Gas‐kinetic unified algorithm for two‐dimensional planar and axisymmetric nozzle flows

Abstract

SummaryFor high‐altitude nozzle or micronozzle flows and other gas flows in the slip or transition flow regime, how to solve it reliably has always been a difficult problem. In this paper, a unified gas kinetic expression is presented to describe the two‐dimensional planar and the axisymmetric nozzle flows, and the computable modeling of the Boltzmann equation is developed at the first time for the nozzle flows by introducing the gas molecular collision relaxing parameter and the local equilibrium distribution function integrated in the unified expression with the flow state controlling parameter, including the macroscopic flow variables, the gas viscosity transport coefficient, the thermodynamic effect, the molecular power law, and molecular models, covering a full spectrum of flow regimes. The boundary conditions involved in the nozzle flow have been mathematically expressed at the level of the gas molecular velocity distribution function, and the model equations have been solved uniformly by the gas‐kinetic unified algorithm (GKUA) for rarefied transition to continuum flows. The presented simulated results from the test cases show promising of simulating gas flow from transitional flow to continuum flow in the same flow domain, especially for those flow involving low‐speed gas flow in rarefied regime, which is otherwise practically difficult using direct simulation Monte Carlo (DSMC).