Effects of Reynolds number and Stokes number on particle-pair relative velocity in isotropic turbulence: A systematic experimental study

The effects of Reynolds number and Stokes number on particle-pair relative velocity (RV) are investigated systematically using a recently developed planar four-frame particle tracking technique in a novel homogeneous and isotropic turbulence chamber. We compare the measured results with direct numerical simulation (DNS), verifying whether the conclusions of the DNS for simplified conditions and limited Rγ are still valid in reality. Two experiments are performed: varying Rγ between 246 and 357 at six values, and varying between 0.02 and 4.63 at five Rγ values. The measured mean inward particle-pair RV 〈w-r〉 as a function of separation distance r is compared with the DNS under closely matched conditions. At all experimental conditions, an excellent agreement is achieved, except when the particle separation distance r ≲ 10η ( is the Kolmogorov length scale), where the experimental 〈w-r〉 is consistently higher, possibly due to particle polydispersity and finite laser thickness in the experiments (Dou et al., arXiv:1712.07506, 2017). At any fixed St, 〈w-r〉 is essentially independent of Rγ, echoing the DNS finding of Ireland et al. (J. Fluid Mech., vol. 796, 2016, pp. 617-658). At any fixed Rγ, 〈w-r〉 increases with St at small r, showing dominance of the path-history effect in the dissipation range when St ≳ 0(1), but decreases with St at large r, indicating dominance of inertial filtering. We further compare the 〈w-r〉 and RV variance 〈w2r〉 from experiments with DNS and theoretical predictions by Pan & Padoan (J. Fluid Mech., vol. 661, 2010, pp. 73-107). For St ≲ 1, experimental 〈w-r〉 and 〈w2r〉 match these values well at r ≳ 10η, but they are higher than both DNS and theory at r ≲ 10η. For St ≳ 1, 〈w-r〉 from all three match well, except for r ≲ 10η, for which experimental values are higher, while 〈w2r〉 from experiment and DNS are much higher than theoretical predictions. We discuss potential causes of these discrepancies. What this study shows is the first experimental validation of Rγ and St effect on inertial particle-pair 〈w-r〉 in homogeneous and isotropic turbulence.