The settling velocity of heavy particles in an aqueous near-isotropic turbulence

The ensemble-average settling velocity, V_s, of heavy tungsten and glass particles with different mean diameters in an aqueous near-isotropic turbulence that was generated by a pair of vertically oscillated grids in a water tank was measured using both particle tracking and particle image velocimetries. Emphasis is placed on the effect of the Stokes number, St, a time ratio of particle response to the Kolmogorov scale of turbulence, to the particle settling rate defined as (V_s - V₁)/ V_t where V_t is the particle terminal velocity in still fluid. It is found that even when the particle Reynolds number Re_p is as large as 25 at which V_t/v_k ≈ 10 where v_k is the Kolmogorov velocity scale of turbulence, the mean settling rate is positive and reaches its maximum of about 7% when St is approaching to unity, indicating a good trend of DNS results by Wang and Maxey (1993) and Yang and Lei (1998). This phenomenon becomes more and more pronounced as values of V_t/v_k decrease, for which DNS results reveal that the settling rate at V_t/v_k = 1 and Re_p<1 can be as large as 50% when St ≈ 1. However, the present result differs drastically with Monte Carlo simulations for heavy particles subjected to nonlinear drag (Re_p> 1) in turbulence in which the settling rate was negative and decreases with increasing St. Using the wavelet analysis, the fluid integral time (T₁), the Taylor microscale (T_λ), and two heavy particles' characteristic times (T_c1, T_c2) are identified for the first time. For St<1, T_c1 < T₁ and T_c2< T_λ, whereas T_c1 ∼ T₁ and T_c2= ≈ T_λ for St ≈ 1. This may explain why the settling rate is a maximum near St ≈ 1, because the particle motion is in phase with the fluid turbulent motion only when St ≈ 1 where the relative slip velocities are smallest. These results may be relevant to sediment grains in rivers and aerosol particles in the atmosphere.