In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles.

中文翻译：

---

使用多重网格虚拟边界方法沉积一般形状的颗粒

在本文中，直接数值模拟技术——有限元虚拟边界法（FBM），被用来模拟不同一般形状颗粒的流固两相流动。固相和液相之间的动量相互作用是通过使用 FBM 来处理的。通过在多网格有限元方法中使用离散投影方案，在独立于流动特征的固定欧拉网格上求解连续性和动量方程。详细描述了流体内部不同一般形状（即圆形、椭圆形、正方形、矩形、三角形和五边形）的二维粒子的几何表示和建模。我们讨论了颗粒形状的影响以及对颗粒沉降行为的影响。比较了质量相同但形状不同的颗粒的沉降轨迹。此外，根据粒子的形状，发现了一些有趣的事实，这些事实对粒子的轨迹和沉降速度有很大的影响。得到了不同颗粒密度比的阻力系数与颗粒雷诺数之间的一些非常重要的相关性。此外，我们还研究了具有不同轴比的椭圆形和矩形颗粒以及具有不同凹角的回旋镖颗粒的沉降行为。得到了不同颗粒密度比的阻力系数与颗粒雷诺数之间的一些非常重要的相关性。此外，我们还研究了具有不同轴比的椭圆形和矩形颗粒以及具有不同凹角的回旋镖颗粒的沉降行为。得到了不同颗粒密度比的阻力系数与颗粒雷诺数之间的一些非常重要的相关性。此外，我们还研究了具有不同轴比的椭圆形和矩形颗粒以及具有不同凹角的回旋镖颗粒的沉降行为。