연속체 영역과 천이 영역의 삼차원 유동 해석을 위한 Kinetic BGK 기법 기반의 Navier-Stokes 해석자의 적용

Abstract

A finite-volume kinetic BGK(Bhatnagar-Gross-Krook) method for the compressible Navier-Stokes equation was presented for three-dimensional flows from continuum to transitional regimes. The unstructured version of the linear interpolation is applied to compute the local equilibrium for left and right states along a cell interface in the reconstruction stage. The explicitly time-dependent fluxes are evaluated from the mathematical relations between the Boltzmann BGK equation and the compressible Navier-Stokes equation. Three-dimensional compressible flow calculations around ONERA-M6 wing were performed to verify the accuracy and robustness of the current Navier-Stokes flow solver using the kinetic BGK scheme. The Navier-Stokes flow solver using the kinetic BGK scheme was applied to the hypersonic flows around flat-nosed cylinder in the continnum and transitional regimes, which includes the typical features of the actual flow around blunt-body vehicles. The flow in the detached normal shock in front of the flat-nosed cylinder experienced very steep gradients in both temperature and density for the continuum-like flow. It is revealed that increasing the asymptotic Knudsen number of the flow reduces the slope of the flow properties within the shock compression layer. A fairly good agreement with the Navier-Stokes results using the kinetic BGK scheme and the DSMC(Direct Simulation Monte Carlo) results is obtained for the flows considered into the transitional regime. Slight discrepancy in the temperature near the solid wall is observed because the temperature jumps are not naturally involved in the Navier-Stokes flow solver using the kinetic BGK scheme.