附壁流动中的近壁相干性及其对流动控制的影响
Near wall coherence in wall-bounded flows and implications for flow control
摘要：
利用数值方法对壁面湍流中近壁条纹的能量循环进行反向控制，已显示出减阻的前景。对于实际实施，只有当控制系统的传感器-致动器对之间存在一定程度的相干性时，才可实现对向控制（这些传感器和致动器通常应该是基于壁的，以避免寄生阻力）。因此，我们在这里检查实时控制的近壁周期的可行性，通过考虑一个可测量的壁量之间的相干性，是壁剪切应力波动，和流向和壁法向速度波动的湍流边界层。同步的空间和时间的速度数据，从数值模拟在$Re_τ\approx 590$和$ 2000$。结果表明，在近壁区，与壁面信号随机不相干的流向速度脉动的谱能量与雷诺数无关。因此，流向的能量份额是随机壁相干的增长与雷诺数由于能量大尺度范围的增加。因此，这意味着基于壁的控制系统具有在较高雷诺数下操纵壁外位置处的总湍流能量的较大部分的能力。相干值为0.55和0.4，这是大大低于最大可能的相干1，被发现之间的流向和壁法向速度波动在近壁的能量谱图中的峰值，分别和流向波动的摩擦速度。这表明，随着雷诺数的增加，仅针对近壁条纹循环的闭环减阻方案在实践中的成功将是有限的。
英文摘要：
Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, opposition control is only realizable if there is a degree of coherence between the sensor--actuator pairs of the control system (these sensors and actuators should typically be wall-based to avoid parasitic drag). As such, we here inspect the feasibility of real-time control of the near-wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from numerical simulations at $Re_τ\approx 590$ and $ 2000$ are employed. It is shown that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region. Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers. Coherence values of 0.55 and 0.4, which are considerably lower than the maximum possible coherence 1, were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. This suggests that a closed-loop drag reduction scheme targeting near wall cycle of streaks alone will be of limited success in practice as the Reynolds number grows.
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