A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects

A concept and model of two critical Reynolds numbers Re_p,cr1 and Re_p,cr2 corresponding respectively to onsets of drag crisis and recovery are proposed. A drag model at limits of zero particle Mach and Knudsen numbers is constructed. On this basis, we develop a general drag coefficient model applicable for a spherical particle traveling in a gas by using a large number of available data derived from the previous experiments, direct numerical simulations and direct simulation Monte-Carlo methods. The scope of applicability of the proposed drag model covers all flow regimes relative to the particle characterized by particle Reynolds and Mach (or Knudsen) numbers and different particle-to-gas temperature ratios. Its comparison with two latest general drag models shows the significantly smaller relative error. Furthermore, quasi-one dimensional simulations against two supersonic nozzle gas-particle flow experiments are conducted with an in-house code to validate its accuracy in comparison with the two drag models.