Scarano Fulvio, Moore Peter
Aerospace Engineering Department, TU Delft, Delft, The Netherlands.
Exp Fluids. 2012;52(4):919-933. doi: 10.1007/s00348-011-1158-3. Epub 2011 Jul 21.
A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor's hypothesis of . In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates , where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when . An additional favorable effect is observed by the analysis in the frequency domain whereby the spectrum becomes significantly less prone to aliasing error for the super-sampled data series.
为提高粒子图像测速（PIV）时间序列的时间分辨率，提出了一种平流方程的数值实现方法。该方法基于速度波动被动传输的原理，类似于泰勒假设。在本工作中，平流模型被扩展到非定常三维流动。该方法的主要目标是将PIV重复率的要求从欧拉频率降低到拉格朗日频率。通过对前一时刻瞬时速度的向前投影和后续时间步的向后投影来获得流体微团的局部轨迹。轨迹由瞬时流线近似，当速度波动幅度相对于对流运动较小时，可得到准确结果。通过在显著高于奈奎斯特准则规定的时间分辨率下进行的两个实验进行验证。绕NACA0012翼型后缘的流动与之非常近似，预计拉格朗日和欧拉时间尺度之间的最大比值会出现在此处。超采样序列的速度谱表明所需采集频率降低了一个数量级。通过对过渡射流的时间分辨层析PIV测量将该方法应用于三维数据。在此，采用三维平流方程来估计流体轨迹。在这种情况下，由于射流剪切层中出现的涡旋在大时间间隔时不能仅通过平流很好地近似，所以使用超采样导致的最小采样率降低较少。两种情况都表明，当……时，当前对时间分辨PIV实验的要求可以修订。通过频域分析还观察到一个额外的有利效果，即超采样数据序列的频谱明显更不易出现混叠误差。
