The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves
The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves
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DOI：
10.1017/jfm.2014.524
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发表时间：
2014-01-01
影响因子：
3.7
通讯作者：
Chung, Yongmann M.
中科院分区：
文献类型：
--
作者：
Hurst, Edward;Yang, Qiang;Chung, Yongmann M.
本文利用流向行波的湍流控制方法(Quadrio et al.J.流体力学，第627卷，2009年，第161-178页)，研究雷诺数对湍流表面摩擦减阻的影响。在雷诺数Re-tau=200~1600范围内，对壁面速度的流向行波作用下的槽道湍流流动进行了直接数值模拟。据作者所知，这是为这类流量控制尝试的最高雷诺数。数值模拟结果表明，随着雷诺数的增加，减阻效果变差，行波减阻效果显著降低。减阻和增阻的强度都随着雷诺数的增加而减小。另一个重要的发现是，当雷诺数增加时，最优控制参数的值会发生变化，即使是在壁面单元中也是如此。在壁面振荡、驻波和流向行波的情况下观察到了这一趋势。这意味着，当所使用的控制参数接近较低雷诺数时的最佳值时，减阻效果随着雷诺数的增加而迅速恶化。在这项研究中，雷诺数对行波的影响是用Re-tau(-α)形式的标度来量化的。没有找到标度参数α的通用常量。取而代之的是，缩放参数Alpha具有广泛的值，具体取决于流量控制条件。进一步讨论了雷诺数标度问题。对湍流统计数据进行了分析，以解释在高雷诺数时观察到的较弱的减阻。斯托克斯层的变化以及平均和均方根(R.M.S.)文中还报道了速度随雷诺数的变化。雷诺剪应力分析表明，在非常高的雷诺数下，有限减阻是一种有趣的可能性。
This paper exploits the turbulent flow control method using streamwise travelling waves (Quadrio et al. J. Fluid Mech., vol. 627, 2009, pp. 161-178) to study the effect of Reynolds number on turbulent skin-friction drag reduction. Direct numerical simulations (DNS) of a turbulent channel flow subjected to the streamwise travelling waves of spanwise wall velocity have been performed at Reynolds numbers ranging from Re-tau = 200 to 1600. To the best of the authors' knowledge, this is the highest Reynolds number attempted with DNS for this type of flow control. The present DNS results confirm that the effectiveness of drag reduction deteriorates, and the maximum drag reduction achieved by travelling waves decreases significantly as the Reynolds number increases. The intensity of both the drag reduction and drag increase is reduced with the Reynolds number. Another important finding is that the value of the optimal control parameters changes, even in wall units, when the Reynolds number is increased. This trend is observed for the wall oscillation, stationary wave, and streamwise travelling wave cases. This implies that, when the control parameters used are close to optimal values found at a lower Reynolds number, the drag reduction deteriorates rapidly with increased Reynolds number. In this study, the effect of Reynolds number for the travelling wave is quantified using a scaling in the form Re-tau(-alpha). No universal constant is found for the scaling parameter alpha. Instead, the scaling parameter alpha has a wide range of values depending on the flow control conditions. Further Reynolds number scaling issues are discussed. Turbulent statistics are analysed to explain a weaker drag reduction observed at high Reynolds numbers. The changes in the Stokes layer and also the mean and root-mean-squared (r.m.s.) velocity with the Reynolds number are also reported. The Reynolds shear stress analysis suggests an interesting possibility of a finite drag reduction at very high Reynolds numbers.