Proceedings of The ASME 2013 Fluids Engineering Division Summer Meeting 13th Symposium on Fundamental Issues and Perspectives in Fluid Mechanics July 7–11, 2013, Incline Village, Nevada, U. S. A. FEDSM2013-16392 NUMERICAL MODELING OF HIGH-SPEED FLOWS OVER A MICROSPHERE IN THE SLIP AND EARLY TRANSITION FLOW REGIMES Chi-Yang Cheng Yi Dai & Genong Li Ansys Inc. Lebanon, NH 03766 chi-yang.cheng@ansys.com yi.dai@ansys.com genong.li@ansys.com Horst J. Richter Thayer School of Engineering Dartmouth College Hanover, NH 03755 horst.j.richter@dartmouth.edu Ming-Chia Lai Dept of Mechanical Engineering Wayne State University Detroit, MI 48202 lai@eng.wayne.edu ABSTRACT The focus of this paper is on using computational fluid dy- namics to investigate the drag and convection heat transfer of high-speed flows over a microsphere. The flow under investi- gation 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. Typ- ical 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 meth- ods (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 or- der 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 mi- crons and the Knudsen number from 1.4 × 10 −3 to 0.14. The CFD results are in good agreement with experimental drag 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 bound- ary condition, the thermal recovery temperature in the slip flow regime can be obtained numerically only by solving the conju- gate 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. Introduction The study of high-speed gas flows over a microsphere was motivated by the need to control micro-particles’ velocity and temperature in a supersonic jet for the development of gas dy- namic cold spray (or “cold spray”) technology [1]. In addition to the cold spray application, high-velocity, compressible, laminar flow over a micro-sphere is found in particle/shock-wave inter- action in multiphase reacting flows, the gas-particle nozzle flows in rocket propulsion, and the study of the collection of interplan- etary dust particles, etc. In the continuum regime where the fluid’s properties and flow characteristics can be treated as continuous functions in space and time, the Navier-Stokes-Fourier (N-S-F) equations are suitable for describing fluid flow and heat transfer. In order 1 Copyright c  2013 by ASME