Drag force of a compressible flow past a random array of spheres

TL;DR

This study uses detailed simulations to analyze how compressible flows past random sphere arrays affect drag, revealing shock formation, hydrodynamic interactions, and proposing a new drag correlation applicable across flow regimes.

Contribution

It introduces an effective Mach number and a new drag correlation for subsonic to weakly supersonic flows past sphere arrays, accounting for compressibility and particle interactions.

Findings

Drag force peaks near a critical Mach number due to shock waves.

Hydrodynamic interactions lower the critical Mach number at higher volume fractions.

Proposed drag correlation applies from dilute to moderately dense suspensions.

Abstract

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The Reynolds number is held at $Re{\approx}300$ to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbour-induced hydrodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on drag. A new drag correlation is proposed valid for subsonic and weakly supersonic flow from dilute to moderately dense suspensions.