Abstract
Low speed shear-driven mixing layers involving fluid streams of different densities due to temperature or compositional variations are described by remarkably similar equations with some differences in the formulations of the molecular transport terms. These differences are related to specifics of the heat conduction and mass diffusion operators, as well as viscosity dependence on mixture molar mass and temperature in the low Mach number limit. Direct numerical simulations are performed in incompressible/low-speed limits to study the differences and similarities in mixing behavior associated with these configurations. The results demonstrate both subtle and significant changes in the mixing behavior for variable composition versus variable temperature mixing. Higher-order statistics related to density field reveal greater differences than are apparent from mean profiles; these differences can be extremely important when the physics is sensitive to mixing, such as in combustion problems. Therefore, conclusions regarding the mixing dynamics drawn from variable temperature mixing are not necessarily applicable to multi-species mixing.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B.W. Spencer, B.G. Jones, Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. AIAA Paper, pp. 71–613 (1971)
J.H. Bell, R.D. Mehta, Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28, 2034–2042 (1990)
R.B. Loucks, J.M. Wallace, Velocity and velocity gradient based properties of a turbulent plane mixing layer. J. Fluid Mech. 699, 280–319 (2012)
M.M. Rogers, R.D. Moser, Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6, 903–923 (1994)
E. Balaras, U. Piomelli, J.M. Wallace, Self-similar states in turbulent mixing layers. J. Fluid Mech. 446, 1–24 (2001)
M. Tanahashi, S. Iwase, T. Miyauchi, Appearance and alignment with strain rate of coherent fine scale eddies in turbulent mixing layer. J. Turbul. 2(6), 1–17 (2001)
Y. Wang, M. Tanahashi, T. Miyauchi, Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer. Int. J. Heat Fluid Flow 28, 1280–1290 (2007)
A. Attili, F. Bisetti, Statistics and scaling of turbulence in a spatially developing mixing layer at \({\rm Re}_{\lambda } =250\). Phys. Fluids 24, 035109 (2012)
G.L. Brown, A. Roshko, On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816 (1974)
A.W. Vreman, N.D. Sandham, K.H. Luo, Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258 (1996)
S. Sarkar, On density and pressure fluctuations in uniformly sheared compressible flow, in Proceedings IUTAM Symposium on Variable Density Low-Speed Flows, Marseille, ed. by L. Fulachier, J.L. Lumley, F. Anselmet (Kluwer Academic Publishers, 1996)
C. Pantano, S. Sarkar, A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371 (2002)
D. Livescu, C.K. Madnia, Small scale structure of homogeneous turbulent shear flow. Phys. Fluids 16, 2864–2876 (2004)
R. Jahanbakhshi, N.S. Vaghefi, C.K. Madnia, Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer. Phys. Fluids 27, 105105 (2015)
A. Almagro, M. GarcÃa-Villalba, O. Flores, A numerical study of a variable-density low-speed turbulent mixing layer. J. Fluid Mech. 830, 569–601 (2017)
J.D. Schwarzkopf, D. Livescu, J.R. Baltzer, R.A. Gore, J.R. Ristorcelli, A two-length scale turbulence model for single-phase multi-fluid mixing. Flow Turbul. Combust. 96, 1–43 (2016)
L. Joly, The structure of some variable density shear flows, in Variable Density Fluid Turbulence, ed. by P. Chassaing, R.A. Antonia, F. Anselmet, L. Joly, S. Sarkar, Chap. 8, pp. 201–234 (Springer, 2002)
W.T. Ashurst, A.R. Kerstein, One-dimensional turbulence: Variable-density formulation and application to mixing layers. Phys. Fluids 17, 025107 (2005)
B.J. Olson, J. Larsson, S.K. Lele, A.W. Cook, Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability. Phys. Fluids 23, 114107 (2011)
I. Gat, G. Matheou, D. Chung, P.E. Dimotakis, Incompressible variable-density turbulence in an external acceleration field. J. Fluid Mech. 827, 506–535 (2017)
C. Pantano, S. Sarkar, F.A. Williams, Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech. 481, 291–328 (2003)
M.S. Day, J.B. Bell, Numerical simulation of laminar reacting flow with complex chemistry. Comb. Theor. Mod. 4, 535–556 (2000)
A.S. Almgren, J.B. Bell, C.A. Rendleman, M. Zingale, Low Mach number modeling of Type Ia supernovae. I. Hydrodynamics. Astrophys. J. 637, 922–936 (2006)
A. Majda, J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Tech. 42, 185–205 (1985)
D. Livescu, Turbulence with large thermal and compositional density variations. Annu. Rev. Fluid Mech.52, 309–341 (2020)
D.R. Chenoweth, S. Paolucci, Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169, 173–210 (1986)
F. Williams, Combustion Theory (Perseus Books, Cambridge, 1985)
P.A. McMurtry, W.-H. Jou, J. Riley, R.W. Metcalfe, Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24, 962–970 (1986)
S. Paolucci, On the filtering of sound from the Navier-Stokes equations. Technical Report SAND82-8257 (Sandia National Laboratories, 1982)
A.W. Cook, J.J. Riley, Direct numerical simulation of a turbulent reactive plume on a parallel computer. J. Comput. Phys. 129, 263–283 (1996)
G. Ahlers, E. Brown, F.F. Araujo, D. Funfschilling, S. Grossmann, D. Lohse, Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection. J. Fluid Mech. 569, 409–445 (2006)
F.J. Higuera, R.D. Moser, Effect of chemical heat release in a temporally evolving mixing layer. Technical Report, 19–40, CTR (1994)
D. Livescu, Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh-Taylor instability. Phil. Trans. R. Soc. A 371, 20120185 (2013)
D.D. Joseph, Fluid dynamics of two miscible liquids with diffusion and gradient stresses. Eur. J. Mech. B 6, 565–596 (1990)
A.W. Cook, P.E. Dimotakis, Transition stages of Rayleigh-Taylor instability between miscible fluids. J. Fluid Mech. 443, 69–99 (2001)
D.L. Sandoval, The dynamics of variable density turbulence. Ph.D. thesis, University of Washington, 1995. LANL Rep. LA-13037-T
D. Livescu, J.R. Ristorcelli, Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591, 43–71 (2007)
W.H. Cabot, A.W. Cook, Reynolds number effects on Rayleigh-Taylor instability with possible implications of Type-Ia supernovae. Nat. Phys. 2, 562–568 (2006)
T. Wei, D. Livescu, Late-time quadratic growth in single-mode Rayleigh-Taylor instability. Phys. Rev. E 86, 046405 (2012)
D. Livescu, J.R. Ristorcelli, M.R. Petersen, R.A. Gore, New phenomena in variable-density Rayleigh-Taylor turbulence. Phys. Scr. T142, 014015 (2010)
E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems (Cambridge University Press, Cambridge, UK, 2009)
Y. Tian, F.A. Jaberi, Z. Li, D. Livescu, Numerical study of variable density turbulence interaction with a normal shock wave. J. Fluid Mech. 829, 551–588 (2017)
R.W. Bilger, Some aspects of scalar dissipation. Flow Turbul. Combust. 72, 93–114 (2004)
N. Taguelmimt, L. Danaila, A. Hadjadj, Effect of viscosity gradients on mean velocity profile in temporal mixing layer. J. Turbul. 17, 491–517 (2016)
Acknowledgements
This work has been authored by employees of Triad National Security, LLC which operates Los Alamos National Laboratory under Contract No. 89233218CNA000001 with the U.S. Department of Energy/National Nuclear Security Administration.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Baltzer, J.R., Livescu, D. (2020). Low-Speed Turbulent Shear-Driven Mixing Layers with Large Thermal and Compositional Density Variations. In: Livescu, D., Nouri, A., Battaglia, F., Givi, P. (eds) Modeling and Simulation of Turbulent Mixing and Reaction. Heat and Mass Transfer. Springer, Singapore. https://doi.org/10.1007/978-981-15-2643-5_1
Download citation
DOI: https://doi.org/10.1007/978-981-15-2643-5_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2642-8
Online ISBN: 978-981-15-2643-5
eBook Packages: EngineeringEngineering (R0)