Volume 41 Issue 7
Jul.  2026
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Wei Xiangzhi, Shi Jingwei, Zhou Li, et al. Experimental investigation of the three-dimensional density field reconstruction in supersonic jets based on BOST methodology[J]. Journal of Aerospace Power, 2026, 41(7):20240686 doi: 10.13224/j.cnki.jasp.20240686
Citation: Wei Xiangzhi, Shi Jingwei, Zhou Li, et al. Experimental investigation of the three-dimensional density field reconstruction in supersonic jets based on BOST methodology[J]. Journal of Aerospace Power, 2026, 41(7):20240686 doi: 10.13224/j.cnki.jasp.20240686

Experimental investigation of the three-dimensional density field reconstruction in supersonic jets based on BOST methodology

doi: 10.13224/j.cnki.jasp.20240686
  • Received Date: 2024-10-10
    Available Online: 2026-04-26
  • The refined characterization of supersonic jet flow fields remains a critical technical challenge for enhancing aircraft aerodynamic performance and suppressing exhaust noise. This study systematically investigated the three-dimensional density field reconstruction of supersonic jets from an axisymmetric convergent-divergent nozzle using background-oriented schlieren tomography (BOST). First, the coupled effects of experimental parameters on the measurement sensitivity and spatial resolution were analyzed, and the BOST three-dimensional reconstruction mathematical model was established. Subsequently, a simulation experiment containing noise was designed to validate the model’s robustness. The results demonstrated that the reconstruction model maintained density field accuracy within 4.5% under high noise levels, confirming the robustness of the method. Finally, a multi-view BOST experimental system was implemented to reconstruct the three-dimensional density fields under typical experimental conditions. Results successfully captured the refined three-dimensional structures including the jet core region, shock trains, and expansion wave systems. The average errors on the centerline between the reconstructed density fields and numerical simulations were determined as 6.4%, 4.7%, and 5.0% under three experimental conditions, with shock positions showing good agreement with schlieren visualization. The BOST effectively visualized the transition process from Mach reflection to regular reflection induced by the increasing total inflow pressure, verifying the reliability of BOST in the three-dimensional diagnostics of supersonic jets. These findings provide high-precision flow field data crucial for nozzle optimization design.

     

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  • [1]
    廉筱纯, 吴虎. 航空发动机原理[M]. 西安: 西北工业大学出版社, 2005. Lian Xiaochun, Wu Hu. Aeroengine principle[M]. Xi’an: Northwestern Polytechnical University Press, 2005. (in Chinese

    Lian Xiaochun, Wu Hu. Aeroengine principle[M]. Xi’an: Northwestern Polytechnical University Press, 2005. (in Chinese)
    [2]
    李周复. 风洞试验手册[M]. 北京: 航空工业出版社, 2015. Li Zhoufu. Handbook of wind tunnel test[M]. Beijing: Aviation Industry Press, 2015. (in Chinese

    Li Zhoufu. Handbook of wind tunnel test[M]. Beijing: Aviation Industry Press, 2015. (in Chinese)
    [3]
    Tam C K W, Tanna H K. Shock associated noise of supersonic jets from convergent-divergent nozzles[J]. Journal of Sound and Vibration, 1982, 81(3): 337-358. doi: 10.1016/0022-460X(82)90244-9
    [4]
    李智豪, 张彪, 李健, 等. 预混旋流燃烧火焰三维折射率场重建[J]. 航空学报, 2023, 44(4): 126480. Li Zhihao, Zhang Biao, Li Jian, et al. Reconstruction of three-dimensional refractive index field of premixed swirl combustion flame[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(4): 126480. (in Chinese

    Li Zhihao, Zhang Biao, Li Jian, et al. Reconstruction of three-dimensional refractive index field of premixed swirl combustion flame[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(4): 126480. (in Chinese)
    [5]
    Feng T, McGuirk J J. Measurements in the annular shear layer of high subsonic and under-expanded round jets[J]. Experiments in Fluids, 2016, 57(1): 7. doi: 10.1007/s00348-015-2090-8
    [6]
    Wernet M P. Application of Tomo-PIV in a large-scale supersonic jet flow facility[J]. Experiments in Fluids, 2016, 57(9): 1-24.
    [7]
    Nicolas F, Donjat D, Léon O, et al. 3D reconstruction of a compressible flow by synchronized multi-camera BOS[J]. Experiments in Fluids, 2017, 58(5): 1-15. doi: 10.1007/s00348-017-2325-y
    [8]
    Dalziel S B, Hughes G O, Sutherland B R. Whole-field density measurements by ‘synthetic schlieren’[J]. Experiments in Fluids, 2000, 28(4): 322-335.
    [9]
    Raffel M, Richard H, Meier G E A. On the applicability of background oriented optical tomography for large scale aerodynamic investigations[J]. Experiments in Fluids, 2000, 28(5): 477-481. doi: 10.1007/s003480050408
    [10]
    Richard H, Raffel M. Principle and applications of the background oriented schlieren (BOS) method[J]. Measurement Science and Technology, 2001, 12(9): 1576-1585. doi: 10.1088/0957-0233/12/9/325
    [11]
    Meier G. Computerized background-oriented schlieren[J]. Experiments in Fluids, 2002, 33(1): 181-187. doi: 10.1007/s00348-002-0450-7
    [12]
    熊渊. 背景纹影测量技术研究与应用进展[J]. 实验流体力学, 2022, 36(2): 30-48. Xiong Yuan. Recent advances in background oriented Schlieren and its applications[J]. Journal of Experiments in Fluid Mechanics, 2022, 36(2): 30-48. (in Chinese doi: 10.11729/syltlx20210173

    Xiong Yuan. Recent advances in background oriented Schlieren and its applications[J]. Journal of Experiments in Fluid Mechanics, 2022, 36(2): 30-48. (in Chinese) doi: 10.11729/syltlx20210173
    [13]
    Raffel M. Background-oriented schlieren (BOS) techniques[J]. Experiments in Fluids, 2015, 56(3): 1-17. doi: 10.1007/s00348-015-1927-5
    [14]
    Settles G S, Hargather M J. A review of recent developments in schlieren and shadowgraph techniques[J]. Measurement Science and Technology, 2017, 28(4): 042001. doi: 10.1088/1361-6501/aa5748
    [15]
    Tipnis T J, Finnis M V, Knowles K, et al. Density measurements for rectangular free jets using background-oriented schlieren[J]. The Aeronautical Journal, 2013, 117(1194): 771-785. doi: 10.1017/S0001924000008447
    [16]
    俞凯凯, 徐惊雷, 唐兰, 等. 基于BOS的过膨胀喷管出口密度测量[J]. 推进技术, 2015, 36(6): 832-838. Yu Kaikai, Xu Jinglei, Tang Lan, et al. Density measurements of nozzle under over-expanded condition using background oriented schlieren technique[J]. Journal of Propulsion Technology, 2015, 36(6): 832-838. (in Chinese doi: 10.13675/j.cnki.tjjs.2015.06.005

    Yu Kaikai, Xu Jinglei, Tang Lan, et al. Density measurements of nozzle under over-expanded condition using background oriented schlieren technique[J]. Journal of Propulsion Technology, 2015, 36(6): 832-838. (in Chinese) doi: 10.13675/j.cnki.tjjs.2015.06.005
    [17]
    Heineck J T, Banks D W, Smith N T, et al. Background-oriented schlieren imaging of supersonic aircraft in flight[J]. AIAA Journal, 2021, 59(1): 11-21. doi: 10.2514/1.J059495
    [18]
    Venkatakrishnan L, Meier G E A. Density measurements using the Background Oriented Schlieren technique[J]. Experiments in Fluids, 2004, 37(2): 237-247. doi: 10.1007/s00348-004-0807-1
    [19]
    Goldhahn E, Seume J. The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field[J]. Experiments in Fluids, 2007, 43(2): 241-249. doi: 10.1007/s00348-007-0331-1
    [20]
    Atcheson B, Ihrke I, Heidrich W, et al. Time-resolved 3D capture of non-stationary gas flows[J]. ACM Transactions on Graphics, 2008, 27(5): 1-9. doi: 10.1145/1457515.1409085
    [21]
    Nicolas F, Todoroff V, Plyer A, et al. A direct approach for instantaneous 3D density field reconstruction from background-oriented schlieren (BOS) measurements[J]. Experiments in Fluids, 2016, 57(1): 13. doi: 10.1007/s00348-015-2100-x
    [22]
    Nicolas F, Donjat D, Plyer A, et al. Experimental study of a co-flowing jet in ONERA’s F2 research wind tunnel by 3D background oriented schlieren[J]. Measurement Science and Technology, 2017, 28(8): 085302. doi: 10.1088/1361-6501/aa7827
    [23]
    Grauer S J, Unterberger A, Rittler A, et al. Instantaneous 3D flame imaging by background-oriented schlieren tomography[J]. Combustion and Flame, 2018, 196: 284-299. doi: 10.1016/j.combustflame.2018.06.022
    [24]
    Liu Hecong, Shui Chongyuan, Cai Weiwei. Time-resolved three-dimensional imaging of flame refractive index via endoscopic background-oriented Schlieren tomography using one single camera[J]. Aerospace Science and Technology, 2020, 97: 105621. doi: 10.1016/j.ast.2019.105621
    [25]
    Liu Hecong, Huang Jianqing, Li Lei, et al. Volumetric imaging of flame refractive index, density, and temperature using background-oriented Schlieren tomography[J]. Science China Technological Sciences, 2021, 64(1): 98-110. doi: 10.1007/s11431-020-1663-5
    [26]
    Guo Guangming, Liu Hong. Density and temperature reconstruction of a flame-induced distorted flow field based on background-oriented schlieren (BOS) technique[J]. Chinese Physics B, 2017, 26(6): 064701. doi: 10.1088/1674-1056/26/6/064701
    [27]
    Gordon R, Bender R, Herman G T. Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography[J]. Journal of Theoretical Biology, 1970, 29(3): 471-481. doi: 10.1016/0022-5193(70)90109-8
    [28]
    Gilbert P. Iterative methods for the three-dimensional reconstruction of an object from projections[J]. Journal of Theoretical Biology, 1972, 36(1): 105-117. doi: 10.1016/0022-5193(72)90180-4
    [29]
    Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J]. Physica D: Nonlinear Phenomena, 1992, 60(1/2/3/4): 259-268. doi: 10.1016/0167-2789(92)90242-f
    [30]
    Lang H M, Oberleithner K, Paschereit C O, et al. Measurement of the fluctuating temperature field in a heated swirling jet with BOS tomography[J]. Experiments in Fluids, 2017, 58(7): 88-108. doi: 10.1007/s00348-017-2367-1
    [31]
    Sipkens T A, Grauer S J, Steinberg A M, et al. New transform to project axisymmetric deflection fields along arbitrary rays[J]. Measurement Science and Technology, 2022, 33(3): 035201. doi: 10.1088/1361-6501/ac3f83
    [32]
    Amjad S, Soria J, Atkinson C. Three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren[J]. Experimental Thermal and Fluid Science, 2023, 142: 110819. doi: 10.1016/j.expthermflusci.2022.110819
    [33]
    Zhang Z. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11): 1330-1334. doi: 10.1109/34.888718
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