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Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

机译:无摩擦球的平面剪切流:动力学理论和3D   软球离散元法模拟

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摘要

We use existing 3D Discrete Element simulations of simple shear flows ofspheres to evaluate the radial distribution function at contact that enableskinetic theory to correctly predict the pressure and the shear stress, fordifferent values of the collisional coefficient of restitution. Then, weperform 3D Discrete Element simulations of plane flows of frictionless,inelastic spheres, sheared between walls made bumpy by gluing particles in aregular array, at fixed average volume fraction and distance between the walls.The results of the numerical simulations are used to derive boundary conditionsappropriated in the cases of large and small bumpiness. Those boundaryconditions are, then, employed to numerically integrate the differentialequations of Extended Kinetic Theory, where the breaking of the molecular chaosassumption at volume fraction larger than 0.49 is taken into account in theexpression of the dissipation rate. We show that the Extended Kinetic Theory isin very good agreement with the numerical simulations, even for coefficients ofrestitution as low as 0.50. When the bumpiness is increased, we observe thatsome of the flowing particles are stuck in the gaps between the wall spheres.As a consequence, the walls are more dissipative than expected, and the flowsresemble simple shear flows, i.e., flows of rather constant volume fraction andgranular temperature.
机译:我们使用球的简单剪切流的现有3D离散元素模拟来评估接触时的径向分布函数,该函数使动力学理论能够正确预测压力和剪切应力,而对于不同的碰撞恢复系数值也是如此。然后,对固定的平均体积分数和壁之间的距离进行固定的平均体积分数和壁之间距离的无摩擦非弹性球体的平面流的weperform 3D离散模拟,该壁在壁之间通过将颗粒粘合成凹凸状而剪切。数值模拟的结果用于得出边界大大小小的颠簸情况适合的条件。然后,利用这些边界条件对扩展动力学理论的微分方程进行数值积分,其中在耗散率的表达中考虑了在大于0.49的体积分数时打破分子混沌假设的情况。我们表明,即使对于恢复系数低至0.50的情况,扩展动力学理论也与数值模拟非常吻合。当颠簸度增加时,我们观察到一些流动的粒子卡在壁球之间的间隙中。结果,壁的耗散性比预期的大,并且流动类似于简单的剪切流动,即,体积分数相当恒定的流动颗粒温度。

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