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 frozen turbulence. 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 frozen turbulence, 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 information is poured from space to time. 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.

中文翻译：

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一种基于平流的模型，用于提高 PIV 时间序列的时间分辨率

提出了对流方程的数值实现，以提高 PIV 时间序列的时间分辨率。该方法基于速度波动被动传递的原理，类似于泰勒关于冻结湍流的假设。在目前的工作中，对流模型扩展到非定常三维流动。该方法的主要目标是降低从欧拉频率到拉格朗日频率对 PIV 重复率的要求。流体块的局部轨迹是通过前一时刻的瞬时速度的前向投影和后一时间步的后向投影获得的。轨迹由瞬时流线近似，当相对于对流运动的速度波动幅度很小时，这会产生准确的结果。验证是通过以显着高于奈奎斯特准则规定的时间分辨率进行的两个实验进行的。通过 NACA0012 机翼后缘的流动非常接近冻结湍流，预计拉格朗日时间尺度和欧拉时间尺度之间的比率最大。超采样系列的速度谱证明了所需采集频率的数量级降低。对 3D 数据的应用是通过对过渡射流的时间分辨断层成像 PIV 测量进行的。在这里，实施 3D 对流方程来估计流体轨迹。在这种情况下，使用超级采样对最小采样率的降低较少，因为在大时间分离时，射流剪切层中发生的涡流不能很好地近似于单一平流。这两种情况都表明，当信息从空间到时间倾泻而出时，可以修改当前对时间分辨 PIV 实验的要求。通过频域中的分析观察到额外的有利影响，由此频谱变得明显更不容易出现超采样数据系列的混叠误差。这两种情况都表明，当信息从空间到时间倾泻而出时，可以修改当前对时间分辨 PIV 实验的要求。通过频域中的分析观察到额外的有利影响，由此频谱变得明显更不容易出现超采样数据系列的混叠误差。这两种情况都表明，当信息从空间到时间倾泻而出时，可以修改当前对时间分辨 PIV 实验的要求。通过频域中的分析观察到额外的有利影响，由此频谱变得明显更不容易出现超采样数据系列的混叠误差。