Abstract
This paper presents a numerical methodology and simulation for three-dimensional transonic flow in Safety Relief Valves. Simulation of safety relief valve flows is very challenging due to complex flow paths, high pressure variation, supersonic flow with shock and expansion waves, boundary layers, etc. The 3D unsteady Reynolds averaged Navier-Stokes (URANS) equations with one-equation Spalart-Allmaras turbulence model is used. A fifth order WENO scheme for the inviscid flux and a second order central differencing for the viscous terms are employed to discretize the Navier-Stokes equations. The low diffusion E-CUSP scheme used as the approximate Riemann solver suggested by Zha et al. is utilized with the WENO scheme to evaluate the inviscid fluxes. Implicit time marching method with 2nd order temporal accuracy using Gauss-Seidel line relaxation is employed to achieve a fast convergence rate. Parallel computing is implemented to save wall clock simulation time. The valve flows with air under different inlet pressures and temperatures are successfully simulated for the full geometry with all the fine leakage channels. A 3D mesh topology is generated for the complex geometry. Detailed simulations of air flow are accomplished with inlet gauge pressure 0.5MPa and 2.1MPa. The simulated air mass flow rate agrees excellently with the experimental results with an error of 0.26% for the inlet pressure of 0.5Mpa, and an error of 2.5% for the inlet pressure of 2.1MPa. The shock waves and expansion waves downstream of the orifice are very well resolved.