Development of a kinetic particle-based method to model the multi-scale physics of expanding flows

Multi-scale transitional flows through a nozzle into vacuum are widely studied flows because of their numerous applications in many fields of science and engineering, and, especially in aerospace sciences. These flows are usually characterized by multiple flow length scales, which significantly complicate their accurate and numerically efficient modeling. Experimental studies under such conditions are rare and expensive. For both micro and meso-sized nozzles operating in the space near-vacuum environment, the interaction of flows with sensitive spacecraft surfaces at high altitudes is important, because back-flows produced by such devices can cause contamination to sensitive electronic devices such as optical instruments and solar panels. This damage can potentially jeopardize the active lifetime of expensive space missions.;The development of accurate numerical tools capable of simulating multi-scale transitional flows is therefore important, but at the same time, challenging, because the flow regime changes from continuum to transitional along the length of the domain. The continuum techniques based on the solution of the Navier-Stokes equations encounter physical challenges when applied to these flows. In such a scenario, the study of high speed rarefied flows, involving strong thermo-chemical non-equilibrium, suggests direct consideration of the Boltzmann equation. The Direct Simulation Monte-Carlo (DSMC) approach provides a good approximation to the solution of the Boltzmann equation, but the method becomes prohibitively expensive for modeling high density flows. The Bhatnagar-Gross-Krook (BGK) method, which solves a simplified form of the Boltzmann equation, is more effective approach in such situations. A computational framework based on a statistical formulation of the BGK method was therefore developed in this work that can handle polyatomic multi-species gas flows. A number of classic fluid flow problems in semi-rarefied flow regime were studied to ascertain the accuracy of the statistical BGK computational framework, such as supersonic flow over a flat plate, planar Couette flow and expanding gas flows in transitional flow regime. These types of flows are commonly found in microfluidic applications. The statistical BGK and a related approach, the Ellipsoidal-Statistical BGK (ESBGK), were found to be equally accurate but more efficient as compared to the benchmark DSMC method for near-equilibrium gas flows, however, for gas flows far from equilibrium, the DSMC method was found to be the preferred approach.;The complimentary features of the statistical (particle) BGK and DSMC methods naturally motivated the development of a new particle-particle hybrid scheme that combines the statistical BGK and DSMC methods for an accurate and numerically efficient modeling of multi-scale flows. The new particle-particle hybrid scheme eliminated the typical numerical issues associated with the continuum-particle hybrid schemes, such as issues related to the imposition of boundary conditions at the interfaces. The key idea behind the new hybrid scheme is the use of DSMC for non-equilibrium flow regions, whereas more efficient BGK for near-equilibrium flow regions. In this work, a new switching criterion between the two methods is developed that is fundamentally linked to the physics of non-equilibrium flows, and is based on the deviation of the velocity distribution function from Maxwellian, called as the Kolmogorov-Smirnov (KS) statistical test. The selection of a particular particle method in each cell in the computational domain is based on the local KS parameter value with respect to a pre-set global switching criterion. A numerically efficient technique to compute the KS parameter is developed so that the degree of non-equilibrium can be calculated for the whole computational domain. To study the new hybrid scheme and its relationship to the rigorous DSMC method, supersonic expanding flow of argon into a vacuum is considered. It is demonstrated that the new hybrid method, composed of DSMC and BGK methods, performed as well as the benchmark DSMC method and better than the two individual component methods in terms of the computational efficiency. The new hybrid scheme can potentially extend the application of particle methods to high density flow regimes. (Abstract shortened by UMI.).