CONTINUUM THEORY FOR RAPID COHESIVE-PARTICLE FLOWS: GENERAL BALANCE EQUATIONS AND DISCRETE-ELEMENT-METHOD-BASED CLOSURE OF COHESION-SPECIFIC QUANTITIES
CONTINUUM THEORY FOR RAPID COHESIVE-PARTICLE FLOWS: GENERAL BALANCE EQUATIONS AND DISCRETE-ELEMENT-METHOD-BASED CLOSURE OF COHESION-SPECIFIC QUANTITIES
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DOI：
10.1017/jfm.2017.642
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发表时间：
2017-12-10
影响因子：
3.7
通讯作者：
Hrenya, Christine M.
中科院分区：
文献类型：
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作者：
Kellogg, Kevin M;Liu, Peiyuan;Hrenya, Christine M.
快速内聚颗粒流的连续体描述包括种群平衡，它跟踪空间和时间上不同的团聚体大小，以及基于动力学理论的动量和颗粒能量平衡。这里，基本闭包以最一般的形式提供。在以前的种群平衡中，即使已经确定碰撞的结果取决于撞击（相对）速度，但给定碰撞导致聚集或破裂的概率（“成功因素”）已被设置为常数。在这里，导出了将成功因素与颗粒温度（冲击速度的连续测量）联系起来的基于物理的闭包。这个推导的一个关键方面是认识到冲击速度的法向分量决定了是否发生团聚。在动力学理论平衡方面，粒子间的内聚使碰撞更具耗散性，从而降低了颗粒温度。由黏聚引起的额外耗散用有效的恢复系数来计算，同样用导出的法向冲击速度分布来确定。这种对种群和动力学理论平衡的集体处理产生了一组一般的方程，其中包含了黏结特异性（范德华、液体桥接等）的几个参数（例如临界团聚速度）。本文还介绍了用简单离散元法模拟确定这些内聚量的方法，以及对所得理论的验证。
The continuum description of rapid cohesive-particle flows comprises the population balance, which tracks various agglomerate sizes in space and time, and kinetic-theory-based balances for momentum and granular energy. Here, fundamental closures are provided in their most general form. In previous population balances, the probability ('success factor') that a given collision results in agglomeration or breakage has been set to a constant even though it is well established that the outcome of a collision depends on the impact (relative) velocity. Here, physically based closures that relate the success factors to the granular temperature, a (continuum) measure of the impact velocity, are derived. A key aspect of this derivation is the recognition that the normal component of the impact velocity dictates whether agglomeration occurs. With regard to the kinetic-theory balances, cohesion between particles makes the collisions more dissipative, thereby decreasing the granular temperature. The extra dissipation due to cohesion is accounted for using an effective coefficient of restitution, again determined using the derived distribution of normal impact velocities. This collective treatment of the population and kinetic-theory balances results in a general set of equations that contain several parameters (e.g.critical velocities of agglomeration) that are cohesion-specific (van der Waals, liquid bridging, etc.). The determination of these cohesion-specific quantities using simple discrete element method simulations, as well as validation of the resulting theory, is also presented.