The Stepped wasteweirs meaningfully decrease dimension of calming basin in forepart of the dikes and lead to hold a big benefit, hence this sort of wasteweirs are extremely attractive to utilize it. The profile of Stepped wasteweir is similar to same Ogee wasteweir profile. Flow lose the energy in the procedure of go throughing over the stairss. Most research workers have focus on factors which are related to energy dissipation. Peyras et al [ 1 ] Ru et Al. [ 2 ] , Liao et Al. [ 3 ] , Rice and Kadavy [ 4 ] , Pegram et Al. [ 5 ] , etc. , have studied on different sort of stepped wasteweirs and studied form of stairss and flow parametric quantities on energy dissipation.

Experimental effect of Chamani and Rajaratnam [ 6 ] have shown that when flow was to the full developed on a stepped wasteweir, the flow divided into upper and lower parts and the air concentration distributions in every parts was equal to the equations which was developed by Straub and Anderson for flow in steep chutes. Olsen et al [ 7 ] have modeled H2O flow over a wasteweir in two and tree dimension. The theoretical account solved the Navier-Stokes equations with the k- Iµ turbulency theoretical account on a structured non-orthogonal grid. Yang Min et Al. [ 8 ] studied hydraulic features of steeped wasteweir. Boes et al. [ 9 ] researched on stepped wasteweir in big theoretical account gulch with fiber-optical instrumentality. Qun Chenet al [ 10 ] used numerical mold for find the H2O surface on the stepped wasteweir. Bhajantri, Eldho and Deolalikar [ 11 ] have studied flow over wasteweir by utilizing numerical theoretical account.

So far, from the literature and our cognition the present survey is new. In the present survey we have simulated stepped spillway overflow for determine features of stepped wasteweir. In this paper, the VOF method ( fractional volume of fluid ) is used for determine some hydraulic features such as: speed coefficient “ I† ” , muffling ration “ K ” and resistance coefficient “ ” on stepped wasteweir.

2 Experimental informations

To formalize the consequences of numerical modeling, a series of experimental informations will be necessary. In this survey, the information is collected from surveies by Yani min et Al ( 2001 ) . In their surveies, all experiments were carried out at the Hydraulic Laboratory of Changchun Institute of Technology, Beijing, China.A Their theoretical account had a armored combat vehicle in the upstream and a wasteweir instantly after it. Model height have been 1.22 m and the width equal to 0.3m. a horizontal floor was jointed to stairss by a curving pail, the radius of pail have been 0.3 m in the theoretical account. The wasteweir had a 3H:4V incline and with 6 cm measure high. The discharge rates changed between 60 L/s to 4 L/s.

General layout of the numerical theoretical account shown in Figure 1. The figure of stairss in the survey is 18 stairss.

3 THEORETICAL Calculation

Velocity coefficient

The Bernoulli energy equation is expressed by:

( 1 )

Where =head upstream of the toe ;

=approach speed ; H = caput on the crest ; P1 = wire heigh ; = shrinkage subdivision deepness ; A =velocity at the shrinking subdivision ; =resistance coefficient ; and ; B= wire breadth, g=A gravitation acceleration. Velocity coefficient I†A is defined as:

( 2 )

( 3 ) A and can rewrite Eq.1 as

where I† = speed coefficient of the stepped wasteweir ; A q=the discharge per unit breadth.

( 4 ) As in experimental method measuring deepness on shrinking subdivision is difficult, so consecutive deepness can be usefull to cipher it.The computation expression is:

where = the sequent deepness Froude Number.A

Coefficient of opposition

In the measure spillway energy loss can be expressed as

( 5 )

Where = the opposition coefficient of stepped wasteweir is defined as: A A A A A A A A A A A A A

( 6 )

Muffling ratio

( 7 ) This parametric quantity is showed by K and it is defined as

where Ec=A shrinking subdivision energy =

4 Numeric modeling

The CFD ( computational fluid kineticss ) solver FLUENT [ 12 ] used in the present survey solves the 3-dimensional Reynolds-averaged Navier-Stokes equations for incompressible flow. FLUENT solves the regulating equations consecutive utilizing the control volume method. The regulating equations are integrated over each control volume to build discretized algebraic equations for the dependent variables. These discretized equations are linearized utilizing an inexplicit method. As the government equations are nonlinear and coupled, loops are needed to accomplish a converged solution. Two-phase sphere ( H2O in the channel with a part of air on the top ) is solved utilizing FLUENT ‘s multiphase preparation, called the volume of fluid ( VOF ) method in order to decide the fluctuation of the H2O surface over spillway. While two continuity equations are solved to account for each stage, the impulse and conveyance equations are shared by both stages.

The base of Navier-Stokes equations are on the saving of impulse and mass within a traveling fluid. The impulse differential equation is described by:

( 8 )

Where in this equation: P= force per unit area, = speed, and g is gravitation. is viscousness of fluid is the turbulency viscousness and is the organic structure force.

The differential equation for mass preservation is described as below:

( 9 )

In this equation is speed and is the unstable denseness.

Turbulence Model:

In this research, K- Iµ criterion is used for disruptive theoretical account. The K- Iµ two equation turbulency theoretical account is an effectual numerical simulation method used in recent decennaries and verified by experimental and field informations. For the K- Iµ turbulency theoretical account given by Launder and Spalding [ 13 ] , the continuity equation, the impulse equation, and the equations for K and Iµ are given as:

( 10 )

( 11 )

( 12 )

( 13 )

where t=time ; ui and xi=velocity constituent and co-ordinate constituent, severally ; I?=density ; Aµt =viscosity ; and P ‘ ( =P+2k/3, P is the force per unit area ) =modified force per unit area. The parametric quantity =turbulence viscousness, which can be calculated by the disruptive kinetic energy K and disruptive dissipation rate Iµ as:

( 14 )

where CI?=0.09=experimental invariable. The turbulency Prandtl Numberss for K and Iµ are 1.0 and.3, severally, and 1.44 and1.92 are invariables for the Iµ equation. The coevals of disruptive kinetic energy G due to the average speed gradients can be defined as:

( 15 )

Volume of Fluid Model of Air-Water Two-Phase Flow

In this survey, the volume of Fluid ( VOF ) method of Hirt and Nichols [ 14 ] is used to interface between the air and H2O. In this method,

the interface is detected by presenting the volume fraction for the stage is the fraction of the volume of a cell is used by that stage. A transport equation is used for the H2O stage to patterning interaction between H2O and air in free surface:

where is the volume fraction of H2O.

Since volume fraction of the other stage can be inferred from the restraint: so one conveyance equation needs to be solved where is the volume fraction of air. In each cell, if it contains merely H2O, so ; if none, so. To work out the mentioned equations and the flow domain the Finite volume method is used. Amount of will be between 0 and 1 for cells that span the interface between the air and H2O. However volume fraction can be assumed is 0.5 for free surface ( Dargahi [ 15 ] ) .The unstable features in the every cells can be assumed is harmonizing to the local volume fraction, for blink of an eye, the cell denseness is: , and dynamic viscousness have a similar look.

## Domain Description

As mentioned earlier, a two-phase sphere incorporating flow of after on wasteweir with a part of air at the top is solved utilizing the multiphase flow theoretical account. The deepness of air part should be big plenty to avoid any consequence from the boundary status at the top of the sphere. If the ratio between the deepness of air to the deepness of H2O ( critical deepness ) is one-third or larger, there is no consequence from the boundary at the top of the sphere ( Salaheldin [ 16 ] ) .Therefore, in all of the numerical tallies performed in the present survey, this ratio is set equal to 0.5 or larger. Although the convergence, overall truth, and stableness of the solution are found to be insensitive to the grid size in the chief organic structure of the flow off from the solid boundaries, finer mesh is required near solid boundaries including the walls and stairss in order to decide the flow inside informations near the solid boundaries ( Figure 2 ) . Accurate representation of flow near the wall part leads to a successful anticipation of the turbulent nucleus of the flow off from the wall and an accurate computation of the bottom shear emphasis. The size of the cells next to solid boundaries is chosen to fulfill the bounds of the wall unit distance 11.225 & lt ; & lt ; 30. The value of should be greater than 11.225 to avoid computation in the laminar bomber bed. The value of should be smaller than 30 to guarantee that the jurisprudence of the wall is applicable. The wall unit distance is defined by the undermentioned equation:

( 17 )

where unstable denseness ; shear speed ; distance from Point P to the wall ; and dynamic viscousness of the fluid. Finer grid is besides provided near the air-water interface to capture the little fluctuation of the free surface. There is no counsel available in the literature for choosing the size of these cells.

In the present research, two sort of meshes were used, unstructured and structured. Number of cell for the survey have been 22818. An unstructured mesh was used on wasteweir ‘s stairss because of complex geometry, and a structural mesh was used for other topographic point. In is necessary to hold full developed flow before the stepped wasteweir, hence there is 8.0m length before wasteweir and 1.8 m after wasteweir toe ( Figure 3 ) .

The Figure 2 shows the wall boundaries meshes for patterning Yani ‘s experimental theoretical account. A finer meshes were used around the stairss to making high accurate at this countries. In the close free surface to following more accurate the figure of mesh in perpendicular position was increased. A high dense mesh is used in the boundary bed to see syrupy in sub bed.

5 Boundary Conditionss and Near Wall Treatment

Base on nature of flow proper conditions must be specified at the boundaries. In this research, two separate recesss for air and H2O are specified. In the recesss unvarying distributions are assigned. In mercantile establishment one escape status are given for both of air and H2O at the downstream. An overall mass balance rectification and zero diffusion flux ( zero normal gradients ) for all flow variables are defined at the downstream boundary. The H2O and air will out from the mercantile establishment. In this boundary status the H2O degree is non defined and is allowed to alter as the hydrodynamic force per unit area at all the boundaries is calculated from inside the sphere. Symmetric boundary status is defined for the top surface which zero normal speed and zero normal gradients of all variables are applied. The upstream recess is placed at sufficient distance from the Spillway to guarantee that the flow becomes to the full developed ( Figure 3 ) .

6 Simulation Results and Analysis

In Figure 4, two stage H2O and air above it are aforethought and In Figure 5, the flow speed vectors on the wasteweir are plotted. In Figure 6, the flow speed vectors on the different stairss of wasteweir are plotted. As shown, the flow type on the wasteweir is non brushed flow but planing flow and there is a clear clockwise ( when the flow way is from left to compensate ) purl on each measure. Stepped spillway dissipate a high rate of energy by interaction between the planing flow and the Eddies. The speed field on the wasteweir is really utile for the design of the energy dissipater downstream. The size of the energy dissipater needed below the wasteweir can be designed based on the residuary energy of the stepped wasteweir flow. The energy ratio or the residuary energy can be calculated harmonizing to the kinetic and possible energy upstream and downstream of the wasteweir.

After impact H2O on stairss, some Eddies make on the stairss. The Eddies both rotate clockwise and are located in the triangular zone of the measure corner. The Centre of the Eddy is near to perpendicular wall and above the horizontal surface of the measure.

In Figure 7 & A ; Figure 8 shows the force per unit area profile on the horizontal and perpendicular surfaces. Steps No. 1 & A ; No.9 & A ; No. 17 in top, center and terminal of wasteweir severally are selected ( Figure-4 ) .

Along the horizontal surface ( Figure 7 ) , the force per unit area decreases somewhat, so force per unit area addition bit by bit to make the maximal degree and at the measure tip lessening once more. The location of the maximal force per unit area is after in-between measure and shut to step tip. This location bit by bit travel to step tip from measure No.1 ( top of wasteweir ) to step No.17 ( underside of wasteweir ) .

Figure 8 shows force per unit area distribution on perpendicular surface. The flow impact to the vaerital surface and force per unit area addition in this surface.On the perpendicular surface, the force per unit area bit by bit decrease from underside to exceed of every measure. The force per unit area is minimal near the top and maximal at the underside. The average force per unit area obtained by is an of import constituent of instantaneous force per unit area and the average minimal force per unit area is necessary for the appraisal of cavitations possible. The consequences shows force per unit area addition bit by bit from top to bottom wasteweir and in terminal of wasteweir there is non any negative force per unit area, therefore The chance of occur cavitations in top of wasteweir will be high.

Table-1 shows compare consequences between numerical modeling and experimental informations for three parametric quantity of speed coefficient “ I† ” , muffling ration “ K ” and resistance coefficient “ ” on stepped wasteweir. As mentioned before, for computation this three parametric quantities, there are used the speed before wasteweir ( V0 ) and after it ( Vc ) , H2O deepness before wasteweir ( H0 ) and after wasteweir ( hc ) . As shown in Figure 9, there is a really good understanding between the numerical mold and experimental information was obtained.

## Decisions

In this research, VOF, k – Iµ turbulency method and unstructured grid was used to imitate the stepped wasteweir. The consequences show force per unit area on the both perpendicular and horizontal surface addition bit by bit from top to bottom of wasteweir, therefore the chance of occur cavitation in top of wasteweir will be higher than bottom.The numerical modeling with this method can imitate the stepped wasteweir overflow really successfully. The trouble in handling the complex boundaries of a stepped wasteweir was overcome by utilizing an unstructured grid to the distinct sphere. Due to less clip demand and lower cost of the numerical method than that of experiments hence numerical method has important advantage in practical undertakings.

## Notation

The undermentioned symbols are used in this paper:

B= breadth of wire

E0= caput upstream

Ec= A energy of the shrinking subdivision

= organic structure force

Fr2= Froude Number of the sequent depth.A

g=A gravitation acceleration

H = caput on the crest

= deepness of the shrinking subdivision

K = muffling ration

P’= force per unit area

P1 = tallness of wire

q= the discharge per unit breadth.

t= clip

Shear speed

ui = speed constituent

V0= attack speed

= speed at the shrinking subdivision

xi= co-ordinate constituent

Distance from Point P to the wall

Grecian symbols

I?= denseness of the fluid

Dynamic viscousness

Aµ0= viscousness of fluid

Aµt = turbulency viscousness

I±a= volume fraction of air

I±w= volume fraction of H2O

I¦= speed coefficient

= opposition coefficient