The emergence of a submerged vortex upstream of a pump can reduce pump intake efficiency and cause structural damage. In this study, we consider the use of active flow control with steady blowing to increase the pressure distribution within a single-phase pump-induced wall-normal vortex model, which is based on the Burgers vortex with a no-slip boundary condition prescribed along its symmetry plane. The goal of our control is to modify the vortex core velocity profile. These changes are sought to increase the core pressure such that detrimental effects on the pump are alleviated. Three-dimensional direct numerical simulations (DNS) are performed to examine the dynamics of the vortex with the application of axial momentum injection at and around the root of the vortex. We find that the active flow control approach can effectively modify the wall-normal vortical structure and significantly increase the low-core pressure by up to 81% compared to that of the uncontrolled case. The result shows that the control setup is also effective when it is introduced in an off-centered manner. Compared to the unsteady blowing and suction based actuation from our previous work (Liu et al. 2018), the current steady control technique offers an effective and simple flow control setup that can support robust operations of pumps.
Interdisciplinary Centre of Energy Sciences, Indian Institute of Science（印度科学学院交叉能源科学中心）；Department of Mechanical Engineering, Indian Institute of Science（印度科学学院机械工程系）
Controlled reattachment in separated flows: a variational approach to recirculation length reduction
采用变分法推导了分离流中回流长度对定常强迫的敏感性的解析表达式。本文对雷诺数为$40 \leq Re \leq 120$的二维圆柱定常绕流进行了亚临界和超临界区域的线性灵敏度分析。确定了对体积强迫和壁吹/吸最敏感的区域。控制配置，减少再循环长度的基础上设计的灵敏度信息，特别是小缸用作控制装置在主缸的尾流，在缸壁和流体吸入。对全非线性Navier-Stokes方程计算的验证表明，对于小振幅控制，具有很好的一致性。系统地研究了受控流的线性稳定性。在中等雷诺数下，我们观察到，控制减少回流长度的区域对应于它对与旋涡脱落相关的最不稳定全局模式具有稳定作用的区域，而该属性在较大雷诺数下不再成立。
本文研究定常粘性为零的Navier-Stokes方程的涡面解。我们称之为湍流极限。这些定常流对应于欧拉哈密顿量的最小值，该最小值作为局部速度的切线不连续性的函数，参数化为$Δ\vec v_t =\vec \nabla Γ$。这一观察结果意味着定常流代表了涡面动力学吉布斯分布的低温极限。涡面的法向位移$δr_\perp$作为哈密顿坐标，$Γ$作为共轭动量。无穷多个欧拉守恒律导致了这个系统的退化真空，这解释了湍流统计的复杂性，并提供了相关的自由度（随机表面）。最简单的例子是一个稳定的解决方案的纳维-斯托克斯方程在湍流极限的球形涡面，我们的调查。这个稳定的解决方案提供了一个例子的欧拉瞬子主张在我们最近的工作，这是应该负责的\NS{}方程的耗散湍流极限。我们进一步得出结论，人们可以得到湍流统计从吉布斯统计的涡面通过添加拉格朗日乘子的封闭表面内的守恒体积，能量泵抽率，和能量耗散。吉布斯分布中的有效温度随雷诺数在湍流极限时的$\mbox{Re}^{-\frac{1}{3}}$而趋于零。\textbf{The Gibbs statistics in this limit reduces to the solvable string theory in two dimensions (so-called $c=1$ critical matrix model)}。这为涡面湍流的非微扰计算开辟了道路…
