Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow (Communications in Computational Physics, 2021)
The fundamental nature of flow instability in wall bounded flows changeswith Mach number. The objectives of this study are two-fold, (i) compute the instability modes in high Mach number Poiseuille flows using linear stability analysis (LSA)and, (ii) perform direct numerical simulations (DNS) of the instability developmentusing a solver based on gas kinetic method (GKM) for the purpose of code validationby comparison against LSA results. The LSA and DNS are performed for the case ofPoiseuille flow over a range of Mach numbers – from moderately supersonic to hypersonic speeds. First, LSA is employed to identify the most unstable mode over the rangeof Mach numbers. We then perform two sets of GKM-DNS to corroborate the LSA results over the Mach number range. In the first set of simulations, the background fieldis initially perturbed with the most unstable mode identified by LSA and the evolutionis monitored. It is shown that GKM-DNS accurately captures the exponential growthin kinetic energy for all Mach numbers. The second set of GKM-DNS simulations isperformed by superposing the background pressure field with random initial perturbations. After an initial transient period, the modes predicted by LSA dominate theDNS flow field evolution. The wave-vector and mode shapes of the dominant instability are well replicated by GKM-DNS at each Mach number. These insights in thelinear regime of high speed Poiseuille flow and validation of GKM are important forunderstanding and simulating wall bounded flows.
Keywords: Gas kinetic method; compressible linear stability theory; hypersonic flows.