Flow of a monatomic rarefied gas over a circular cylinder: Calculations based on the ab initio potential method

摘要

Two-dimensional flows of argon and helium over a circular cylinder are calculated by the Direct Simulation Monte Carlo (DSMC) method in the range of the free stream Mach number Ma_∞ from 0.5 to 10 in nearly free molecular, transitional, and nearly continuum flows. In DSMC simulations, inter-particle collisions are calculated with the ab initio (AI) potential method based on the interatomic interaction potentials established in quantum mechanical calculations. It is shown that the AI potential method enables computationally efficient simulations of multidimensional rarefied gas flows without introducing semi-empirical models of collision cross sections. The calculated values of the drag C_D and heat flux C_Q coefficients of the cylinder for Ar and He at the same values of Ma_∞, rarefaction parameter, and surface-to-free-stream temperature ratio are found to be different in less than 1%, ensuring small sensitivity of C_D and C_Q to the species of a monatomic gas. The simulation results obtained with the AI potential method are systematically compared with results obtained with the hard sphere (HS) molecular model. It is found that the choice of the HS diameter based on the condition of the identical viscosity of the real and HS gases at the free stream temperature ensures calculations of C_D and C_Q in sub- and supersonic flows at Ma_∞⩽2 with errors less than 3% and 6.5%, correspondingly. For hypersonic flows, this choice of the HS diameter is unsatisfactory and results in the errors up to 7% in C_D and 28% in C_Q. A semi-empirical rule that defines an optimum HS diameter in super- and hypersonic flows is suggested. With the use of this rule, the HS model is capable of predicting C_D and C_Q with errors less than 1% and 3%, correspondingly, and also provides a good accuracy in calculations of local flow parameters.