# 椭球体集合曳力的统计学分析

ABSTRACT：In this study，Particle-Resolved Simulations（PRS）are performed for suspensions of different ellipsoids that are randomly oriented and the drag forces are calculated for each individual particle in the flow. The investigated conditions include Reynolds number from 10 to 200，solid volume fraction from low（0.1）to intermediate（around 0.3）with ellipsoid aspect ratios（AR）of 2.5，5 and 10.
Keywords：Particle suspensions;Particle-Resolved Simulation;prolate ellipsoids;drag force;statistical analysis.
1.INTRODUCTION
Fluid drag forces acting on particles in suspension are of critical importance for capturing the dynamics of fluid-particle systems accurately. In this paper，particle-resolved simulations are performed for suspensions of ellipsoids with aspect ratio（defined as the ratio between length of the particle along rotational symmetry axis and the diameter of the equatorial plane）of 2.5，5 and 10. Reynolds number range of [10，200] with solid fraction of [0.1，0.35]，[0.1，0.3] and [0.1，0.2] for these three ellipsoids，respectively are investigated with derivation of drag force for each individual particle in the suspensions. To get a better understanding of the drag force distribution. Statistical analysis are carried out including the PDF，standard deviation to provide more insight in such problem aside from the ensemble mean drag force.
2.METHODS
Detailed explanation about the computational algorithm and validation can be found in [1] The particle suspensions are generated using a physical simulation engine PhysX developed by Nvidia [2] which has been implemented in the previous works [3，，4]. Detailed procedure can be found in the work of He et al. [3]，which contains the process of particle collision detection，resolving the post-collision translational and rotational velocity and kinetic energy decaying to finally reach a stationary state. Examples of the particle suspension for AR5 ellipsoid under solid fraction of 0.1 are shown in Figure 1. The total amount of particle required for a specific solid fraction is calculated by：
Where represents the amount of particles needed under. is the volume of the domain that contains the particles with a dimension of .
3.RESULTS
3.1Drag Force Distribution in the Whole Suspension
As is demonstrated in the study of Rong et al. [5]，drag force of spheres in suspension follow an approximate Gaussian distribution. In this work，the geometry is extended to ellipsoids of aspect ratio of 2.5，5 and 10. The drag force at Reynolds number of 10 with solid fraction of 0.1 is shown in Figure 2. Figures on the right share the same y-axis title as the figures on the left. The left three plots present the drag force distribution with respect to the particle inclination angle. Considering ellipsoids with aspect ratio of 2.5，the analysis of He and Tafti [4] indicates that increase of pressure force and decrease of viscous force results in an almost constant total drag with respect to. Besides，it can be observed that the data has insignificant variation of spread under different，which is due to the almost constant dispersity of viscous drag under varying and its dominant effect on the total drag force. However，for data of ellipsoids with aspect ratio of 5 and 10，a significant increasing trend in drag force can be observed with respect to.

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