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

The effects of Reynolds number ( $R_{\unicode[STIX]{x1D706}}$ ) 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 $R_{\unicode[STIX]{x1D706}}$ are still valid in reality. Two experiments are performed: varying $R_{\unicode[STIX]{x1D706}}$ between 246 and 357 at six $St$ values, and varying $St$ between 0.02 and 4.63 at five $R_{\unicode[STIX]{x1D706}}$ values. The measured mean inward particle-pair RV $\langle w_{r}^{-}\rangle$ 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 $r\lesssim 10\unicode[STIX]{x1D702}$ ( $\unicode[STIX]{x1D702}$ is the Kolmogorov length scale), where the experimental $\langle w_{r}^{-}\rangle$ 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 $St,\langle w_{r}^{-}\rangle$ is essentially independent of $R_{\unicode[STIX]{x1D706}}$ , echoing the DNS finding of Ireland et al. (J. Fluid Mech., vol. 796, 2016, pp. 617–658). At any fixed $R_{\unicode[STIX]{x1D706}}$ , $\langle w_{r}^{-}\rangle$ increases with $St$ at small $r$ , showing dominance of the path-history effect in the dissipation range when $St\gtrsim O(1)$ , but decreases with $St$ at large $r$ , indicating dominance of inertial filtering. We further compare the $\langle w_{r}^{-}\rangle$ and RV variance $\langle w_{r}^{2}\rangle$ from experiments with DNS and theoretical predictions by Pan & Padoan (J. Fluid Mech., vol. 661, 2010, pp. 73–107). For $St\lesssim 1$ , experimental $\langle w_{r}^{-}\rangle$ and $\langle w_{r}^{2}\rangle$ match these values well at $r\gtrsim 10\unicode[STIX]{x1D702}$ , but they are higher than both DNS and theory at $r\lesssim 10\unicode[STIX]{x1D702}$ . For $St\gtrsim 1$ , $\langle w_{r}^{-}\rangle$ from all three match well, except for $r\lesssim 10\unicode[STIX]{x1D702}$ , for which experimental values are higher, while $\langle w_{r}^{2}\rangle$ 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 $R_{\unicode[STIX]{x1D706}}$ and $St$ effect on inertial particle-pair $\langle w_{r}^{-}\rangle$ in homogeneous and isotropic turbulence.