Abstract The particle-source-in-cell Euler-Lagrange (PSIC-EL) method is widely used to simulate flows laden with particles. Its accuracy, however, is known to deteriorate as the ratio between the particle diameter ( d p ) and the mesh spacing ( h ) increases, due to the impact of the momentum that is fed back to the flow by the Lagrangian particles. Although the community typically recommends particle diameters to be at least an order of magnitude smaller than the mesh spacing, the errors corresponding to a given d p / h ratio and/or flow regime have not been systematically studied. In this paper, we provide an expression to estimate the magnitude of the flow velocity disturbance resulting from the transport of a particle in the PSIC-EL framework, based on the d p / h ratio and the particle Reynolds number, Re p . This, in turn, directly relates to the error in the estimation of the undisturbed velocity, and therefore to the error in the prediction of the particle motion. We show that the upper bound of the relative error in the estimation of the undisturbed velocity, for all particle Reynolds numbers, is approximated by ( 6 / 5 ) d p / h . Moreover, for all cases where d p / h ≲ 1 / 2 , the expression we provide accurately estimates the value of the errors across a range of particle Reynolds numbers that are relevant to most gas-solid flow applications ( Re p 500 ).

中文翻译：

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量化细胞内粒子源 Euler-Lagrange 方法的误差

摘要 细胞内粒子源欧拉-拉格朗日 (PSIC-EL) 方法被广泛用于模拟载有粒子的流动。然而，众所周知，由于拉格朗日粒子反馈给流动的动量的影响，随着颗粒直径 (dp) 和网格间距 (h) 之间的比率增加，其精度会下降。尽管社区通常建议颗粒直径至少比网格间距小一个数量级，但尚未系统地研究与给定 dp/h 比和/或流态相对应的误差。在本文中，我们提供了一个表达式来估计由 PSIC-EL 框架中的粒子传输引起的流速扰动的大小，基于 dp / h 比和粒子雷诺数 Re p 。这反过来，与原状速度估计误差直接相关，因此与粒子运动预测误差直接相关。我们表明，对于所有粒子雷诺数，在未受干扰速度估计中的相对误差的上限近似为 ( 6 / 5 ) dp / h 。此外，对于 dp / h ≲ 1 / 2 的所有情况，我们提供的表达式准确估计了与大多数气固流应用相关的一系列粒子雷诺数的误差值 (Re p 500)。