Numerical simulation of water surface profiles on ogee and Stepped Spillway by finite volume and finite element methods

The spillway is one of the most important elements of dam building. So studying and designing of the spillway hydraulic should be considered in dams and other similar projects. The ogee spillway, because of its superb hydraulic characteristics, has been widely studied. Its ability to pass flow efficiently and safely, when has been properly designed, with relatively good flow measuring capabilities, has enabled engineers to use it in a wide variety of situations. In the last two decades, there has been an increasing interest in the stepped spillways in various laboratory experiments around the world. This is partly because of technical advances in the construction of Roller Compacted Concrete (RCC) dams and considerable amount of energy dissipation along the chute, leading to reduction in the size of the stilling basin. Flow analysis using laboratory experiments usually involves considerable time and cost requirements .Nowadays, availability of computational fluid dynamic (CFD) programs and powerful computers has resulted in increasing usage of numerical methods of flow analysis. Free surface flows are encountered in hydraulic engineering problems including water jets, weirs and around gates. For the numerical modelling of a steady flow, the area of calculation and therefore the position of the free surface have to be known. The main object of this study is numerical analysis of free surface profiles on ogee and stepped spillways by finite volume and finite element methods and comparison of the two methods. The physical laws governing a fluid flow problem are represented by a system of partial differential equations regrouping the continuity equation, the Navier-Stokes equations and any additional conservation equations. The numerical analysis resolves these equations by accurate and complex numerical schemes. A program or code, where the numerical algorithm is implemented, is then solved on a computer. In recent study experimental results offered by Tabara and CHatila (2005) have been used to investigate stepped spillway physics models of Tabara and Chatara (2004) for studying ogee spillway. FLUENT and ADINA software have been used to simulate flow field of types of stepped and ogee spillways. It should be noted that k-£ model has been applied in order to modeling turbulence. Gambit preprocessor software is a tool for networking flow field. In recent study we have used PRESTO scheme for discretization of pressure, quick plan for discretization of terms of displacement of momentum equations, turbulence formulas and PISO algorithm for coupling velocity and pressure. In finite element method, Galerkin relation has the second order accuracy. SUPG method is used in momentum equations and turbulence for discretization of term advection which is effective in problem convergence. Meshing type has been selected as triangle form in ADINA code, but quadrilateral in FLUENT code regarding the spillway geometry. In some area structured mesh and in some other ones non-structured mesh have been chosen. Due to existence of rotatory flows over the steps, more fine meshes have been used in both codes near to body of stepped spillway as well as ogee spillway, because of the velocity gradient nearby wall, where flow enters spillway channel from reservoir. In recent study, water surface profile has been simulated in four types of stepped spillways and 3 types of ogee spillways on the basis of finite element method using FLUENT code and finite volume method using ADINA code. Relatively close consistency has been observed between water surface profiles in both codes by comparing experimental results. Note that free surface profile simulated over the ogee spillway was closer to water surface profile evaluated in laboratory than the profile by finite element method. There were observed better consistency in results from free surface profile over stepped spillway with finite volume method. Maximum differences between results of water surface profile in numerical model of FLUENT and ADINA were nearly 1.2 cm and 1.6 cm, comparing with laboratory results respectively. This value in numerical simulation is acceptable regarding to different meshing in model networking. On this basis, numerical methods of FLUENT and ADINA are proper in order to simulate similar structures for saving costs due to construction of physical model. Flow surface can be determined considering the lower error of FLUENT model in measuring free surface flow; thereby, designing lateral walls of spillway is realized with more precise.