Flow, Turbulence and Combustion

, Volume 96, Issue 1, pp 163–181 | Cite as

Effects of Viscosity Variations in Temporal Mixing Layer

  • Noureddine Taguelmimt
  • Luminita DanailaEmail author
  • Abdellah Hadjadj


The objective of the present investigation is to assess the effects of viscosity variations in low-speed temporally-evolving turbulent mixing layer. The two streams are density-matched, but the slow fluid is R ν times more viscous than the rapid stream. Direct Numerical Simulations (DNS) are performed for several viscosity ratios, R ν = ν h i g h /ν l o w , varying between 1 and 9. The space-time evolution of Variable-Viscosity Flow (VVF) is compared with that of the Constant-Viscosity Flow (CVF), for which R ν = 1. The initial Reynolds number, based on the initial momentum thickness, δ 𝜃,0, is \(Re_{\delta _{\theta ,0}}=160\) for the considered cases. The study focuses on the first stages of the temporal evolution of the mixing-layer. It is shown that in VVF (with respect to CVF): (i) the velocity fluctuations occur earlier and are more enhanced for VVF. In particular, the kinetic energy peaks earlier and is up to three times larger for VVF than for CVF at the earliest stages of the flow. Over the first stages of the flow, the temporal growth rate of the fluctuations kinetic energy is exponential, in full agreement with linear stability theory. (ii) large-scale quantities, i.e. mean longitudinal velocity and momentum thickness, are affected by the viscosity variations, thus dispelling the myth that viscosity is a small-scale quantity that affects little the large scales. (iii) the transport equation for the fluctuations kinetic energy is derived and favourably compared with simulations data. The enhanced kinetic energy for VVF is mainly due to an increased production at the interface between the two fluids, in tight correlation with enlarged values of mean velocity gradient at the inflection point of the mean velocity profile.


Variable viscosity Temporal mixing layer Kinetic energy Energy dissipation rate DNS 


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  1. 1.
    Antkowiak, A., Brancher, P.: On vortex rings around vortices: an optimal mechanism. J. Fluid Mech. 578, 295–304 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Brown, G.L., Roshko, A.: On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816 (1974)CrossRefGoogle Scholar
  3. 3.
    Chaudhuri, A., Hadjadj, A., Chinnayya, A., Palerm, S.: Numerical study of compressible mixing layers using high-order WENO schemes. J. Sci. Comput. 47, 170–197 (2011)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Dimotakis, P.E.: On the convection velocity of turbulent structures in supersonic shear layers. AIAA J. 91, 1724 (1991)Google Scholar
  5. 5.
    Elliott, G., Samimy, M.: Compressibility effects in free shear layers. Phys. Fluids 2, 1231–1240 (1990)CrossRefGoogle Scholar
  6. 6.
    Govindarajan, R.: Effect of miscibility on the linear instability of two-fluid channel flow. Int. J. Multiphase Flow 30, 1177–1192 (2004)CrossRefzbMATHGoogle Scholar
  7. 7.
    Govindarajan, R., L’vov, V., Procaccia, I.: Retardation of the onset of turbulence by minor viscosity contrasts. Phys. Rev. Lett. 87, 174,501–1–174,501–4 (2001)CrossRefGoogle Scholar
  8. 8.
    Govindarajan, R., Sahu, K.C.: Instabilities in viscosity-stratified flow. Ann. Rev. Fluid Mech. 46, 331–353 (2014)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Harang, A., Thual, O., Brancher, P., Bonometti, T.: Kelvin-helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries. Environ. Fluid Mech. 14, 743–769 (2014)CrossRefGoogle Scholar
  10. 10.
    Hazel, P.: Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39–61 (1972)CrossRefzbMATHGoogle Scholar
  11. 11.
    Jonathan, B., Freund, S., Lele, S., Moin, P.: Compressibility effects in a turbulent annular mixing layer. part 1. turbulence and growth rate. J. Fluid Mech. 421, 229–267 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Klein, M., Sadiki, A.: Janicka: A digital filter based generation of in flow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186, 652–665 (2003)CrossRefzbMATHGoogle Scholar
  13. 13.
    Kolmogorov, A.N.: Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32(1), 16–18 (1941)zbMATHGoogle Scholar
  14. 14.
    Laizet, S., Lardeau, S., Lamballais, E.: Direct numerical simulation of a mixing layer downstream a thick splitter plate. Phys. Fluids 22, 015,104 (2010)CrossRefGoogle Scholar
  15. 15.
    Lu, G., Lele, S.: On the density ratio effect on the compressible mixing layer. Phys. Fluids 6, 1073 (1994)CrossRefGoogle Scholar
  16. 16.
    Masayuki, H., Michihisa, T., Leung, R.: Numerical simulation of sound generation in a mixing layer by the finite difference lattice boltzmann method. Computers and Mathematics with Applications 59, 2403–2410 (2010)CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Mehta, R.: Effect of velocity ratio on plane mixing layer development: Influence of the splitter plate wake. Exp. Fluids 10, 194–204 (1991)CrossRefGoogle Scholar
  18. 18.
    Pantano, C., Sarkar, S.: A study of compressible effects in the high -speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371 (2002)CrossRefzbMATHGoogle Scholar
  19. 19.
    Papamoschou, D., Lele, S.K.: Vortex-induced disturbance field in a compressible shear layer. Phys. Fluids 5, 1412 (1993)CrossRefGoogle Scholar
  20. 20.
    Pullin, D., O’Reilly, G.: Structure and stability of the compressible stuart vortex. J. Fluid Mech. 493, 231–254 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Reid, R., Prausnitz, J., Poling, B.: The properties of gases and liquids. McGraw-Hill, Inc., New York (1987)Google Scholar
  22. 22.
    Talbot, B., Danaila, L., Renou, B.: Variable-viscosity mixing in the very near field of a round jet. Phys. Scr. T155, 014,006 (2013)CrossRefGoogle Scholar
  23. 23.
    Yih, C.S.: Instability due to viscosity stratification. J. Fluid Mech. 27(2), 337–352 (1967)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Noureddine Taguelmimt
    • 1
  • Luminita Danaila
    • 1
    Email author
  • Abdellah Hadjadj
    • 1
  1. 1.CORIA-UMR 6614, Normandie University, CNRS-University & INSA of RouenSaint Etienne du RouvrayFrance

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