Effect of bulk viscosity and relaxation model on nonequilibrium shock structure of diatomic gases

This paper investigates the impact of bulk viscosity and relaxation model on the shock transition of diatomic gases using the nonlinear coupled constitutive relations (NCCR), which is an extended model to Navier-Stokes equations for simulating nonequilibrium compressible flows. To elucidate their roles in the mechanism of shock transition, a modified NCCR model including temperature-dependent bulk-shear-viscosity ratio and a thermal nonequilibrium NCCR model with rotational mode are developed from various physical perspectives. Subsequently, these models are employed to investigate the shock structure in nitrogen for Mach numbers up to 10. It is found that the shock profiles and shock thicknesses computed by proposed NCCR models are in close agreement with the experimental data and direct simulation Monte Carlo results across all Mach numbers, with an observation that introducing bulk viscosity or relaxation model improves the physical consistency of NCCR theory and thereby shock solutions in nonequilibrium flows. Moreover, the rationality of assuming a constant viscosity ratio in the original NCCR model for diatomic gases is validated. It is important to note that the relaxation model brings in a skewing of shock profiles towards downstream and strengthens the non-Newton-Fourier behavior and asymmetry in heat flux phase planes, whereas the bulk viscosity leads to a skewing of shock profiles towards upstream and enhances the nonNewton-Fourier behavior and asymmetry in stress phase planes. These findings highlight the distinct mechanisms through which the bulk viscosity and relaxation model improve the shock profiles, offering deeper insight into the physical mechanism inside the shock structures of diatomic gases.