论文标题
量化粒子源中的euler-lagrange方法的误差
Quantifying the errors of the particle-source-in-cell Euler-Lagrange method
论文作者
论文摘要
粒子源欧拉 - 拉格朗日（PSIC-EL）方法被广泛用于模拟带有颗粒的流量。然而，由于粒子直径〜（$ \ smash {d_ \ text {p}} $）之间的比率，它的准确性会恶化，而网状间距〜（$ h $）增加，这是由于拉格吉尼亚粒子回到流动的动量的影响。尽管社区通常建议粒子直径至少比网格间距小的数量级，但尚未系统地研究与给定$ \ smash {d_ \ text {p} / h} $比率和 /或流动状态相对应的错误。在〜本文中，我们提供了一种表达式，以根据$ \ smash {d_ \ smash {d_ \ text {p} / h} $比率和粒子reynolds编号，$ \ smash samash {\ smash {\ re} {re} =反过来，这直接与未触及速度的估计中的误差有关，因此与粒子运动预测中的误差有关。我们表明，对于所有粒子雷诺数，估计不受干扰的速度的估计中相对误差的上限均由$ \ smash {（6/5）\，d_ \ d_ \ text {p} / h} $近似。此外，在所有情况下，$ \ smash {d_ \ text {p} / h \ lyssim 1/2} $，我们提供的表达式准确地估算了与大多数气体固体流量相关的一系列粒子雷诺数中错误的值（$ \ smash {$ \ smash {\ smash {\ smash {re} re} $}
The particle-source-in-cell Euler-Lagrange (PSIC-EL) method is widely used to simulate flows laden with particles. Its accuracy, however, is known to deteriorate as the ratio between the particle diameter~($\smash{d_\text{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 $\smash{d_\text{p} / h}$ 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 $\smash{d_\text{p} / h}$ ratio and the particle Reynolds number, $\smash{\text{Re}_\text{p}}$. 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 $\smash{(6/5)\,d_\text{p} / h}$. Moreover, for all cases where $\smash{d_\text{p} / h \lesssim 1/2}$, 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 ($\smash{\text{Re}_\text{p} < 500}$).
