3-Civil - IJCSEIERD - Role of - Gholam Hossein Akbari - Iran-p

International Journal of Civil, Structural, Environmental and Infrastructure Engineering Research and Development (IJCSEIERD) ISSN 2249-6866 Vol.2, Issue 3, Sep 2012 30-41 Š TJPRC Pvt. Ltd.,

ROLE OF ENHANCED SPILLWAY DESIGN TO SUSTAIN EFFICIENT WATER SYSTEM 1

GHOLAM HOSSEIN AKBARI & 2ALI AKBAR ETESAM

1

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

Research 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

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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 USACE 1 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. The close 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 Cassidy’s 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 NavierStokes (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 2

- U.S. Army Crops of Engineers - U.S. Bureau of Reclamation

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Gholam Hossein Akbari & Ali Akbar Etesam

the laboratory, analytical solution of equations) require us to make simplifications and to justify approximated solutions which are liable to errors. However, we do need to be able to choose between different model formulations, and to advise when the benefits of a more sophisticated process representation outweigh the associated increase in computational and data collection costs. Data, with all their problems, still help us to do this, although other approaches are also of value. It is perhaps here, where CFD meets the real world, that the new challenges are emergent, as we deal with flooding errors subjected to a compound system of floodplains, rivers-reservoirs, ogee spillways, with complex structures and hence strong horizontal and vertical process gradients, and where traditional simplification of model geometry removes the critical aspects of the processes that are driving the system.

PHYSICAL MODEL A physical model of typical ogee spillway similar to UWRL1, as shown Figure 1, with design head

H d of 35cm was fabricated and tested. The model was constructed of Plexiglas and was fabricated

to confirm to the distinctive shape of an ogee crest. The model also included a tangent section and a typical flip bucket. Plexiglas was chosen because it could be fabricated with smooth curves and easily instrumented with pressure taps. The model was 2m wide with 90cm height. The

P / H d ratio (height of

crest/design head) was related as (18/7). The spillway model was placed in flume measuring approximately 2m wide by 12m long by 125cm depth. The ogee section was installed in the flume in an area with Plexiglas sliders so that flow could be observed. The flume had a flat bottom and was equipped with baffles and wave suppressors to provide a uniform approach flow.

To ensure that sidewall effects did not influence the pressure data, the main pressure taps were located at the center of the sectional model. To assess whether or not there were sidewall effects, several pressure taps were placed laterally across the model crest axis and were observed during testing. Testing showed that the pressure taps located centrally on the model were not affected by the sidewalls of the flume. However, a tap that was located approximately 31cm away from the sidewall of flume was influenced by sidewall effects. To ensure that the center taps would not interface with adjacent taps, the taps were staggered laterally. Every third tap was placed in the center of the spillway with the other two taps placed on either side. The tap spacing was approximately 15cm apart in the flow directions and staggered approximately 15cm.

1

- Utah Water Res. Lab.

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Role of Enhanced Spillway Design to Sustain Efficient Water System

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  ď Ľ ) 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; FAVOR2: which is an applied technique used for simulation of solid areas and volume changed, that is also 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 of flow such as velocity

1

2

-Volume of Fluid -Fractional Area/Volume Obstacle Representation

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Gholam Hossein Akbari & Ali Akbar Etesam

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)

 (2)

   (uAx )  ( vAy )  ( wAz )  0 x y z  ui 1 u 1 p   (u j A j i )   g i  fi  t VF dx j  dxi

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;

VF is volume fraction of fluid in each cell; Ax , Ay and Az is

fractional areas open to flow in subscript directions;

 is density; p is defined as the pressure; gi is

gravitational force in the subscript direction; and

fi represents the Reynolds stresses for which a

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

VF and A j

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 crest’s 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 (

Ax , Ay and Az ) 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, defining the 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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Role of Enhanced Spillway Design to Sustain Efficient Water System

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.

COMPARISON AND DISCUSSION OF RESULTS 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:

H e / H d (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 misleading errors. The design head was set at 0.3 and corresponding design flow rate, as determined from the model, 3

was 0.4 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 Q Qd Qd

Figure 2, Results of different techniques for comparing discharge Also tests were carried for the effective head H e , 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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Gholam Hossein Akbari & Ali Akbar Etesam

dimensionless divided by Qd 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 this comparison differences between models were significant shown up to 8% errors.

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

percent

of

errors

introduced

for

given,

X/Hd

which

was

defined

(Qc  Qm ) / Qm 100 where Qm is discharge in the physical model and Qc 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

H e / H d =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

H e / H d =0.8 and Figure 7 provides a comparison of average

crest pressure for flow head, for ratio equaled to

H e / H d =1.2

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Role of Enhanced Spillway Design to Sustain Efficient Water System

Figure 4, Crest pressure comparison with respect to error of H e / H d =0.5

Figure 5, Crest pressure comparison with respect to error of H e / H d =0.8

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Gholam Hossein Akbari & Ali Akbar Etesam

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

X / H d , with

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

H p / Hd

on the ordinate where

Hp

is 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

X / Hd

at the position for a ratio equaled to

He / Hd

=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

X / H d value at position for a ratio equaled to H e / H d =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 problem solution.

X / H d at a position for ratio equaled to H e / H d =1.2, as sensitive to the

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Role of Enhanced Spillway Design to Sustain Efficient Water System

Figure 7, Free surface height (cm) of flood over spillway at H e / H d =0.51

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

Figure 9, Free surface height (cm) of flood over spillway at H e / H d =1.20

Gholam Hossein Akbari & Ali Akbar Etesam

40

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.

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2. LE T. V. H., HARUYAM S., LE B. H., BUI D. L., Historical Flood/Inundation and Hydrological Regime 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 and initially unknown discharge. J. Hydr. Res., Delft, the Netherlands, 1998, 36(5), 785–801.

7. KRUGAR S., BURGISSER M., RUTSCHMANN P., Advances in calculating supercritical flow in spillway contractions. Hydro- Informatics, Babovic and L. Larsen, eds., Balkema, Rotterdam, The Netherlands, 1998, 1., 63–170

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Role of Enhanced Spillway Design to Sustain Efficient Water System

8. BRUCE M. S., MICHAEL C. J., Flow over Ogee spillway; physical and numerical model case study. J. Hydrology. Eng. ASCE, 2001, 127, 640–649.

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

10. NICHOLAS. B. D., HIRT C. W., HOTCHKISS R. S., Volume of fluid (VOF) method for the dynamics of free boundaries. Los Alamos Scientific Lab. Rep. LA-8355, Los Alamos, N.M., 2008.