Understanding plume expansion in transitional/rarefied media using multiscale computations

Plume expansion in a near-vacuum background involves a continuum flow near the nozzle exit, highly rarefied (free molecular) flow far away from the exit, and transitional flow in between. Hybrid numerical methods that combine Navier-Stokes (NS) and Direct Simulation Monte Carlo (DSMC) approaches have been widely employed for studying such multiscale flows. These methods, however, face difficulties in identifying and classifying the domain into different flow regimes and the imposition of boundary/interface conditions between the two solvers. We address these challenges in multiscale plume computation by adapting the Unified Gas Kinetic Wave-Particle (UGKWP) method to a curvilinear grid framework for axisymmetric plume simulations. The unified method, based on Bhatnagar-Gross-Krook (BGK) model for Boltzmann equation, reduces to an NS-type gas kinetic scheme at the continuum limit, while at the free molecular limit, it becomes a Monte-Carlo-type particle-dominant method. In between, an adaptive weighting balances the two, allowing for multiscale modeling without the need to explicitly classify the domain (as in hybrid methods) or discretize the velocity space (as in discrete velocity methods). The method is used to systematically investigate how the shock structure in plume flow changes as the background conditions are varied from continuum to rarefied conditions. These changes include variations in the mach-cell shape, structure, and shock thickness, especially within the transitional regime. Additionally, similarity parameters that collapse the center-line flow properties into a single profile for the transitional regime are examined.