A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

作者：Marxen Olaf^*; Magin Thierry E; Shaqfeh Eric S G; Iaccarino Gianluca

来源：Journal of Computational Physics, 2013, 255: 572-589.

DOI：10.1016/j.jcp.2013.07.029

• Navier-Stokes equations
• Finite difference methods
• Instability of boundary layers
• Direct numerical simulations
• Supersonic and hypersonic flows
• Chemically reactive flows
• Viscosity
• diffusion
• and thermal
• conductivity
• Thermodynamic properties
• equations of
• state

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier-Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier-Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of nonequilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.

• 出版日期2013-12-15