Skip to main content
×
×
Home

A numerical study of a variable-density low-speed turbulent mixing layer

  • Antonio Almagro (a1), Manuel García-Villalba (a1) and Oscar Flores (a1)
Abstract

Direct numerical simulations of a temporally developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier–Stokes equations in the low-Mach-number approximation are solved using a novel algorithm based on an extended version of the velocity–vorticity formulation used by Kim et al. (J. Fluid Mech., vol 177, 1987, 133–166) for incompressible flows. Four cases with density ratios $s=1,2,4$ and 8 are considered. The simulations are run with a Prandtl number of 0.7, and achieve a $Re_{\unicode[STIX]{x1D706}}$ up to 150 during the self-similar evolution of the mixing layer. It is found that the growth rate of the mixing layer decreases with increasing density ratio, in agreement with theoretical models of this phenomenon. Comparison with high-speed data shows that the reduction of the growth rates with increasing density ratio has a weak dependence with the Mach number. In addition, the shifting of the mixing layer to the low-density stream has been characterized by analysing one-point statistics within the self-similar interval. This shifting has been quantified, and related to the growth rate of the mixing layer under the assumption that the shape of the mean velocity and density profiles do not change with the density ratio. This leads to a predictive model for the reduction of the growth rate of the momentum thickness, which agrees reasonably well with the available data. Finally, the effect of the density ratio on the turbulent structure has been analysed using flow visualizations and spectra. It is found that with increasing density ratio the longest scales in the high-density side are gradually inhibited. A gradual reduction of the energy in small scales with increasing density ratio is also observed.

Copyright
Corresponding author
Email address for correspondence: aalmagro@ing.uc3m.es
References
Hide All
Ashurst, W. T. & Kerstein, A. R. 2005 One-dimensional turbulence: variable-density formulation and application to mixing layers. Phys. Fluids 17, 025107.
Bell, J. H. & Mehta, R. D. 1990 Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28 (12), 20342042.
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21 (6), 926927.
Bretonnet, L., Cazalbou, J.-B., Chassaing, P. & Braza, M. 2007 Deflection, drift, and advective growth in variable-density, laminar mixing layers. Phys. Fluids 19 (10), 103601.
Brown, G. L. 1974 The entrainment and large structure in turbulent mixing layers. In Proceedings of the 5th Australasian Conference on Hydraulics and Fluid Mechanics, pp. 352359.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775816.
Carlier, J. & Sodjavi, K. 2016 Turbulent mixing and entrainment in a stratified horizontal plane shear layer: joint velocity-temperature analysis of experimental data. J. Fluid Mech. 806, 542579.
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarkar, S. 2002 Variable Density Fluid Turbulence. Springer.
Clemens, N. T. & Mungal, M. G. 1992 Two-and three-dimensional effects in the supersonic mixing layer. AIAA J. 30 (4), 973981.
Cook, A. W. & Riley, J. J. 1996 Direct numerical simulation of a turbulent reactive plume on a parallel computer. J. Comput. Phys. 129 (2), 263283.
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24 (11), 17911796.
Dimotakis, P. E. 1991 Turbulent free shear layer mixing and combustion. High Speed Flight Propulsion Systems 137, 265340.
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37 (1), 329356.
Driscoll, T. A, Bornemann, F. & Trefethen, L. N 2008 The chebop system for automatic solution of differential equations. BIT Num. Math. 48 (4), 701723.
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.
Fontane, J. & Joly, L. 2008 The stability of the variable-density Kelvin–Helmholtz billow. J. Fluid Mech. 612, 237260.
Gatski, T. B. & Bonnet, J.-P. 2013 Compressibility, Turbulence and High Speed Flow. Academic.
Hall, J. L., Dimotakis, P. E. & Rosemann, H. 1993 Experiments in nonreacting compressible shear layers. AIAA J. 31 (12), 22472254.
Higuera, F. J. & Moser, R. D. 1994 Effect of chemical heat release in a temporally evolving mixing layer. CTR Report 1940.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Jahanbakhshi, R. & Madnia, C. K. 2016 Entrainment in a compressible turbulent shear layer. J. Fluid Mech. 797, 564603.
Jang, Y. & de Bruyn Kops, S. M. 2007 Pseudo-spectral numerical simulation of miscible fluids with a high density ratio. Comput. Fluids 36 (2), 238247.
Kaneda, Y. & Ishihara, T. 2006 High-resolution direct numerical simulation of turbulence. J. Turbul. 7, N20.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Knio, O. M. & Ghoniem, A. F. 1992 The three-dimensional structure of periodic vorticity layers under non-symmetric conditions. J. Fluid Mech. 243, 353392.
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561583.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 1642.
Lele, S. K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26 (1), 211254.
Mahle, I., Foysi, H., Sarkar, S. & Friedrich, R. 2007 On the turbulence structure in inert and reacting compressible mixing layers. J. Fluid Mech. 593, 171180.
McMullan, W., Coats, C. & Gao, S. 2011 Analysis of the variable density mixing layer using large eddy simulation. In 41st AIAA Fluid Dynamics Conference and Exhibit, pp. 20113424. AIAA.
McMurtry, P. A., Jou, W.-H., Riley, J. & Metcalfe, R. W. 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24 (6), 962970.
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30 (1), 539578.
Nicoud, F. 2000 Conservative high-order finite-difference schemes for low-Mach number flows. J. Comput. Phys. 158 (1), 7197.
O’Brien, J., Urzay, J., Ihme, M., Moin, P. & Saghafian, A. 2014 Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers. J. Fluid Mech. 743, 554584.
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329371.
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453477.
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.
Pickett, L. M. & Ghandhi, J. B. 2001 Passive scalar measurements in a planar mixing layer by PLIF of acetone. Exp. Fluids 31 (3), 309318.
Ramshaw, J. D. 2000 Simple model for mixing at accelerated fluid interfaces with shear and compression. Phys. Rev. E 61, 53395344.
Reinaud, J., Joly, L. & Chassaing, P. 2000 The baroclinic secondary instability of the two-dimensional shear layer. Phys. Fluids 12 (10), 24892505.
Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6 (2), 903923.
Sekimoto, A., Dong, S. & Jiménez, J. 2016 Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows. Phys. Fluids 28 (3), 035101.
da Silva, C. B. & Pereira, J. C. F 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20 (5), 055101.
Soteriou, M. C. & Ghoniem, A. F. 1995 Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys. Fluids 7 (8), 20362051.
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297324.
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.
Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235258.
Wang, P., Fröhlich, J., Michelassi, V. & Rodi, W. 2008 Large-eddy simulation of variable-density turbulent axisymmetric jets. Intl J. Heat Fluid Flow 29 (3), 654664.
Williams, F. A. 1985 Combustion Theory. Westview Press.
Wyngaard, J. C. 2010 Turbulence in the Atmosphere. Cambridge University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed