
1. 中国航空工业空气动力研究院,沈阳,110034
2. 高速高雷诺数气动力航空科技重点实验室,沈阳,110034
3. 西北工业大学 航空学院 超声速客机研究中心,西安,710072
4. 西北工业大学 航空学院气动与多学科优化设计研究所,西安,710072
Published:2019
移动端阅览
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 Zhansen, HAN Zhonghua. Progress and challenges of sonic boom research[J]. 2019, 37(4): 601-619.
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. DOI: 10.7638/kqdlxxb-2019.0054.
QIAN Zhansen, HAN Zhonghua. Progress and challenges of sonic boom research[J]. 2019, 37(4): 601-619. DOI: 10.7638/kqdlxxb-2019.0054.
声爆是超声速飞行器所特有的一种气动声学现象,其涉及空气动力学和非线性声学等研究领域,开展相关研究具有重要的学术意义和应用前景。本文简述了声爆的基本概念、主要特征和主要危害,简要回顾了声爆的产生、发展和演化的研究历史,重点介绍了声爆的数值模拟、风洞试验和飞行试验预测方法,以及近年来提出的声爆抑制方法和低声爆气动优化设计方法的发展现状;最后总结了当前声爆预测方法面临的技术难点和挑战。
Sonic boom is a special aero-acoustic phenomenon for supersonic aircraft
which contains both the fields of aerodynamics and nonlinear acoustics
so it is of important academic significance and application prospect. The present paper introduces its basic conception and major characteristics
the research history of its generation
development and evolution
and its harmfulness; Then the numerical simulation method
wind tunnel experiment method and flight test method of sonic boom researches are emphatically presented
and also including the recently proposed sonic boom inhibition and low boom optimization design methods; Finally
the current technique difficulties and challenges of sonic boom prediction are summarized.
MAGLIERI D J, BOBBITT P J, PLOTKIN K J, et al. Sonic boom six decades of research: NASA SP-622[R]. Hampton, VA: NASA, 2014.
PAWLOWSKI J W, GRAHAM D H, BOCCADORO C H, et al. Origins and overview of the shaped sonic boom demonstration program[R]. AIAA 2005-0005, 2005.
PLOTKIN K J, HAERING E A, MURRAY J E, et al. Ground data collection of shaped sonic boom experiment aircraft pressure signature[R]. AIAA 2005-0010, 2005.
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)
CHEN P, LI X D. Frequency domain method for predicting sonic boom propagation based on Khokhlov-Zabolotskaya-Kuznetsov equation[J]. Journal of Aerospace Power, 2010, 25(2):359-365. (in Chinese)
FENG X Q, LI Z K, SONG B F. Preliminary analysis on the sonic boom of supersonic aircraft[J]. Flight Dynamics, 2010, 28(6):21-23. (in Chinese)
QIAO J L, HAN Z H, DING Y L, et al. Sonic boom prediction method for supersonic transports based on nonlinear Burgers equation[C]//The First Chinese Conference of Aerodynamics. 15-19 August 2018, Mianyang, Sichuan.
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(01):169-181. (in Chinese)
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)
QIAN Z S, LIU Z C, LENG Y. Flight measurement and numerical simulation of sonic boom signatue of OS-X0 experimental aircraft[C]//The First Chinese Conference of Aerodynamics. 15-19 August 2018, Mianyang, Sichuan.
LENG Y, QIAN Z S, LIU Z C. Analysis on typical parameters of bodies of revolution affecting the sonic boom[C]//The First Chinese Conference of Aerodynamics. 15-19 August 2018, Mianyang, Sichuan.
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. 15-19 August 2018, Mianyang, Sichuan.
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)
HUO M, TAN L H, LIN D K, et al. The effects of near field calculation to far field prediction for a standard model[C]//The First Chinese Conference of Aerodynamics. 15-19 August 2018, Mianyang, Sichuan.
QIAN Z S. Current status and challenge of the sonic boom prediction techniques for supersonic aircraft[C ] //The First Chinese Aeronautical Future Scientist Forum. 30 th April, 2019, Beijing.
QIAN Z S, LEE Chun-Hian High order upwind compact scheme and ETA buffer zone-type non-reflecting boundary condition for LEE[R]. AIAA 2016-2720, 2016.
LANDAU L D. On shock waves at large distances from the place of their origin[J]. Sov J Phys, 1945, 9:496-500.
YEAGER, CHUCK. Yeager:An Autobiography[M]. Bantam Press, 1986.
LEATHERWOOD J D, SULLIVAN B M, SHEPHERD K P, et al. Summary of recent NASA studies of human response to sonic booms[J]. J Acoust Soc Am, 2002, 111:586-598.
MORGENSTERN M J, STELMACK M, JHA D P. Advanced concept studies for supersonic commercial transports entering service in 2030-35 (N+3)[R]. AIAA 2010-5114, 2010.
COULOUVRAT F. The challenges of defining an acceptable sonic boom overland[R]. AIAA 2009-3384, 2009.
WHITHAM G. The flow pattern of a supersonic project[J]. Communications on Pure and Applied Mathematics, 1952, 5(3):301-347.
HAYES D W. Brief review of basic theory[R]. NASA SP-147, 1967.
CHEUNG S, EDWARDS T, LAWRENCE S. Application of CFD to sonic boom near and mid flow-field prediction[R]. AIAA 1990-3999, 1990.
SICLARI M J, DARDEN C M. Euler code prediction of near-field to midfield sonic boom pressure signatures[J]. Journal of Aircraft, 1993, 30(6):911-917.
WALKDEN F. The Shock pattern of a wing-body combination, far from the flight path[J]. Aeronautical Quarterly, 1958, Ⅸ(2):164-194.
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):169-181. (in Chinese)
LENG Y, QIAN Z S. Sonic boom signature prediction and analysis for a type of hypersonic long-range civil vehicle[R]. AIAA 2017-4422, 2017.
PARK M A, AFTOSMIS M J, CAMPBELL R L, et al. Summary of the 2008 NASA fundamental aeronautics program sonic boom prediction workshop[R]. AIAA 2013-649, 2013.
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.
PARK M A, NEMEC M. Near field summary and statistical analysis of the second AIAA sonic boom prediction workshop[R]. AIAA 2017-3256, 2017.
BLOKHINTZEV D. The propagation of sound in an inhomogeneous and moving medium I[J]. The Journal of the Acoustical Society of America, 1945, 18(2):322-328.
ONYEONWU R O. The effects of wind and temperature gradients on sonic boom corridors[R]. AFOSR-TR-71-3087, 1971.
THOMAS L C. Extrapolation of sonic boom pressure signatures by waveform parameter method[R]. NASA TN D-6832, 1972.
PIERCE A D. Acoustics: an introduction to its physical principles and applications[M]. Acoustical Soc of America, 1981.
KANG J. Nonlinear acoustic propagation of shock waves through the atmosphere with molecular relaxation[D]. Ph. D. thesis, Pennsylvania: The Pennsylvania State University, 1991.
ROBINSON L D. Sonic Boom Propagation through an Inhomogeneous, Windy Atmosphere[D]. Ph. D. thesis, Texas: University of Texas at Austin, 1991.
CLEVELAND R O. Propagation of sonic booms through a real, stratified atmosphere[D]. Ph. D. thesis, Texas: The University of Texas at Austin, 1995.
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)
KANAMORI M, TAKAHASHI T, MAKINO Y, et al. Comparison of simulated sonic boom in stratified atmosphere with flight test measurements[J]. AIAA Journal, 2018, 56(7):2743-2755.
TAKENO J, MISAKA T, SHIMOYAMA K, et al. Analysis of sonic boom propagation based on the KZK equation[R]. AIAA 2015-0745, 2015.
FUJINO K, KIKUCHI R, SHIMOYAMA K, et al. Effects of uncertainties in atmospheric turbulence and weather predictions on sonic boom[R]. AIAA 2017-0280, 2017.
CARLSON H W. An investigation of some aspects of the sonic boom by means of wind-tunnel measurements of pressures about several bodies at a Mach number of 2.01[R]. NASA TN D-161, 1959.
CARLSON H W, MORRIS O A. Wind-tunnel sonic-boom testing techniques[J]. Journal of Aircraft, 1967, 4(3):245-249.
BOBBITT P J, DARDEN C M. A wedge-shaped supersonic flow field probe[R]. NASA CP-10133, Ⅱ: 379-398, 1993.
DURSTON D, CLIFF S, WAYMAN T, et al. Near field sonic boom test on two low-boom configurations using multiple measurement techniques at NASA ames[R]. AIAA 2011-3333, 2011.
CHERNYSHEV S L, IVANOV A L, KISELEV A P, et al. Development of the technique of sonic boom experimental researches[C]//Proceeding of International Conference on High-Speed Vehicle Science Technology (HiSST), 26-29 November 2018, Moscow, Russia.
MORGENSTERN J. Distortion correction of low sonic boom measurements in wind tunnels[R]. AIAA 2012-3216, 2012.
MAKINO Y, NOGUCHI M. Near field pressure measurements of several models in JAXA's 1 m×1 m supersonic wind tunnel[R]. AIAA 2013-648, 2013.
CLIFF S, ELMILIGUI A, AFTOSMIS M, et al. Design and evaluation of a pressure rail for sonic boom measurement in wind tunnels[C]//Seventh International Conference on Computational Fluid Dynamics (ICCFD7-2006), Big Island, Hawaii. 2012.
DURSTON D A, CLIFF S E, DENISON M, et al. Nozzle plume/shock interaction sonic boom test results from the NASA Ames 9-by 7-foot supersonic wind tunnel[R]. AIAA 2017-0041, 2017.
MORGENSTERN J M. Measurements supporting 1st sonic boom prediction workshop cases[R]. AIAA 2014-2007, 2014.
CLIFF S E, DENISON M F, MOINI-YEKTA S, et al. Wind tunnel model design for sonic boom studies of nozzle jet flow with shock interactions[R]. AIAA 2016-2035, 2016.
DURSTON D, CLIFFF S, DENISON M, et al. Nozzle plume/shock interaction sonic boom test results from the NASA Ames 9-by 7-Foot supersonic wind tunnel[R]. AIAA 2017-0041, 2017.
WINSKI C S, CARTER M B, ELMILIGUI A A, et al. Computational and experimental study of plume and shock interaction effects on sonic boom in the NASA Ames 9x7 supersonic wind tunnel[R]. AIAA 2018-0331, 2018.
BAUER A B, BAGLEY C J. Sonic boom modeling investigation of topographical and atmospheric effects[R]. Report No. FAA NO-70-10, July 1970.
SASOH A, IWAKAWA A, FURUKAWA D, et al. Near-field measurement of post-shock pressure modulation induced by supersonic flight model past a grid turbulence[R]. AIAA 2016-3583, 2016.
TOYODA A, OKUBO M, OBAYASHI S, et al. Ballistic range experiment on the low sonic boom characteristics of supersonic biplane[R]. AIAA 2010-0873, 2010.
DAVY B A, BLACKSTOCK D T. Measurements of the refraction and diffraction of a short N-wave by a gas-filled soap bubble[J]. J Acoust Soc Am, 1971, 49(3):732-737.
LIPKENS B, BLACKSTOCK D T. Model experiment to study sonic boom propagation through turbulence. Part Ⅰ:General results[J]. J Acoust Soc Am, 1998, 103(1):148-158.
LIPKENS B, BLACKSTOCK D T. Model experiment to study sonic boom propagation through turbulence. Part Ⅱ. Effect of turbulence intensity and propagation distance through turbulence[J]. J Acoust Soc Am, 1998, 104(1):1301-1309.
LIPKENS B. Model experiment to study sonic boom propagation through turbulence. Part Ⅲ:Validation of sonic boom propagation models[J]. J Acoust Soc Am, 2002, 111(1):509-519.
RIBNER H S, MORRIS P J, CHU W H. Laboratory simulation of development of superbooms by atmospheric turbulence[J]. J Acoust Soc Am, 1973, 53(3):926-928.
TUBBS P E. Measured effects of turbulence on the rise time of a weak shock[R]. AIAA 1975-0453, 1975.
DOMENIC J M, VERA H, HERBERT R H. Sonic-boom measurements for SR-71 aircraft operating at Mach numbers to 3.0 and altitudes to 24384 meters[R]. NASA TN D-6823, 1972.
MAGLIERI D J, et al. Summary of XB-70 s onic boom signature data for flights during March 1965 through May 1966[R]. NASA CR-189630, 1992.
HILTON D A, HENDERSON H R, MCKINIZEY R. Sonic-boom ground-pressure measurements from APOLLO 15[R]. NASA TN D-6950, 1972.
HICKS R M, MENDOZA J P, GARCIA F J. A wind tunnel-flight correlation of Apollo 15 sonic boom[R]. Ames TM X-62111, 1972
GARCIA F J, HICKS R M, MENDOZA J P. A wind tunnel flight correlation of Apollo 16 sonic boom[R]. NASA TM X-62073, 1972.
HENDERSON H R, HILTON D A. Sonic-boom ground pressure measurement from the launch and reentry of Apollo 16[R]. NASA TN D-7606, 1974.
HENDERSON H R, HILTON D A. Sonic-boom measurements in the focus eegion during the ascent of Apollo 17[R]. NASA TN D-7806, 1974
PAGE J, et al. Superboom caustic analysis and measurement program (SCAMP) final report[R]. NASA CR-2015-218871, 2015
PLOTKIN K J, MAGLIERI D J. SCAMP: experimental design of a sonic boom focus flight test[R]. AIAA 2013-0931, 2013.
KAWAGUCHI J, et al. Post-flight evaluation of the guidance and control for D-SEND#2 2nd drop test[R]. AIAA 2017-0939, 2017.
FOMIN V M, KISELEVA T A, VOLKOV V F, et al. Sonic boom problem: past, present and future[C]//Proceeding of the 1st International Conference on High-Speed Vehicle Science and Technology (HiSST), Moscow, Russia, November 26th-29th, 2018.
HAERING E A, EHERNBERGERL J, WHITMORES A. Preliminary airborne measurements for the SR-71, sonic boom propagation experiment[R]. NASA TM 104307, 1995.
BENSON L R. Queiting the Boom[M]. NASA Aeronautic Book Series, 2013.
WEINSTEIN L, STACY K, VIEIRA J, et al. Imaging supersonic aircraft shock waves[J]. Journal of Flow Visualization and Image Processing, 1997, 4(3):189-1990.
MAGLIERI D J, BOBIT P J, PLOTKIN K J, et al. Sonic boom six decades of research[R]. NASA/SP-201-622, 2014.
LEE R A, DOWNING J M. Sonic booms produced by the united states air force and united states navy aircraft: measured data[R]. AL-TR-1991-0099, 1991.
BATDORF S B. On a new approach to the alleviation of the sonic boom[R]. Rept. ATR-70 (S9990)-1, Aerospace Corp, 1969.
MILES R B, MARTINELLI L, MACHERET S O, et al. Suppression of sonic boom by dynamic off-body energy addition and shape optimization[R]. AIAA 2002-0150, 2002.
RETHORST S. Supersonic aircraft shock wave energy recovery system: U. S. Patent 5, 676, 333[P]. 1997-10-14.
GOETHERT B H. Fundamental research on advanced techniques for sonic boom suppression[J]. The Journal of the Acoustical Society of America, 1973, 54(6):1766-1766.
HENNE P A, HOWE D C, WOLZ R R, et al. Supersonic aircraft with spike for controlling and reducing sonic boom: U. S. Patent 6, 698, 684[P]. 2004-3-2.
SIMMONS F, FREUND D, SPIVEY N, et al. Quiet Spike TM : the design and validation of an extendable nose boom prototype[R ] . AIAA 2007-1774, 2007.
HOWE D, SIMMONS Ⅲ F, FREUND D. Development of the gulfstream quiet spike tm for sonic boom minimization[R]. AIAA 2008-0124, 2008.
ZHA G, IM H, ESPINAL D. Toward zero sonic-boom and high efficiency supersonic flight, Part Ⅰ: a novel concept of supersonic bi-directional flying wing[R]. AIAA 2010-1013, 2010.
ESPINAL D, LEE B, SPOSATO H, et al. Supersonic bi-directional flying wing, Part Ⅱ: Conceptual design of a high speed civil transport[R]. AIAA 2010-1393, 2010.
HORINOUCHI S. Variable forward swept wing supersonic aircraft having both low-boom characteristics and low-drag characteristics: U. S. Patent Application 11/103, 549[P]. 2005-10-20.
KUSUNOSE K. Supersonic biplane-A review[J]. Progress in Aerospace Sciences, 2011, 47:53-87.
JONES L B. Lower bounds for sonic bangs[J]. The Aeronautical Journa, 1961, 65(606):433-436 l.
JONES L B. Lower bounds for sonic bangs in the far field[J]. The Aeronautical Quarterly, 1967, 18(1):1-21.
JONES L B. Lower bounds for the pressure jump of the bow shock of a supersonic transport[J]. The Aeronautical Quarterly, 1970, 21(1):1-17.
SEEBASS R. Minimum sonic boom shock strengths and overpressures[J]. Nature, 1969, 221(5181):651, 1969.
SEEBASS R, GEORGE A R. Sonic-boom minimization[J]. The Journal of the Acoustical Society of America, 1972, 51(2C):686-694.
GEORGE A R, SEEBASS R. Sonic boom minimization including both front and rear shocks[J]. AIAA Journal, 1971, 9(10):2091-2093.
DARDEN C M. Sonic-boom minimizationwith nose-bluntness relaxation[R]. NASA TP-1348, 1979.
HAGLUND G. HSCT designs for reduced sonic boom[R]. AIAA 1991-3103, 1991.
PLOTKIN K, RALLABHANDI S, LI W. Generalized formulation and extension of sonic boom minimization theory for front and aft shaping[R]. AIAA 2009-1052, 2009.
HAAS A, KROO I. A multi-shock inverse design method for low-boom supersonic aircraft[R]. AIAA 2010-0843, 2010.
MAKINO Y, KEN', SUZUKI I, et al. Nonaxisymmetrical fuselage shape modification for drag reduction of low-sonic-boom airplane[J]. AIAA Journal, 2003, 41(8):1413-1420.
JUNG T P, STARKEY R P, ARGROW B. Lobe balancing design method to create frozen sonic booms using aircraft components[J]. Journal of Aircraft, 2012, 49(6):1878-1893.
WINTZER M, KROO I. Optimization and adjoint-based CFD for the conceptual design of low sonic boom aircraft[R]. AIAA 2012-0963, 2012.
LI W, SHIELDS E, LE D. Interactive inverse design optimization of fuselage shape for low-boom supersonic concepts[J]. Journal of Aircraft, 2008, 45(4):1381-1397.
CHEUNG S H, EDWARDS T A. Supersonic airplane design optimization method for aerodynamic performance and low sonic boom[R]. NASA 19920076743, 1992.
KIRZ J. Surrogate based shape optimization of a low boom axisymmetric body[R]. AIAA 2018-2849, 2018.
QIAO Jianling, HAN Zhonghua, SONG Wenping. An efficient surrogate-based global optimization for low sonic boom design[J]. Acta Aeronauticaet et Astronautica Sinica, 2018, 39(5):67-80.
REUTHER J, JAMESON A. Supersonic wing and wing-body shape optimization using an adjoint formulation[R]. NASA CR-199150, 1995.
RALLABHANDI S K, NIELSEN E J, DISKIN B. Sonic-boom mitigation through aircraft design and adjoint methodology[J]. Journal of Aircraf, 2014, 51(2):502-510.
HUANG J T, ZHANG Y D, GAO Z H. et al. The supersonic jet sonicboom optimization based on flow/sonic boom coupled adjoint equations[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(5):122505. (in Chinese).
RALLABHANDI S K, MAVRIS D N. Sonic boom minimization using inverse design and probabilistic acoustic propagation[J]. Journal of aircraft, 2006, 43(6):1815-1828.
YANG X R. Atmospheric acoustics[M]. Science Press Beijing, 2015.
ZHU Z Q. Applied computational fluid dynamics[M]. Beihang Univerisity Press, Beijing, 1998. (In chinese)
ZHANG H X, SHEN M Y. Computational fluid dynamics——then theory and application of finite difference method[M]. National Defense Industrial Press, Beijing, 2003. (In chinese)
LEVEQUE R J. Finite volume methods for hyperbolic problems[M]. Cambridge Texts in Applied Mathematics. 2002.
PARK M A, MORGENSTERN J M. Summary and statistical analysis of the first AIAA sonic boom prediction workshop[R]. AIAA 2014-2006, 2014.
PARK M A, NEMEC M. Nearfield summary and statistical analysis of the second AIAA sonic boom prediction workshop[R]. AIAA 2017-3256, 2017.
HAYES W D, HAEFELI R C, KULSRUD H E. Sonic boom propagation in a stratified atmosphere with computer program[R]. NASA CR-1299, 1968.
THOMAS C L. Extrapolation of wind-tunnel sonic boom signatures without use of a Whitham F-Function[R]. NASA SP-255, 205-217, 1970.
PLOTKIN K J. PCBoom3 sonic boom prediction model-Version 1.0e[R]. Wyle Research Report WR 95-22E, 1998.
CLEVELAND R O. Time-domain modeling of finite-amplitude sound in relaxing fluids[J]. J Acoust Soc Am, 1996, 99(6):3312-3318.
YAMAMOTO M, HASHIMOTO A, AOYAMA T. A unified approach to an augmented Burgers equation for the propagation of sonic booms[J]. J Acoust Soc Am, 2015, 137(4):1857-1866.
TAYLOR M E. Partial differential equations:nonlinear equations[M]. Springer-verlag, 1996.
YEE H C, SJÖGREEN B. Designing adaptive low-dissipative high order schemes for long-time integrations[J]. Fluid Mechanics Its Applications, 2002, 66:141-198.
HADJADJ A, YEE H C, SJÖGREEN B. LES of temporally evolving mixing layers by an eighth-order filter scheme[R]. AIAA 2012-0453, 2012.
RANDALL D G. Sonic bang intensities in a stratified, still atmosphere[J]. J Sound Vib, 1968, 8(2):196-214.
ROBINSON L D. A numerical model for sonic boom propagation through an inhomogeneous, windyatmoshpere[R]. NASA CP-1992-1372, 1992.
CROW S C. Distortion of sonic bangs by atmospheric turbulence[J]. J FluidMech, 1969, 37:529-563.
PLOTKIN K J, GEORGE A R. Propagation of weak shock waves through turbulence[J]. Journal of Fluid Mechanics, 1972, 54(3):449-467.
MAGLIERI D J. Sonic boom flight research: Some effects of airplane operations and the atmosphere on sonic boom signatures[R]. NASA SP-147, 1967.
KANE E J. Some effects of the atmosphere on sonic boom[R]. NASA SP-147, 1967.
PIERCE A D. Progress in modeling atmospheric propagation of sonic booms[R]. NASA N94-28189, 1994.
YAMASHITA H, OBAYASHI S. Sonic boom variability due to homogeneous atmospheric turbulence[J]. Journal of Aircraft, 2015, 46(6):1886-1893.
PIACSEK A A. Atmospheric turbulence conditions leading to focused and folded sonic boom wave fronts[J]. The Journal of the Acoustical Society of America, 2002, 111(1):520-529.
LOCEY L L. Sonic boom postprocessing functions to simulate atmospheric turbulence effects[D]. Ph. D Thesis, The Pennsylvania State University, 2008.
LUQUET D. 3D simulation of acoustical shock waves propagation through a turbulent atmosphere: Application to sonic boom[D]. Ph D Thesis, Sorbone Unicversity (UPMC), 2016.
MCDONALD B E, CAINE P, WEST M. A tutorial on the Nonlinear Progressive wave Equation (NPE)-Part 1[J]. Applied Acoustics, 1994, 43:159-167.
CAINE P, WEST M. A Tutorial on the Non-Linear Progressive Wave Equation (NPE). Part 2. Derivation of the three-dimensional Cartesian version without use of perturbation expansion[J]. Applied Acoustics, 1995, 45:155-165.
MAGLIERI D J, HILTON D A, MCLEOD N J. Experiments on the effects of atmospheric refraction and airplane accelerations on sonic-boom ground-pressure patterns[R]. NASA TN D-3520, 1966.
PLOTKIN K J, CANTRIL J W. Prediction of sonic boom at focus[R]. AIAA 1976-0002, 1976.
PIACSEK A. A numerical study of weak step shocks that focus in two dimensions[D]. Ph. D thesis, The Pennsylvania State University, 1995.
PILON A R. Spectrally resolved prediction of sonic boom focusing[R]. AIAA 2011-2858, 2011.
0
Views
0
下载量
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution
京公网安备11010802024621