Yang Rui, Chong Kai Leong, Wang Qi, Verzicco Roberto, Shishkina Olga, Lohse Detlef
Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, MESA+ Institute and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands.
Max Planck Institute for Dynamics and Self-Organisation, Am Fassberg 17, 37077 Göttingen, Germany.
Phys Rev Lett. 2020 Oct 9;125(15):154502. doi: 10.1103/PhysRevLett.125.154502.
Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency f) on global transport properties has hardly been studied. Here, we perform numerical simulations of Rayleigh-Bénard convection with time periodic modulation in the temperature boundary condition and report how this modulation can lead to a significant heat flux (Nusselt number Nu) enhancement. Using the concept of Stokes thermal boundary layer, we can explain the onset frequency of the Nu enhancement and the optimal frequency at which Nu is maximal, and how they depend on the Rayleigh number Ra and Prandtl number Pr. From this, we construct a phase diagram in the 3D parameter space (f, Ra, Pr) and identify the following: (i) a regime where the modulation is too fast to affect Nu; (ii) a moderate modulation regime, where Nu increases with decreasing f, and (iii) slow modulation regime, where Nu decreases with further decreasing f. Our findings provide a framework to study other types of turbulent flows with time-dependent forcing.
许多自然和工业湍流都受到随时间变化的边界条件的影响。尽管这种情况很普遍，但时间调制（频率为f）对整体传输特性的影响却几乎没有得到研究。在此，我们对温度边界条件随时间周期性调制的瑞利-贝纳德对流进行了数值模拟，并报告了这种调制如何导致显著的热通量（努塞尔数Nu）增强。利用斯托克斯热边界层的概念，我们可以解释Nu增强的起始频率和Nu达到最大值时的最佳频率，以及它们如何依赖于瑞利数Ra和普朗特数Pr。据此，我们在三维参数空间（f，Ra，Pr）中构建了一个相图，并确定了以下内容：（i）调制太快而无法影响Nu的区域；（ii）适度调制区域，其中Nu随f的减小而增加；以及（iii）缓慢调制区域，其中Nu随f的进一步减小而减小。我们的研究结果为研究其他类型的随时间变化强迫的湍流提供了一个框架。
