van Hinsberg M A T, Clercx H J H, Toschi F
Fluid Dynamics Laboratory and J.M. Burgers Centre for Fluid Dynamics, Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands.
Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands.
Phys Rev E. 2017 Feb;95(2-1):023106. doi: 10.1103/PhysRevE.95.023106. Epub 2017 Feb 9.
The Stokes drag force and the gravity force are usually sufficient to describe the behavior of sub-Kolmogorov-size (or pointlike) heavy particles in turbulence, in particular when the particle-to-fluid density ratio ρ_{p}/ρ_{f}≳10^{3} (with ρ_{p} and ρ_{f} the particle and fluid density, respectively). This is, in general, not the case for smaller particle-to-fluid density ratios, in particular not for ρ_{p}/ρ_{f}≲10^{2}. In that case the pressure gradient force, added mass effects, and the Basset history force also play important roles. In this study we focus on the understanding of the role of these additional forces, all of hydrodynamic origin, in the settling of particles in turbulence. In order to qualitatively elucidate the complex dynamics of such particles in homogeneous isotropic turbulence, we first focus on the case of settling of such particles in the flow field of a single vortex. After having explored this simplified case we extend our analysis to homogeneous isotropic turbulence. In general, we found that the pressure gradient force leads to a decrease in the settling velocity. This can be qualitatively understood by the fact that this force prevents the particles from sweeping out of vortices, a mechanism known as preferential sweeping which causes enhanced settling. Additionally, we found that the Basset history force can both increase and decrease the enhanced settling, depending on the particle Stokes number. Finally, the role of the nonlinear Stokes drag has been explored, confirming that it affects settling of inertial particles in turbulence, but only in a limited way for the parameter settings used in this investigation.
斯托克斯曳力和重力通常足以描述亚科尔莫戈罗夫尺度（或点状）重粒子在湍流中的行为，特别是当粒子与流体的密度比ρₚ/ρբ≳10³时（其中ρₚ和ρբ分别为粒子和流体的密度）。一般来说，对于较小的粒子与流体密度比，情况并非如此，特别是对于ρₚ/ρբ≲10²时。在这种情况下，压力梯度力、附加质量效应和巴塞特历史力也起着重要作用。在本研究中，我们专注于理解这些均源于流体动力学的附加力在湍流中粒子沉降过程中的作用。为了定性地阐明此类粒子在均匀各向同性湍流中的复杂动力学，我们首先关注此类粒子在单个涡旋流场中沉降的情况。在探究了这个简化情况之后，我们将分析扩展到均匀各向同性湍流。一般来说，我们发现压力梯度力会导致沉降速度降低。这可以从定性的角度理解为，该力阻止粒子扫出涡旋，这种机制被称为优先扫掠，它会导致沉降增强。此外，我们发现巴塞特历史力根据粒子的斯托克斯数既可以增加也可以降低增强沉降。最后，我们探讨了非线性斯托克斯曳力的作用，证实它会影响惯性粒子在湍流中的沉降，但对于本研究中使用的参数设置，其影响有限。
