用于平面壁附近的Euler-Lagrange模拟的稳态未扰动速度修正方案
Steady undisturbed velocity correction scheme for Euler-Lagrange simulations near planar walls
AI总结：
本文提出一种用于平面壁附近稀疏气固两相流的稳态未扰动速度修正框架，通过镜像法求解Stokes方程的Green's函数并结合网格相关卷积，高效实现了大规模双向耦合Euler-Lagrange模拟的精确修正。
摘要：
Euler-Lagrange (EL) 点粒子模拟依赖于流体动力学力闭合模型来准确预测流动中的粒子动力学。目前用于稀疏颗粒负载流动的闭合模型需要估计在粒子中心处的未扰动流体速度。恢复该未扰动速度需要对粒子引起的流动扰动进行建模。在本研究中，我们提出了一种用于无滑移壁附近速度扰动建模的新框架，适用于以大Stokes数为特征的稀疏气固流动。对于小扰动Reynolds数，速度扰动控制方程简化为稳态Stokes方程。为了在平面壁位置精确满足速度扰动的无滑移和无穿透边界条件，我们采用镜像法推导了Wendland和Gaussian力正则化核的Stokes方程的Green's函数。通过与依赖于网格间距的Gaussian核进行额外的卷积运算，以匹配离散流动求解器生成的解。我们通过比较计算网格上生成的速度扰动与模型预测结果，验证了所提出的解析模型。通过在无界域中乘以Oseen修正因子，提出了针对有限粒子Reynolds数的模型扩展。该修正方案使用涉及粒子在多种Stokes数、粒子Reynolds数以及粒子直径与网格间距比下平行和垂直于壁运动的经典测试用例进行了验证。由于Wendland力正则化的速度扰动采用多项式表示，当前模型计算效率高，非常适合大规模、双向耦合的EL模拟。
英文摘要：
Euler-Lagrange (EL) point-particle simulations rely on hydrodynamic force closure models to accurately predict particle dynamics in flows. The closure models currently employed for dilute particle-laden flows require the undisturbed fluid velocity estimated at the particle center. Recovering this undisturbed velocity necessitates modeling the particle-induced disturbance on the flow. In this work, we present a new framework for velocity disturbance modeling near no-slip walls, suited for dilute gas-solid flows characterized by large Stokes numbers. For small disturbance Reynolds numbers, the velocity disturbance governing equations reduce to the steady Stokes equations. To exactly satisfy the no-slip and no-penetration boundary conditions for the velocity disturbance at the location of the planar wall, we employ the method of images to derive the Green's functions of the Stokes equations for Wendland and Gaussian force regularization kernels. An additional convolution product with a mesh-spacing dependent Gaussian kernel is performed to match the solution produced by a discrete flow solver. We verify the proposed analytical model by comparing the velocity disturbance generated on a computational mesh with the model predictions. An extension of the model for finite particle Reynolds numbers is proposed by multiplying an Oseen correction factor in an unbounded domain. The correction scheme is validated using canonical test cases involving the motion of a single particle parallel and perpendicular to a wall at various Stokes numbers, particle Reynolds numbers, and particle diameter to mesh-spacing ratios. Owing to the polynomial representation of the velocity disturbance for a Wendland force regularization, the current model is computationally efficient and well-suited for large-scale, two-way coupled EL simulations.
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