3-civil - ijcseierd - role of - gholam hossein akbari - iran-p

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ROLE OF ENHANCED SPILLWAY DESIGN TO SUSTAIN EFFICIENT

WATER SYSTEM

1GHOLAM HOSSEIN AKBARI &

2ALI AKBAR ETESAM

1Assistant Professor, Civil Eng. Dept., University of Sistan & Baluchestan, Iran

1Research fellows, Civil Eng. Dept., University of Sistan & Baluchestan, Iran

ABSTRACT

This work present an engineering system to sustain water required for a community. An efficient

water way system was designed. Several numerical run tests performed for highlighting errors involved

in design of ogee spillways subjected to overflowing flood from a catchment. Flow-3D software capable

of handling turbulent models (Prandtel mixing length, One-equation transport, Two equations transport,

Re- Normalized Group (RNG)) were utilized. Two techniques (volume of fluid (VOF) and Fractional

Area/Volume Obstacle Representation (FAVOR)) were adopted for geometric simulations. Reynolds -

Averaged Navier-Stokes (RANS) equations was solved for possible errors subjected to: design flood

head, maximum instantaneous flood head based on probable maximum discharge predictions. Results

were compared to graphical models (the U.S. Bureau of reclamation (USBR) and the U.S. Corp of

Engineers (USACE)) included with extensive data. A Physical model fabricated, employed, compared to

powerful and efficient computational fluid dynamic (CFD) codes, found not errors free and expensive.

Results indicated numerical methods as convenient, time saving with least errors.

KEYWORDS: Overflow structures errors, efficient modeling, sustainable water system,

enhanced CFD techniques

INTRODUCTION

The spillways are flow measurement structures with good hydraulic engineering characteristics.

They are widely used in water fields found sensitive hydraulic structures. Their ability to pass flooding

flows efficiently, safely, properly designed, with relatively good measuring capabilities, have enabled

engineers to use them in wide range of flow situations. Hydraulics of flooding flows over barrier

structures have been subject of broad research works, but investigations regarding errors from measured

floods (hydrometric stations in hydrologic catchments) have not been carried in coupled fashion through

hydrologic -hydraulics and CFD analysis. No research has been carried on sensitive parameters

introduced errors, involved in the solution procedure and great efforts have not been made dealing with

the errors precisely. Slight modification in flow geometry, varying shape and hydraulic properties of the

flow, cause great difference on the problem solution. These changes appear as errors beyond the values

often required by experts to evaluate and determine the performance of the overflowing spillway

working under flooding conditions. With fast developments in computational simulation for solving the

International Journal of Civil, Structural, Environmental

and Infrastructure Engineering Research andDevelopment (IJCSEIERD)

ISSN 2249-6866

Vol.2, Issue 3, Sep 2012 30-41 TJPRC Pvt. Ltd.,


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31 Role of Enhanced Spillway Design to Sustain Efficient Water System

governing equations of flooding flows, recently engineers have broader choice for selecting various

methods of solutions in evaluating varied flow analysis . The choices of a physical model,

computational model, information from the USACE1

or USBR2

there exist for engineers. To correlate

this study with the existing USBR and USACE data, a standard ogee-crested spillway design was used.

As part of this study, several numerical techniques were compared using flow 3-D software and

physical models data. Research carried out here provides practitioners, engineers with an additional

assurance for analysis and design of flooding overflow spillways.

BACKGROUND

Considerable research has been done to determine the shape of the crest of an overflow spillway,

and different methods are available that depend on the relative height and upstream face slope of the

spillway. An early attempt of modeling spillway flows was completed by Cassid . By using potential

flow theory and mapping into the complex potential plane, he was able to solve free surfaces and crest

pressure head and found good agreement with experimental data for a limited number of solutions. Theclose agreement let Cassidy to conclude that viscosity had a negligible influence on the location of free

surface. He also concluded that the point of minimum pressure for a given head was dependent on the

boundary configuration. Convergence of Cassidys solution was dealt by others using linear finite

elements and variation principle. Li et a , completed additional improvements on the two dimensional

irrigational gravity flows by using higher-order elements to model the curved water surface and spillway

surface.

Guo ET al expanded on the potential flow theory by applying the analytical functional boundary

value theory with the substitution of variable to derive nonsingular boundary integral equations. This

method was applied successfully to spillway with a free drop. Further researches used the standard

( k ) equations to model turbulence, included viscous effects, solved the Reynolds-averaged Navier-

Stokes (RANS) equations in two and three dimensions, shown excellent agreement for water surface and

discharge coefficients for a limited number of flows.

Majority of the existing information, derived from extensive data, taken from physical models,

are completed by the USBR and the USACE. Researchers attempted to solve similar problems with a

variety of mathematical models and computational methods. The main difficulty of the problem was flow

transition from sub-critical to supercritical flow. In addition, the discharge was unknown, solved as part

of the solution. This is especially critical when the velocity head at upstream end from

the spillway is significant part of the total upstream head.

Despite all progress made to minimize computational errors of flooding flow, key research questions

remain. A particularly central issue is how to validate models. A newly view, somewhat strange

preoccupation, given that all of our other research approaches (fieldwork, experimental data collection in

1- U.S. Army Crops of Engineers2- U.S. Bureau of Reclamation


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Figure 1, Dimension of spillway with pressure taps on crest

NUMERICAL MODEL AND GOVERNING EQUATIONS

Initially a simple computer program was written, compiled and run for conceptualizing the

physical model data analysis. Flow-3D model, having broad application in water engineering, a suitable

model for the 3D- fluids, widely used in literatures, was employed for analysis, supported three

dimensional flows with free surface, complex geometry, flooding flow over spillway. The software is

designed with five algorithms used in a regular grid network substituting equations in forms of finite and

second order precision relations for solving the problems. Numerical testing included in the software are

five turbulent models (Prandtel mixing length, One-equation transport, Two-equations ( k ) transport,

Re- Normalized Group (RNG), Large Eddy Simulation (LES7-8)). The LES was excluded here because

of lack of available data. The software adopts two techniques, used for geometric simulation, the first

scheme named as: VOF1: shows properties of flow with free surface. The second method named as;

FAVOR

2

: which is an applied technique used for simulation of solid areas and volume changed, that isalso used for boundary simulation. Model was used for solving Reynolds-Averaged Navier-Stokes

(RANS) equations. The computational region is covered by Cartesian coordinate grid. This grid has

variable-sized hexahedral cells. For each cell, software computes parameters offlow such as velocity

1-Volume of Fluid

2-Fractional Area/Volume Obstacle Representation


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Gholam Hossein Akbari & Ali Akbar Etesam 34

and pressure. Free surface modeling divided the computational cells to five regions: Completely solid,

Part solid with semi fluid, completely fluid, Part fluid and empty, and completely empty.

The general governing RANS and continuity equations for incompressible flow, including the

VOF and FAVOR variables, are outlined as the following (1) and (2) equations:

(1)

( ) ( ) ( ) 0x y zuA vA wAx y z

(2)

1 1( )i i

j j i i

F j i

u u pu A g f

t V dx dx

Equation 1 and 2 are continuity and momentum equations. The variables u, v and w represent the

velocities in the x, y and z directions; FV

is volume fraction of fluid in each cell; xA

, yA

and zA

is

fractional areas open to flow in subscript directions;

is density;p

is defined as the pressure; ig

is

gravitational force in the subscript direction; and if represents the Reynolds stresses for which a

turbulence model is required for closure. It can be seen that, in cells completely full of fluid FV

and jA

equal 1, thereby reducing the equations to the basic incompressible RANS equations.

The FAVOR numerical algorithm in Flow-3D, outlined by Hirt and Sicilian (1985) and Hirt

(1992), is a porosity technique used to define obstacles. The grid porosity value is zero within obstacles

and one for cells without the obstacle. Cells only partially filled with an obstacle have a value between

zero and 1, based on the percent volume that is solid. Therefore, the ogee crests surface is defined by

cells within the grid that have a porosity value between 1 and0. The location of the interface in each cell

is defined as first-order approximation, a straight line in two dimensions and a plane in three dimensions,

determined by the points where the obstacle intersects the cell faces. The slicing plane not only defines

the fractional volume that can contain fluid but also determines the fraction area ( xA

, yA

and zA

) on

each cell face through which flux (fluid flow) can occur. This method presented good performances

between numerical models.

`Another numerical algorithm in Flow-3D, used in this study to simulate flow over ogee spillway

is VOF method. To numerically solve the rapidly varying flow over ogee spillway, it is important that the

free surface be accurately tracked. Tracking involves three sections: locating the free surface, definingthe surface as a sharp interface between the fluid and air and applying boundary conditions at the

interface.

VOF method is a tool for tracking the free surface. This method is described by Hirt and Nichols

(1975), Nichols et al. (1980) and Hirt and Nichols (1981). The VOF method is similar to the FAVOR

method in defining cells that are empty, full, or partially filled with fluid. Therefore, empty cells assigned


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zero, full cells assigned one and partially filled cells are assigned between 0 and 1. The slope of free

surface in the cells that partially filled is found by an algorithm that uses the surrounding cells to define a

surface angle and surface location. In VOF method similar to FAVOR method, free surface definition

done by series of connected chords in two dimensions or by connected planes in three dimensions, the

VOF method allows for changing free surface over time and space.

COMPARISONANDDISCUSSIONOFRESULTS

The main purpose of this study was to compare results between physical model and numerical

analysis for flooding flow over an ogee spillway. This was also to see how numerical algorithms, VOF,

FAVOR, used in Flow-3D working side by side to graphical methods of USBR and USACE utilized with

extensive laboratory data. For wider application and simplicity, the results have been non-dimensioned.

The design parameters involved are: eH

/ dH

(Maximum flood head (m) over design head (m)), and the

maximum probable flood discharge divided by design flood discharge (Q/Qd ), also design flow rate per

unit length from the physical model which are used as the basic parameters subjected to misleadingerrors. The design head was set at 0.3 and corresponding design flow rate, as determined from the model,

was 0.43/ .m s m . In figure 2 VOF scheme was used and its performance was compared to three models.

The effects of flood discharge relationships against design head is examined varied uniformly. This was

expected, as recommended for design purpose13 .

Q dQ

Q dQ

Figure 2, Results of different techniques for comparing discharge

Also tests were carried for the effective heade

H , which included the velocity head,

dimensionless divided by the design head and shown on the horizontal axis. The discharge Q is


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dimensionless divided bydQ as shown on the vertical axis in the same figure. For next analysis, the

relative percent errors introduced for discharge ratios calculated and shown in Figure 3. In thiscomparison differences between models were significant shown up to 8% errors.

Figure 3, Results of introducing a relative percent of error for X/Hd

Relative percent of errors introduced for given, X/Hd which was defined

by:( ) / 100

c m mQ Q Q

where mQ

is discharge in the physical model and cQ

is the discharge in the

numerical model. This was also compared with interpolated data from the USBR the USACE design

graphs. The relative error introduced shown to be sensitive to the problem solution, in which the

numerical model shown varied for selected range of X/Hd. A variation of 2 to 8% from the physical

model was observed due to a value of X/Hd changed from 0.1 to 1.2 as shown in the figure 3.

Numerical experiments were continued as shown in the following figures. In the following

Figures 4-7, the different algorithms within the Numerical model named as RNG9-10, used and tested

against other available physical model data13-14. In this Figure comparison of average crest pressure for

flow head, for a ratio equaled to/e dH H =0.5 was made having satisfactory agreement. Further run

tests made to see greater differences between models. Figure 5 provides a comparison of average crest

pressure for flow head, for ratio equaled to/

e dH H

=0.8 and Figure 7 provides a comparison of average

crest pressure for flow head, for ratio equaled to/

e dH H =1.2


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Figure 4, Crest pressure comparison with respect to error of /e d

H H =0.5

Figure 5, Crest pressure comparison with respect to error of /e d

H H =0.8


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Figure 6, Crest pressure comparison with respect to error of /e dH H =1.2

The physical and numerical model crest pressures were interpolated at these heads from the

USACE data. The pressure distribution on the spillway is shown to be dimensionless as/

dX H

, with

X being the horizontal distance from the crest axis. The pressures are shown dimensionless as

/p d

H Hon the ordinate where p

His the pressure head.

Further analysis and comparison were made for introducing any error affecting results, as

followed, and shown in figure 7, the absolute pressure error (cm) of water for numerical model and

USACE data for a given value of/

dX H

at the position for a ratio equaled to/

e dH H

=0.51 This was

also expected to happen. In figure 8 it was shown that absolute pressure error (cm) of water for numerical

model and USACE data for a given/ dX H value at position for a ratio equaled to

/e dH H =0.82, had

the same expectation which confirms the sensitivity of the solution to any error. Figure 9 also reaffirmed

the case study and results shown for an absolute pressure error (cm) of water in numerical model and

USACE data for a given / dX H at a position for ratio equaled to /e dH H =1.2, as sensitive to the

problem solution.


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Figure 7, Free surface height (cm) of flood over spillway at /e d

H H =0.51

Figure 8, Free surface height (cm) of flood over spillway at /e dH H =0.82

Figure 9, Free surface height (cm) of flood over spillway at /e d

H H =1.20


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CONCLUSIONS

Initially a hand written computer program carefully compiled and run working with physical data.

Several numerical techniques then were tested with physical data, compared with available software of

3-D flow predictions. Research carried out in this study provides practicing engineers with an additional

assurance for design and analysis of flooding flows over spillways. This tool can also be very useful for

reevaluating a dam for any higher unsteady flow under provided conditions. An improvement to

hydrologic event flood calculations also was dealt in this work for misleading flood prediction errors. It

was shown that, within different ranges tested, the numerical method had an improved accuracy over the

design graphs for flow rates and pressure heads used. The increased accuracy dictates that the developed

algorithms used are powerful, having wider application, more convenient and adequate for covering

huge flood studies cases. Physical model studied are also considered as the basis for which numerical

methods are to be compared. However, a physical model may have limitation in dimensions and

applications, cost more money and take more time to complete than numerical studies. It also may be

concluded that for limited cases when only approximate flood discharge and pressure heads are required,

published design graphs provide quick solutions, within given parameters, at a cost and time which are

reasonable but not less than numerical studies.

REFERENCES

1.LIN B., WICKS J. M., FALCONER R. A., and ADAMS K. Integrating 1D and 2D hydrodynamicmodels for flood simulation. Proceedings of the Institution of Civil Engineers, Water

Management, 2006, 159, No. 1, 19-25.

2.LE T. V. H., HARUYAM S., LE B. H., BUI D. L., Historical Flood/Inundation and HydrologicalRegime in the Mekong River Delta in Vietnam. Environmental Change and Social Environment

of Large River, 2005, 38-50

3.MAYNORD S. T., General Spillway Investigation. Tech. Rep. Hl-85-1, U.S. Army Engineers,Waterways Experiment Station, Vicksburg, Miss.

4.CASSIDY J. J., I rotational Flow over Spillways of Finite Height. J. Eng. Mech. Div. ASCE,91(6), 155-173.

5.LI W., XIE Q., CHEN C. J., Finite Analytic Solution of Flow over Spillways. J. Eng. Mech.ASCE, 1989, 115(12), 2635-2648.

6.GUO Y., WEN X., WU C., FANG D. Numerical modeling of spillway flow with free drop andinitially unknown discharge. J. Hydr. Res., Delft, the Netherlands, 1998, 36(5), 785801.

7.KRUGAR S., BURGISSER M., RUTSCHMANN P., Advances in calculating supercritical flowin spillway contractions. Hydro- Informatics, Babovic and L. Larsen, eds., Balkema, Rotterdam,

The Netherlands, 1998, 1., 63170


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8.BRUCE M. S., MICHAEL C. J., Flow over Ogee spillway; physical and numerical model casestudy. J. Hydrology. Eng. ASCE, 2001, 127, 640649.

9.FLOW-3D User manual; excellence in flow modeling software, v 9.0. Flow Science, Inc., SantaFe, N.M., 2008. www.flow3d.com.

10. NICHOLAS. B. D., HIRT C. W., HOTCHKISS R. S., Volume of fluid (VOF) method for thedynamics of free boundaries. Los Alamos Scientific Lab. Rep. LA-8355, Los Alamos, N.M.,

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