90度弯道水流的线性稳定性
Linear stability of flow in a 90-degree bend
摘要：
本文考虑由直进、出口支管和90度圆弧弯曲段组成的二维通道内的流动。不可压缩的粘性流体在入口和出口之间的恒定压力梯度的作用下流过弯管。采用高保真谱/hp元方法数值求解了纳维-斯托克斯方程。在一定的雷诺数范围内，采用自适应选择频率阻尼方法获得稳态流场。结果表明，在弯管内存在三个分离泡和旋涡脱落。研究了二维和三维扰动的模态稳定性。通过低雷诺数的计算结果外推得到了二维扰动的临界雷诺数。它比三维流动大得多，但二维流动对于外加的小振幅白噪声可能是亚临界不稳定的。对于三维扰动，得到了临界雷诺数对弯曲半径的依赖关系。对于一个中等弯曲半径的情况下，中性曲线提供和本征函数进行了详细研究：三维不稳定性可以引起周期性或单调增长模式，这些不稳定的模式考虑到再循环气泡发生后的弯曲。
英文摘要：
The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant pressure gradient between the inlet and outlet. Navier-Stokes equations were solved numerically using a high-fidelity spectral/hp element method. In a range of Reynolds numbers, an adaptive selective frequency dumping method was used to get a steady-state flow. It was found that three separation bubbles and vortex shedding can exist in the bend. The modal stability of two- and three-dimensional perturbations was investigated. Critical Reynolds number of the two-dimensional disturbances was found as extrapolation by lower Reynolds number results. It is much greater than three-dimensional one, but the two-dimensional flow could subcritically unstable with respect to the imposed small-amplitude white noise. For three-dimensional perturbations, the dependence of the critical Reynolds numbers on the bending radius is obtained. For a case of a moderate bending radius the neutral curve is provided and eigenfunctions are studied in detail: three-dimensional instability can be caused by periodic or monotonically growing mode, these unstable modes regard to the recirculation bubbles that occur after the bend.
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