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Skin-friction drag reduction in laminar and turbulent boundary layers.

机译：层流和湍流边界层中的皮肤摩擦阻力减小。

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The skin-friction drag in a constant, mass-flux plane channel flow is sustained below that corresponding to laminar flow when wall-normal blowing and suction at the upper and lower walls are applied as upstream traveling waves. The control is distributed such that the net mass-flux of the channel is not modified. Direct numerical simulations demonstrate that these upstream traveling waves can induce sublaminar viscous drag in fully developed laminar and turbulent flows. Furthermore, it is found that the observed phenomena can be characterized by the linearized governing equations.; The Navier-Stokes equations can be linearized by describing the flow velocities as perturbations about a mean, resulting in equations that describe the dynamics of the perturbations. A spectral decomposition, involving a two-dimensional Fourier expansion in the streamwise and spanwise directions and a Galerkin projection of Chebyshev polynomials in the wall-normal direction, is used to spatially discretize these equations, leading to a state space model. The traveling wave control is then introduced as a temporally, phase-shifting, wall-normal velocity wall boundary condition at a particular Fourier wavenumber.; This linear model was used to develop reduced-order linear-quadratic-Gaussian (LQG) controllers. While these controls could achieve significant drag reduction, they appeared to be a performance limit. However, they could induce transient sublaminar drag under certain conditions. A nonlinear minimization using full-order nonlinear simulations was attempted to capture this transient behavior on a periodic basis. The upstream traveling wave was discovered in the course of that study.; The same linear models can represent the sustained sublaminar drag. Using a recent formulation which expresses the viscous drag of a fully developed channel flow as a sum of laminar drag and the Reynolds shear stress, it is shown that the Reynolds shear stress calculated from the controlled linear model state provides good predictions of how the nonlinear flow will respond. This provides a computationally efficient environment in which to find the optimal amplitude and speed to set a traveling wave to gain the most predicted drag reduction for a specific level of input power.
机译：当上壁和下壁的壁面正常吹扫和吸力作为上游行波施加时，皮肤摩擦阻力在恒定的质量流量平面通道流中保持在低于层流的水平。分配控制，以使通道的净质量通量不变。直接数值模拟表明，这些上游行波可以在充分发展的层流和湍流中诱发层下粘性阻力。此外，发现观察到的现象可以通过线性化控制方程来表征。通过将流速描述为围绕平均值的扰动，可以使Navier-Stokes方程线性化，从而生成描述扰动动力学的方程。频谱分解涉及在流向和跨度方向上的二维傅立叶展开以及在壁法线方向上的切比雪夫多项式的Galerkin投影，用于在空间上离散这些方程式，从而得到状态空间模型。然后将行波控制作为在特定傅立叶波数处的时间，相移，壁法向速度壁边界条件引入。该线性模型用于开发降阶线性二次高斯（LQG）控制器。尽管这些控件可以实现显着的减阻效果，但它们似乎是性能的极限。但是，它们可能在某些条件下引起瞬时的层下阻力。尝试使用全阶非线性仿真进行非线性最小化以定期捕获此瞬态行为。在研究过程中发现了上游行波。相同的线性模型可以表示持续的层下阻力。使用最新的公式将完全展开的通道流的粘性阻力表示为层流阻力和雷诺剪切应力的总和，结果表明，根据受控线性模型状态计算出的雷诺剪切应力可以很好地预测非线性流动会回应。这提供了一种计算有效的环境，在该环境中，可以找到最佳振幅和速度来设置行波，以针对特定水平的输入功率获得最可预测的阻力减小。

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