Energy transfer in turbulent flows behind two side-by-side square cylinders
Energy transfer in turbulent flows behind two side-by-side square cylinders
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DOI：
10.1017/jfm.2020.611
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
Yi Zhou;K. Nagata;Y. Sakai;Tomoaki Watanabe;Yasumasa Ito;T. Hayase
中科院分区：
文献类型：
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作者：
Yi Zhou;K. Nagata;Y. Sakai;Tomoaki Watanabe;Yasumasa Ito;T. Hayase
摘要我们以前的研究（J. Fluid Mech.，第874卷，2019年，第。677-698）证实了在两个并排方柱后面的湍流流动中可以发现两种不同类型的$-5/3$能谱（即非Kolmogorov和准Kolmogorov $-5/3$能谱）。在上游区域（即$X/T_0=6$，其中$T_0$为圆柱体厚度），尽管湍流是高度不均匀的和间歇的，Kolmogorov的假设不成立，但能谱在十年以上的时间里表现出一个明确的$-5/3$幂律范围。同时，对应的二阶结构函数的幂律指数为1，显著大于期望值，即2/3。相反，在下游位置，即X/T_0=26$，可以识别准Kolmogorov $-5/3$能谱（以及2/3标度的二级结构）。通过将流向速度脉动分解为瞬时速度展向平均值和湍流余项，证明了X/T_0=6$处的非Kolmogorov $-5/3$谱是由湍流余项引起的。为了阐明逐尺度能量转移的物理学，我们求助于卡门-豪沃思-莫宁-希尔方程。在X/T_0=6时，不能检测到非线性项和耗散项之间的预期平衡。相反，来自非局部压力、平流、非线性输送和湍流输送项的贡献占主导地位。此外，由于相应的流场具有高度间歇性，非局部压力、平流、非线性输送和湍流输送项的大小明显大于耗散项的大小。在远下游位置，即$X/T_0=26$，双尾流完全是湍流，变得更加均匀和各向同性，在一个短的中间范围内，两点湍流动能收支中的两个主要项是非线性输运项和耗散项，这在某种程度上与Kolmogorov的情景相呼应，尽管来自大尺度平流项的贡献不能被忽略。通过比较一点和两点能量传递的行为，可以看出，这两种不同的能量传递过程实际上是密切相关的，即粘性耗散的相似的相对重要性和不可忽略的项作为源项或汇项的相同作用。
Abstract Our previous study (J. Fluid Mech., vol. 874, 2019, pp. 677–698) confirmed that two different types of $-5/3$ energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov $-5/3$ spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. $X/T_0=6$ with $T_0$ being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined $-5/3$ power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. $2/3$. At the downstream location, i.e. $X/T_0=26$, in contrast, the quasi-Kolmogorov $-5/3$ energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov $-5/3$ spectrum at $X/T_0=6$ is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán–Howarth–Monin–Hill equation. At $X/T_0=6$, the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e. $X/T_0=26$, where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.