论文标题
内部流结构与湍流雷利 - 纳德对流中的传热效率的相关性
Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh-Bénard convection
论文作者
论文摘要
为了了解内部流量结构如何在全球传热中表现出来，我们研究了不同流量模式与瞬时正方形雷利 - 贝纳德对流单元中的瞬时努塞尔数（$ nu $）之间的相关性。高分辨率和长时间直接数值模拟的瑞利号码在$ 10^{7} $和$ 10^{9} $和PrandTL数字为5.3之间。 The investigated Nusselt numbers include the volume-averaged $Nu_{\text{vol}}$, the wall-averaged $Nu_{\text{wall}}$, the kinetic energy dissipation based $Nu_{\text{kinetic}}$, and the thermal energy dissipation based $Nu_{\text{thermal}}$.采用傅立叶模式分解和正确的正交分解来提取相干的流量结构。我们的结果表明，单次滚动模式，水平堆叠的双滚模式和四极流模式平均更有效地进行传热。相反，垂直堆叠的双滚模式平均效率低下。体积平均$ nu _ {\ text {vol}} $以及基于基于动能的$ nu _ {\ text {kinetic}} $可以更好地再现内部流结构与热传递效率的相关性，而不是壁 - veraged $ nu _ { $ nu _ {\ text {thermal}} $，即使这四个努塞尔特数字给出了一致的时间平均值。在流动逆转过程中，$ nu $的合奏平均时间痕迹表明，只有体积平均$ nu _ {\ text {vol}} $才能重现先前实验研究中观察到的过时现象。我们的结果表明，$ NU $的适当选择对于获得有意义的解释至关重要。
To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Bénard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{\text{vol}}$, the wall-averaged $Nu_{\text{wall}}$, the kinetic energy dissipation based $Nu_{\text{kinetic}}$, and the thermal energy dissipation based $Nu_{\text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{\text{vol}}$ and the kinetic energy dissipation based $Nu_{\text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{\text{wall}}$ and the thermal energy dissipation based $Nu_{\text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{\text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.
