The inter-scale energy budget in a von Kármán mixing flow
The inter-scale energy budget in a von Kármán mixing flow
复制标题
DOI：
10.1017/jfm.2020.277
复制
发表时间：
2020-05
影响因子：
3.7
通讯作者：
Anna N. Knutsen;P. Baj;J. Lawson;E. Bodenschatz;J. Dawson;N. Worth
中科院分区：
文献类型：
--
作者：
Anna N. Knutsen;P. Baj;J. Lawson;E. Bodenschatz;J. Dawson;N. Worth
基于两组广泛的实验数据，对冯·Kármán混合槽内湍流的尺度间能量收支进行了详细的评估。测量采用泰勒微尺度雷诺数$Re{\Unicode[STIX]{x1D706}}=199$，使用扫描粒子图像测速仪(PIV)来完全解析速度梯度张量(VGT)，并使用立体PIV来扩大视场。在基本流动特征的基础上，用Kármán-Howarth-Monin-Hill方程研究了尺度间的能量传递。使用完整的VGT，可以在没有任何假设或近似值的情况下评估能源预算不同条款的贡献。文中还报道了主导项的尺度-空间分布，以评估能量传递的各向同性。结果表明，能量传递在尺度空间上呈高度各向异性分布。能量传递在球平均意义上表现为在小尺度上由非线性尺度间传递项主导。然而，与以前研究中考虑的流动不同，我们发现局部能量转移严重依赖于与平均流动相关的线性贡献。对能量从尺度到尺度转移的分析还可以直接评估能量级联的经典图景。结果表明，虽然湍流涨落驱动的尺度间能量级联总是向前推进，但湍流涨落和平均流共同驱动的总能量级联呈现出明显的逆级联区，能量从小尺度向大尺度转移。
A detailed assessment of the inter-scale energy budget of the turbulent flow in a von Kármán mixing tank has been performed based on two extensive experimental data sets. Measurements were performed at a Taylor microscale Reynolds number of $Re_{\unicode[STIX]{x1D706}}=199$ in the central region of the tank, using scanning particle image velocimetry (PIV) to fully resolve the velocity gradient tensor (VGT), and stereoscopic PIV for an expanded field of view. Following a basic flow characterisation, the Kármán–Howarth–Monin–Hill equation was used to investigate the inter-scale energy transfer. Access to the full VGT enabled the contribution of the different terms of the energy budget to be evaluated without any assumptions or approximations. The scale-space distribution of the dominant terms was also reported to assess the isotropy of the energy transfer. The results show a highly anisotropic distribution of energy transfer in scale space. Energy transfer was shown in a spherically averaged sense to be dominated at the small scales by the nonlinear inter-scale transfer term. However, in contrast to flows considered in previous studies, the local energy transfer is found to depend heavily on the linear contribution associated with the mean flow. Analysis of the scale-to-scale transfer of energy also allowed direct assessment of the classical picture of the energy cascade. It was found that while the inter-scale energy cascade driven by the turbulent fluctuations always proceeds in the forward direction, the total energy cascade driven by both the turbulent fluctuations and the mean flow exhibits significant inverse cascade regions, where energy is transferred from smaller to larger scales.