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首页> 外文期刊>Journal of Computational Physics >An accurate and efficient method for treating aerodynamic interactions of cloud droplets
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An accurate and efficient method for treating aerodynamic interactions of cloud droplets

机译：一种准确有效的处理云滴空气动力相互作用的方法

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Motivated by a need to improve the representation of short-range interaction forces in hybrid direct numerical simulation of interacting cloud droplets, an efficient method for treating the aerodynamic interaction of two spherical particles settling under gravity is developed. An effort is made to ensure the accuracy of our method for any inter-particle separation by considering three separation ranges. The first is the long-range interaction where a multipole method is applied. After a decomposition into six simple configurations, explicit formulae for drag forces and torques are derived from an approximate Force-Torque- Stresslet (FTS) formulation. The FTS formulation is found to be accurate when the separation distance normalized by the average radius is larger than 5. The second range concerns the short-range interaction where the interaction force could be very large. Leading- order lubrication expansions are employed for this range and are found to be accurate when the normalized separation is less than about 0.01. Finally, for the intermediate range where no simple method is available, a third-order polynomial fitting is proposed to bridge the treatments for long-range and short-range interactions. After optimizing the precise form of polynomial fitting and matching locations, the force representation is found to be highly accurate when compared with the exact solution for Stokes flows. Using this method, collision efficiencies of cloud droplets sedimenting under gravity have been calculated. It is shown that the results of collision efficiency are in excellent agreement with results based on the exact Stokes flow solution. Collision efficiency results are also compared to previous results to further illustrate the accuracy of our calculations. The effects of particle rotation and the attractive van der Waals force on the collision efficiency are also studied. The efficient force representation developed here is more general than the usual lubrication expansion and thus can serve as a better approach to correct unresolved short-range interactions in particle-resolved simulations.
机译：由于需要在相互作用的云滴的混合直接数值模拟中改善短程相互作用力的表示，因此开发了一种有效的方法来处理两个在重力作用下沉降的球形颗粒的空气动力学相互作用。通过考虑三个分离范围，努力确保我们的方法对任何颗粒间分离的准确性。第一个是应用多极方法的远程相互作用。在分解为六个简单的配置后，可从近似的力-扭矩-应力（FTS）公式中得出拖曳力和扭矩的明确公式。当通过平均半径归一化的分离距离大于5时，发现FTS公式是准确的。第二个范围涉及的是短程相互作用，其中相互作用力可能非常大。前导润滑扩展用于此范围，当归一化间隔小于约0.01时，发现是精确的。最后，对于没有简单方法可用的中间范围，建议使用三阶多项式拟合来桥接长距离和短距离相互作用的处理方法。在优化多项式拟合和匹配位置的精确形式之后，与斯托克斯流的精确解相比，力表示被发现是非常精确的。使用这种方法，已经计算出了在重力作用下沉淀的云滴的碰撞效率。结果表明，碰撞效率的结果与基于精确斯托克斯流解的结果非常吻合。碰撞效率结果也与以前的结果进行了比较，以进一步说明我们计算的准确性。还研究了粒子旋转和范德华力对碰撞效率的影响。与常规的润滑扩展相比，此处开发的有效力表示更为通用，因此可以作为一种更好的方法来纠正粒子解析模拟中未解析的短程相互作用。

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