Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method
Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method
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DOI：
10.1088/1361-6501/ab6c28
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发表时间：
2020-01
影响因子：
2.4
通讯作者：
Xiaofeng Liu;J. Moreto
中科院分区：
文献类型：
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作者：
Xiaofeng Liu;J. Moreto
本文对由PIV测量的压力梯度重建压力的全向积分法的误差传播特性进行了理论分析和相应的数值和实验验证。分析表明，全方位积分为降低重建压力对测量压力梯度中随机噪声的敏感性提供了一种有效的机制。准确确定边界压力值是保证重建压力精度的第一步。边界压力误差由两部分组成，一部分以指数形式递减并最终消失，另一部分通过迭代保持不变，但幅度较小。利用各向同性湍流在不同噪声水平下叠加噪声的直接数值模拟数据库和模拟噪声嵌入数据的空间分布方案对这些结果进行了验证。对于Neumann边界条件下的压力泊松方程、圆形虚边界全向积分和旋转平行射线全向积分，基于噪声水平40%的统计独立压力梯度场实现的重构压力的无量纲化平均误差分别为0.854±0.406、0.154±0.015和0.149±0.015。如果将旋转平行射线得到的收敛边界压力值作为狄利克雷边界条件，则泊松平均压力误差为0.151±0.015。在全向方法的不同变体中，平行射线方法表现出最好的性能，因此是可选择的方法。利用实验获得的开口空腔湍流剪切层流动，对这些压力重建方法的性能进行了比较，结果与用数值模拟数据得到的结论是一致的。通过添加噪声的DNS数据，还识别和量化了在确定压力波动统计中关于压力重建方法的限制。
This paper reports a theoretical analysis and the corresponding numerical and experimental validation results of the error propagation characteristics of the omnidirectional integration method used for pressure reconstruction from the PIV measured pressure gradient. The analysis shows that the omnidirectional integration provides an effective mechanism in reducing the sensitivity of the reconstructed pressure to the random noise embedded in the measured pressure gradient. Accurate determination of the boundary pressure values is the first step in ensuring the accuracy of the reconstructed pressure. The boundary pressure error consists of two parts, with one part decreasing exponentially in magnitude and eventually vanishing, and the other remaining as a constant with small magnitude through iteration. These results are verified by using a direct numerical simulation database of isotropic turbulence flow superimposed with noise at various noise levels and spatial distribution schemes to simulate noise embedded data. The nondimensionalized average error of the reconstructed pressure based on 1000 statistically independent pressure gradient field realizations with a 40% added noise level is 0.854 ± 0.406 for the pressure Poisson equation with Neumann boundary condition, 0.154 ± 0.015 for the circular virtual boundary omnidirectional integration and 0.149 ± 0.015 for the rotating parallel ray omnidirectional integration. If the converged boundary pressure values obtained by the rotating parallel ray are used as Dirichlet boundary conditions, the average pressure error by Poisson is reduced to 0.151 ± 0.015. Of the different variations of the omnidirectional methods, the parallel ray method shows the best performance and therefore is the method of choice. Comparisons of the performance of these pressure reconstruction methods using an experimentally obtained turbulent shear layer flow over an open cavity are in agreement with the conclusions obtained with the DNS simulation data. With the noise added DNS data, limitations regarding the pressure reconstruction methods in determining pressure fluctuation statistics are also identified and quantified.