Accurate simulation of sonic boom is of great importance for the study of low-boom design. It is hard to conduct direct full-field simulation of sonic boom at the cruising altitude of supersonic aircraft due to limitation of computing capacity. Current methods for sonic boom prediction usually have two steps. Firstly, the near field over-pressure is obtained according to the supersonic linearized theory or computational fluid dynamics. Then the near field signal is advanced to the far field using acoustic methods to get the ground pressure signature of aircraft. During the calculation of the far field, the traditional waveform parameter method does not take into consideration the loss of sound energy resulting from classical attenuation or molecular relaxation effect in propagation, so that the final shock waves obtained do not have thickness, making the far field sound pressure level inaccurate. This paper, based on the splitting method, investigates the numerical methods of the augmented Burgers equation in nonlinear acoustics. Two standard numerical examples published in the SBPW-2 are calculated, verifying that the method proposed can accurately predict the ground signature. It can be found that adding a zero-amplitude buffer signal to the near field signal is very effective to improve the simulation accuracy in the rising of ‘N’ wave. A study of mesh convergence demonstrates that it is useful to refine the grid density properly. A study of atmospheric sound absorption finds that the effect of relaxation effect is stronger than classical attenuation. Dry and cold atmosphere is found to have adverse effect on over-pressure of sonic boom signal based on an analysis of influence of humidity and temperature on ground pressure signature.
ZHANG Yidian
,
HUANG Jiangtao
,
GAO Zhenghong
. Far field simulation and applications of sonic boom based on augmented Burgers equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018
, 39(7)
: 122039
-122039
.
DOI: 10.7527/S1000-6893.2018.22039
[1] 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).
[2] PLOTKIN K J. State of the art of sonic boom modeling[J]. Journal of the Acoustical Society of America, 2002, 111(2):530-536.
[3] PLOTKIN K J. Sonic boom research:History and future (Invited):AIAA-2003-3575[R].Reston, VA:AIAA, 2003.
[4] 冯晓强. 超声速客机低声爆机理及设计方法研究[D].西安:西北工业大学, 2014:15. FENG X Q. The research of low sonic boom mechanism and design method of supersonic aircraft[D]. Xi'an:Northwestern Polytechnical University, 2014:15(in Chinese).
[5] CARLSON H W. Simplified sonic-boom prediction:NASA TR-1978-1122[R]. Washington, D.C.:NASA, 1978.
[6] PLOTKIN K. Review of sonic boom theory:AIAA-2003-3575[R]. Reston, VA:AIAA, 1989.
[7] RALLABHANDI S. Advanced sonic boom prediction using augmented burger's equation[J]. Journal of Aircraft, 2011, 48(4):1245-1253.
[8] YAMASHITA R, SUZUKI K. Full-field sonic boom simulation in stratified atmosphere[J]. AIAA Journal, 2016, 54(10):1-9.
[9] THOMAS C L. Extrapolation of sonic boom pressure signatures by the waveform parameter method:NASA TN D-6832[R]. Washington, D.C.:NASA, 1972.
[10] ANDERSON M D. The propagation of a spherical N wave in an absorbing medium and its diffraction by a circular aperture[R]. Austin:University of Texas at Austin, 1974.
[11] CLEVELAND R O. Propagation of sonic booms through a real, stratified atmosphere[D]. Austin:The University of Texas at Austin, 1995.
[12] 王刚, 马博平, 雷知锦, 等. 典型标模声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 prediction on several typical calculation models[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(1):121458.
[13] FENG X, LI Z, SONG B. Research of low boom and low drag supersonic aircraft design[J]. Chinese Journal of Aeronautics, 2014, 27(3):531-541.
[14] 冯晓强, 宋笔锋, 李占科, 等. 超声速飞机低声爆布局混合优化方法研究[J]. 航空学报, 2013, 34(8):1768-1777. FENG X Q, SONG B F, LI Z K, et al. Hybrid optimization approach reaseach for low sonic boom supersonic aircraft configuration[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(8):1768-1777(in Chinese).
[15] RALLABHANDI S, LOUBEAU A. Summary of propagation cases of the second AIAA sonic boom prediction workshop:AIAA-2017-3257[R]. Reston,VA:AIAA, 2017.
[16] BLACKSTOCK D T. Thermoviscous attenuation of plane, periodic, finite amplitude sound waves[J]. Journal of the Acoustical Society of America, 1964, 36(3):534.
[17] CARLTON T W, BLACKSTOCK D T. Propagation of plane sound waves of finite amplitude in inhomogeneous fluids[J]. Journal of the Acoustical Society of America, 1974, 56(6):S42.
[18] PIERCE A D. Acoustics:An introduction to its physical principles and applications[M]. Columbus, OH:Mc-Graw-Hill Book Co., 1981:56-57.
[19] HAMILTON M F, BLACKSTOCK D T. Nonlinear acoustics[M]. New York:Academic Press, 1998:55.
[20] PLOTKIN K, MAGLIERI D. Sonic boom research:History and future (Invited):AIAA-2003-3575[R]. Reston, VA:AIAA, 2003.
[21] PARK M A, MORGENSTERN J M. Summary and statistical analysis of the first AIAA sonic boom prediction workshop[J]. Journal of Aircraft, 2016, 53(2):578-598.
[22] PARK M A, NEMEC M. Near field summary and statistical ananalysis of the second AIAA sonic boom prediction workshop:AIAA-2017-3256[R]. Reston, VA:AIAA, 2017.
[23] RALLABHANDI S K. Application of adjoint methodology in various aspects of sonic boom design:AIAA-2014-2271[R]. Reston,VA:AIAA, 2014.
[24] 杨训仁, 陈宇. 大气声学[M]. 北京:科学出版社, 2007. YANG X R, CHEN Y. Atmosphericacoustics[M]. Beijing:Science Press, 2007(in Chinese).
[25] BAUER H J. Influences of transport mechanisms on sound propagation in gases[J]. Advances in Molecular Relaxation Processes, 1972, 2(2-4):319-376.
[26] EVANS L B, SUTHERLAND L C. Absorption of sound in air[J]. Journal of the Acoustical Society of America, 1971, 49(1):110.
[27] MARTINS J R, LAMBE A B. Multidisciplinary design optimization:A survey of architectures[J]. AIAA Journal, 2013, 51(9):2049-2075.
[28] HUAN Z, ZHENGHONG G, FANG X, et al. Review of robust aerodynamic design optimization for air vehicles[J/OL]. Archives of Computational Methods in Engineering, (2018-02-19)[2018-03-19]. https://doi.org/10.1007/s11831-018-9259-2.
[29] ZHAO H, GAO Z, GAO Y, et al. Effective robust design of high lift NLF airfoil under multi-parameter uncertainty[J]. Aerospace Science and Technology, 2017, 68:530-542.
[30] LEE Y S, HAMILTON M F. Time-domain modeling of pulsed finite-amplitude sound beams[J]. Journal of the Acoustical Society of America, 1995, 97(2):906-917.
[31] ATKINSON K E. An introduction to numerical analysis[M]. Hoboken, New Jersey:Wiley, 1978.
[32] BLOKHINTZEV D. The propagation of sound in an inhomogeneous and moving medium I[J]. Journal of the Acoustical Society of America, 1946, 18(2):322-328.
[33] ONYEONWU R O. The effects of wind and temperature gradients on sonic boom corridors:UTIAS No.168[R]. Toronto:University of Toronto, 1971.
[34] YAMAMOTO M, HASHIMOTO A, AOYAMA T, et al. A unified approach to an augmented Burgers equation for the propagation of sonic booms[J]. Journal of the Acoustical Society of America, 2015, 137(4):1857.
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