hydraulics of stepped spillways.pdf

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TECHNICAL PAPER

Hydraulics of stepped spillwayswith different numbers of stepsThis paper describes the study of two physical models that were

built to investigate the energy dissipation and flow regimes for

different discharges over stepped spillways with different numbers

of steps. These physical models had a general slope of 19?2% and

had 12 and 23 steps respectively. Experiments were carried out for

a wide range of discharges. The hydraulic parameters of the flow

over the models were measured and the energy dissipation of flow

was also calculated. Results showed that the 12-step model

dissipated more energy than the 23-step model. However, the flow

regimes that occurred in the 23-step model were considered more

acceptable than in the 12-step model. The experiments showed

that energy dissipation at lower flow rates were similar in both

cases. However, in the skimming flow regime at higher discharges,

energy dissipation was about 12% less in the 23-step model than in

the 12-step model.

IntroductionStepped spillways, in which a series of steps are built

into the sloping floor of the spillway, can be used to

convey flood flows at dams, dissipating some of the

energy of the flow as it passes over the steps.

Depending upon the flow rate for a given stepped

spillway geometry, the flow over a stepped spillway may

be divided into three distinct flow regimes nappe,

transition and skimming flow in the order of

increasing flow rates.1 Nappe flow is observed for a

small dimensionless discharge dc/h (where dc is the

critical flow depth and h is the step height) and is

characterised by a succession of free-falling nappes at

each step edge, followed by nappe impact on the

downstream step. The skimming flow regime is

observed for the largest discharges; the water skims

over the pseudo-bottom formed by the step edges as a

coherent stream. Beneath the pseudo-bottom, intense

recirculation vortices fill the cavities between all step

edges.2 These recirculation eddies are maintained by

the transmission of shear stress from the main stream

flow and contribute significantly to the energy

dissipation. Gonzalez1 observed air cavities of different

size, alternating with fluid-filled recirculation vortices,

between step edges below the main stream of the flow.

In the recent past, much research on stepped spillways

has been carried out on different hydraulic parameters

such as flow regimes, inception of air entrainment, air

concentration, velocity distributions and energy

dissipation (examples being Gonzalez,1 Barani et al.3

and Meireles and Matos4).

Experiments on a moderately sized stepped spillway by

Christodoulou5 indicated that the energy loss owing to

the steps depended primarily on dc/h as well as on N

(the number of steps). For values of dc/h near unity, or

near the limit of skimming flow, the stepped surface

was very effective in dissipating energy. For higher

values of dc/h, the effect of N became appreciable at a

certain dc/h, which indicated that the relative energy

loss increased with N.

Pegram et al.6 studied two different physical models of

stepped spillways of slope 60% with the same crest shape,

30 m height and a range of step sizes (0?25 to 2?0 m in a

1:10 scale model and 0?5 to 2?0 m in a 1:20 scale model).

They showed that the residual specific energy was

independent of the step sizes. But this energy at the toe of

a stepped spillway of height 50 m (or higher), within the

range of step heights tested, was less than 60% of the

residual specific energy at the same level on a similar

smooth spillway experiencing flows up to 20 m3/m2.

In the present study, two sets of experiments were

carried out using physical models. In the first set,

experiments were performed to investigate the effects

of different discharges and numbers of steps on the

flow regimes at stepped spillways. In the second set,

energy dissipation on the same flow and geometry

131

Dams and Reservoirs2010 20, No. 3, 131136DOI: 10.1680/dare.2010.20.3.131

R. RoshanMSc

Hydraulic StructuresDivision, Water ResearchInstitute, Tehran, Iran

A. Ab GhaniMSc, PhD

River Engineering andUrban DrainageResearch Centre(REDAC), Penang,Malaysia

H. Md.AzamathullaME, PhD

River Engineering andUrban DrainageResearch Centre(REDAC), Penang,Malaysia

M. MarosiMSc

Shahid ChamranUniversity of Ahvaz,Ahvaz, Iran

H. PahlavanMSc

Shahrood University ofTechnology, Shahrood,Iran

H. SarkardehMSc

Hydraulic StructuresDivision, Water ResearchInstitute, Tehran, Iran

www.damsandreservoirs.com ISSN 1368-1494 f 2010 ICE Publishing

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conditions was measured to assess the effect of thenumber of steps and of the different step heights.

Experimental set-upThe physical model of the Khansar Dam and Spillway(Yazd-Iran) was built in the hydraulic structureslaboratory of Irans Water Research Institute (WRI) tostudy the spillways energy losses and flow regimes. The

toe elevation of this dam was 1941?9 m, crest elevation1953?5 m, width of the spillway was 65 m, the maximumflow per unit width of the spillway (q) was 16?15 m3/m2

and the maximum flow passing over the spillway (Q)was 1050 m3/s. The scale of this physical model wasselected as 1:20. The vertical height of the model(difference between crest and toe elevations) was0?78 m. The maximum flow in the modelled spillway

132

Figure 1. Views of the physical models

1957.50

1953.50

1951.5011 1

1

23

Spillw

ay a

xis

Figure 2. A schematic view of ogee spillway of the model

Table 1. Flow regimes of 12-step and 23-step models

qm : m3/m2 dc: m 12-step 23-step

0?026 0?041 NA TRA

0?034 0?049 NA TRA

0?045 0?059 TRA TRA-SK

0?052 0?065 TRA TRA-SK

0?069 0?078 TRA SK

0?086 0?091 TRA SK

0?095 0?097 TRA-SK SK

0?103 0?103 TRA-SK SK

0?120 0?114 TRA-SK SK

0?138 0?125 SK SK

0?155 0?135 SK SK

0?172 0?144 SK SK

0?181 0?149 SK SK

The types of flow regimes in Table 1 are: NA5 nappe flow, TRA5 transition flow, SK5 skimming flow and TRA-SK5 transitionto skimming flow.

ROSHAN ET AL.

Dams and Reservoirs 2010 20, No. 3, 131136

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On: Sun, 14 Nov 2010 11:42:18 133

00 0.60.4

h/l

d c/h

0.2

2.0

1.5

1.0

0.5

2.5

Upper limit of transition flow7Lower limit of transition flow7

12-step: lower limit

12-step: upper limit23-step: upper limit

Figure 3. Flow observations in comparison with Chanson and Toombes7 equations

Step 3

Step 2Step 1

Nappe flow

Solid flow

Figure 4. Nappe flow at low flow rates

Step 2

Step 3

Step 4

Step 5

Step 6

Figure 5. Skimming flow at high flow rates

HYDRAULICS OF STEPPED SPILLWAYS WITH DIFFERENT NUMBERS OF STEPS



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was 0?118 m3/s. The general slope of the model was

19?2%. A rectangular weir, which was installed in the

canal at the downstream end of the model, was used to

measure the flow rate passing the stepped spillway. A

water gauge with 0?1 mm accuracy was used to measure

the depths of flow at the upstream and downstream

ends of the model.

To evaluate the effect of the number of steps, two cases

with 12 and 23 steps were built (by fixing the other

parameters of the Khansar dam model). These two

laboratory cases with the same slope were made of

PerspexR and the step properties were as follows:

length 5 33?7 cm, height 5 6?5 cm for 12-step case and

length 5 16?8 cm, height 5 3?25 cm for 23-step case

(Figures 1 and 2).

Experimental resultsFlow regime observationOn the stepped spillway, the nappe and transition flow

regimes were observed for the low range of water

discharges and skimming flow regime occurred for the

upper range of water discharges. In the 12-step case, for

water discharges less than 0?138 m3/m2, nappe or

transition flows was observed and skimming flow was

observed for discharges of 0?138 m3/m2 and larger. In

the 23-step case, the limit between skimming and

transition flows was 0?069 m3/m2 (Table 1).

134

Figure 6. Strong spray and splashing in transition flows

Figure 7. Strong hydrodynamic fluctuations downstream of the inception point

ROSHAN ET AL.



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Chanson and Toombes7 presented two equations whichshowed the lower and upper limits of transition flows.In this part, experimental observations using the samedefinitions of nappe, transition and skimming flows areplotted in Figure 3. For the lower limit this equation is

1dchw0:9174{0:381 h

l0vh

lv1:7

and for the upper limit is

2dchv 0

:9821

h=l z0:388 0:384 0vh

lv1:5

where l is the step length. Equations 1 and 2 are plottedin Figure 3. The measured data of changes in flowregimes showed good agreement with the findings ofChanson and Toombes7 for the threshold betweennappe flow and transition flow, at a dc/h value ofbetween 0?75 and 0?91 in the 12-step model. However,

there was a rather higher threshold for the boundary

between transition flow and skimming flow, at between

1?75 and 1?92 in the 12-step model and between 2?0

and 2?4 in the 24-step model.

Experimental observations of flow regime for the 12-

step case showed that, for discharges less than 0?045

m3/m2, water cascaded down the spillway as a

succession of free-falling nappes from one step to

another (Figure 4). Flow visualisations permitted clear

and precise views of the intense recirculation taking

place in the cavities between step edges for both

transition and skimming flow regimes. Skimming and

transition flows have distinct appearances. In skimming

flows, the water skimmed smoothly over the pseudo-

bottom formed by the steps (Figure 5).

In transition flows, the water exhibited a chaotic

behaviour associated with the intensive recirculation in

cavities, strong spray and splashing (Figure 6).

Downstream of the inception point, splashing and spray

135

Figure 8. Air entrainment in transition flows

HYDRAULICS OF STEPPED SPILLWAYS WITH DIFFERENT NUMBERS OF STEPS



On: Sun, 14 Nov 2010 11:42:18

were observed next to the free surface with waterdroplets that jump out of the flume (Figure 7).

Free-surface aeration was very intense in all transitionflow rates downstream of the inception point of free-surface aeration; rapid free-surface aeration wasobserved. The location of the inception of free-surfaceaeration was clearly defined (Figure 8).

Energy dissipationTo determine the energy dissipation from upstream todownstream, experiments with different flow rates andnumbers of steps (two cases) were carried out. Bymeasuring the hydraulic characteristics of flow upstreamand downstream of the model and based on theBernoulli equation, the total head losses in each casewere calculated. The percentage of dissipated energy ineach case was then determined and plotted (Figure 9).

As can be seen from Figure 9, generally, the energydissipation decreased with increasing dimensionlessdischarge number in both models. This non-dimensional discharge parameter is defined byq

g hp

P , where P is the height of spillway from crestto toe. Also, the 12-step case results in greater energydissipation than the 23-step case. Thus, it can be statedthat increasing the number of steps in a given height ofthe spillway decreases energy dissipation, because of

the reduced step height. Moreover it should be notedthat flow regimes over a stepped spillway have a greateffect on energy dissipation. For example, a nappe flowregime is more efficient for energy loss than a skimmingflow. This phenomenon could occur in lowerdischarges or higher steps (in the present study, thisoccurred in the 12-step case). Overall it could beconcluded from Figure 9 that the 12-step casedissipated about 12% more energy than the 23-stepcase.

ConclusionsIn this research work, two different models were usedto show the effect of the number of steps on flowregimes and energy dissipation over stepped spillways.Experiments were conducted over a wide range ofdischarges. By observing and measuring the hydraulicparameters, the effect of the number of steps wasevaluated.

Flow regimes visualisation indicated that, in the 12-stepcase, for water discharges less than 0?138 m3/m2, nappeor transition flows were observed and skimming flowsoccurred for discharges larger than 0?138 m3/m2. In the23-step case, the limit between skimming and transitionflows was equal to 0?069 m3/m2. It is interesting to notethat the 12-step case had more effect on energydissipation than the 23-step case.

REFERENCES1. GONZALEZ C. A. An Experimental Study of Free Surface Aeration on Embankment Stepped Chutes. PhD Thesis, Department of Civil

Engineering, University of Queensland, Australia, 2005.2. CHAMANI M. R. and RAJARATNAM N. Characteristics of skimming flow over stepped spillways. Journal of Hydraulic Engineering, ASCE,

1999, 125, No. 4, 361368.3. BARANI G. A., RAHNAMA M. B. and SOHRABIPOOR N. Investigation of flow energy dissipation over different stepped spillways. Journal of

Applied Science, 2005, 2, No. 6, 11011105.4. MEIRELES I. and MATOS J. Skimming flow in the nonaerated region of stepped spillways over embankment dams. Journal of Hydraulic

Engineering, 2009, 135, No. 8, 685689.5. CHRISTODOULOU C. Energy dissipation on stepped spillways. Journal of Hydraulic Engineering, 1993, 119, No. 5, 644650.6. PEGRAM G. G. S., OFFICER A. K. and MOTTRAM, S. R. Hydraulics of skimming flow on modeled stepped spillways. Journal of Hydraulic

Engineering, 1999, 125, No. 5, 500510.7. CHANSON H. and TOOMBES L. Hydraulics of stepped chutes: the transition flow. Journal of Hydraulic Research, 2004, 42, No. 1, 4354.

136

00

23-step model 12-step model NA TRA TRA-SK SK

Ener

gy d

issi

patio

n: %

0.05 0.15

q/(gdc)0.5P

0.10 0.20

90

80

70

60

50

40

30

20

10

100

Figure 9. Energy dissipation for the 12-step and 23-step models

ROSHAN ET AL.


hydraulics of stepped spillways.pdf

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