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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

  • 摘要: 利用平板湍流边界层四相机阵列大视场高时间分辨率TRPIV实验数据库,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。首先,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,依据能量最大准则确定了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.提取湍动能最大的第9尺度下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9尺度转移.结合分尺度子波系数自相关函数法,依据检测喷射事件和扫掠事件的子波系数极值准则,检测流向脉动速度能量最大尺度的子波系数取得局部正的极大值,代表扫掠事件中心;检测流向脉动速度取得负的局部极小值,代表喷射事件中心,分别获得喷射事件和扫掠事件对应的流向脉动速度、法向脉动速度、瞬时雷诺应力的条件相位平均波形,结果符合喷射和扫掠的特征. 对不同法向位置的流向瞬时速度分量进行流向空间多尺度分解,对4个不同法向位置的第6尺度子波系数进行喷射事件和扫掠事件检测,以检测点为中心分别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: 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. Firstly, 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 9th scale as the wall-normal locations vary from the buffer layer to the logarithmic layer. Taking advantage of the autocorrelation function of wavelet coefficients at the maximum energy time-scale and the wavelet coefficients extremum detection criterion, The wavelet coefficient at maximum energy time-scale of longitudinal velocity component are point-by-point examined for the local positive maximum, which represents the center of sweep event and the negative minimum which represents a eject event center. According to the autocorrelation function of wavelet coefficients at the maximum energy time-scale, the average burst period of turbulence is determined, and 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 fifth 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.

     

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