A loosely-coupled gas-kinetic BGK scheme for conjugate heat transfer in hypersonic flows

Abstract

The gas-kinetic BGK scheme has shown to be a promising method in hypersonic flow simulation from many previous studies. In this paper, a loosely-coupled BGK scheme is developed for solving conjugate heat transfer (CHT) problems in hypersonic flows. For more accurate evaluation of heat flux and better numerical stability, some modifications to the original BGK scheme are suggested, including using an improved way to calculate slopes of distribution functions and applying a non-simplified Prandtl number fix. Different from most CHT solvers that adopt different methods in fluid and solid domains, the BGK scheme can also be extended to simulate the heat transfer in structures, as long as an appropriate BGK model for the heat conduction equation is constructed. The dual-time steeping approach and a recently-developed implicit JFNK–BGK method are used to obtain the time-accurate solutions in individual domains. To achieve the fluid-thermal coupling, two loosely-coupled algorithms are employed, which are based on quasi-steady and unsteady flow computations, respectively. For comprehensive validation of the developed method, several cases of standalone hypersonic flows, standalone structural heat transfers and a typical CHT problem are investigated, and its performances are shown by comparisons with other numerical and experimental results.