多相流欧拉-拉格朗日模拟中粒子分辨精度的机器学习和两两相互作用扩展点粒子（PIEP）近似
Towards Particle-Resolved Accuracy in Euler-Lagrange Simulations of Multiphase Flow Using Machine Learning and Pairwise Interaction Extended Point-particle (PIEP) Approximation
摘要：
本研究提出了两种不同的机器学习方法，用于建模的流体动力颗粒在一个颗粒负载的多相流。从颗粒分辨直接数值模拟（PR-DNS）的结果，在一个随机阵列的静止颗粒的八个组合的颗粒雷诺数（$Re$）和体积分数（$ϕ$）的流动被用于模型的发展。第一种方法遵循两步过程。在第一个流动预测步骤中，由于一个粒子的扰动流是作为一个轴对称的叠加尾流使用线性回归。在第二个力的预测步骤中，一个粒子上的力的评估方面的扰动流引起的所有邻居使用广义Faxén形式的力的表达式。在第二种方法中，使用PR-DNS模拟的所有颗粒上的力数据来开发用于直接预测颗粒上的力的人工神经网络（ANN）模型。由于PR-DNS模拟中完全分辨的粒子数量不可避免的限制，使用ANN模型的直接力预测往往会过拟合数据，并且在预测测试数据时表现不佳。相比之下，由于PR-DNS模拟中使用了数百万个网格点，因此可以进行准确的流量预测，从而可以准确预测粒子力。这种多相物理学和机器学习的混合是特别重要的，因为它混合了每一种的强度，并且由此产生的成对相互作用扩展点粒子（PIEP）模型不能单独由物理学或机器学习开发。
英文摘要：
This study presents two different machine learning approaches for the modeling of hydrodynamic force on particles in a particle-laden multiphase flow. Results from particle-resolved direct numerical simulations (PR-DNS) of flow over a random array of stationary particles for eight combinations of particle Reynolds number ($Re$) and volume fraction ($ϕ$) are used in the development of the models. The first approach follows a two step process. In the first flow prediction step, the perturbation flow due to a particle is obtained as an axisymmetric superposable wake using linear regression. In the second force prediction step, the force on a particle is evaluated in terms of the perturbation flow induced by all its neighbors using the generalized Faxén form of the force expression. In the second approach, the force data on all the particles from the PR-DNS simulations is used to develop an artificial neural network (ANN) model for direct prediction of force on a particle. Due to the unavoidable limitation on the number of fully resolved particles in the PR-DNS simulations, direct force prediction with the ANN model tends to over-fit the data and performs poorly in the prediction of test data. In contrast, due to the millions of grid points used in the PR-DNS simulations, accurate flow prediction is possible, which then allows accurate prediction of particle force. This hybridization of multiphase physics and machine learning is particularly important, since it blends the strength of each, and the resulting pairwise interaction extended point-particle (PIEP) model cannot be developed by either physics or machine learning alone.
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