Abstract: In gas-solid two-phase flows, complex spatiotemporal mesoscale structures are present, making the development of accurate mesoscale drag models essential for precisely simulating fluidization dynamics. The filtered gas pressure gradient, as a key physical quantity in mesoscale drag modeling, has been extensively studied and applied in the simulation of mesoscale resistance. Typically, during the filtering process, the pressure gradient is derived at two discrete scales: the fine-grid scale and the filter scale. The pressure gradients calculated at these two scales often differ significantly, leading to considerable discrepancies when used in numerical simulations of fluidized beds. These discrepancies can affect the predictive accuracy of mesoscale drag models and hinder their practical application in simulating industrial-scale systems. To address these challenges, an artificial neural network (ANN) approach is employed to systematically analyze the influence of pressure gradients at different filtering scales on the construction of mesoscale drag models. Two drag models are developed based on the pressure gradients at the fine-grid and filter scales, referred to as model A and model B, respectively. Through extensive validation and analysis, the performance of these models is compared across a range of filtering scales and flow regimes. The results reveal that model B, which uses the pressure gradient at the filter scale, exhibits superior predictive capabilities compared to model A, particularly at larger filter scales. This superiority is further substantiated through posterior analysis. Simulations of fluidized beds under three typical flow regimes—bubbling, turbulent, and fast fluidization—demonstrate that model B provides axial solid volume fraction distributions that align more closely with resolved results than those predicted by model A. These findings confirm that constructing mesoscale drag models based on the pressure gradient at the filter scale enhances their accuracy and applicability, making them more suitable for simulating complex fluidized bed dynamics in industrial and research contexts.

Key words: gas-solid flow, fluidization bed, filtered drag force, computational fluid dynamics, machine learning

摘要： 滤波气相压力梯度是介尺度曳力建模中的重要物理量。在滤波过程中，压力梯度可分别从细网格尺度和滤波网格尺度计算得到。然而，这两种尺度下计算的滤波压力梯度存在显著差异，从而影响介尺度曳力模型的预测精度及其在流化床模拟中的实际应用。基于此，采用人工神经网络方法，探究不同的滤波压力梯度对介尺度曳力建模的影响。基于细网格尺度和滤波网格尺度的压力梯度构建的曳力模型分别被称为模型A和模型B。结果表明，模型B具有更优越的预测性能。这一优势通过后验得到进一步验证。在鼓泡、湍动和快速流化等典型流化状态下，模型B预测的轴向固含率分布与解析结果更为接近，而模型A的偏差较大。研究表明，基于滤波网格尺度压力梯度构建的介尺度曳力模型能够显著提升精度与适用性，更适用于工业尺度的复杂流化床动力学的模拟。

关键词: 气固流动, 流化床, 滤波曳力, 计算流体力学, 机器学习