Model-based design of transverse wall oscillations for turbulent drag reduction
Model-based design of transverse wall oscillations for turbulent drag reduction
复制标题
基于模型的湍流减阻横向壁振动设计
DOI：
10.1017/jfm.2012.272
复制
发表时间：
2012
影响因子：
3.7
通讯作者：
M. Jovanovi'c
中科院分区：
文献类型：
--
作者：
R. Moarref;M. Jovanovi'c
在过去的二十年里，实验和模拟都表明，适当选择振幅和频率的横向壁面振荡可以减少湍流阻力多达40美元。在本文中，我们开发了一种基于模型的方法来设计振荡，抑制湍流的通道流。我们利用涡粘性增强线性化的湍流与控制结合湍流建模，以确定表面摩擦阻力的模拟自由的方式。Boussinesq涡粘性假设被用来量化的平均速度的波动的影响，在流受到控制。与依赖于数值模拟的传统方法相比，我们确定了湍流粘度从二阶统计的线性化模型驱动的白色时间随机强迫。强迫的空间功率谱的选择，以确保非受控流的线性化模型再现湍流能谱。由此产生的修正引起的小振幅壁运动的湍流平均速度，然后用于确定减阻振荡的最佳频率。此外，我们得到的控制净效率和湍流结构与数值模拟和实验结果吻合得很好。这证明了我们基于模型的方法控制湍流的预测能力，预计将为在比目前可能的更高雷诺数下成功控制流量铺平道路。
Abstract Over the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as $40\hspace{0.167em} \% $ . In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modelling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on the mean velocity in flow subject to control. In contrast to the traditional approach that relies on numerical simulations, we determine the turbulent viscosity from the second-order statistics of the linearized model driven by white-in-time stochastic forcing. The spatial power spectrum of the forcing is selected to ensure that the linearized model for uncontrolled flow reproduces the turbulent energy spectrum. The resulting correction to the turbulent mean velocity induced by small-amplitude wall movements is then used to identify the optimal frequency of drag-reducing oscillations. In addition, the control net efficiency and the turbulent flow structures that we obtain agree well with the results of numerical simulations and experiments. This demonstrates the predictive power of our model-based approach to controlling turbulent flows and is expected to pave the way for successful flow control at higher Reynolds numbers than currently possible.