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Linear Interaction Approximation for Shock/Perturbation Interaction

  • Pierre Sagaut
  • Claude Cambon
Chapter

Abstract

This chapter is devoted to the Linear Interaction Approximation for the interaction between a shock wave and turbulent disturbances, with extension to the case of a rarefaction wave. Coupling with the Kovasznay decomposition into physical modes is discussed, with extension to mixture of perfect gas, detonation waves. The derivation of analytical solutions via a Laplace-tranform-based approach is also discussed.

References

  1. Fabre, D., Jacquin, L., Sesterhenn, J.: Linear interaction of a cylindrical entropy spot with a shock wave. Phys. Fluids 13(8), 2403–2422 (2001)ADSCrossRefzbMATHGoogle Scholar
  2. Griffond, J.: Linear interaction analysis applied to a mixture of two perfect gases. Phys. Fluids 24, 115108 (2005)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. Griffond, J., Soulard, O., Souffland, D.: A turbulent mixing Reynolds stress model fitted to match linear interaction analysis prediction. Phys. Scr. 142, 014059 (2010)CrossRefGoogle Scholar
  4. Griffond, J., Soulard, O.: Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves. Phys. Fluids 17, 086101 (2012)CrossRefGoogle Scholar
  5. Huete, C., Jin, T., Martinez-Ruiz, D., Williams, F.A.: Reacting Shock Wave Effects on Isotropic Turbulent Flows. Linear interaction analysis and direct numerical simulations. Private Communication (2016)Google Scholar
  6. Huete, C., Sanchez, A.L., Velikovich, A.L.: Theory of interactions of thin strong detonations with turbulent gases. Phys. Fluids 25, 076105 (2013)ADSCrossRefGoogle Scholar
  7. Huete, C., Sanchez, A.L., Velikovich, A.L.: Linear theory for the interaction of small-scale turbulence with overdriven detonations. Phys. Fluids 26, 116101 (2014)ADSCrossRefGoogle Scholar
  8. Huete, C., Wouchuk, J.G., Canaud, B., Velikovich, A.L.: Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities. J. Fluid Mech. 700, 214–245 (2012a)ADSCrossRefzbMATHGoogle Scholar
  9. Huete, C., Wouchuk, J.G., Velikovich, A.L.: Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field. Phys. Rev. E 85, 026312 (2012b)ADSCrossRefGoogle Scholar
  10. Jackson, T.L., Hussaini, M.Y., Ribner, H.S.: Interaction of turbulence with a detonation wave. Phys. Fluids A 5(8), 745–749 (1993)ADSCrossRefzbMATHGoogle Scholar
  11. Lasseigne, D.G., Jackson, T.L., Hussaini, M.Y.: Nonlinear interaction of a detonation/vorticity wave. Phys. Fluids A 3, 1972–1979 (1991)ADSCrossRefzbMATHGoogle Scholar
  12. Lee, S., Lele, S.K., Moin, P.: Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562 (1993)ADSCrossRefGoogle Scholar
  13. Mahesh, K., Lele, S.K., Moin, P.: The interaction of an isotropic field of acoustic waves with a shock wave. J. Fluid Mech. 300, 383–407 (1995)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. Mahesh, K., Moin, P., Lele, S.K.: The interaction of a shock wave with a turbulent shear flow. Report No. TF-69, Department of Mecanical Engineering, Stanford University (1996)Google Scholar
  15. Miller, G.H., Ahrens, T.J.: Shock wave viscosity measurement. Rev. Modern Phys. 63, 919–948 (1991)ADSCrossRefGoogle Scholar
  16. Moore, F.K.: Unsteady oblique interaction of a shock wave with a plane disturbance. Technical report 2879, NACA (1954)Google Scholar
  17. Ribner, H.S.: Convection of a pattern of vorticity through a shock wave. Technical report 1164, NACA (1953)Google Scholar
  18. Ryu, J., Livescu, D.: Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756(R1), 1–13 (2014)ADSCrossRefGoogle Scholar
  19. Wouchuk, J.G., Huete, C., Velikovich, A.L.: Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 79, 066315 (2009)ADSMathSciNetCrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

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