Second-Order Viscous/Heat Fluxes Scheme: Hyperbolic System for RANS Flow and Conjugate Heat Transfer Problem in Gas Turbine

Abstract

Accurate and robust scheme of diffusive flux is critical for the numerical simulations of turbulence flow and CHT problem. In this work, a general framework of constructing upwind diffusive flux scheme is investigated based on the first order hyperbolic system. The governing equations of RANS flow and CHT problem are discretized as a unified hyperbolic Convection-Diffusion system and Navier-Stokes system. One approximation approach, assuming the numerical fluxes of equations solution gradients are independent on the fluids’ compressibility, is proposed to simplify the calculation of diffusive flux for the Hyperbolic Navier-Stokes system, and the numerical accuracy is tested by several verification cases. To stabilize the computations, Lr=O(h) is suggested, and the upwind diffusive fluxes are applied to the RANS flow and CHT problem successfully. Moreover, the accuracy analysis and the convergence feature of hyperbolic CHT system are carried on. Preliminary results show that hyperbolic CHT system has a potential to simulate the distribution of temperature on the fluid-solid interface more accurately, and has some superiority to speed up the convergence.