Competition of natural convection and thermal creep in a square enclosure

Abstract

Although natural convection and thermal creep have been well recognized in the continuum and rarefied regimes, respectively, the study of the competition of them in a wide flow regime is very scarce. From a theoretical point of view, natural convection can be described by Navier–Stokes–Fourier (NSF) equations at the macroscopic level, while thermal creep needs descriptions at the molecular level. Therefore, it is quite challenging to capture these two effects simultaneously. In this work, we employ the unified stochastic particle Bhatnagar–Gross–Krook (USP-BGK) method to investigate thermally driven gas flow in a square enclosure. The simulation results obtained by the USP-BGK method are validated by comparing to those from NSF solutions and direct simulation Monte Carlo method for the continuum and transitional regimes, respectively. We find that the flow patterns in the whole flow regime cannot be determined by just one nondimensional parameter, i.e., the Rayleigh number (Ra), but needs two nondimensional parameters, i.e., the Knudsen number (Kn) and the Froude number (Fr), or Kn and Ra. Specifically, small Knudsen and Froude numbers tend to generate natural convection, while large Knudsen and Froude numbers tend to cause thermal creep. Moreover, our simulation results and analyses demonstrate that when Kn < 0.12, thermal creep is dominant if Ra < 1.0, while natural convection is dominant if Ra/Fr > 0.28, or equivalently, L/L* > 1.0, where L is the characteristic length of the system and L* is the equivalent characteristic length of molecules. These findings provide useful guidance for better understanding of the complex gas flows resulting from the competition of natural convection and thermal creep under microscale or low-density conditions such as on Mars.