Similarity of ideal gas flow at different scales

The similarity of ideal gas flow at different scales is investigated analytically and numerically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, are proposed as the similarity criterions, because the Reynolds number can be expressed by the Mach number and the Knudsen number of ideal gases. A DSMC method is used to simulate flows at different scales with the same Ma and Kn, including subsonic channel flows and the supersonic flows over a hot plate. Comparisons between the results of different scales show that the normalized fields of macroscopic quantities are the same. This confirms the similarity. Especially, the results indicate that the micro flow are similar to the rarefied flow of ideal gas, which suggests that many transformations are available from the existing rarefied flow results to the micro flow.