The mean radial component of relative velocity (MRV) between pairs of inertial particles is studied, where the particles are advected by turbulent flow and undergo collision and coalescence. The direct numerical simulation (DNS) is conducted to illustrate the relationship between the DNS-produced MRV and particle or turbulent parameters. The results show that for particles with near-zero Stokes numbers (St), the MRV is roughly independent of St. The MRV for particles of this St range is mainly related to the characteristics of local velocity difference of turbulent flow at particle diameter scale. This conclusion holds for small St particles $(\text{St}<0.1)$ in turbulent flow with different Reynolds number. At larger St, the magnitude of MRV increases with St, and this change is most pronounced when $\text{St}>0.2$. Using the fact that the turbulent velocity difference increases with length scale and assuming that the relative velocities of the colliding particle pairs are derived from fluid velocity differences associated with a nominal resonant length scale, we propose an empirical relation between this resonant scale and Stokes number such that the resonant scale has the form $d+\alpha {\text{St}}^{\beta }$, and we found by curve fitting that $\beta \approx 1.86$. By studying the MRV under different Reynolds numbers $({\text{Re}}_{\lambda }=84,124,189)$, we find that for particles with $\text{St}>0.1$, ${\text{Re}}_{\lambda }$ dependence is observed such that the coefficients $\alpha$ and $\beta$ decrease with ${\text{Re}}_{\lambda }$.

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• Particle-laden flows
• Turbulence
• Turbulence simulations
• Multiphase flows
• Direct numerical simulations
• Navier-Stokes equation