstream water level for data point 2 (30.97 m T.A.W. vs. 29.3 m
T.A.W.), which leads to a larger flow section, combined with a lower discharge (91.3 m³/s vs. 99.9
m³/s).
From these curves, especially for data point 2, it can be seen that there is a contraction of the flow in
vertical direction. Then the velocity decreases, as Figure 123 indicates. For data point 2, the contraction
is noticed around a distance of 8 m upstream of the inlet of the structure. For data point 1, this
contraction seems to occur around a distance of ± 5 m relative to the inlet section. These locations are
also indicated on Figure 123. Hence, for higher upstream levels, the contraction takes place more
upstream of the structure.
Throughout the measurements on the F_LWh_U_B&C-configuration, a small number of stationary
waves were observed upstream of the inlet of the hydraulic structure. These are shown in Figure 124.
Figure 124: Stationary wave pattern on the side of the Meuse
Visual observations of the wave pattern in combination with the results from Figure 123, indicate that
the longitudinal position at which the vertical contraction takes place, is at the location of the
stationary waves. Since the measurements from Figure 123 were taken about 1.2 m below the water
surface, the location of the contraction in these curves, is at a small distance downstream of the
stationary waves.
The observations on these stationary waves indicated that the position of the waves relative to the
inlet, depends on the upstream water level. The higher the water level, the larger the distance between
131
the inlet and the waves. Confirming the conclusions from Figure 123, that the higher the upstream
water level, the further upstream the contraction occurs.
These observations suggest the presence of a region with almost no velocity towards the scale model
and a contraction of the flow starting on the water surface near the location of the waves. This region
will also have an impact on the formation of vortices, which is discussed in chapter 3, paragraph 5.2.
4.2.2 Testing procedure I
Furthermore, velocity profiles were measured to verify velocities upstream of the structure. The
measurements have been executed according to testing procedure I, which was described previously
in chapter 4, paragraph 4.2.1. The measured data points (Q, hupstream) are named 3 and 4 and are shown
in Table 15.
Table 15: Discharge and corresponding hupstream and Δh for which velocity measurements have been executed
Nr. Q [m³/s] hupstream [m T.A.W.]
3 98.70 29.23
4 95.15 31.71
To situate these points, they are indicated in Figure 124 on the experimentally obtained Qh-relation of
the F_LWh_U_B&C-configuration.
Figure 125: Indication of the measured data points on the experimentally obtained Qh-relation of the F_LWh_U_B&C-
configuration
0
20
40
60
80
100
120
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Q [
m³/
s]
hupstream[ m T.A.W.]
F_LWh_U_B&C
3 4
132
4.2.2.1 Data point 3
The velocity measurements on data point 3 (29.2 m T.A.W.) can be seen in Figure 126, showing the
velocity on the x-axis against the height at which the measurement was taken (hmeasurement). These
velocities were measured at a longitudinal distance of 5 m upstream of the inlet of the structure. The
same graph for a longitudinal distance of 10 m upstream of the inlet of the structure can be seen in
Figure 127. The location of the bottom slab of the hydraulic structure is indicated on these graphs by
a black line.
Figure 126: Velocity measurements for data point 3 and a distance of 5 m upstream of the inlet
Figure 127: Velocity measurements for data point 3 at a distance of 10 m upstream of the inlet
22.7
23.7
24.7
25.7
26.7
27.7
28.7
1.05 1.1 1.15 1.2 1.25 1.3
h m
easu
rem
ent[m
T.A
.W.]
V [m/s]
Data point 3, 5 m upstream of the inlet
middle of the flume middle of the inlet section side of the flume
22.7
23.7
24.7
25.7
26.7
27.7
28.7
1.05 1.1 1.15 1.2 1.25 1.3
h m
easu
rem
ent[m
T.A
.W.]
V [m/s]
Data point 3, 10 m upstream of the inlet
middle of the flume middle of the inlet section side of the flume
133
As can be seen from these figures, the velocity is higher close to the water surface and decreases in
depth for most of the measured points. The velocity is slightly higher at the middle of the flume than
at the middle of the inlet section of a single cycle. The measurements at the side of the flume show a
lot of variation. No clear trend can be discerned for the measurements at the side of the flume. Figures
comparing the data at a different longitudinal location at a fixed transverse location can be seen in
Figure 128, Figure 129 and Figure 130.
Figure 128: Velocity measurements for data point 3 in the middle of the flume
Figure 129: Velocity measurements for data point 3 in the middle of the inlet section of a single cycle
22.7
23.7
24.7
25.7
26.7
27.7
28.7
1.05 1.1 1.15 1.2 1.25 1.3
h m
easu
rem
ent
[m T
.A.W
.]
V [m/s]
Data point 3, middle of the flume
5 m relative to the inlet 10 m relative to the inlet
22.7
23.7
24.7
25.7
26.7
27.7
28.7
1.05 1.1 1.15 1.2 1.25 1.3
h m
easu
rem
ent
[m T
.A.W
.]
V [m/s]
Data point 3, middle of the inlet section of a single cycle
5 m relative to the inlet 10 m relative to the inlet
134
Figure 130: Velocity measurements for data point 3 at the side of the flume
These figures show that the velocities in the middle of the flume and the middle of the inlet section
are lower at a distance of 10 m relative to the inlet section, compared to a similar measurement at a
distance of 5 m relative to the inlet section. It is also noted that the difference between both 5 m and
10 m relative to the inlet, decreases in height. The differences imply that for an upstream distance of
5 m, the velocities should be smaller at the side of the flume (since more discharge passes through the
centre of the flume) when compared to the velocities at the side of the flume at a distance of 10 m
upstream of the inlet section. However, based on Figure 130, no real conclusions can be made on this
matter. Distortion may be caused by effects due to the presence of the wall of the flume or due to a
narrow gap between the side of the honeycombs, located more upstream in the flume, and the wall
of the flume. This is shown in Figure 131.
22.7
23.7
24.7
25.7
26.7
27.7
28.7
1.05 1.1 1.15 1.2 1.25 1.3
h m
easu
rem
ent
[m T
.A.W
.]
V [m/s]
Data point 3, side of the flume
5 m relative to the inlet 10 m relative to the inlet
135
Figure 131: Indication of the gap between the side of the honeycombs and the wall of the flume
4.2.2.2 Data point 4
For the data point 4 (hupstream of 31.71 m T.A.W.), velocities have only been measured at the centre of
the inlet section of a single cycle.
Figure 132: Velocity measurements for data point 4 at the middle of the inlet section
For the data corresponding to a distance of 10 m relative to the inlet, the velocities increase in height.
The velocities are again smaller, or have approximately the same magnitude for a relative distance of
10 m compared to a relative distance of 5 m to the inlet section.
22.7
23.7
24.7
25.7
26.7
27.7
28.7
29.7
30.7
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
h m
easu
rem
ent
[m T
.A.W
.]
V [m/s]
Data point 4, middle of the inlet section
5 m relative to inlet 10 m relative to inlet
136
4.2.2.3 Comparison of both data points
When comparing the measurements on data point 3 (hupstream of 29.2 m T.A.W.) and data point 4
(hupstream of 31.71 m T.A.W.) for the middle of the inlet section, the graph in Figure 133 is obtained.
Figure 133: Comparison of the velocity measurements for Q = 98.7 m³/s and Q = 95.15 m³/s at the middle of the inlet
section
From this figure, it can be seen that lower velocities occur for data point 4 (hupstream = 31.71 m T.A.W.,
Q = 95.15 m³/s) than for data point 3 (hupstream = 29.2 m T.A.W., Q = 98.7 m³/s). This can be explained
by the higher upstream water level at data point 4, leading to a larger section through which the water
flows, combined with a slightly lower discharge.
When comparing the measurements from data point 4 for an upstream distance of 5 m and 10 m,
several conclusions can be made. The velocity increases in the lower half of the flume (i.e. from the
bottom of the flume up to a height of ± 27.0 m T.A.W.) from a distance of 10 m relative to the inlet to
a distance of 5 m relative to the inlet. This can be explained by the contraction of the flow in vertical
direction towards the inlet section. Note that the soffit of the U-beam (i.e. the top of the inlet section)
is at 26.7 m T.A.W.. The velocities close to the water level have approximately the same value, while
at lower height the velocity at 5 m is higher than the velocity at 10 m. This indicates that more discharge
goes through the section at 5 m than at 10 m. A possible hypothesis for this, is that besides a vertical
contraction also a contraction in horizontal direction occurs towards both openings of the inlet.
No velocity measurements for this data point (i.e. data point 4, hupstream = 31.71 m T.A.W., Q = 95.15
m³/s) at the middle of the flume are available to check this theory concerning the horizontal
22.7
23.7
24.7
25.7
26.7
27.7
28.7
29.7
30.7
0.54 0.64 0.74 0.84 0.94 1.04 1.14 1.24 1.34
h m
easu
rem
ent
[m T
.A.W
.]
V [m/s]
Middle of the inlet section of a single cycle
Data point 4, 5 m relative to inlet Data point 4, 10 m relative to inlet
Data point 3, 5 m relative to inlet Data point 3, 10 m relative to inlet
137
contraction. The measurements from data point 3 do not confirm this theory. However for data point
3, less difference in velocity is measured between the section at 5 m and the section at 10 m, than for
data point 4. Additionally, no contraction in vertical direction was observed data point 3.
Assuming that the stationary waves indicate the location of the flow contraction in vertical direction,
as explained in paragraph 4.2.1, an explanation for the absence of vertical flow contraction for data
point 3 (hupstream = 29.2 m T.A.W., Q = 98.7 m³/s) can be given. The stationary waves are located at a
distance less than 5 m upstream of the structure for data point 3. For data point 4, the waves are
located further upstream, conform to the theory explained in paragraph 4.2.1. This explains why no
vertical contraction is noticed for data point 3. The contraction starts at approximately 5 m upstream
of the structure, as was indicated at Figure 123 from paragraph 4.2.1. For data point 4, the
measurements are influenced by the wave pattern. Two conceptual drawings, sketching the situation
for both discharges, can be seen in Figure 134 and Figure 135.
Figure 134: Conceptual drawing indicating the contraction of the velocity profiles for data point 3
Data point 3 (hupstream = 29.2 m T.A.W., Q = 98.7
m³/s)
V [m/s] V [m/s]
138
Figure 135: Conceptual drawing indicating the contraction of the velocity profiles data point 4
4.3 Velocities downstream of the structure
No velocity measurements have been executed on the downstream side of the structure.
Whitecapping on the downstream side of the hydraulic structure disappears at a distance of 15 to 20
m more downstream, for the peak discharge (i.e. ± 99 m³/s). Hence, the turbulence at the outlet, is
limited to a region of 18 to 20 m downstream of the structure. This value is obtained based on visual
observations.
4.4 Critical remarks
Two (main) critical remarks concerning the velocity measurements have to be made. They concern the
interpretation of the velocities measured on the scale model in the flume in function of the structure
at Heerenlaak.
Firstly, the presence of a standing wave pattern in front of the structure influences the velocity
measurements, as was stated above. Questions can be raised whether this standing wave pattern will
occur for the structure at Heerenlaak, since the labyrinth weir in a culvert is not located in a canal or
Data point 4 (hupstream = 31.71 m T.A.W., Q = 95.15
m³/s)
V [m/s] V [m/s]
139
wave flume, and the flow approach conditions at Heerenlaak do not match these of the tested
configuration. A second remark concerns the position of the bottom of the flume relative to the height
of the bottom slab. During the scale model test, the bottom of the current flume is at 22.7 m T.A.W..
Since no details concerning the bottom of the Meuse at the location are available, the influence of the
embankment on the velocities is not included in the velocity measurements on the scale model study.
5. Quantification of vortices
During some experiments, the formation of vortices was noticed. Consequently, this phenomenon was
investigated based upon the most important findings stated in the literature review. The presence and
the different types of vortices are investigated and the application of the theories given in the literature
about vortices is explored.
5.1 Presence of vortices
For the experiments in the F_LWh_U_B&C configuration at different upstream water levels (keeping
the difference with the downstream level at a constant value of 2 m), observations are made. If
present, vortices are classified according to the classification system of Knauss (1987), as discussed in
the literature review.
Figure 136: Example of a full air core vortex at a discharge of 91 m³/s and an upstream water level of 28.24 m T.A.W.
For low flows, no vortices were observed. At an upstream level of approximately 27.4 to 27.5 m T.A.W.
(i.e. the water level is 0.8 to 0.9 m above the soffit of the U-beams) and a discharge of 50 to 60 m3/s,
surface dimples (type II) start to appear. At higher flows, full air core vortices (type VI) appear. These
140
are observed when the upstream water level reaches a height of 28.2 to 28.3 m T.A.W., corresponding
to a discharge of about 92 m3/s. These findings are consistent with the literature, stating that the
formation of vorticity starts rapidly after the inlet section becomes submerged and grow in intensity
with increasing submergence.
The intensity of the vortices is highest for flows of about 92 to 98 m³/s, corresponding to an upstream
water level of 28.5 to 29.4 m T.A.W.. For even higher flows, the intensity of the vortices diminishes
again.
5.2 Critical submergence
As explained in the literature, the critical submergence is defined by different researchers in a
somewhat different manner. The definition used in this paragraph is the one adopted in most research,
i.e. the threshold at which air-entraining vortices change into non air-entraining vortices. The definition
of critical submergence is thus partly based on subjective evaluation of the presence and the type of
the vortices and is as a result subject to uncertainty.
Numerous formulas for the determination of the critical submergence have been proposed by the
different researchers. Some formulas take into account more influence factors than others. The
formulas applied to the data from the hydraulic model are given below with further explanation in
Table 16.
- The formula of Gordon (1970) for symmetrical approach flow conditions:
- The formula of Ahmad et al. (2008) used when the bottom clearance is zero (e = 0):
and for when the bottom clearance is equal to half of the diameter (e = D/2):
- The formula of Gürbüzdal (2009) :
141
is the critical submergence above the top of the intake [m]
is height of the intake [m]
is the average velocity through the inlet [m/s]
is the intake Froude number, given by [-]
e is the distance from the bottom of the channel to the intake invert [m]
is the distance of the side wall to the centre of intake for a symmetrical geometry [m]
is the Reynolds number, given by [-]
is the Weber number, given by [-]
The formulas of Ahmad et al. are drafted for a distance between the bottom of the approach channel
and the invert of the intake of either 0 or Di/2. In case of the model tested in the flume, this distance
is equal to 1/3 Di. The submergence should thus be in between both formulas of Ahmed et al.
The critical submergence of the scale model is velocity dependent, which is derived through the known
discharge:
For each measurement of the Qh-relation, the critical submergence is calculated and compared with
the actual submergence of the inlet. When the calculated submergence is smaller than the measured
submergence, air-entraining vortices should not be present anymore. These thresholds are given in
Table 16 and a graphical representation is given in Figure 136.
Table 16: Critical submergence
Formula Utilized parameters * Critical submergence
Gordon (1970)
29.8 m T.A.W.
Ahmad et al. (2008) , for e = 0
29.69 m T.A.W.
142
Ahmad et al. (2008), for e = D/2
e = D/2 = 1.5 m
28.81 m T.A.W.
Gürbüzdal (2009)**
29.42 m T.A.W.
*In the table above, is the width of the flume, rescaled with a factor 18 for comparison in
prototype values. The same remark is applicable on , which is the upstream water level
relative to the bottom of the flume, rescaled with a factor 18 for comparison in prototype values
** In case of the formula by Gürbüzdal, the accompanying boundary condition of
is not fulfilled, hence the results of this formula might be incorrect.
Figure 137: Graphic representation of the measured submergence, compared to the calculated critical submergences
0
1
2
3
4
5
6
7
26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7
Sub
mer
gen
ce [
m]
hupstream [m T.A.W.]
Experimentally measured submergence Critical Submergence by Gordon (1970)Critical submergence by Ahmad (e=0) Critical submergence by Ahmad (e=D/2)Critical submergence by Gurbuzdal
Observed critical submergence
143
In our observations, the threshold between air entraining vortices and non-air entraining vortices (i.e.
the critical submergence) was denoted at an upstream water level of about 31.5 m T.A.W.. This
corresponds to a submergence of 3.8 m. Note that, as explained before, defining the critical
submergence is based on a subjective evaluation of the presence and strength of the vortices. Above
the denoted critical submergence, small vortices were still present but they were very weak, with no
air-entrainment.
As the results in Table 16 and Figure 137 indicate, the critical submergence of the scale model is a lot
higher than the theoretical values proposed by Gordon, Ahmad et al. and Gürbüzdal would suggest.
This means the vortices still remain present at high upstream water levels.
The most likely explanation is that this is caused by the geometry of the front of the hydraulic structure.
In the literature review about vortices, it was mentioned that vortices are formed by rotational motions
of fluid regions and they find their origins in discontinuities in the flow pattern. Gordon (1970, see
Baykari, 2013) explains one of the influencing aspects on the formation of vortices to be the geometry
of the approach flow to the intake. Since the U-beam creates the possibility for the water to rotate in
a water zone with no velocity, swirling motion and hence vorticity is stimulated significantly. This is
illustrated in Figure 138.
Figure 138: Stimulation of vorticity caused by the geometry of the structure front, top view of F_LWh_U_B&C
144
This was established before (see section 2.8), by comparing two identical scale models having a
different front section. In the scale model with a flat front geometry (S_LWh_U, see, Figure 139)
significantly less vortices were observed. However, no systematic classification of the vortices in the
S_LWh_U configuration has been made.
Figure 139: The front of S_LWh_U
Since all the formulas mentioned above have been based upon intakes with a flat front surface (i.e. a
vertical plane with an orifice), this could explain the poor agreement in critical submergence between
the theory and observations.
5.3 Application to the future hydraulic structure
When considering the observed vortices on the scale model, it is verified whether scale effects could
play an important role. In the literature review about vortices (chapter 3, paragraph 5.4), it was
concluded that the surface tension of water can be neglected when the Weber number
is higher than 720 and the viscosity can be neglected if the Reynolds number ( ) is
higher than . The Reynolds number and Weber number of the data in the scale model were
calculated, reaching higher values than the prescribed ones at a discharge of about 85 m³/s and an
upstream water level of 27.86 m T.A.W. and higher. Thus, it can be concluded that scale effects should
be negligible when researching the critical submergence of the vortices.
Because the future hydraulic structure is built inside a dike (Figure 140), the rotational motion above
the inlet may even be enhanced, considering the flow of the Meuse is perpendicular to the flow
145
through the structure. This flow through the Meuse could create extra angular momentum on the
water above the U-beam, which could enhance the presence of vortices and their strength. However,
this is dependent on the actual construction and flow conditions, thus care should be given after the
implementation on the Meuse.
Figure 140: Cross-section of the hydraulic structure inside the body of the dike
By the presence of vortices, debris could be drawn inside the structure. The U-beams are designed to
prevent the ingress of floating debris, but the vortices might suck this floating debris inside, diminishing
the effectiveness of the U-beams. To verify this, some tentative tests were performed by use of floating
polypropylene-particles with a diameter of about 3 mm and paper lumps (diameter of about 1.5 – 2
cm). These tests confirm the possibility of trash intake caused by vortices. It must be remarked,
however, that these tests were tentative and no scaling was done to verify this.
Figure 141: Examples of the tentative trashtests
Meuse
Sheetpiles Spillway
Heerenlaak pond
146
Trash intake by vortices must be avoided for structural, maintenance and environmental reasons.
Some possibilities for vortex mitigation are given in the literature review, such as trashracks, floating
or submerged rafts, … However, for the future hydraulic structure, nv de Scheepvaart is not in favour
of trash racks, while the other solutions might hinder the intended function of the U-beams, namely
to intercept debris of the Meuse. Small adaptions to the surrounding geometry at the inlet might be a
solution, in order to decrease the rotational motion of the water.
147
Chapter 7: Conclusions
To remove one of the remaining bottlenecks in the Common Meuse, a hydraulic structure has been
designed by ir. H. Gielen (nv de Scheepvaart) to be built in a levee near the Heerenlaak pond. This
structure consists of a labyrinth weir integrated in culvert and consists of two labyrinth cycles, further
referred to as one unit (see chapter 2, paragraph 1). The intention is to implement a number of these
units to discharge water from the Meuse through the Heerenlaak pond, at times of high discharges in
the Meuse.
The Q-h relation of the proposed structure and the corresponding maximum discharge capacity, have
been estimated by means a desktop study by Flanders Hydraulics Research (FHR, Vercruysse et al.,
2013). Given the many uncertainties, it was recommended to make a scale model study of the
hydraulic structure. This was the main objective of the present master thesis. In the Hydraulics
Laboratory of Ghent University, a study (at scale 1 to 18) has been carried out, in cooperation with FHR
and nv De Scheepvaart. To acquire more insight into the Qh-relation, a literature survey has been
carried out as well as a scale model study of variant configurations of the proposed design. The latter
was also meant to explore possible optimizations of the design.
The main conclusions derived from the scale model study of the proposed design are:
(1) The stage-discharge relation of the hydraulic structure consists out of 3 regimes. The first
regime corresponds to free overflow over a labyrinth weir, in which the discharge only
depends on the upstream water level. The second regime starts when the inlet of the structure
becomes internally drowned, i.e. at an upstream water level of 28.0 m T.A.W.. This regime
seems comparable to flow through a culvert, regime V. The third regime starts when the outlet
of the hydraulic structure is submerged as well, i.e. when the downstream water level reaches
the soffit of the downstream U-beam. During this regime, the discharge capacity of the
structure decreases slightly before reaching a more or less constant value for high upstream
water levels. In the third regime, the capacity depends on the difference in water levels
upstream and downstream of the structure and seems comparable to flow through culverts,
regime IV. This difference is about 2 m at Heerenlaak, although it slightly increases for higher
discharges through the Common Meuse.
(2) A peak discharge of 100 m³/s was reached at the transition from the second to the third
regime, i.e. when the downstream water level is at the soffit of the outlet. This value, however,
148
is somewhat underestimated, since the tested model geometry has some minor discrepancies
with the proposed design (which were induced by choices of commercially available scale
model components, with slightly different thicknesses and sizes as the dimensions suggested
by the conceptual design). When taking into account the effect of these discrepancies, it is
estimated that the capacity of the structure might increase up to 10%. Thus a capacity of 110
m³/s may be reached.
Other conclusions, which were made based on a comparative testing of a wide variety of related
hydraulic structures (integrated in a culvert or not) are:
(1) When the inlet section of the culvert is smaller than the available area over the weir, integrated
in the culvert, the culvert section is the most limiting factor for the capacity of the structure.
However, by reducing the head losses inside the structure the discharge capacity can be
increased.
(2) The occurrence of vortices at the inlet, as well as the presence of eddies inside the structure,
can decrease the capacity of the hydraulic structure. As such, measures preventing the
creation of these vortices could increase the discharge capacity of the structure. Punctilious
design of both the inlet section and the U-beam at the Meuse side of the structure could
ensure this.
(3) Experiments have proven that removing the beams, supporting the roof structure, out of the
flow area between the culvert ceiling and the crest of the labyrinth weir –meaning those
beams have to be integrated either into or on top of the ceiling slab of the culvert –leads to a
discharge increase of 12 to 17%. This is due to the afore mentioned reduction in head losses.
(4) An increase in discharge of about 14% can be reached by removing the downstream U-beam
of the structure, as was demonstrated in the experiments.
(5) Higher differences in Δh between the water levels upstream and downstream of the structure,
result in higher discharge capacities.
Based on the literature review, it is concluded that the proposed design can possibly be improved in
several respects (crest shape, rounded upstream abutments, rounded U-beams, filled alveoli …). Yet,
the influence of most improvements diminishes for large ratios of the total upstream head HT to the
height of the labyrinth weir P. Nonetheless, the use of filled alveoli and its corresponding merits
(smaller required wall thickness, the possibility to use a stair step and facilitating the practical
construction process) seem to be promising for the structure at Heerenlaak.
149
For the proposed design, 3 units (each consisting out of two labyrinth weir cycles) are required to allow
the passage of the target discharge of 300 m³/s. It is expected that these three units will have a
maximum capacity of about 320-330 m³/s. Taking into account possible improvements to this design
(e.g. integrating the supporting beams into or on top the roof) and the fact that for higher upstream
levels, the difference between the upstream and downstream side of the structure increases, it is
believed that a discharge of 390 m³/s can be reached. This implies that a total of 5 cycles will be
sufficient to allow the passage of 300 m³/s (assuming a discharge capacity of 65 m³/s for each cycle).
However, it is unknown if this is practically possible.
During the scale model experiments, the approach flow was uniform and aligned with the longitudinal
axis of the culvert. When finalizing the design, the approach channel between the river Meuse and the
hydraulic structure should preferably be made such that comparable approach flow conditions are
present. Otherwise, the abovementioned number of units to reach the target discharge of 300 m³/s
should be taken with caution.
150
Chapter 8: Recommendations for further research
Several aspects regarding the hydraulic structure at Heerenlaak have been investigated. The
experimental measurements highlighted some new areas of interest, while other facets of the
structure still remain unaddressed. Therefore some recommendations for further research can be
made.
Scale model testing on the S_LWh_U_Raisedroof configuration showed, somewhat surprisingly, a
decrease in discharge capacity of the structure. The explanation given for this is the creation of eddies
in the structure. Therefore it is highly recommended to further investigate the occurrence of these
eddies and possible measures of preventing them.
In the different configurations, where a linear or labyrinth weir is incorporated in a culvert, a slight
decrease in discharge was noticed in the third regime. Afterwards the discharge increased again slightly
and/or became constant. This dip in the Qh-relation was discussed in chapter 6, paragraph 2.12, where
some possible theories were given and some disproved. However, the origin of this dip was not
investigated further, hence it might interesting to conduct additional research.
The experimental scale model tests have been executed as described in chapter 4. The scale model is
inserted in a channel and the height of the bottom slab of the tested hydraulic structure to the bottom
of the current flume is small ( < 1 m, on prototype scale). The influence of the embankment of the dike
and the approach flow conditions of the Common Meuse (the hydraulic structure is located in a bend,
see chapter 1, Figure 1) are not taken into account during the experimental tests. Additional research
concerning the influence of the approach section could be an interesting topic for further research.
Proceeding on these approach conditions, it might be worth investigating more in depth the formation
of vortices on the Heerenlaak structure. These vortices were observed during the experiments and it
was concluded that they impacted the discharge through the structure. Moreover, the inlet geometry
is assumed to have a major influence on their presence. Hence, researching the specific influence of
the geometry could result in possible improvements of the hydraulic structure.
151
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Appendix A: Proposed design of the hydraulic
structure
158
159
Appendix B: Valeport Model 801 Electromagnetic Flow
Meter
As part of our policy of continuing development, we reserve the right to alter at any time, without notice, all specifications, designs, prices and conditions of supply of all equipment
MODEL 801 Electromagnetic Flow Meter
Datasheet Reference: MODEL 801 version 2A, Feb 2011
The Model 801 Electromagnetic Flow Meters measure the speed of
water in Open Channel environments with exceptional accuracy. Two
sensor types are available, to suit different application requirements,
but both offer excellent durability, reliable accurate data, and are
suitable for use in clean water and dirty or difficult environments.
Specifications
Model 801 - Cylindrical Type
Range: -5m/s to +5m/s
Accuracy: ±0.5% of reading plus 5mm/s
Zero Drift: <5mm/s
Sensing Volume: Sphere of approx 12cm diameter around sensor
Minimum Depth: 15cm
Model 801 - Flat Type
Range: -5m/s to +5m/s
Accuracy: ±0.5% of reading plus 5mm/s
Zero Drift: <5mm/s
Sensing Volume: Cylinder of approx 20mm Ø x 10mm high
Minimum Depth: 5cm
Calibration
Both instruments are calibrated to NAMAS traceable standards at
Valeport’s own premises up to speeds of 1m/s. Higher speed
measurements are based on linear extrapolation. Specific high speed
calibrations can be arranged at a third party facility on request.
Display Unit
Size: 244mm x 163mm x 94mm, 2kg
Environmental: Sealed to IP67
Power: 8 x alkaline C cells, lasting for up to 37 hours
Operating Temp.: -5°C to +50°C (display unit)
-5°C to + 40°C (sensor)
Configuration
Both instruments are available for use as hand held “Wading Sets” only,
with the operator standing in the channel, holding the instrument in position.
The system is supplied with 1.5m wading rod (3 x 0.5m sections),
graduated in cm, and a 3m cable from instrument to display unit.
Alternatively, a “top-setting” wading rod system is available, which allows
the vertical position of the instrument to be set without removing the wading
rods from the water.
Software
System is supplied with CDUExpress Windows based PC software, for data
extraction from display unit. CDU Express is license free.
Shipping
Standard: 62 x 42 x 34cm, 9kg (wading set)
Ordering
0801001 Single axis cylindrical sensor, c/w 3m cable, control
display unit (with logging facility), and operation
manual. Supplied in ABS transit case.
0801002 Single axis flat sensor, c/w 3m cable, control display
unit (with logging facility), and operation manual.
Supplied in ABS transit case.
0801003 Wading rod set c/w 3 x 0.5m graduated rods, base,
direction knob, and canvas carrying bag.
0801011 Option - Large transit case to take instrument and
wading rods.
What’s the Difference?
The smaller sampling volume of the flat sensor makes it very much more
suitable for shallow flows, or measurements in confined spaces. However,
it is also very much more sensitive to turbulent flows, which may manifest
as apparently noisy real time readings. This effect can be minimised by
using a long (>30secs) average period. The larger sampling volume of the
cylindrical sensor effectively eliminates the turbulence noise, but also
means that a greater depth of water is required for measurements.
Data Acquisition
The Model 801 Flow Meters are supplied with a dedicated surface display
unit, which both drives the sensor and provides data display of the
measured water velocity.
Data is updated at 1Hz, and may be averaged over any number of seconds
from 1 to 600. The display will show real time speed data at a resolution of
1mm/s, as well as the result of the data average, and a Standard Deviation
figure to give added data confidence. A solid state memory records all
results (up to 999 averaged readings), and the data may be downloaded to
PC using the RS232 interface lead supplied.