Mean Velocity Scaling in Dilute Particle-Laden Channel Flow at Moderate Mass Loading*

In wall-bounded particle-laden turbulent flows with sufficiently high volume or mass loading, the mean velocity profile differs from a single-phase incompressible flow at the same Reynolds number. This alteration depends on the Stokes number and the mass loading of the particle phase, among other parameters. For a dilute mixture of heavy particles in a gas at moderate mass loading, we demonstrate how the mean fluid velocity and viscous stresses can be scaled using ideas from compressible flow transforms and rough-wall turbulent flows. This results in an improved collapse of mean velocity profiles, which we demonstrate with numerical simulations of particle-laden channel flow.

The suite of channel flow simulations were conducted at Re_τ≈235, using Lagrangian point particles, with a range of Stokes numbers (St⁺≈1-60) and particle mass loadings (Φ =10%-300%).