Keywords: stepped spillway cavity, turbulent eddy viscosity, partial flow boundary conditions.

In order to solve the circulating flow in a triangular cavity of a step spillway, the non-dimensional incompressible form of the two-dimensional continuity and momentum equations are solved using unstructured finite volumes. By application of the pseudo compressibility technique, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner. This technique helps coupling the pressure and the velocity fields during the explicit computation procedure of the incompressible flow steady state problem. The sub-grid scale model is used to compute the turbulent eddy viscosity coefficient in diffusion terms of the momentum equations.

In the present work, the pressure and velocity are imposed at the top flow boundary of the triangular cavity. In order to achieve better computational performance, the free stream velocity is imposed at the central part of the flow boundary, while the free stream pressure is imposed the corner parts of the flow boundary. The effects of considering various ratios of these parts on convergence and accuracy of the circulation formation is studied for various low Reynolds numbers inside an equilateral triangular cavity.

Examining various percentages for the free stream pressure and velocity imposing parts, it is found that considering 10% free stream pressure imposed part at both sides of the free stream velocity imposing part of the flow boundary of an equilateral triangular cavity may provide good convergence behaviour. The computed results reported in the literature for the similar case [1,2,3,4] were used for comparison and assessment of the quality of the results of the model presented. The position of the centre of the main circulation for various low Reynolds numbers were used for accuracy assessments and the comparison shows that the results of the present modelling method agree with the results of the previously published methods. The plot of the convergence behaviour of the computed parameters shows that the method presents good convergence behaviour for the Reynolds numbers larger than 100.

Finally, the optimum combination of partial free stream pressure and velocity flow boundary condition is used for solving velocity and pressure fields inside one of the triangular cavities of a step spillway.

1

W.D. McQuain, C.J. Ribbens, C.Y. Wang, L.T. Watson, "Steady viscous flow in a trapezoidal cavity", Journal of Computers and Fluids, 23, 613-626, 1994. doi:10.1016/0045-7930(94)90055-8

2

E. Erturk, C. Gokcol, "Fine grid numerical solutions of triangular cavity flow", Eur. Phys. J. Appl. Phys., 38, 97-105, 2007. doi:10.1051/epjap:2007057

3

M. Li, T. Tang, "Steady viscous flow in a triangular cavity by efficient numerical techniques", Journal of Computers and Mathematics with Applications, 31, 55-65, 1996. doi:10.1016/0898-1221(96)00052-1

4

P.H. Gaskell, H.M. Thompson, M.D. Savage, "A finite element analysis of Steady viscous flow in Triangular cavities", Proceedings of the Institution of Mechanical Engineers Part C- Journal of Mechanical Engineering Science, 213, 263-276, 1999. doi:10.1243/0954406991522635

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