On the influence of forced homogeneous-isotropic turbulence on the settling and clustering of finite-size particles
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We investigate the motion of heavy particles with a diameter of several multiples of the Kolmogorov length scale in the presence of forced turbulence and gravity, resorting to interface-resolved direct numerical simulation based on an immersed boundary method. The values of the particles’ relative density (1.5) and of the Galileo number (180) are such that strong wake-induced particle clustering would occur in the absence of turbulence (Uhlmann and Doychev in J Fluid Mech 752:310–348, 2014. https://doi.org/10.1017/jfm.2014.330). The forced turbulence in the two present cases (with Taylor-scale Reynolds number 95 and 140) would lead to mild levels of clustering in the absence of gravity (Uhlmann and Chouippe in J Fluid Mech 812:991–1023, 2017. https://doi.org/10.1017/jfm.2016.826). Here we detect a tendency to cluster with an intensity (quantified via the standard deviation of the distribution of Voronoï cell volumes) which is intermediate between these two limiting cases, meaning that forced background turbulence decreases the level of clustering otherwise observed under ambient settling. However, the clustering strength does not monotonically decay with the relative turbulence intensity. Various mechanisms by which coherent structures can affect particle motion are discussed. It is argued that the reduced interaction time due to particle settling through the surrounding eddy (crossing trajectories) has the effect of shifting upward the range of eddies with a time-scale matching the characteristic time-scale of the particle. In the present cases this shift might bring the particles into resonance with the energetic eddies of the turbulent spectrum. Concerning the average particle settling velocity, we find very small deviations (of the order of one percent) from the value obtained for an isolated particle in ambient fluid when defining the relative velocity as an apparent slip velocity (i.e., as the difference between the averages computed separately for the velocities of each phase). This is consistent with simple estimates of the nonlinear drag effect. However, the relative velocity based upon the fluid velocity seen by each particle (computed via local averaging over a particle-attached sphere) has on average a smaller magnitude (by 5–7%) than the ambient single-particle value.
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This work was supported by the German Research Foundation (DFG) under Project UH 242/1-2. The simulations were partially performed at LRZ München (under Grant pr83la) and at SCC Karlsruhe (Project DNSPARTHIT). The computer resources, technical expertise, and assistance provided by these centers are thankfully acknowledged.
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