Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-10T11:21:53.074Z Has data issue: false hasContentIssue false
  • English
  • Français

The interaction of an isotropic field of acoustic waves with a shock wave

Published online by Cambridge University Press:  26 April 2006

Krishnan Mahesh ,
Sangsan Lee ,
Sanjiva K. Lele  and
Parviz Moin
Krishnan Mahesh
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Sangsan Lee
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Sanjiva K. Lele
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Parviz Moin
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Moore's (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail.

The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuations decreases across the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 300 , 10 October 1995 , pp. 383 - 407
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, M. C. 1949 On shock waves in inhomogeneous flow. J. Aero. Sci. 16, 685–690.Google Scholar
Burgers, J. M. 1946 On the transmissions of sound waves through a shock wave. Koninklijke Nederlandsche Akademie Van Wetenschappen, Proc. XLIX, 273–281.Google Scholar
Cambon, C., Coleman, G. N. & Mansour, N. N. 1993 Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number. J. Fluid Mech. 257, 641–665.Google Scholar
Carrier, G. F. 1949 On the stability of the supersonic flows past a wedge. Q. Appl. Maths 6, 367–378.Google Scholar
Chang, C. T. 1957 Interaction of a plane shock and oblique plane disturbances with special reference to entropy waves. J. Aero. Sci. 24, 675–682.Google Scholar
Chu, B. T. 1952 On weak interaction of strong shock and Mach waves generated downstream of a shock. J. Aero. Sci. 19, 433–446.Google Scholar
Crow, S. C. 1969 Distortion of sonic bangs by atmospheric turbulence. J. Fluid Mech. 37, 529–563.Google Scholar
Cuadra, E. 1968 Flow perturbations generated by a shock wave interacting with an entropy wave. AFOSR-UTIAS S
Hannappel, R. & Friedrich, R. 1994 DNS of a M=2 shock interacting with isotropic turbulence. In Proc. First ERCOFTAC Workshop on DNS and LES, Guildford, Surrey, UK.
Honkan, A. & Andreopoulous, J. 1992 Rapid compression of grid-generated turbulence by a moving shock wave. Phys. Fluids A 4, 2562–2572.Google Scholar
Jacquin, L., Blin, E. & Geffroy, P. 1991 Experiments on free turbulence/shock wave interaction. In Proc. Eighth Symp. on Turbulent Shear Flows, Munich (ed. F. Durst, R. Friedrich, B. E. Launder, F. W. Schmidt, U. Schumann & J. H. Whitelaw). Springer.
Jacquin, L., Cambon, C. & Blin, E. 1993 Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids A 5, 2539–2550.Google Scholar
Johnson, W. R. & Laporte, O. 1958 Interaction of cylindrical sound waves with a stationary shock wave. Phys. Fluids 1, 82–94.Google Scholar
Kantrowitz, A. 1947 The formation and stability of normal shock waves in channel flow. NACA TN 1225.
Keller, J. & Merzkirch, W. 1990 Interaction of a normal shock wave with a compressible turbulent flow. Exps. Fluids 8, 241–248.Google Scholar
Kerrebrock, J. L. 1956 The interaction of flow discontinuities with small disturbances in a compressible fluid. PhD thesis, California Institute of Technology.
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero. Sci. 20, 657–682.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1982 Fluid Mechanics. Course of Theoretical Physics, Vol. 6, pp. 332–333. Pergamon Press.
Lee, S., Lele, S. K. & Moin, P. 1993 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1994a Corrigendum to 251, 1993, 533–562. J. Fluid Mech. 264, 373–374.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1994b Interaction of isotropic turbulence with a strong shock wave. AIAA Paper 94–0311.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Ann. Rev. Fluid Mech. 26, 211–254.Google Scholar
Lighthill, M. J. 1949 The flow behind a stationary shock. Phil. Mag. (7) 40, 214–220.Google Scholar
Lowson, M. V. 1968 Pressure fluctuations resulting from shock interactions. J. Sound Vib. 7, 380–392.Google Scholar
Mahesh, K. 1995 The interaction of a shock wave with a turbulent shear flow. PhD thesis, Dept of Mechanical Engineering, Stanford University.
Mckenzie, J. F. & Westphal, K. O. 1968 Interaction of linear waves with oblique shock waves. Phys. Fluids 11, 2350–2362.Google Scholar
Meadows, K. R., Caughey, D. A. & Casper, J. 1993 Computing unsteady shock waves for aeroacoustic applications. AIAA Paper 93–4329.
Moore, F. K. 1954 Unsteady oblique interaction of a shock wave with a plane disturbance. NACA TN 2879.
Pierce, A. D. 1971 Statistical theory of atmospheric turbulence effects on sonic-boom rise times. J. Acoust. Soc. Am. 49, 906–924.Google Scholar
Pierce, A. D. 1981 Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill.
Pierce, A. D. 1992 Wave equations and computational models for sonic boom propagation through a turbulent atmosphere. NASA CP 3172.
Poinsot, T. J. & Lele, S. K. 1990 Boundary conditions for direct simulation of compressible viscous reacting flow. Center for Turbulence Research Manuscript 102. Stanford University/NASA Ames.
Ribner, H. S. 1953 Convection of a pattern of vorticity through a shock wave. NACA TN 2864.
Ribner, H. S. 1954 Shock-turbulence interaction and the generation of noise. NACA TN 3255.
Ribner, H. S. 1987 Spectra of noise and amplified turbulence emanating from shock-turbulence interaction AIAA J. 25, 436–442.Google Scholar
Rotman, D. 1991 Shock wave effects on a turbulent flow. Phys. Fluids A 3, 1792–1806.Google Scholar
Rusak, Z. & Cole, J. D. 1993 Interaction of the sonic boom with atmospheric turbulence. AIAA Paper 93–2943.
Wray, A. A. 1986 Very low storage time-advancement schemes. Internal Rep. NASA-Ames Research Center.
Zang, T. A., Hussaini, M. Y. & Bushnell, D. M. 1984 Numerical computations of turbulence amplification in shock-wave interactions. AIAA J. 22, 13–21.Google Scholar