The energetics of flow through a rapidly oscillating tube. Part 2. Application to an elliptical tube
The energetics of flow through a rapidly oscillating tube. Part 2. Application to an elliptical tube
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DOI：
10.1017/s0022112009992916
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发表时间：
2010-04
影响因子：
3.7
通讯作者：
R. Whittaker;M. Heil;J. Boyle;O. Jensen;S. Waters
中科院分区：
文献类型：
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作者：
R. Whittaker;M. Heil;J. Boyle;O. Jensen;S. Waters
在本工作的第1部分中，我们推导出了三维流场和能量通量的一般渐近结果，管内流动的壁执行规定的小振幅周期性振荡的高频和大的轴向波长。在目前的文件中，我们说明了如何将这些结果可以应用到通过一个有限长度的轴向非均匀管的椭圆形横截面的流动的情况下，在一个Starling电阻器的流动模型。三个模型问题（压力-流量和压力-压力边界条件下的轴向均匀管和轴向非均匀管与指定的流量）与指定的壁面运动的数值模拟的结果进行了比较，在第1部分的理论预测，每个显示出良好的协议。当上游和下游的压力是规定的，我们显示了如何调整的平均通量缓慢的雷诺应力的作用下，使用多尺度分析。我们测试的平均能量转移E从流动到壁在一段时间内的运动获得的渐近表达式。特别是，在E = 0的临界点被准确地预测：这一点对应于能量中性振荡，这是相关的Starling电阻器的全局不稳定性的发病条件。
In Part 1 of this work, we derived general asymptotic results for the three-dimensional flow field and energy fluxes for flow within a tube whose walls perform prescribed small-amplitude periodic oscillations of high frequency and large axial wavelength. In the current paper, we illustrate how these results can be applied to the case of flow through a finite-length axially non-uniform tube of elliptical cross-section – a model of flow in a Starling resistor. The results of numerical simulations for three model problems (an axially uniform tube under pressure–flux and pressure–pressure boundary conditions and an axially non-uniform tube with prescribed flux) with prescribed wall motion are compared with the theoretical predictions made in Part 1, each showing excellent agreement. When upstream and downstream pressures are prescribed, we show how the mean flux adjusts slowly under the action of Reynolds stresses using a multiple-scale analysis. We test the asymptotic expressions obtained for the mean energy transfer E from the flow to the wall over a period of the motion. In particular, the critical point at which E = 0 is predicted accurately: this point corresponds to energetically neutral oscillations, the condition which is relevant to the onset of global instability in the Starling resistor.