In this study, we quantify the accuracy of a simple pressure estimation method from 2D snapshot PIV in attached and separated flows. Particle image velocimetry (PIV) offers the possibility to acquire a field of pressure instead of point measurements. Multiple methods may be used to obtain pressure from PIV measurements, however, the current state-of-the-art requires expensive equipment and data processing. As an alternative, we aim to quantify the efficacy of estimating instantaneous pressure from snapshot (non-time resolved) two-dimensional planar PIV (the simplest type of PIV available). To make up for the loss of temporal information, we rely on Taylor’s hypothesis (TH) to replace temporal information with spatial gradients. Application of our approach to high-resolution 2D velocity data of a turbulent boundary layer flow over ribs shows moderate to good agreement with reference pressure measurements in average and fluctuations. To assess the performance of the 2D TH method beyond average and fluctuation statistics, we acquired a time-resolved measurement of the same flow and determined temporal correlation values of the pressure from our method with reference measurements. Overall, the correlation attains good values for all measured locations. For comparison, we also applied two time-resolved approaches, which attained values of correlation similar to our approach. The performance of the 2D TH method is further assessed on 3D time-resolved velocity data for a turbulent boundary layer and compared with 3D methods. The root-mean-square (RMS) pressure fluctuations of the 2D TH, 3D TH and 3D pseudo-Lagrangian methods closely follow the pressure fluctuation distribution from DNS. These observations on the RMS pressure estimates are further supported by similar analysis on synthetic PIV data (based on DNS) of a turbulent channel flow. The values of spatial correlation between the 2D TH method and the DNS pressure fields in this case, are similar to the temporal correlations achieved in the turbulent flow over the ribs. Finally, we discuss the accuracy of instantaneous pressure estimates and provide a rule of thumb to determine regions where the pressure fluctuation estimate from the 2D TH methods is likely to fail.Graphical abstract

中文翻译：

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来自 2D 快照 PIV 的压力

在这项研究中，我们量化了一种简单压力估计方法的准确性，该方法来自 2D 快照 PIV 在附加流和分离流中。粒子图像测速 (PIV) 提供了获取压力场而不是点测量的可能性。可以使用多种方法从 PIV 测量中获得压力，但是，当前的最新技术需要昂贵的设备和数据处理。作为替代方案，我们旨在量化从快照（非时间分辨）二维平面 PIV（可用的最简单的 PIV 类型）估计瞬时压力的功效。为了弥补时间信息的损失，我们依靠泰勒假设（TH）将时间信息替换为空间梯度。将我们的方法应用于肋骨上湍流边界层流动的高分辨率二维速度数据，显示出与参考压力测量值的平均值和波动有中等至良好的一致性。为了评估 2D TH 方法在平均和波动统计之外的性能，我们获得了相同流量的时间分辨测量值，并从我们的方法与参考测量值确定了压力的时间相关值。总体而言，所有测量位置的相关性都达到了良好的值。为了比较，我们还应用了两种时间分辨方法，它们获得了与我们的方法相似的相关值。在湍流边界层的 3D 时间分辨速度数据上进一步评估 2D TH 方法的性能，并与 3D 方法进行比较。2D TH、3D TH 和 3D 伪拉格朗日方法的均方根 (RMS) 压力波动密切遵循来自 DNS 的压力波动分布。对湍流通道流的合成 PIV 数据（基于 DNS）的类似分析进一步支持了对 RMS 压力估计的这些观察。在这种情况下，2D TH 方法和 DNS 压力场之间的空间相关性值类似于在肋骨上的湍流中实现的时间相关性。最后，我们讨论了瞬时压力估计的准确性，并提供了一个经验法则来确定 2D TH 方法的压力波动估计可能失败的区域。图形摘要 对湍流通道流的合成 PIV 数据（基于 DNS）的类似分析进一步支持了对 RMS 压力估计的这些观察。在这种情况下，2D TH 方法和 DNS 压力场之间的空间相关性值类似于在肋骨上的湍流中实现的时间相关性。最后，我们讨论了瞬时压力估计的准确性，并提供了一个经验法则来确定 2D TH 方法的压力波动估计可能失败的区域。图形摘要 对湍流通道流的合成 PIV 数据（基于 DNS）的类似分析进一步支持了对 RMS 压力估计的这些观察。在这种情况下，2D TH 方法和 DNS 压力场之间的空间相关性值类似于在肋骨上的湍流中实现的时间相关性。最后，我们讨论了瞬时压力估计的准确性，并提供了一个经验法则来确定 2D TH 方法的压力波动估计可能失败的区域。图形摘要 类似于在肋骨上的湍流中实现的时间相关性。最后，我们讨论了瞬时压力估计的准确性，并提供了一个经验法则来确定 2D TH 方法的压力波动估计可能失败的区域。图形摘要 类似于在肋骨上的湍流中实现的时间相关性。最后，我们讨论了瞬时压力估计的准确性，并提供了一个经验法则来确定 2D TH 方法的压力波动估计可能失败的区域。图形摘要