High-order scheme discretization of sonic boom propagation model based on augmented Burgers equation

WANG Di; QIAN Zhansen; LENG Yan

doi:10.7527/S1000-6893.2021.24916

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2022 , Vol. 43 >Issue 1: 124916 - 124916

DOI: https://doi.org/10.7527/S1000-6893.2021.24916

Fluid Mechanics and Flight Mechanics

High-order scheme discretization of sonic boom propagation model based on augmented Burgers equation

WANG Di ,
QIAN Zhansen ,
LENG Yan

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1. AVIC Aerodynamics Research Institute, Shenyang 110034, China;
2. Aviation Key Laboratory of Science and Technology on High Speed and High Reynolds Number Aerodynamic Force Research, Shenyang 110034, China

Received date: 2020-10-23

Revised date: 2021-01-22

Online published: 2021-01-21

Supported by

National Natural Science Foundation of China (11672280)

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Abstract

The sonic boom prediction is one of the key technologies in the development of the new generation low-boom supersonic transport aircraft. In view of the low accuracy of the numerical scheme for the far-field propagation model of sonic boom based on the augmented Burgers equation, we study the discretization method for high-order scheme. After the physical properties of each effect term in the model is analyzed, an appropriate high-order accuracy scheme is used to discretize each term, and the classical geometric acoustic ray tracing method is adopted to calculate the propagation path of sonic boom, so as to realize the accurate prediction of ground waveform. The reliability of the high-order discrete method used in this paper is verified by the numerical simulation of the sonic boom flight test of F-5E aircraft and the standard numerical examples of the 2nd AIAA Sonic Boom Prediction Workshop on sonic boom prediction. Further results show that the high-order scheme has lower dissipation than the traditional second-order scheme, and thus can obtain higher resolution results with the same number of grids, with the grid convergence much higher than that of the traditional second-order scheme. Meanwhile, the high-order scheme also has advantages in computational efficiency. Among the effect terms of the augmented Burgers equation, the influence of the nonlinear term is more noticeable, explaining the prominence of the advantages of the adopted high-order scheme. The influence of the thermoviscous absorption term on the numerical results is small, and the improvement of calculation accuracy by using high-order scheme is not obvious. Therefore, the traditional discrete scheme can still be used in actual calculations, and the contribution of this term can even be ignored.

Key words： supersonic civil aircraft; augmented Burgers equation; sonic boom prediction; high-order scheme; computational fluid dynamics

Cite this article

WANG Di , QIAN Zhansen , LENG Yan . High-order scheme discretization of sonic boom propagation model based on augmented Burgers equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(1) : 124916 -124916 . DOI: 10.7527/S1000-6893.2021.24916

References

[1] 钱战森, 韩忠华. 声爆研究的现状与挑战[J]. 空气动力学学报, 2019, 37(4): 601-619. QIAN Z S, HAN Z H. Progress and challenges of sonic boom research[J].Acta Aerodynamica Sinica, 2019, 37(4): 601-619(in Chinese).
[2] 韩忠华, 乔建领, 丁玉临, 等. 新一代环保型超声速客机气动相关关键技术与研究进展[J]. 空气动力学学报, 2019, 37(4): 620-635. HAN Z H,QIAO J L, DING Y L, et al. Key technologies for next-generation environmentally-friendly supersonic transport aircraft: a review of recent progress[J]. Acta Aerodynamica Sinica, 2019, 37(4): 620-635(in Chinese).
[3] 朱自强, 兰世隆. 超声速民机和降低音爆研究[J]. 航空学报, 2015, 36(8): 2507-2528. ZHU Z Q, LAN S L. Study of supersonic commercial transport and reduction of sonic boom[J].Acta Aeronautica et Astronautica Sinica, 2015, 36(8): 2507-2528(in Chinese).
[4] 黄江涛, 张绎典, 高正红, 等. 基于流场/声爆耦合伴随方程的超声速公务机声爆优化[J]. 航空学报, 2019, 40(5): 122505. HUANG J T, ZHANG Y D, GAO Z H, et al. Sonic boom optimization of supersonic jet based on flow/sonic boom coupledadjoint equations[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(5): 122505(in Chinese).
[5] 王刚, 马博平, 雷知锦, 等. 典型标模音爆的数值预测与分析[J]. 航空学报, 2018, 39(1): 121458. WANG G, MA B P, LEI Z J, et al. Simulation and analysis for sonic boom on several benchmark cases[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(1): 121458(in Chinese).
[6] 钱战森, 刘中臣, 冷岩, 等. OS-X0试验飞行器声爆特性飞行测量与数值模拟分析[J]. 空气动力学学报, 2019, 37(4): 675-682. QIAN Z S, LIU Z C, LENG Y, et al. Flight measurement and numerical simulation of sonic boom signature of OS-X0 experimental aircraft[J].Acta Aerodynamica Sinica, 2019, 37(4): 675-682(in Chinese).
[7] WHITHAM G B. The flow pattern of a supersonic projectile[J]. Communications on Pure and Applied Mathematics, 1952, 5(3): 301-348.
[8] WALKDEN F. The shock pattern of a wing-body combination, far from the flight path[J]. Aeronautical Quarterly, 1958, 9(2): 164-194.
[9] CARLSON H W. Simplified sonic-boom prediction: TP-1978-1122[R]. Washington, D.C.: NASA, 1978.
[10] PLOTKIN K. A rapid method for the computation of sonic booms[C]//15th Aeroacoustics Conference. Reston: AIAA, 1993.
[11] YAMASHITA R, SUZUKI K. Full-field sonic boom simulation in real atmosphere[C]//32nd AIAA Applied Aerodynamics Conference. Reston: AIAA, 2014.
[12] YAMASHITA R, SUZUKI K. Full-field sonic boom simulation in stratified atmosphere[J]. AIAA Journal, 2016, 54(10): 3223-3231.
[13] KANDIL O, YANG Z, BOBBITT P. Prediction of sonic boom signature using Euler-full potential CFD with grid adaptation and shock fitting[C]//8th AIAA/CEAS Aeroacoustics Conference & Exhibit. Reston: AIAA, 2002.
[14] OZCER I. Sonic boom prediction using Euler /full potential methodology[C]//45th AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2007.
[15] CARLSON H W. An investigation of some aspects of the sonic boom by means of wind-tunnel measurements of pressures about several bodies of revolution at a Mach number of 2.01: NASA TND-161[R]. Washington, D.C.: NASA, 1959.
[16] CLIFF S, ELMILIGGUI A, AFTOSMIS M, et al. Design and evaluation of a pressure rail for sonic boom measurement in wind tunnels[C]//7th International Conference on Computational Fluid Dynamics (ICCFD7). Washington, D.C.: NASA, 2012.
[17] 刘中臣, 钱战森, 冷岩. 声爆近场空间压力分布风洞试验精确测量技术研究[C]//首届中国空气动力学大会, 2018. LIU Z C, QIAN Z S, LENG Y. Research on accurate measurement techniques of pressure distribution in wind tunnel near field sonic boom test[C]//The First Chinese Conference of Aerodynamics, 2018(in Chinese).
[18] PAWLOWSKI J, GRAHAM D, BOCCADORO C, et al. Origins and overview of the shaped sonic boom demonstration program[C]//43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2005.
[19] 徐悦, 宋万强. 典型低音爆构型的近场音爆计算研究[J]. 航空科学技术, 2016, 27(7): 12-16. XU Y, SONG W Q. Near field sonic boom calculation on typical LSB configurations[J]. Aeronautical Science & Technology, 2016, 27(7): 12-16(in Chinese).
[20] PARK M A, NEMEC M.Nearfield summary and statistical analysis of the second AIAA sonic boom prediction workshop[J]. Journal of Aircraft, 2018, 56(3): 851-875.
[21] THOMAS C L. Extrapolation of sonic boom pressure signatures by waveform parameter method: NASA-TN-D-6832[R]. Washington, D.C.: NASA, 1972.
[22] LENG Y, QIAN Z S. Sonic boom signature analysis for a type of hypersonic long-range civil vehicle[C]//21st AIAA International Space Planes and Hypersonics Technologies Conference. Reston: AIAA, 2017.
[23] KANG J. Nonlinear acoustic propagation of shock waves through the atmosphere with molecular relaxation[D]. Philadelphia: The Pennsylvania State University, 1991.
[24] ROBINSON L D. Sonic boom propagation through an inhomogeneous, windy atmosphere[D]. Austin: University of Texas at Austin, 1991.
[25] CLEVELAND R O. Propagation of sonic booms through a real, stratified atmosphere[D]. Austin: The University of Texas at Austin, 1995.
[26] RALLABHANDI S K. Advanced sonic boom prediction using the augmented Burgers equation[J]. Journal of Aircraft, 2011, 48(4): 1245-1253.
[27] YAMAMOTO M, HASHIMOTO A, TAKAHASHI T, et al. Long-range sonic boom prediction considering atmospheric effects[C]//INTER-NOISE and NOISE-CON Congress and Conference Proceedings. Reston: INCE-USA, 2011: 2282-2289.
[28] YAMAMOTO M, HASHIMOTO A, TAKAHASHI T, et al. Numerical Simulation for sonic boom propagation through an Inhomogeneous atmosphere with winds[J]. AIP Conference Proceedings, 2012, 1474(1): 339-342.
[29] YAMAMOTO M, HASHIMOTO A, AOYAMA T, et al. A unified approach to an augmented Burgers equation for the propagation of sonic booms[J]. The Journal of the Acoustical Society of America, 2015, 137(4): 1857-1866.
[30] 张绎典, 黄江涛, 高正红. 基于增广Burgers方程的音爆远场计算及应用[J]. 航空学报, 2018, 39(7): 122039. ZHANG Y D, HUANG J T, GAO Z H. Far field simulation and applications of sonic boom based on augmented Burgers equation[J].Acta Aeronautica et Astronautica Sinica, 2018, 39(7): 122039(in Chinese).
[31] 乔建领, 韩忠华, 丁玉临, 等. 基于广义Burgers方程的超声速客机远场声爆高精度预测方法[J]. 空气动力学学报, 2019, 37(4): 663-674. QIAO J L, HAN Z H, DING Y L, et al. Sonic boom prediction method for supersonic transports based on augmented Burgers equation[J].Acta Aerodynamica Sinica, 2019, 37(4): 663-674(in Chinese).
[32] LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115(1): 200-212.
[33] JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228.
[34] BALSARA D S, SHU C W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy[J]. Journal of Computational Physics, 2000, 160(2): 405-452.
[35] LELE S K. Compact finite difference schemes with spectral-like resolution[J]. Journal of Computational Physics, 1992, 103(1): 16-42.
[36] COCKBURN B, SHU C W. Nonlinearly stable compact schemes for shock calculations[J]. SIAM Journal on Numerical Analysis, 1994, 31(3): 607-627.
[37] 冷岩, 钱战森, 刘中臣. 超声速条件下旋成体声爆典型影响因素分析[J]. 空气动力学学报, 2019, 37(4): 655-662, 689. LENG Y, QIAN Z S, LIU Z C. Analysis on typical parameters of bodies of revolution affecting the sonic boom[J].Acta Aerodynamica Sinica, 2019, 37(4): 655-662, 689(in Chinese).
[38] 冷岩, 钱战森, 杨龙. 均匀各向同性大气湍流对声爆传播特性的影响[J]. 航空学报, 2020, 41(2): 123290. LENG Y, QIAN Z S, YANG L. Homogeneous isotropic atmospheric turbulence effects on sonic boom propagation[J].Acta Aeronautica et Astronautica Sinica, 2020, 41(2): 123290(in Chinese).
[39] PARK M. 2nd AIAA sonic boom prediction workshop[EB/OL]. (2017-01-17)[2020-07-22]. https://lbpw.larc.nasa.gov/sbpw2/S.
[40] RALLABHANDI S K, LOUBEAU A. Summary of propagation cases of the second AIAA sonic boom prediction workshop[J]. Journal of Aircraft, 2018, 56(3): 876-895.
[41] BASS H E, SUTHERLAND L C, ZUCKERWAR A J, et al. Atmospheric absorption of sound: Further developments[J]. The Journal of the Acoustical Society of America, 1995, 97(1): 680-683.
[42] PIERCE D A. Acoustics-an introduction to its physical principles and applications[M]. New Youk: Acoustical Society of America, 1989: 587-588.
[43] VAN LEER B. Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme[J]. Journal of Computational Physics, 1974, 14(4): 361-370.
[44] ROE P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics, 1981, 43(2): 357-372.
[45] HARTEN A. High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49(3): 357-393.
[46] SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock capturing schemes[J]. Journal of Computational Physics, 1988, 77(2): 439-471.

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