Numerical study on rarefied unsteady jet flow expanding into vacuum using the Gas-Kinetic Unified Algorithm

The unsteady process of rarefied jet flows expanding into a vacuum is numerically solved by the Gas-Kinetic Unified Algorithm (GKUA) based on the Boltzmann model equations. The discrete velocity ordinate method (DVOM) is adopted to discretize the velocity space of the molecular velocity distribution function, while the corresponding numerical integral technique is developed to evaluate macroscopic flow variables, including number density, flow velocity, temperature and so on. The time-explicit finite difference scheme is constructed to capture the unsteady evolution of the discrete velocity distribution functions at each DVO point by using the unsteady time-splitting method. The multi-block docking grid technique is designed for different regions of flow field in physical space with self-adaptive adjustment. Then, the supersonic planar jet flows with the wide range of Knudsen numbers, from 100 to 0.1, are solved numerically and discussed, including startup to steady state and shutting down. The GKUA results of free-molecule jet flows are analyzed and compared with the Maxwellian analytical solutions for collisionless plume flows, in which good agreement shows the validity and accuracy of the present numerical method. When taking the collision effect into account, the unsteady jet flows with different Knudsen numbers are computed by the present GKUA method. It is shown that the collision term of the Boltzmann model equation plays an important role in this rarefied gas diffusion into the back flow when Kn ≤ 10. However, the colliding relaxation term have a little influence on the kernel region in the startup process for Kn ≥ 0.1. In general, the convective transport term of the Boltzmann model equation dominates the kernel region of the jet flow during the unsteady process of gas expanding into a vacuum. The numerical experience indicates that the present GKUA can provide a vital tool for solving unsteady flow problems covering various flow regimes by directly tracing the time evolution of the Boltzmann-type velocity distribution function.