Effects of Reynolds Number and Stokes Number on Particle-pair Relative Velocity in Isotropic Turbulence: An Experimental Study

Effects of Reynolds number ($R_{\lambda } )$ and Stokes number ($St)$ on particle-pair relative velocity (RV) were studied using four-frame particle tracking in an enclosed turbulence chamber. Two tests were 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. By comparing experimental and DNS results of mean inward particle-pair RV, $\left\langle {w_{r}^{-} } \right\rangle $, we observed excellent agreement for all test conditions across a large range of particle separation distance ($r)$; however at $r\le 10\eta $ ($\eta $: Kolmogorov length scale), experimental $\left\langle {w_{r}^{-} } \right\rangle $values were higher than simulation. At fixed $St$,$\left\langle {w_{r}^{-} } \right\rangle $ was found to be independent of $R_{\lambda } $ in the observable $St$, $r$, and $R_{\lambda } $ ranges. At fixed $R_{\lambda } $, $\left\langle {w_{r}^{-} } \right\rangle $ increased with $St$at small $r$ and decreased with $St$ at large $r$. We further compared $\left\langle {w_{r}^{-} } \right\rangle $ and variance of RV, $\left\langle {w_{r}^{2} } \right\rangle $, between experiments, DNS and theoretical predictions by Pan and Padoan (2010). At $0