Stabilisation and drag reduction of pipe flows by flattening the base profile
Stabilisation and drag reduction of pipe flows by flattening the base profile
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DOI：
10.1017/jfm.2018.1012
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发表时间：
2018-06
影响因子：
3.7
通讯作者：
Elena Marensi;A. Willis;R. Kerswell
中科院分区：
文献类型：
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作者：
Elena Marensi;A. Willis;R. Kerswell
最近的实验观察(k<s:1> hnen等人，物理学报。（vol. 14, 2018b, pp. 386-390）已经表明，在管道流动中，平坦化湍流的流向速度剖面会破坏湍流的稳定性，从而使流动重新分层。我们证明了层流管道流型也存在类似的现象，即层流状态的非线性稳定性随着流型变得更平坦而增强。层流基础轮廓的平坦化是由人造的局部体力产生的，该体力被设计成模拟k<e:1>等人（流动涡轮）实验中使用的障碍物。燃烧。， vol. 100, 2018a, pp. 919-943)和由触发跃迁所需的初始扰动的能量大小测量的非线性稳定性。当被足够大的扰动触发时，还观察到紊流的显著阻力减小。为了提高非线性稳定性计算的效率，我们研究了最小种子（最小能量扰动）在测量过渡阈值时的指示性。我们首先证明了最小种子对基轮廓变化和谱滤波具有较强的鲁棒性。然后，我们将最小种子的（非强制）跃迁行为与雷诺数$Re=2400$ - $10\ 000$范围内的几种形式的随机初始条件进行比较，发现最小种子在其演化的Orr和斜相之后的能量接近于临界局部随机扰动的能量。从这个意义上说，斜相位末端的最小种子可以看作是典型扰动（这里取局部随机扰动）的一个很好的代理，因此在具有体力的模拟中用作初始条件。本研究中预测的增强的非线性稳定性和减阻是k<s:1> hnen等人的实验建模中令人鼓舞的第一步，并且应该激励未来的发展，以充分利用这一有前途的流动控制方向的好处。
Recent experimental observations (Kühnen et al., Nat. Phys., vol. 14, 2018b, pp. 386–390) have shown that flattening a turbulent streamwise velocity profile in pipe flow destabilises the turbulence so that the flow relaminarises. We show that a similar phenomenon exists for laminar pipe flow profiles in the sense that the nonlinear stability of the laminar state is enhanced as the profile becomes more flattened. The flattening of the laminar base profile is produced by an artificial localised body force designed to mimic an obstacle used in the experiments of Kühnen et al. (Flow Turbul. Combust., vol. 100, 2018a, pp. 919–943) and the nonlinear stability measured by the size of the energy of the initial perturbations needed to trigger transition. Significant drag reduction is also observed for the turbulent flow when triggered by sufficiently large disturbances. In order to make the nonlinear stability computations more efficient, we examine how indicative the minimal seed – the disturbance of smallest energy for transition – is in measuring transition thresholds. We first show that the minimal seed is relatively robust to base profile changes and spectral filtering. We then compare the (unforced) transition behaviour of the minimal seed with several forms of randomised initial conditions in the range of Reynolds numbers $Re=2400$ – $10\,000$ and find that the energy of the minimal seed after the Orr and oblique phases of its evolution is close to that of a critical localised random disturbance. In this sense, the minimal seed at the end of the oblique phase can be regarded as a good proxy for typical disturbances (here taken to be the localised random ones) and is thus used as initial condition in the simulations with the body force. The enhanced nonlinear stability and drag reduction predicted in the present study are an encouraging first step in modelling the experiments of Kühnen et al. and should motivate future developments to fully exploit the benefits of this promising direction for flow control.