Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

Abstract

We report experimental measurements of kinematic and dynamic particle concentration kernels conditioned by the separation distances of solid inertialess particles in isotropic turbulence by three-dimensional particle tracking velocimetry with particle diameters smaller than the Kolmogorov length scale. Particle radial relative velocity statistics are measured from the dissipation to the integral length-scale range. The radial scaling of particle and fluid relative velocity variance $\langle w_r(r)^{2} \rangle \sim r^{2/3}$ in the inertial subrange, consistent with Kolmogorov's theory, is reported, while a new scaling is found for small distances due to finite-size effects between particles. The measured concentration kernels at small separation distances therefore deviate from those in the theory of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) at small inter-particle distances due to hydrodynamic interactions. A real kernel taking into account the history of the particle tracks and excluding multiple events is also calculated, while the normalised particle concentration kernels are found to be essentially insensitive to the flow Reynolds number.