Investigation of safety relief behavior by discontinuous finite element method

This paper deals with the application of a finite element Discontinuous Galerkin (DG) method to compute and study the steady two-dimensional axisymmetric transonic flow in a research model of a safety relief valve. The code solves the RANS and k−w turbulence model governing equations with arbitrarily (here presented up to third) high-order discretization on complex meshes. Key features include original formulation of "realizable" k−w model as well as a novel shock-capturing technique to deal with oscillations near discontinuities. When compared against experiments, results show the remarkable accuracy of the method. On the other hand, commercial codes such as Fluent and ANSYS-CFX encounters difficulties in obtaining a stable solution on the same, relatively coarse, grid, if second-order schemes are employed. Both DG and CFX codes are here used to compute the flow field in the safety valve at maximum lift (fully open position) for a range of total-to-static expansion pressure ratios spanning from subsonic to supersonic exit conditions. The aim of the CFD simulations is to investigate and clarify the complex flow patterns occurring and to explain the measured trends. Results show that different codes can sometimes lead to the occurrence of quite different fluid dynamic fundamental structures, such as sonic throat and emerging jet positions. These reflect themselves onto different discharge coefficients and pressure distribution along the cap surface, which are indeed parameters of crucial importance for the correct behavior of the valve. Other test cases conducted at valve partial lift, not reported here for the sake of brevity, confirm the illustrated trends. The characteristics of accuracy and robustness displayed by the DG method shed confidence over its capability of correctly predict the three-dimensional flow field of the complete valvebody-connection system.