Abstract Particle-resolved direct numerical simulations (PR-DNSs) are employed to simulate flows past various stationary clusters of spheres in low-particle-Reynolds-number regime. The results show that the drag force at the interface between the dilute and dense phases is significantly different from the prediction of the traditional homogeneous BVK law (AIChE Journal, 2007, 53(2):489-501). The drag force at the interface is found to be the function of the solid volume fraction gradient, the superficial velocity gradient and the size of the grid on which the drag force is computed. Based on the PR-DNS data, a new microscopic drag model considering the interface effect is formulated. The effectiveness of the new drag models is demonstrated in flows past ellipsoidal clusters of particles. The results show that, in terms of the global drag force on the clusters, the difference between the prediction of the new model and the PR-DNS data is generally less than 17%. While the prediction of the BVK law is more than 200% larger than the PR-DNS data. The comparison is made at the grid size of three times of the particle diameter, which is a commonly adopted size in fine-grid two fluid model as well as computational fluid dynamics-discrete element method simulations. Therefore, the new drag model is very promising in resolving the detailed interactions between the gas and solid phases in flows with complex fine structures such as riser flows.

中文翻译：

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考虑稀密相界面影响的微观气固阻力模型

摘要 采用粒子分辨直接数值模拟 (PR-DNS) 来模拟低粒子雷诺数状态下通过各种静止球体簇的流动。结果表明，稀相和密相界面处的阻力与传统均质 BVK 定律的预测显着不同（AIChE Journal, 2007, 53(2):489-501）。发现界面处的阻力是固体体积分数梯度、表面速度梯度和计算阻力的网格尺寸的函数。基于PR-DNS数据，建立了一种新的考虑界面效应的微观阻力模型。新阻力模型的有效性在流过椭圆形粒子簇的过程中得到了证明。结果表明，在集群上的全局阻力方面，新模型的预测与 PR-DNS 数据的差异一般小于 17%。而 BVK 定律的预测比 PR-DNS 数据大 200% 以上。比较是在三倍粒径的网格尺寸下进行的，这是细网格二流体模型以及计算流体动力学-离散元方法模拟中常用的尺寸。因此，新的阻力模型非常有希望解决具有复杂精细结构的流动（例如立管流）中气固相之间的详细相互作用。比较是在三倍粒径的网格尺寸下进行的，这是细网格二流体模型以及计算流体动力学-离散元方法模拟中常用的尺寸。因此，新的阻力模型非常有希望解决具有复杂精细结构的流动（例如立管流）中气固相之间的详细相互作用。比较是在三倍粒径的网格尺寸下进行的，这是细网格二流体模型以及计算流体动力学-离散元方法模拟中常用的尺寸。因此，新的阻力模型非常有希望解决具有复杂精细结构的流动（例如立管流）中气固相之间的详细相互作用。