A series of direct numerical simulations of a fully developed turbulent channel flow is conducted in order to clarify the effects of travelling wave-like wall blowing and suction on dissimilar heat transfer enhancement. While the wave form is kept sinusoidal and its amplitude is set to be 5 % of the bulk mean velocity, the wavelength and phase speed of the travelling wave are systematically changed in a wide parameter space. As a result, the global optimum of the parameter set for maximizing the analogy factor, which is defined as the ratio between the Stanton number and the skin-friction coefficient, is identified. Interestingly, the obtained globally optimal mode agrees well with that predicted from the optimal control theory taking into account the future dynamics within a limited time horizon by Yamamoto et al. (J. Fluid Mech., vol. 733, 2013, pp. 189–220). The instantaneous velocity and thermal fields are decomposed into coherent and random components in order to evaluate the contribution from each component to dissimilar heat transfer enhancement. The detailed mechanisms of dissimilarity are explained by the budget analyses of the coherent and random contributions. Also, their relationships with the near-wall turbulent structures modified by the applied control are discussed through flow visualization. It is found that the random component makes a dominant contribution to dissimilarity, and this can be explained by an indirect effect through the modification of the coherent field by the applied control. Based on the above mechanisms, we propose a simple unsteady Reynolds-averaged Navier–Stokes (URANS) approach, where the phase-averaged velocity and thermal fields are solved directly whereas the effects of the random component are modelled by the Boussinesq eddy viscosity and diffusivity hypothesis. It is shown that the present URANS can capture the overall trend of dissimilar heat transfer enhancement in a wide parameter range. The present results also explain why the optimal control theory with a limited time horizon succeeds in predicting the globally optimal control mode.

中文翻译：

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壁吹和吸力的流动行波引起的湍流热和动量传递之间的差异

对完全发展的湍流通道流动进行了一系列直接数值模拟，以阐明行波状壁吹和吸力对不同传热增强的影响。当波形保持为正弦波并且其幅度设置为总体平均速度的 5% 时，行波的波长和相位速度在一个宽参数空间中系统地改变。结果，确定了用于最大化类比因子的参数集的全局最优值，该因子被定义为斯坦顿数和皮肤摩擦系数之间的比率。有趣的是，获得的全局最优模式与 Yamamoto 等人 考虑到有限时间范围内的未来动态的最优控制理论预测的一致。(J. Fluid Mech., vol. 733, 2013, 第 189-220 页）。瞬时速度和热场被分解为相干和随机分量，以评估每个分量对不同传热增强的贡献。相干和随机贡献的预算分析解释了差异的详细机制。此外，通过流动可视化讨论了它们与由应用控制修改的近壁湍流结构的关系。发现随机分量对相异性做出了主要贡献，这可以通过应用控制修改相干场的间接影响来解释。基于上述机制，我们提出了一种简单的非定常雷诺平均 Navier-Stokes (URANS) 方法，其中相位平均速度和热场直接求解，而随机分量的影响由 Boussinesq 涡流粘度和扩散率假设建模。结果表明，目前的 URANS 可以在很宽的参数范围内捕捉不同传热增强的整体趋势。目前的结果也解释了为什么有限时间范围的最优控制理论能够成功预测全局最优控制模式。