Atmospheric turbulence is known to randomly distort the “N-wave” sonic boom signature emitted by conventional, unshaped supersonic aircraft. To predict the effect of turbulence on the signature from shaped aircraft, a numerical model has been developed based on the nonlinear Khokhlov–Zabolotskaya–Kuznetzov (KZK) propagation equation coupled with an approximate atmospheric turbulence model. The effects of turbulence on an archetypal N-wave and a shaped signature are compared via a series of numerical experiments propagating the signatures through multiple random realizations of turbulence in varying atmospheric and propagation conditions. The simulated results generally show that the variance of the Stevens Mark VII perceived level metric related to loudness is decreased by boom shaping and that the shocks in the shaped signature are less distorted than for the N-wave. Additionally, the probabilities of high-level and high-amplitude signatures are decreased for the shaped signature. Thus, the model predicts that boom shaping results in a signature with more consistent loudness and amplitude after propagation through turbulence.
References
1.
Averiyanov
, M.
, Blanc-Benon
, P.
, Cleveland
, R. O.
, and Khokhlova
, V.
(2011a
). “Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media
,” J. Acoust. Soc. Am.
129
, 1760
–1772
.2.
Averiyanov
, M.
, Ollivier
, S.
, Khokhlova
, V.
, and Blanc-Benon
, P.
(2011b
). “Random focusing of nonlinear acoustic N-waves in fully developed turbulence: Laboratory scale experiment
,” J. Acoust. Soc. Am.
130
, 3595
–3607
.3.
Aver'yanov
, M.
, Khokhlova
, V.
, Sapozhnikov
, O.
, Blanc-Benon
, P.
, and Cleveland
, R.
(2006
). “Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media
,” Acoust. Phys.
52
, 623
–632
.4.
Blanc-Benon
, P.
, Lipkens
, B.
, Dallois
, L.
, Hamilton
, M. F.
, and Blackstock
, D. T.
(2002
). “Propagation of finite amplitude sound through turbulence: Modeling with geometrical acoustics and the parabolic approximation
,” J. Acoust. Soc. Am.
111
, 487
–498
.5.
Bradley
, K.
, Hobbs
, C.
, Wilmer
, C.
, Sparrow
, V.
, Stout
, T.
, Morgenstern
, J.
, Cowart
, R.
, Collmar
, M.
, Underwood
, K.
, Maglieri
, D.
, Shen
, H.
, and Blanc-Benon
, P.
(2020
). “Sonic booms in atmospheric turbulence (SonicBAT): The influence of turbulence on shaped sonic booms
,” NASA Contractor Report 20200002482 (NASA Langley Research Center
, Hampden, VA
).6.
Chevret
, P.
, Blanc‐Benon
, P.
, and Juvé
, D.
(1996
). “A numerical model for sound propagation through a turbulent atmosphere near the ground
,” J. Acoust. Soc. Am.
100
, 3587
–3599
.7.
Cleveland
, R. O.
, Hamilton
, M. F.
, and Blackstock
, D. T.
(1996
). “Time‐domain modeling of finite‐amplitude sound in relaxing fluids
,” J. Acoust. Soc. Am.
99
, 3312
–3318
.8.
Haering
, E.
, Cliatt
, L.
, Bunce
, T.
, Gabrielson
, T.
, Sparrow
, V.
, and Locey
, L.
(2008
). “Initial results from the variable intensity sonic boom propagation database
,” in Proceedings of AIAA 2008-3034, 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference)
, May 5–7, Vancouver, Canada.9.
Hamilton
, M. F.
, and Blackstock
, D. T.
(1998
). Nonlinear Acoustics
(Academic
, San Diego
).10.
Hammerton
, P.
(2001
). “Effect of molecular relaxation on the propagation of sonic booms through a stratified atmosphere
,” Wave Motion
33
, 359
–377
.11.
Hobbs
, C.
, and Page
, J.
(2011
). “PCBoom model prediction comparisons with flight test measurement data
,” in Proceedings of AIAA 2011-1277, 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
, January 4–7, Orlando, FL.12.
Kanamori
, M.
, Takahashi
, T.
, Naka
, Y.
, Makino
, Y.
, Takahashi
, H.
, and Ishikawa
, H.
(2017
). “Numerical evaluation of effect of atmospheric turbulence on sonic boom observed in D-SEND#2 flight test
,” in Proceedings of AIAA 2017-0278, 55th AIAA Aerospace Sciences Meeting
, January 9–13, Grapevine, TX.13.
Leatherwood
, J. D.
, Sullivan
, B. M.
, Shepherd
, K. P.
, McCurdy
, D. A.
, and Brown
, S. A.
(2002
). “Summary of recent NASA studies of human response to sonic booms
,” J. Acoust. Soc. Am.
111
, 586
–598
.14.
Lee
, Y.-S.
(1993
). “Numerical solution of the KZK equation for pulsed finite amplitude sound beams in thermoviscous fluids
,” Ph.D. dissertation, University of Texas
, Austin, TX
.15.
Lee
, Y.-S.
, and Hamilton
, M. F.
(1995
). “Time‐domain modeling of pulsed finite‐amplitude sound beams
,” J. Acoust. Soc. Am.
97
, 906
–917
.16.
Lipkens
, B.
, and Blackstock
, D. T.
(1998
). “Model experiment to study sonic boom propagation through turbulence. Part I: General results
,” J. Acoust. Soc. Am.
103
, 148
–158
.17.
Locey
, L. L.
, and Sparrow
, V. W.
(2007
). “Modeling atmospheric turbulence as a filter for sonic boom propagation
,” Noise Control Eng. J.
55
, 495
–503
.18.
Luquet
, D.
(2016
). “3D simulation of acoustical shock waves propagation through a turbulent atmosphere. Application to sonic boom
,” Ph.D. dissertation, Université Pierre et Marie Curie-Paris VI
, Paris
.19.
Maglieri
, D. J.
, Bobbitt
, P. J.
, Plotkin
, K. J.
, Shepherd
, K. P.
, Coen
, P. G.
, and Richwine
, D. M.
(2014
). “Sonic boom: Six decades of research
,” NASA/SP-2014-622 (NASA Langley Research Center
, Hampden, VA
).20.
Ostashev
, V. E.
, and Wilson
, D. K.
(2015
). Acoustics in Moving Inhomogeneous Media
(CRC
, Boca Raton, FL
).21.
Salze
, É.
, Yuldashev
, P.
, Ollivier
, S.
, Khokhlova
, V.
, and Blanc-Benon
, P.
(2014
). “Laboratory-scale experiment to study nonlinear N-wave distortion by thermal turbulence
,” J. Acoust. Soc. Am.
136
, 556
–566
.22.
Shepherd
, K. P.
, and Sullivan
, B. M.
(1991
). “A loudness calculation procedure applied to shaped sonic booms
,” NASA Technical Paper 3134 (NASA Langley Research Center
, Hampden, VA
).23.
Stevens
, S.
(1972
). “Perceived level of noise by Mark VII and decibels (E)
,” J. Acoust. Soc. Am.
51
, 575
–601
.24.
Stout
, T. A.
(2018
). “Simulation of N-wave and shaped supersonic signature turbulent variations
,” Ph.D. dissertation (The Pennsylvania State University
, State College, PA
).25.
Stout
, T. A.
, and Sparrow
, V. W.
(2018a
). “Nonlinear propagation of shaped supersonic signatures through turbulence
,” Proc. Mtgs. Acoust.
34
, 045011
.26.
Stout
, T. A.
, and Sparrow
, V. W.
(2018b
). “Time-domain spline interpolation in a simulation of N-wave propagation through turbulence
,” J. Acoust. Soc. Am.
144
, EL229
–EL235
.27.
Stout
, T. A.
, Sparrow
, V. W.
, and Blanc-Benon
, P.
(2021
). “Evaluation of numerical predictions of sonic boom level variability due to atmospheric turbulence
,” J. Acoust. Soc. Am.
149
, 3250
–3260
.28.
Takahashi
, H.
, Kanamori
, M.
, Naka
, Y.
, and Makino
, Y.
(2017
). “Characteristic scales of atmospheric turbulence responsible for sonic boom propagation
,” in Proceedings of AIAA 2017-0279, 55th AIAA Aerospace Sciences Meeting
, January 9–13, Grapevine, TX.29.
Wilson
, D. K.
(2000
). “A turbulence spectral model for sound propagation in the atmosphere that incorporates shear and buoyancy forcings
,” J. Acoust. Soc. Am.
108
, 2021
–2038
.30.
Wintzer
, M.
, and Ordaz
, I.
(2015
). “Under-track CFD-based shape optimization for a low-boom demonstrator concept
,” in Proceedings of the 33rd AIAA Applied Aerodynamics Conference
, June 22–26, Dallas, TX, p. 2260
.31.
Yuldashev
, P. V.
, Ollivier
, S.
, Karzova
, M. M.
, Khokhlova
, V. A.
, and Blanc-Benon
, P.
(2017
). “Statistics of peak overpressure and shock steepness for linear and nonlinear N-wave propagation in a kinematic turbulence
,” J. Acoust. Soc. Am.
142
, 3402
–3415
.© 2022 Acoustical Society of America.
2022
Acoustical Society of America
You do not currently have access to this content.
