In this study, we derive a spatially averaged two-fluid model for heat transport in moderately dense gas–particle flows. In the context of multiphase turbulence modeling, closure models for the unresolved terms in the filtered transport equations in the presence of mesoscale heterogeneous particle clusters are postulated. In analogy to the drift velocity correction for the resolved gas–particle drag force, we propose to approximate the filtered interphase heat transfer by the resolved heat transfer corrected by a drift temperature. This drift temperature represents the gas-phase temperature fluctuations seen by the particles and can be expressed as a correlation between the solid volume fraction variations and the gas-phase temperature fluctuations, i.e., the turbulent internal energy. Therefore, transport equations for the turbulent internal energies of the phases are derived, where a cluster-induced turbulence production term arises in the gas-phase. Except for the interphase exchange terms, we find that closure models based on single phase turbulence modeling can be applied to the unresolved terms in the transport equations for both the filtered and turbulent internal energies. The interphase exchange terms can be expressed by the variances of the temperatures scaled by correlation coefficients. A dynamic adjustment of the correlation coefficients by using test-filters in coarse-grid simulations is proposed. In an a priori study, the developed closure models show good agreement with the predictions obtained by filtering fine-grid, two-fluid model simulation data of Geldart type A and B particles in three-dimensional wall-bounded fluidized beds.

中文翻译：

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中等密度气体-颗粒流中热传输的动态空间平均双流体模型

在这项研究中，我们推导出了一个空间平均的双流体模型，用于中等密度气体-颗粒流中的热传输。在多相湍流建模的背景下，假设存在中尺度异质粒子簇时过滤传输方程中未解析项的闭合模型。类似于解析气体-粒子阻力的漂移速度校正，我们建议通过由漂移温度校正的解析传热来近似过滤相间传热。该漂移温度代表颗粒所见的气相温度波动，可以表示为固体体积分数变化与气相温度波动之间的相关性，即湍流内能。所以，导出了相的湍流内能的输运方程，其中在气相中出现了簇引起的湍流产生项。除了相间交换项，我们发现基于单相湍流建模的闭合模型可以应用于过滤和湍流内能的输运方程中的未解析项。相间交换项可以用相关系数缩放的温度方差来表示。建议通过在粗网格模拟中使用测试滤波器来动态调整相关系数。在先验研究中，开发的闭合模型与通过过滤细网格获得的预测非常吻合，