Spatial clustering of polydisperse inertial particles in turbulence: I. Comparing simulation with theory

Particles that are heavy compared to the fluid in which they are embedded (inertial particles) tend to cluster in turbulent flow, with the degree of clustering depending on the particle Stokes number. The phenomenon is relevant to a variety of systems, including atmospheric clouds; in most realistic systems particles have a continuous distribution of sizes and therefore the clustering of 'polydisperse' particle populations is of special relevance. In this work a theoretical expression for the radial distribution function (RDF) for mono- and bidisperse inertial particles in the low Stokes number limit (Chun et al 2005 J. Fluid Mech. 536 219-51) is compared with the results of a direct numerical simulation of particle-laden turbulence. The results confirm the power-law form of the RDF for monodisperse particles with St less than or similar to 0.3. The clustering signature occurs at scales less than or similar to 10-30 times the Kolmogorov scale, consistent with a dissipation-scale mechanism. The theory correctly predicts the decorrelation scale below which bidisperse particles cease to cluster because of their distinct inertial response. A 'saturation' effect was observed, however, in which the power-law exponent is limited by the least clustered particle population. An expression is presented with which a polydisperse RDF can be obtained from the mono-and bidisperse RDFs and the particle size distribution. The DNS data clearly show that the effect of polydispersity is to diminish clustering, and place a bound on the level of polydispersity required to approximate a monodisperse system; this result is of relevance to experimental studies and realistic systems.