Implementation and research on the reconstruction algorithms of pressure fields based on PIV
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摘要: 介绍了有限容积法、直接积分法和Poisson方程法3种基于PIV瞬时速度场重构压力场的基本原理以及相应的计算方法，选取管流突扩流场和偏置方块绕流流场两个不可压缩流场的瞬时速度场数据，采用上述3种压力场重构算法，分别研究了图像噪声、速度场精度、插值算法以及边界条件的类型与精度对重构压力场的影响。最后针对管流突扩过程第20ms的流场，给出了3种重构算法下的压力场云图以及对应的CFD模拟结果。研究表明，有限容积法和直接积分法容易受到噪声的影响而产生剧烈震荡，但是可以在较大的速度场误差范围内保持较高的精度，通过采用双线性插值可以获得更高精度的重构压力场；Poisson方程法不易受到噪声的影响而产生震荡，同时在高精度PIV速度场下的优势较为突出，通过采用双三次差值可以获得更高精度的重构压力场；混合边界条件仅仅测定边界上有限个点的压力值，就获得了接近狄利克雷边界条件下重构压力场的精度，远高于诺依曼边界条件；边界条件的误差严重降低重构压力场的精度，其影响程度比速度场误差还要大。Abstract: The basic principles and the corresponding algorithms of the finite volume method, the direct integral method and the Poisson equation method are introduced in detail, which are used to reconstruct the pressure fields based on PIV velocity fields. The instantaneous velocity fields of two incompressible flows, including the pipe flow with a sudden expansion and the flow around a square, are selected to study the influence of picture noise, velocity error, interpolation methods, the type and the precision of boundary conditions on reconstructed pressure fields by using different reconstruction algorithms. Finally, the transient pressure distributions of the pipe flow with a sudden expansion at 20ms are obtained by using the three algorithms respectively as well as the CFD. It shows that the finite volume method and the direct integral method are easily affected by noise to produce rude shocks, but maintain high accuracy in a larger range of error in velocity fields while they can get higher precision of reconstructed pressure fields with bilinear interpolation; the Poisson equation method isn't easily affected by noise so it produces few shocks, and has great advantages with the accurate PIV velocity fields while it can get higher precision of reconstructed pressure fields with bicubic interpolation; by measuring only several pressure points on the boundaries, the mixed boundary condition gets the accurate reconstructed pressure fields which are close to those of the Dirichlet boundary condition and far better than those of the Neumann boundary condition; the error of boundary conditions reduces the precision of reconstructed pressure fields, which is more severe than the error of velocity fields.
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Key words:
- PIV /
- velocity fields /
- reconstructed pressure fields /
- Poisson equation /
- Riemann iteration /
- boundary conditions
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图 6 管流突扩过程中的模拟PIV速度场
Figure 6. Simulated PIV velocity fields during the process of pipe flow
图 8 偏置方块绕流模拟PIV速度场图像
Figure 8. Simulated PIV velocity field of the flow around a square
图 9 距左侧测量边界40mm处截面的压力分布（无噪声）
Figure 9. Pressure distribution of the cross section at 40mm from the left side of the measurement area (no noise)
图 10 距左侧测量边界40mm处截面的压力分布（有噪声或滤波）
Figure 10. Pressure distribution of the cross section at 40mm from the left side of the measurement area (with noise or filter)
图 11 重构压力场误差与速度场误差的关系
Figure 11. Relationship between the error of reconstructed pressure fields and velocity fields
图 12 重构压力场误差与插值算法的关系
Figure 12. Relationship between the error of reconstructed pressure fields and interpolation algorithms
图 13 重构压力场误差与边界条件误差的关系
Figure 13. Relationship between the error of reconstructed pressure fields and boundary conditions
表 1 管流突扩流场在不同边界条件下的重构压力场误差
Table 1. The error of reconstructed pressure fields with different boundary conditions of the pipe flow
重构算法 管流突扩流场 狄利克雷 诺依曼 混合 有限容积法 0.0654 0.2393 0.0954 直接积分法 0.0649 0.29 0.1418 Poisson方程法 0.0362 0.0928 0.0374 
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表 2 方块绕流流场在不同边界条件下的重构压力场误差
Table 2. The error of reconstructed pressure fields with different boundary conditions of the flow around a square
重构算法 偏置方块绕流流场 狄利克雷 诺依曼 混合 有限容积法 0.1805 1.801 0.4271 直接积分法 0.1794 1.7894 0.4862 Poisson方程法 0.0204 1.5176 0.0894
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[1] 李丹勋, 曲兆松, 王兴奎, 等. 粒子示踪测速技术原理与应用[M]. 北京: 科学出版社, 2012: 1-15.Li D X, Qu Z S, Wang X K. Principle and application of particle tracing technique[M]. Beijing: Science Press, 2012: 1-15. [2] Henning A, Kaepernick K, Ehrenfried K, et al. Investigation of aeroacoustic noise generation by simultaneous particle image velocimetry and microphone measurements[J]. Experiments in Fluids, 2008, 45(6): 1073-1085. doi: 10.1007/s00348-008-0528-y [3] Larsson J, Davidson L, Olsson M, et al. Aeroacoustic investigation of an open cavity at low Mach number[J]. AIAA Journal, 2004, 42(12): 2462-2473. doi: 10.2514/1.1339 [4] 徐惊雷. PIV技术在超及高超声速流场测量中的研究进展[J]. 力学进展, 2012, (01): 81-90. http://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201201008.htmXu J L. The research progress of PIV in the measurement of ultra-and hypersonic flow fields[J]. Advances in Mechanics, 2012, (01): 81-90. http://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201201008.htm [5] 王勇, 陈鹏, 耿子海, 等. 基于PIV速度场测量重构压强场的研究进展[J]. 实验流体力学, 2014, 04: 1-8, 24. http://www.syltlx.com/CN/abstract/abstract10745.shtmlWang Y, Chen P, Geng Z H, et al. Development of PIV based instantaneous pressure determination[J]. Journal of Experiments in Fluid Mechanics, 2014, 04: 1-8, 24. http://www.syltlx.com/CN/abstract/abstract10745.shtml [6] Gurka R, Liberzon A, Hefetz D, et al. Computation of pressure distribution using PIV velocity data[C]//Workshop on Particle Image Velocimetry, 1999. http://cn.bing.com/academic/profile?id=2120662661&encoded=0&v=paper_preview&mkt=zh-cn [7] Hosokawa S, Moriyama S, Tomiyama A, et al. PIV measurement of pressure distributions about single bubbles[J]. Journal of Nuclear Science and Technology, 2003, 40(10): 754-762. doi: 10.1080/18811248.2003.9715416 [8] Fujisawa N, Nakamura Y, Matsuura F, et al. Pressure field evaluation in microchannel junction flows through μPIV measurement[J]. Microfluidics and Nanofluidics, 2006, 2(5): 447-453. doi: 10.1007/s10404-006-0088-5 [9] Fujisawa N, Tanahashi S, Srinivas K. Evaluation of pressure field and fluid forces on a circular cylinder with and without rotational oscillation using velocity data from PIV measurement[J]. Measurement Science and Technology, 2005, 16(4): 989. doi: 10.1088/0957-0233/16/4/011 [10] Van Oudheusden B W. Principles and application of velocimetry based planar pressure imaging in compressible flows with shocks[J]. Experiments in Fluids, 2008, 45(4): 657-674. doi: 10.1007/s00348-008-0546-9 [11] Van Oudheusden B W, Scarano F, Roosenboom E W M, et al. Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible andcompressible flows[J]. Experiments in Fluids, 2007, 43(2-3): 153-162. doi: 10.1007/s00348-007-0261-y [12] Charonko J J, King C V, Smith B L, et al. Assessment of pressure field calculations from particle image velocimetry measurements [J]. Measurement Science and Technology, 2010, 21(10): 105401. doi: 10.1088/0957-0233/21/10/105401 [13] De Kat R, Van Oudheusden B W, Scarano F. Instantaneous planar pressure field determination around a square-section cylinder based on time resolved stereo-PIV [C]//Proceedings of the 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Posrtugal, 2008. [14] De Kat R, Van Oudheusden B W, Scarano F. Instantaneous planar pressure field determination around a square-section cylinder based on time resolved stereo-PIV [C]//Proceedings of the 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Posrtugal, 2008. [15] De Kat R, Van Oudheusden B W. Instantaneous planar pressure determination from PIV in turbulent flow[J]. Experiments in Fluids, 2012, 52(5): 1089-1106. doi: 10.1007/s00348-011-1237-5 [16] De Kat R, Van Oudheusden B W. Instantaneous planar pressure from PIV: analytic and experimental[3] test-cases[C]//Proceedings of the 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2010. http://cn.bing.com/academic/profile?id=2004953817&encoded=0&v=paper_preview&mkt=zh-cn [17] Adrian R J. Twenty years of particle image velocimetry[J]. Experiments in Fluids, 2005, 39(2): 159-169. doi: 10.1007/s00348-005-0991-7 [18] Raff M, Willert C, Wereley S, et al. Particle image velocimetry: a practical guide[M]. 2nd ed. Berlin: Springer-Verlag, 2007. [19] 马静. 超燃冲压发动机内流通道冷态流场的PIV试验研究[D]. 南京: 南京航空航天大学, 2010. http://cdmd.cnki.com.cn/article/cdmd-10287-1011291906.htmMa J. PIV experiment study of scramjet internal cold flow field[D]. Nanjing: Nanjing University of Aeronautics & Astronautics, 2010. http://cdmd.cnki.com.cn/article/cdmd-10287-1011291906.htm [20] 林春峰. 超声速冲击射流的PIV实验研究[D]. 南京: 南京航空航天大学, 2006. http://cdmd.cnki.com.cn/article/cdmd-10287-2007194304.htmLin C F. A PIV study of supersonic impinging jet[D]. Nanjing: Nanjing University of Aeronautics & Astronautics, 2006. http://cdmd.cnki.com.cn/article/cdmd-10287-2007194304.htm [21] 王大伟, 王元. 由PIV的速度场获取压强分布的数值方法. 北京: 中国科技论文在线. http://www.paper.edu.cn/releasepaper/content/200611-227.Wang D W, Wang Y. A numerical method for obtaining the pressure distribution of the velocity field by PIV. Beijing: Science Paper Online. http://www.paper.edu.cn/releasepaper/content/200611-227. [22] Van Oudheusden B W. PIV-based pressure measurement[J]. Measurement Science and Technology, 2013, 24(3): 032001. doi: 10.1088/0957-0233/24/3/032001 [23] 周正贵, 等. 计算流体力学基础理论与实际应用[M]. 南京: 东南大学出版社, 2008.Zhou Z G, et al. Basic theories and practical applications of computational fluid dynamics[M]. Nanjing: Southeast University Press, 2008 [24] Baur T, Köngeter J. PIV with high temporal resolution for the determination of local pressure reductions from coherent turbulence phenomena[C]//3rd International Workshop on Particle Image Velocimetry, Santa Barbara, CA, USA, 1999. doi: 10.1007%2Fs00348-008-0546-9 -
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