壁湍流相干结构的时空多尺度条件平均模态
SPATIOTEMPORAL MULTI-SCALE ANALYSIS AND CONDITIONAL PHASE-AVERAGED WAVEFORM OF WALL TURBULENCE
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摘要: 对湍流边界层中“喷射”和“扫掠”事件的时间历程和空间物理形态进行描绘并研究其统计特性, 是深入认识湍流的重要途经. 利用平板湍流边界层四相机阵列大视场高时间分辨率TRPIV(time-resolved particle image velocimetry)实验数据库, 获取流-法向平面u \text- v瞬时速度场的时间序列样本, 依据子波分析能量最大准则及条件相位平均统计分析方法, 对平板湍流边界层瞬时速度场进行时-空多尺度分析, 开展壁湍流相干结构的时空多尺度条件平均模态研究. 结果发现: 对瞬时速度场中不同法向位置的流向脉动速度信号进行空间多尺度分解得到能量最大流向空间尺度为第9尺度, 该尺度湍动能达到峰值, 湍流猝发最活跃. 提取不同法向位置对应的流向脉动速度时间序列, 进行时间多尺度子波分解, 发现流向湍动能最大时间尺度随着法向位置远离壁面, 逐渐从小尺度第6尺度向大尺度第8尺度转移. 获得第6时间尺度喷射和扫掠事件的流向脉动速度、法向脉动速度和瞬时雷诺应力的条件相位平均波形, 结果呈现很好拟序性. 此外, 对4个不同法向位置的第6空间尺度喷射事件和扫掠事件锁定流线和涡量场的空间相位平均模态, 发现对数律区的检测点处流线出现明显鞍点-焦点动力系统结构, 且在鞍点-焦点动力系统四角的涡量场呈现明显四极子结构, 在缓冲层区域, 四极子的下层涡对消失, 四极子上层涡对诱导流体产生喷射和扫掠事件. 该项研究为湍流边界层多尺度涡结构的动力系统模型提供了实验依据.Abstract: Describing the time and spatial statistical characteristics of "eject" and "sweep" events in turbulent boundary layers is an important way to gain a deeper understanding of turbulence. The experimental database of turbulent boundary layer TRPIV (time-resolved particle image velocimetry) measurement with a large field of view and high time resolution of a four-camera array is employed in order to carry out the multi-scale analysis of the instantaneous velocity field of the turbulent boundary layer and investigate the spatiotemporal multi-scale conditional-averaged modes of coherent structures in wall-bounded turbulence. Based on the maximum energy criterion of wavelet analysis and the statistical analysis method of conditional phase averaging, the fluctuating velocity was analyzed at multiple scales in time and space in the turbulent boundary layer of a flat plate, and the spatiotemporal multi-scale phase-averaged modes of the coherent structure of wall turbulence was carried out. The results show that at different wall-normal heights, the fluctuating longitudinal velocity signals along the streamwise spatial direction is decomposed into multi-scale components using wavelet analysis. Based on the maximum energy criterion, the fluctuating velocity signals corresponding to maximum-energy space-scale (the 9th scale) is obtained, where the turbulent fluctuating kinetic energy reaches the peak and the turbulence burst is the most active. And then at different wall-normal locations, the time series of fluctuating longitudinal velocity component are unfolded into multi-scale components by wavelet analysis. It was found that the peak-scale with the maximum turbulent energy in the streamwise direction gradually varies from the 6th scale to the 8th scale as the wall-normal locations vary from the buffer layer to the logarithmic layer. According to the autocorrelation function of wavelet coefficients at the maximum energy time-scale, the average phase waveform of the streamwise fluctuating velocity component, the normal-wall fluctuating velocity component and instantaneous Reynolds stress is obtained during eject event and sweep event occurs, and the results fit the features of eject event and sweep event well. Spatial multi-scale decomposition for the instantaneous velocity field is performed along the longitudinal direction at different normal positions. Eject and sweep are detected at four different normal positions of the sixth spatial scale, as well as the spatial phase-averaged modes of the streamline and vorticity are obtained around the detected points. It is found that in the logarithmic layer, there is a saddle-focal point dynamics system around the detection point, and the vorticity fields at the four corners of the saddle-focal point dynamics system show a quadrupole vortex structure, while in the buffer layer, the lower vortex-pair of the quadrupole disappears and the upper vortex-pair induces the ejection and sweep events. This study provides an experimental foundation for establishing the dynamics system model of multi-scale vortex structure in turbulent boundary layer.