Boltzmann-Rykov model equation gas-kinetic unified algorithm and nozzle flow

The kinetic Boltzmann-Rykov model is used to explore the influence of rotating non-equilibrium on the inner flow of the nozzle, based on the computing principle of the gas-kinetic unified algorithm (GKUA). Mathematical models for the boundary conditions of nozzle flows were developed under the level of molecular velocity distribution function, and a numerical scheme of gas-kinetic was constructed to solve the molecular velocity distribution function directly. The Boltzmann-Rykov model equation considering the effect of rotational energy was numerically solved. The inner flow problems including the one-dimensional unsteady shock tube, one-dimensional steady positive shock structure, and two-dimensional planar nozzle flow were numerically simulated. The computed results match the theoretical solution, simulation value, and experimental data. It verifies the feasibility and accuracy of the unified algorithm for the inner flow problems. Lastly, an analysis was conducted on the nozzle’s inner flow field while taking rotational energy into account. The results show that the Knudsen number can be used as the characterization of nozzle flow characteristics and performance.