Multi-Species Compressible Solver for Non-Continuum Flow Through a Micro-Channel

Abstract

Compressible multi species flow solver, developed by the authors Kumar and Maheshwari [May 15, 2020. “Viscous Multi-Species Lattice Boltzmann Solver for Simulating Shock-Wave Structure.” Computers and Fluids 203. Article ID 104539], has been extended further to non-continuum flows. The approach uses the Onsager-BGK model, which ensures Onsager's maximum entropy production principle is followed, thus avoids unphysical solutions. Equations for velocity slip and temperature jump have been derived. The viscous slip, thermal slip and diffusion slip coefficients have been successfully validated with 13-moment solver's and experimental data. The departure from equilibrium in such flows has been approximated by a collision probability function ($P_{Kn}$), instead of using the complicated second order perturbation over the Knudsen number (that leads to Burnett equations). This provided the necessary reduction in (viscous, thermal, mass) dissipation and the developed approximate solver is able to predict the thermal and viscous profiles in a non-continuum regime and validates against DSMC simulations. Test cases consisting of flow through micro-channels demonstrated the ability of solver to handle monoatomic, diatomic and poly atomic gases. The developed non-continuum solver is in a finite volume framework and is easily adaptable to legacy in-house Navier–Stokes solvers.

Keywords:

• Collision probability function
• compressible viscous flow
• multi species
• Onsager-BGK kinetic model
• micro-channel flow
• high Knudsen number
• viscous slip
• thermal slip
• diffusive slip

Disclosure statement

No potential conflict of interest was reported by the author(s).