General drag correlations for subsonic to supersonic flow past ordered particle arrays at low and moderate Reynolds numbers

Abstract

The drag coefficient (CD) is an important and fundamental parameter for particle-fluid systems. In this study, we employed pseudo-particle modeling (PPM), which integrates a time-driven algorithm with the hard-sphere model, to investigate subsonic to supersonic flows past ordered particle arrays with three typical configurations, i.e., simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC), at low and moderate Reynolds numbers. The relationships between the drag coefficient and various factors including Reynolds number (Re), Mach number (Ma), solid volume fraction (εs) and array configuration were analyzed. The study found: 1) Under identical conditions, the drag coefficient varies with configurations. In most cases, CD of SC is the smallest and that of FCC is the largest. 2) At low and moderate Re (Re≤20), the CD decreases with increasing Re and Ma; when Ma≤1.0, the CD increases with increasing εs; when Ma>1.0, the variation of CD with εs differs qualitatively for the SC and BCC particle arrays. 3) For Re≤20, the CD for FCC particle arrays can be tentatively expressed as CD(Re, Ma, εs)=CD(Re) [aexp(-bMa)+(1-a)](1 + Kεsn), while the coefficients a and b are related to Re and K and n are related to Re and Ma. This study fills the absence of drag data for multi-particles in slip flow and transitional flow, thereby providing drag laws for a wide range of particle-fluid systems important for micro-chemical-engineering and aero-space technologies.