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Unsteady unidirectional flow of Bingham fluid between parallel plates with different given volume flow rate conditions

机译：在给定体积流量条件下平行板之间的Bingham流体非稳态单向流动

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摘要

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of Bingham fluid between parallel plates are solved by the Laplace transform method. The flow motion between the plates is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved; these are a suddenly started, and a constant acceleration, flow respectively. These two results are then applied to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered. The result indicates when the yield stress TO is equal to zero; the solution to the problem reduces to that of a Newtonian fluid.
机译：本文利用拉普拉斯变换法求解了平行板之间宾汉流体非稳态单向流动的速度分布和压力梯度。板之间的流动运动是由规定的随时间变化的任意入口体积流量引起的。根据所描述的流动条件，解决了两种基本流动情况；这些分别是突然开始的和恒定的加速度。然后将这两个结果应用于梯形活塞运动的实际情况，该运动包含三个阶段的活塞运动，即从静止状态到固定速度的恒定加速度，然后保持该速度，然后恒定减速度直至停止。另外，还考虑了振荡流。结果表明屈服应力TO何时等于零；屈服应力TO等于零。问题的解决方案简化为牛顿流体。

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