Evaluation of a Numerical Modeling for Flow over an OGEE Spillway

8th International River Engineering Conference

Shahid Chamran University , 26-28 Jan. 2010 , Ahwaz�

Evaluation of a Numerical Modeling for Flow over an OGEE

Spillway

Fatema Zandi Goharrizi1, Mehdi Azhdary Moghadam2

1 Msc student of water engineering, [email protected] 2 Assistant Professor, University of Sistan and Baluchestan, [email protected]

ABSTRACT

The main objectives of the present research were to simulate flow

over an ogee spillway by a commercial numerical model and

investigate the ability of the model to predict several characteristics of

flow. At ten different flow head, discharge and pressure were obtained

by physical model, that constructed with Plexiglas and placed in a test

flume. k-� Standard is used for turbulent modeling in finite volume

method and volume of fluid is used to predict free surface of flow.

Numerical results have a good agreement with physical model results

and also with data interpolated from U.S. Army Corps of Engineering

and U.S. Bureau of Reclamation design monographs. This

compatibility has shown in nondimensional curves. The numerical

modeling has shown efficiency in studies due to saving time and money

and ability of monitoring all necessary data in several conditions.

Keywords: Ogee spillway, numerical model, finite volume method, volume

of fluid, CFX

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Introduction

One of the most popular hydraulic structures in studies is the ogee-crested spillway,

because of its fine hydraulic characteristics. Engineers widely use it in situations and know if

properly designed. It has ability to pass flows efficiently and safely, with relatively good flow

measuring capabilities. Engineer’s need to understand flow characteristics changing due to

variety of hydraulic and geometry design modifications such as hydraulics head, make them

to use modeling, both physical and numerical. These days computational fluid dynamics

(CFD) is used extensively by engineers to model and analyse complex issues related to

hydraulic design, planning studies for future generation stations, civil maintenance, supply

efficiency, and dam safety. However it is necessary to evaluate artificial models with

experimental models due to the rapidly changing advances in computational modeling for

solving the governing equations of fluid flow.

The choice of a physical model, computational model, or interpolating/extrapolating the

needed information from the U.S. Army Corps of Engineers (USACE) or the U.S. Bureau of

Reclamation (USBR) design/performance curves is up to engineer and his knowledge of

capabilities and limitations of state-of-the-art computational modeling or if the effects of

extrapolating. This study was completed at to compare the discharge and crest pressures

from flow over an uncontrolled ogee-crested spillway using a physical model, computational

model, and design curves from the USBR and USACE.

A standard ogee-crested spillway design was used for comparison the numerical model

with USBR and USACE data. These nondimensional data could be interpolated from

USACE (1990) and USBR (Design 1977) published reports and here we cached them from

the research done by Savage and Johnson (2001). The crest geometry is shown in Fig. 1. The

physical model data was obtained from the Plexiglas model used by Savage and Johnson

(2001). Commercial available computational fluid dynamics (CFD) software package,

ANSYS CFX (in brief: CFX) was used as numerical model.

Background

Variety of researches has been done in this field of modeling to help hydraulic designers to

obtain pressure, velocity and free surface level data for ogee spillway. In the hydraulic design

head the flow over crest acts as an aerated napped flowing over sharp-crested weir. At the

lower heads, the discharge is less than sharp-crested design discharge because of crest

resistance. At heads higher than design head, the discharge is greater than an aerated sharp-

crested weir because the negative crest pressure suctions more flow.

Although designing a crest allows small negative pressures at the design head because it

increases the efficiency of the spillway, there is also a prohibition for large negative pressures

on the crest. Because large negative pressures lead to cavitation damage, destabilization of

the structure, and possible safety failure. Large negative pressures can also be caused by

discontinuities in the crest shape and surface roughness.

Considerable works on understanding overflow spillways are available that depend on the

relative height and upstream face slope of the spillway (Maynord 1985) (Savage and Johnson

2001). Bazin (Chow 1959), in 1888, completed a comprehensive laboratory investigation and

was the first to study the ogee shape. After Bazin, a big area of the existing information was

developed from extensive data cached from physical models done by the USBR and the

USACE. For more information respect these references: USACE (1990), Design (1977), and

Chow (1959), Savage and Johnson (2001).

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Fig.1. Ogee Dimensions and Flow Parameters

In the recent years several attempts provided for CFD solutions and mathematical

methods. In some of them there is a good agreement with experimental data for a limited

numbers of their solutions. One of them did it by potential flow theory and mapping into the

complex potential plane. This attempt led to conclude that viscosity has a negligible influence

on the location of the free surface. Also another one obtained that the minimum pressure

point for a given head is up to the boundary condition configuration. And a good one showed

excellent agreement for water surfaces and discharge coefficients for a limited number of

flows. However, pressure data were only recorded at five locations downstream from a

nonstandard crest at one flow and showed some variability.

Some recent researches are due to, Savage and Johnson (2001), Savage and Johnson

(2001) studied a two-dimensional simulation of flow over an ogee spillway using a

commercial CFD code Flow-3D. They found a good agreement with experiments for both

pressures and discharge. Dargahi (2006) used Fluent to investigate flow field over an

overflow spillway and compare it with 3D flows simulations, he used commercial code to

simulate water surface, discharge coefficient and wall shear stresses. Chanel and Doering

(2007) presented in their research a comparison of discharge rating curves obtained through

numerical modeling with the CFD software Flow-3D to data acquired from physical model

studies on three Manitoba Hydro generating stations with significantly different spillway

height, P, to design head, Hd ,ratios. The objective of this study is investigate the problem and

solve the RANS equations by CFX.

The Ogee Crest Spillway Information

As you see in the Fig. 1 the ogee crested spillway is one of the standard one with tree

curves upstream of the crest axis. Downstream section from the crest axis to the tangent

section has been standardized to the equation shown in Fig. 1. The coefficients and

exponents may change, depending on the dam geometry and design flow rate. Tangent

section is located at X/Hd =1.4 and a typical flip buckets placed at the end of the obstacle.

P/Hd = 2.70, where P is the dam height and Hd is the design head over the dam.

The discharge equation is:

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23

0 23

2eLHgCQ = (1)

The variable Q represent the total discharge; L = lateral crest length or width; He = total

head upstream from the crest; g = gravitational constant; and C0 = discharge coefficient. The

discharge coefficient C0 is not constant, which is influenced by a variety of factors including

the depth of approach, relation of the actual crest shape to the ideal napped shape, upstream

face slope, downstream apron interference, and downstream submergence (Design 1977).

Note that there are ranges and design curves for each of conditions to describe the effect of

the parameters.

Experimental Model

The physical model data was obtained from the experiment that Savage and Johnson

(2001) have done, as mentioned before. The spillway model with a design head, Hd of 301

mm in 1.83 m width and 0.80 m height, was constructed of Plexiglas placed in flume (in an

area with Plexiglas sides) approximately 1.83 m wide by 12 m long by 1.22 m deep. The

model was tested and fabricated in UWRL. Plexiglas was chosen because it could be

fabricated with smooth curves and easily instrumented with pressure taps (Savage and

Johnson 2001). The Plexiglas also has another advantage that flow could be observed. The

P/Hd ratio was 2.7.

The flume bottom was flat and equipped with baffles and wave suppressors to provide a

uniform approach flow. The main pressure taps were placed at the center of the sectional

model (0.92 m from sidewall) to ensure that sidewall effects did not influence the pressure

data. However, several pressure taps were located laterally across the model crest axis and

were observed during testing. They showed just that the tap that was located approximately

305 mm away from the sidewall of the flume was influenced by sidewall effects. The

pressure taps along the spillway was shown in Fig. 2. The flowmeters and tanks were used to

control the flow rate. A piezometer board with glass tubes vented to the atmosphere was

applied for measuring pressures on the spillway that leveled and connected to the pressure

taps. An average pressure was recorded.

FIG. 2. Grid Dimensioning for Ogee Crest

The flow was set by a control valve in the model. Ten different flow rates are used to

calculate a discharge rating curve for crest. The heads were ranging from He /Hd = 0.07 to

1.20, where He is the effective head upstream above the crest.

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By allowing the free discharge from flip bucket to the flume the tailwater was kept below

critical depth and had no influence on the pressure taps on the spillway. At a distance of 2.04

m upstream from the model crest, the headwater elevation was measured.

Numerical Model

Computational Fluid Dynamics (CFD) is a computer-based tool for simulating the

behavior of systems involving fluid flow, heat transfer, and other related physical processes.

It works by solving the equations of fluid flow (in a special form) over a region of interest,

with specified (known) conditions on the boundary of that region. ANSYS CFX is a general

purpose Computational Fluid Dynamics (CFD) software suite that combines an advanced

solver with powerful pre- and post-processing capabilities. ANSYS CFX consists of five

software modules that pass the information required to perform a CFD analysis that is shown

in Fig. 3. (CFX 2006)

The set of equations solved by ANSYS CFX are the unsteady Navier-Stokes equations in

their conservation form.

FIG. 3. Five software modules of ANSYS CFX

A number of models have been developed that can be used to approximate turbulence

based on the Reynolds Averaged Navier-Stokes (RANS) equations. The following turbulence

models based on the RANS equations are some of the available models in ANSYS CFX :

Eddy-viscosity Models such as Zero equation model, Standard k-� model, RNG k-� model,

standard k-� model and Reynolds-Stress Models (RSM) (CFX 2006).

FIG. 4. Boundary conditions

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General Governing Equation

The continuity equation for incompressible flow:

0=∂

∂�

i

i

x

u (2)

The momentum equations:

ii

ij

i

j

i fgx

p

x

uu

t

u++

∂

∂=

∂

∂+

∂

∂

ρ

1 (3)

In VOF Method, in order to find the interface of two phases, another equation of momentum

for fraction volume has to be solved:

0=∂

∂+

∂

∂

i

q

i

q

xu

t

αα (4)

When oq=α for the cell in the domain is empty of the qth

fluid, 1=qα for the cell in the domain is full

of the qth

fluid, and 10 << qα for the cell contains the interface between fluids. Also for n phases there

are:

11

=�−

n

q

qα (5)

After completing the solution if we reach to 5.0=α , the correct interface has been obtained.

In above equations iu =velocity in the i=1,2,3 directions; qα = volume fraction of fluid in

each cell; ρ = density; p is defined as the pressure; ig = gravitational force in the subscript

direction; and if represents the Reynolds stresses.

Boundary Condition

The information of boundary conditions is represented in Fig. 4.

Results

The discharge per unit of length of the spillway for the physical model has been obtained

0.376 (m3/s.m). Then all the discharges of the effective head have been nondimensionalized

by Hd: hydraulic design head and the curve is presented the comparison of discharges in the

simplest form (Fig. 5). The discharge relative error by (Qc –Qm)/Qc×100 where Qc is

numerical model discharge, and Qm is physical modeling (Fig. 6).

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FIG. 5. Normalized Discharge Comparison

FIG. 6. Relative Percent Error in Discharge Using Physical Model as Basis

The most of error is belonged to USBR, because the crest design has two radii in the

compound curve, upstream of crest axis, where other spillway has 3 radii here. The relative

error for numerical model is less than 3% for He/Hd.

The comparison of crest pressure for three different flow rates is shown in Fig. 7. The axis

is nondimensional by Hd. Hp is the pressure head; Hp=P/�g and � is density of water.

He/Hd=0.51

He/Hd=0.82

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He/Hd=1.2

FIG. 7. Crest Pressure Comparison

Absolute pressures’ error with physical model data as basis is shown at the cm of water in

Fig. 8. The relative pressure instead of absolute pressure causes large relative error in the near

zero pressure zones.

He/Hd=0.51

He/Hd=0.82

He/Hd=1.2

FIG. 8. Absolute Pressure Differences Using Physical Model as Baseline

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Conclusion

In this research by using CFD model and ANSYS CFX software flow over an ogee

spillway were simulated. k-� Standard is used for turbulent modeling in finite volume method

and volume of fluid is used to predict free surface of flow. The results were compared with

physical at ten different flow head. Numerical results have a good agreement with physical

model results and also with data interpolated from U.S. Army Corps of Engineering and U.S.

Bureau of Reclamation design monographs. The numerical modeling has shown efficiency

in studies due to saving time and money and ability of monitoring all necessary data in

several conditions.

References

ANSYS CFX user manual; v 11.0. (2006) ANSYS, Inc. ANSYS Europe, Ltd.

Chanel, P. G. and Doering, J. c. (2007). An Evaluation of Computational Fluid Dynamics for

Spillway Modeling, 16th Australasian Fluid Mechanics Conference Crown Plaza, Gold

Coast, Australia.

Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, New York.

Dargahi, B. (2006). Experimental Study and 3D Numerical Simulations for a Free-Overflow

Spillway, J. Hydr. Engrg., ASCE, 132(9).

Design of small dams. (1977). U.S. Bureau of Reclamation, U.S. Government Printing

Office, Washington, D.C.

Nichols, B. D., Hirt, C. W. (1981). ‘‘Volume of fluid (VOF) method for the dynamics of free

boundaries.’’ Los Alamos Scientific Lab., Los Alamos, N.M.

Savage, B. M. and Johnson, M. C. (2001). Flow Over Ogee Spillway: Physical and numerical

Model Case Study, J. Hydr. Engrg., ASCE, 127(8).

U.S. Army Corp of Engineers (USACE). (1990). ‘‘Hydraulic design of spillways.’’ EM

1110-2-1603, Dept. of the Army, Washington, D.C.

Versteeg, H. K., and Malalasekera, W. (1995). An introduction to computational fluid

dynamics, Longman Scientific and Technical, New York.

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