Non-equilibrium effects of diatomic and polyatomic gases on the shock-vortex interaction based on the second-order constitutive model of the Boltzmann-Curtiss equation

Abstract

The rotational mode of molecules plays a critical role in the behaviour of diatomic and polyatomic gases away from equilibrium. In order to investigate the essence of the non-equilibrium effects, the shock-vortex interaction (SVI) problem was investigated by employing an explicit modal discontinuous Galerkin method. In particular, the first-and second-order constitutive models for diatomic and polyatomic gases derived rigorously from the Boltzmann-Curtiss kinetic equation were solved in conjunction with the physical conservation laws. As compared with a monatomic gas, the non-equilibrium effects result in a substantial change in flow fields in both macroscale and microscale shock-vortex interactions. Specifically, the computational results showed three major effects of diatomic and polyatomic gases on the shock-vortex interaction; (i) the generation of third sound waves and additional reflected shock waves with strong and enlarged expansion, (ii) the dominance of viscous vorticity generation, (iii) an increase in enstrophy with increasing bulk viscosity, related to the rotational mode of gas molecules. Moreover, it was shown that there is a significant discrepancy in flow fields between the microscale and macroscale shock-vortex interactions in diatomic and polyatomic gases. The quadrupolar acoustic wave source structures, which are typically observed in macroscale shock-vortex interactions, were not found in any microscale shock-vortex interactions. The physics of the shock-vortex interaction was also investigated in detail to examine vortex deformation and evolution dynamics over an incident shock wave. A comparative study of first-and second-order constitutive models was also conducted for enstrophy and dissipation rate. Finally, the study was extended to the shock-vortex pair interaction (SVPI) case to examine the effects of pair interaction on vortex deformation and evolution dynamics.

Contribution of Mach number on the evolution of Richtmyer-Meshkov instability induced by shock-accelerated square light bubble

“…Discontinuous Galerkin (DG) approaches have recently gained prominence in fields ranging from fluid mechanics to acoustics and electromagnetics [44,45,[56][57][58][59][60][61][62][63][64][65][66]. These methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements.…”

“…These methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements. In this paper, the two-dimensional compressible avier-Stokes-Fourier equations ( 1) are solved by an in-house developed explicit mixed-type modal DG solver based on structured meshes [37,38,58,63]. The computational domain is discretized into rectangular elements, and scaled Legendre polynomial functions are employed for the elements.…”

Role of Atwood number on flow morphology of a planar shock-accelerated square bubble: A numerical study

“…The DG methods combine the main features associated with the finite element (FE) and finite volume (FV) methods and have been successfully applied to a wide range of applications in gas dynamics, acoustics waves, plasma physics, quantum physics, and magneto-hydrodynamics. [39][40][41][42][43][44][45][46] As a traditional FE method, accuracy is obtained by approximating the solution based on a series of the higher-order polynomials within each element of the domain, rather than employing wide stencils, as in the case of the traditional FV method. However, similar to the FV method, the physics of wave propagation is considered in order to determine the physical solution among multiple solutions at the interfaces of the elements.…”

“…In this study, the compressible NSF equations ( 2) are solved by an in-house developed explicit mixed-type discontinuous Galerkin solver based on rectangular meshes. 43,44 The computational domain is discretized into rectangular elements, and scaled Legendre polynomial functions are employed for elements. The Gauss-Legendre quadrature rule is implemented for both the volume and the boundary integrations, and the local Lax-Friedrichs (LLF) is applied for the inviscid term, 47 while the local discontinuous Galerkin (LDG) scheme is employed for the auxiliary and viscous fluxes at elemental interfaces.…”

“…Interestingly, the bulk viscosity beyond the Stokes's hypothesis plays an essential role in determining non-equilibrium effects in diatomic and polyatomic gases in compressible flows. 43,50 It is also expected that the bulk viscosity will affect significantly the development of the RM instability in compressible fluid flows. Therefore, in this context, the current methodology based on the high-order discontinuous Galerkin method will be extended to investigate the impacts of bulk viscosity on the flow morphology in shock-accelerated polygonal bubbles with different types of interface shapes in future investigations.…”