Self‐similar solution of the second kind for a convergent viscous gravity current
Self‐similar solution of the second kind for a convergent viscous gravity current
复制标题
收敛粘性重力流的第二类自相似解
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
J. Gratton
中科院分区：
文献类型：
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作者：
J. Diez;R. Gratton;J. Gratton
研究了极粘性流体向中心孔的轴对称流动。在最近的一篇论文中，我们找到了这个问题的自相似解。自相似性是第二类的，因此流动只能通过一个表征它的无量纲常数来记住它的初始条件。在这项工作中，通过测量作为时间函数的前沿位置和高度轮廓，对这种收敛流动进行了实验研究（使用硅油）。验证了自相似解正确地描述了空腔半径的一定区间内的流动，其中获得的相似指数δ值与理论值0.762一致（考虑实验误差）。 .数值模拟了向自相似流的过渡，并获得了不同初始条件下的时间闭合的数值。这些模拟还显示了理论上的自相似流动后，空腔关闭，这是很难观察到的。
The axisymmetric flow of a very viscous fluid toward a central orifice is studied. In a recent paper, a self‐similar solution for this problem has been found. The self‐similarity is of the second kind and hence the flow remembers its initial condition only through a nondimensional constant which characterizes it. In this work this convergent flow is studied experimentally (using silicone oils) by measuring the front position and the height profile as a function of time. It is verified that the self‐similar solution properly describes the flow within a certain interval of the cavity radius, where values are obtained for the similarity exponent δ in agreement (accounting for experimental errors) with the theoretical value 0.762... . The transition to the self‐similar flow is also simulated numerically and numerical values are obtained for the time closure for different initial conditions. These simulations also show the theoretical self‐similar flow after the cavity closure, which is very difficult to obser...