Numerical Modeling of High-Speed Flows Over a Microsphere in the Slip and Early Transition Flow Regimes

Abstract

The focus of this paper is on using computational fluid dynamics to investigate the drag and convection heat transfer of high-speed flows over a microsphere. The flow under investigation is steady-state, subsonic, transonic or supersonic laminar flow over a sphere. Due to the small size of the particle (< 80 microns), the flow is in the slip and early transition regimes. Typical Reynolds number based on sphere’s diameter is between 10 and 6000, and the Knudsen number is between 0.001 and 0.75. For the slip flow as well as the early transition regimes, instead of using the Direct Simulation Monte Carlo methods (DSMC) or lattice Boltzmann methods, we use ANSYS FLUENT, a Navier-Stokes-Fourier solver with the first-order velocity-slip and temperature-jump boundary conditions. In order to capture the non-equilibrium effects in the Knudsen layer, a constitutive scaling model for gas viscosity and conductivity is also implemented in the CFD model. CFD simulations were performed at the free-stream Mach number from 0.6 to 3.0, with particle diameter from 1 to 80 microns and the Knudsen number from 1.4 × 10−3 to 0.14. The CFD results are in good agreement with experimental data. The deviations from the data are within 10%. The numerical model also provides additional insight to the concept of the thermal recovery temperature in high-speed convection. Due to the nature of the temperature-jump boundary condition, the thermal recovery temperature in the slip flow regime can be obtained numerically only by solving the conjugate heat transfer problem. A “thin-wall” model is introduced in this paper in order to determine the thermal recovery temperature (or recovery factor) for the given Mach and Reynolds numbers. Although a number of publications have been devoted to particle drag correlations as functions of particle Reynolds and Mach numbers, the dependence of drag on particle temperature has not been investigated. By using the rarefied gas flow model in this study, we have not only confirmed that the drag increases as particle temperature goes higher, but also found that rate of drag increase is higher for the transonic than for the supersonic flows.