Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-23T12:33:24.997Z Has data issue: false hasContentIssue false

Organised large structure in the post-transition mixing layer. Part 2. Large-eddy simulation

Published online by Cambridge University Press:  03 December 2014

Abstract

Three-dimensional large-eddy simulations of two-stream mixing layers developing spatially from laminar boundary layers are presented, replicating wind-tunnel experiments carried out in Part 1 of this study. These simulations have been continued through the mixing transition and into the fully turbulent self-similar flow beyond. In agreement with the experiments, the simulations show that the familiar mechanism of growth by vortex amalgamation is replaced at the mixing transition by a previously unrecognised mechanism in which the spanwise-coherent large structures individually undergo continuous linear growth. In the post-transition flow it is this continuous linear growth of the individual structures that produces the self-similar growth of the mixing-layer thickness, the large-structure interactions occurring as a consequence of the growth, not its cause. New information is also presented on the topography of the organised post-transition flow and on its cyclical evolution through the lifetimes of the individual large structures. The dynamic and kinematic implications of these findings are discussed and shown to define quantitatively the growth rate of the homogeneous post-transition mixing layer in its organised state.

Type
Papers
Copyright
© 2014 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

Attili, A. & Bisetti, F. 2012 Statistics and scaling of turbulence in a spatially developing mixing layer at $\mathit{Re}_{{\it\lambda}}=250$ . Phys. Fluids 24, 035109.Google Scholar
Balaras, E., Piomelli, U. & Wallace, J. M. 2001 Self-similar states in turbulent mixing layers. J. Fluid Mech. 446, 124.Google Scholar
Bell, J. H. & Mehta, R. D. 1992 Measurements of the streamwise vortical structures in a plane mixing layer. J. Fluid Mech. 239, 213248.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structures in plane mixing layers. J. Fluid Mech. 170, 499525.Google Scholar
Biancofiore, L. 2014 Crossover between two- and three-dimensional turbulence in spatial mixing layers. J. Fluid Mech. 745, 164179.CrossRefGoogle Scholar
Boersma, B. J., Brethouwer, G. & Nieuwstadt, F. T. M. 1998 A numerical investigation of the effect of the inflow conditions on the self-similar region of a round jet. Phys. Fluids A 10, 899909.Google Scholar
Bogey, C. & Bailly, C. 2010 Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets. J. Fluid Mech. 663, 507538.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 124.Google Scholar
Brown, G. L. 1974 The entrainment and large structure in turbulent mixing layers. In Proceedings of the Fifth Australasian Conference on Hydraulics and Fluid Dynamics, University of Canterbury, Christchurch, New Zealand, pp. 352359.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 2012 Turbulent shear layers and wakes. J. Turbul. 13 (51), 132.CrossRefGoogle Scholar
Buell, J. C. & Mansour, N. N. 1989 Asymmetric effects in three-dimensional spatially-developing mixing layers. In Proceedings of the Seventh Symposium on Turbulent Shear Flows (ed. Durst, F., Friedrich, R., Launder, B. E., Schmidt, F. W., Schumann, U. & Whitelaw, J. H.), 9.2.1–9.2.6. Springer.Google Scholar
Comte, P., Lesieur, M. & Lamballais, E. 1992 Large- and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer. Phys. Fluids A 4, 27612778.Google Scholar
Comte, P., Silvestrini, J. H. & Bégou, P. 1998 Streamwise vortices in large-eddy simulations of mixing layers. Eur. J. Mech. (B/Fluids) 17, 615637.Google Scholar
Damms, S. M. & Küchemann, D. 1974 On a vortex-sheet model for the mixing between two parallel streams. I. Description of the model and experimental evidence. Proc. R. Soc. Lond. A 339, 451461.Google Scholar
De Bruin, I. C. C.2001 Direct and large eddy simulation of the spatial turbulent mixing layer. PhD thesis, University of Twente.Google Scholar
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 17911796.Google Scholar
D’Ovidio, A. & Coats, C. M. 2013 Organised large structure in the post-transition mixing layer. Part 1. Experimental evidence. J. Fluid Mech. 737, 466498.CrossRefGoogle Scholar
Ferrero, P., Kartha, A., Subbareddy, P. K., Candler, G. V. & Dimotakis, P. E.2013 LES of a high-Reynolds number, chemically reacting mixing layer. AIAA Paper 2013-3185.Google Scholar
Gao, S. & Voke, P. R. 1995 Large eddy simulation of turbulent heat transfer in enclosed impinging jets. Intl J. Heat Fluid Flow 16, 349356.Google Scholar
Glansdorff, P. & Prigogine, I. 1964 On a general evolution criterion in macroscopic physics. Physica 30, 351374.Google Scholar
Goldshtik, M. & Hussain, F. 1995 Structural approach to the modelling of a turbulent mixing layer. Phys. Rev. E 52, 25592568.Google Scholar
Hernan, M. A. & Jimenez, J. 1982 Computer analysis of a high-speed film of a plane turbulent mixing layer. J. Fluid Mech. 119, 323345.Google Scholar
Huang, L.-S. & Ho, C.-M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475500.Google Scholar
Jaberi, F. A., Colucci, P. J., James, S., Givi, P. & Pope, S. B. 1999 Filtered mass density function for large-eddy simulation of turbulent reacting flows. J. Fluid Mech. 401, 85121.Google Scholar
Jimenez, J. 1980 On the visual growth of a turbulent mixing layer. J. Fluid Mech. 96, 447460.Google Scholar
Jimenez, J., Cogollos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125143.Google Scholar
Jimenez, J., Linan, A., Rogers, M. M. & Higuera, F. J. 1997 A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows. J. Fluid Mech. 349, 149171.Google Scholar
Ko, S.-H. & Lessen, M. 1969 Low Reynolds number instability of an incompressible half-jet. Phys. Fluids 12, 404407.Google Scholar
Konrad, J. H.1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. PhD thesis, California Institute of Technology (Issued as Project SQUID Tech. Report CIT-8-PU).Google Scholar
Koochesfahani, M. M. & Dimotakis, P. E. 1986 Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170, 83112.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.Google Scholar
Lesieur, M. & Metais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 4582.Google Scholar
Li, N., Balaras, E. & Piomelli, U. 2000 Inflow conditions for large-eddy simulations of mixing layers. Phys. Fluids A 12, 935938.Google Scholar
Li, N., Balaras, E. & Wallace, J. M. 2010 Passive scalar transport in a turbulent mixing layer. Flow Turbul. Combust. 85, 124.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139178.Google Scholar
Masutani, S. M. & Bowman, C. T. 1986 The structure of a chemically reacting plane mixing layer. J. Fluid Mech. 172, 93126.Google Scholar
McMullan, W. A.2005 Numerical experiments on spatially developing mixing layers using large eddy simulation. PhD thesis, University of Leicester.Google Scholar
McMullan, W. A., Gao, S. & Coats, C. M. 2007 A comparative study of inflow conditions for two- and three-dimensional spatially developing mixing layers using large eddy simulation. Intl J. Numer. Meth. Fluids 55, 589610.Google Scholar
McMullan, W. A., Gao, S. & Coats, C. M. 2009 The effect of inflow conditions on the transition to turbulence in large eddy simulations of spatially developing mixing layers. Intl J. Heat Fluid Flow 30, 10541066.Google Scholar
McMullan, W. A., Gao, S. & Coats, C. M.2010 Investigation of coherent structures in turbulent mixing layers using large eddy simulation. AIAA Paper 2010-1291.Google Scholar
Metais, O. & Lesieur, M. 1992 Spectral large eddy simulations of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157194.Google Scholar
Metcalfe, R. W., Orzag, S. A., Brachet, M. E., Menon, S. & Riley, J. J. 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207243.Google Scholar
Michalke, A. 1965 Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech. 22, 371383.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of organized vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465473.Google Scholar
Moser, R. D. & Rogers, M. M. 1991 Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3, 11281134.Google Scholar
Moser, R. D. & Rogers, M. M. 1993 The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247, 275320.Google Scholar
Mungal, M. G. & Dimotakis, P. E. 1984 Mixing and combustion with low heat release in a turbulent mixing layer. J. Fluid Mech. 148, 349382.Google Scholar
Nicoud, F. & Ducros, D. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183200.Google Scholar
Pedley, T. J.1990 An experimental investigation into coherent structures in free shear layer flows. PhD thesis, University of Leeds.Google Scholar
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 17661771.Google Scholar
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup. J. Fluid Mech. 243, 183226.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99164.Google Scholar
Spencer, B. W. & Jones, B. G.1971 Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. AIAA Paper 71-613.Google Scholar
Tenaud, C., Pellerin, A., Dulieu, L. & Ta Phuoc, L. 2005 Large eddy simulations of a spatially developing incompressible 3D mixing layer using the $v{-}{\it\omega}$ formulation. Comput. Fluids 34, 6796.Google Scholar
Vreman, B., Guerts, B. & Kuerten, H. 1997 Large eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357390.Google Scholar
Wang, J. K. & Milane, R. E. 2006 Large eddy simulation (2D) of spatially developing mixing layer using vortex-in-cell for flow field and filtered density function for scalar field. Intl J. Numer. Meth. Fluids 50, 2761.Google Scholar
Wang, Y., Tanahashi, M. & Miyauchi, T. 2007 Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer. Intl J. Heat Fluid Flow 28, 12801290.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.Google Scholar
Yang, W. B., Zhang, H. Q., Chan, C. K., Lau, K. S. & Lin, W. Y. 2004a Investigation of plane mixing layer using large eddy simulation. Comput. Mech. 34, 423429.Google Scholar
Yang, W. B., Zhang, H. Q., Chan, C. K. & Lin, W. Y. 2004b Large eddy simulation of mixing layer. J. Comput. Appl. Math. 163, 311318.Google Scholar
Zhou, X. Y. & Pereira, J. C. F. 2000 Large eddy simulation (2D) of a reacting plane mixing layer using filtered density function closure. Flow Turbul. Combust. 64, 279300.Google Scholar