Multiscale Modelling of the Erosive Impact of Particles

侵蚀是一种影响许多行业的现象，人们对颗粒侵蚀效应的建模越来越感兴趣。其影响包括风力涡轮机叶片前缘的侵蚀，以及石油和天然气管道因沙子而恶化。工业应用通常涉及数百万个颗粒。为了模拟大规模的工程应用，由于计算成本过高，我们不能直接计算每个粒子上的流体力。因此，我们需要估计粒子上的各种流体力，包括阻力和升力。在过去几十年中，已经开发了几种模型。然而，这些模型是基于在非常低的雷诺数周围的自由球，然后扩展使用实验数据，以提供半经验方程的解析解。为了研究壁面附近粒子的运动，我们需要了解固体壁面对阻力和升力的影响。此外，当颗粒更靠近壁时，可压缩性效应变得重要。在本计画中，将使用精确的数值格式离散可压缩的Navier-Stokes方程，以数值分析近壁区域中单一粒子的绕流。高保真模拟使我们能够研究球体尾流与壁面之间的各种复杂相互作用，以及壁面和球体上边界层之间的相互作用，以了解固体壁附近的阻力和升力如何演变。该项目将建立在现有的2D模拟的基础上，将工作扩展到接近固体壁的球形颗粒的完整3D模型。数值格式的精确性使我们能够以高精度研究不同马赫数和雷诺数以及差距尺寸（到壁面的距离）对颗粒所经受的力的影响。

Erosion is a phenomenon affecting many industries and there is a growing interest in modelling the erosive effect of particles. Effects include the erosion of the leading edge of wind turbine blades, and deterioration of oil and gas pipelines due to sand. Industrial applications usually involve millions of particles. To model a large scale engineering application, we cannot directly calculate the fluid forces on each particle due to prohibitive computational cost. Therefore, we need to estimate the various fluid forces on the particle including drag and lift. Several models have been developed over the past several decades. However, these models are based on the analytical solution at very low Reynolds number around a free sphere which are then extended using experimental data to provide semi-empirical equations. To investigate the motion of particles near walls, we need to understand the effect of solid walls on the drag and lift forces. Furthermore, the compressibility effect becomes important as the particle gets closer to the wall. In this project accurate numerical schemes will be used to discretise the compressible Navier-Stokes equation to numerically analyse the flow around a single particle in the near wall region. The high-fidelity simulations allow us to investigate various complex interactions between the sphere's wake and the wall and also the interactions between the boundary layers on the wall and sphere to understand how the drag and lift evolve near a solid wall. This project will build upon the available 2D simulations to extend the work to a full 3D model of a spherical particle close to a solid wall. The accuracy of the numerical scheme allows us to investigate the effects of varying Mach and Reynolds number and the gap size (distance to the wall) on the forces experienced by the particle with high precision.