Similarity of Microscale and Rarefied Gas Flows

The similarity between micro gas flow and rarefied gas flow was numerically investigated using a DSMC method. With compressibility and rarefaction effects, the similarity parameters are the Mach number and the Knudsen number, since the Reynolds number is dependent on the Mach number and the Knudsen number for an ideal gas. Comparisons of numerical results for various scales show that the normalized fields for the macroscopic quantities are quite similar, which shows that the microscale flow is similar to rarefied flow of an ideal gas. Therefore, existing rarefied flow results can be applied to microscale flows. However, for dense gas flows, the three dimensionless parameters are independent, so the similarity breaks down for dense gas flows. Simulation results for an ideal gas using nitrogen as an example show that the similarity holds for densities less than 7–8 times the density at standard conditions.