How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent flows tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that a rod settles preferentially with its tip first, wheras a disk settles with its edge first, therefore minimizing the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating velocity gradients, and ask under which circumstances either one or the other dominate. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds number flows. In this case non-spherical particles are expected to settle with a maximal drag. But when the Reynolds number is small then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its broad side first.

中文翻译：

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流体惯性对于在湍流中沉降的球体方向的重要性

非球形粒子在流动时如何定向，在许多科学和工程问题中具有重要的实际意义。在静止流体中，缓慢沉降的颗粒会定向，使其宽边先沉降。这是由于由沉降颗粒运动的流体的对流惯性引起的扭矩效应，这使颗粒受到的阻力最大化。湍流倾向于使粒子取向随机化。最近分析了湍流中非球形粒子的沉降，忽略了对流流体惯性的影响，但考虑了湍流流体速度梯度对粒子取向的影响。这些研究得出了相反的结论，即棒优先以其尖端先沉降，而圆盘首先以其边缘沉降，因此最小化对粒子的阻力。在这里，我们考虑了两种效应，对流惯性扭矩以及由于速度梯度波动引起的扭矩，并询问在哪种情况下一种或另一种占主导地位。为此，我们估计两个扭矩的大小之比。我们的估计表明流体惯性扭矩在高雷诺数流动中占优势。在这种情况下，非球形颗粒预计会以最大阻力沉降。但是当雷诺数很小时，由于流体速度梯度引起的扭矩可能占主导地位，导致粒子首先以其宽边沉降。并询问在哪种情况下一种或另一种占主导地位。为此，我们估计两个扭矩的大小之比。我们的估计表明流体惯性扭矩在高雷诺数流动中占优势。在这种情况下，非球形颗粒预计会以最大阻力沉降。但是当雷诺数很小时，由于流体速度梯度引起的扭矩可能占主导地位，导致粒子首先以其宽边沉降。并询问在哪种情况下一种或另一种占主导地位。为此，我们估计两个扭矩的大小之比。我们的估计表明流体惯性扭矩在高雷诺数流动中占优势。在这种情况下，非球形颗粒预计会以最大阻力沉降。但是当雷诺数很小时，由于流体速度梯度引起的扭矩可能占主导地位，导致粒子首先以其宽边沉降。