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

The effects of Reynolds number (R-lambda) and Stokes number (St) 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 R-lambda are still valid in reality. Two experiments are performed: varying R-lambda between 246 and 357 at six St values, and varying St between 0.02 and 4.63 at five R-lambda 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 less than or similar to 10 eta (eta 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 R-lambda, echoing the DNS finding of Ireland et al. (J. Fluid Mech., vol. 796, 2016, pp. 617-658). At any fixed R-lambda, < W-r(-)> increases with St at small r, showing dominance of the path-history effect in the dissipation range when St less than or similar to 0(1), but decreases with St at large r, indicating dominance of inertial filtering. We further compare the < w(r)(-)> and RV variance < w(r)(2)> from experiments with DNS and theoretical predictions by Pan & Padoan (J. Fluid Mech., vol. 661, 2010, pp. 73-107). For St less than or similar to 1, experimental < w(r)(-)> and (w(r)(2)) match these values well at r greater than or similar to 10 eta, but they are higher than both DNS and theory at r less than or similar to 10 eta. For St greater than or similar to 1, (w(r)(-)) from all three match well, except for r less than or similar to 10 eta, for which experimental values are higher, while < w(r)(2)> 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 R-lambda and St effect on inertial particle-pair < w(r)(-)> in homogeneous and isotropic turbulence.