Compressibility and Rarefaction Effects on Drag of a Spherical Particle

Abstract

A review of compressibility and rarefaction effects on spherical particle drag was conducted based on existing experimental data, theoretical limits, and direct simulation Monte Carlo method results. The data indicated a nexus point with respect to effects of Mach number and Knudsen number. In particular, it was found that a single drag coefficient (of about 1.63) is obtained for all particle conditions when the particle Reynolds number is about 45, and is independent of compressibility or rarefaction effects. At lower Reynolds numbers, the drag is dominated by rarefaction, and at higher Reynolds numbers, it is dominated by compressibility. The nexus, therefore, allows construction of two separate models for these two regimes. The compression-dominated regime is obtained using a modification of the Clift-Gauvin model to specifically incorporate Mach number effects. The resulting model was based on a wide range of experimental data and showed superior prediction robustness compared with previous models. For the rarefaction-dominated regime, the present model was constructed to directly integrate the theoretical creeping flow limits, including the incompressible continuum flow limit (Stokes drag), the incompressible weak rarefaction limit (Basset-Knudsen correction), and the incompressible free-molecular flow limit (Epstein theory). Empirical correlations are used to extend this model to finite particle Reynolds numbers within the rarefaction-dominated regime.

Fast Numerical Solutions of Gas-Particle Two-Phase Vacuum Plumes

“…The overall tendency of particle drag coefficient decreases with an increase of particle Reynolds number Re as shown in [10]. Before the Nexus point, Re = 45, the rarefaction effects are leading, whereas after that the compressibility effects dominate.…”

“…The drag is the main force for particle motion, but the calculation of drag coefficient needs a modification in compressible and rarefied flows. Loth indicated that the rarefaction dominates the modifications of drag force for low slip or small particle Reynolds number flows, but the compressibility dominates the effects on drag force for high particle Reynolds number flows [10]. However, there are few investigations on two-phase vacuum plumes utilizing particle Lagrangian tracking method.…”

Analysis of pressure blips in aft-finocyl solid rocket motor

“…(1)) evaluation and, in turn, to assess the drag force (D) acting on the droplet, a strong deviation from the situation Re p = 1 and M p ≪ 1 is expected to occur for the §ow¦eld conditions inside the SRM and, therefore, a correction to the classical Stokes solution has to be considered. This is done employing the expression of the compressibility/high Reynolds correction provided in [15] that is a modi¦ca-tion of the CliftGauvin drag coe©cient expression [16]. Moreover, the upper and lower limits selected for the drag coe©cient in Fig.…”

Experimental characterization of energetic material dynamics for multiphase blast simulation.

“…from the standard drag model of Clift and Gauvin [25] and the compressible drag model of Loth [26]... ...... 38 [26], Parmar et al [27], Henderson [23], and Clift and Gauvin [25] Figure 33. Comparison of current data to correlations of Loth [26], Parmar et al [27], and Clift and Gauvin [25].…”