Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T02:24:30.056Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of flow topology and dilatation on scalar mixing in compressible turbulence

Published online by Cambridge University Press:  18 March 2016

Mohammad Danish ,
Sawan Suman  and
Sharath S. Girimaji
Mohammad Danish*
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
Sawan Suman
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
Sharath S. Girimaji
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: mddanish.me@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The kinematics of passive scalar mixing and its relation to local flow topology and dilatation in compressible turbulence are examined using direct numerical simulations (DNS) of decaying isotropic turbulence. The main objective of this work is to characterize the dependence of various evolution mechanisms of scalar dissipation on local streamline topology and normalized dilatation. The DNS results indicate that the topology has a stronger influence on the nonlinear amplification mechanism than the dilatation level of a fluid element. In its appropriately normalized form, the amplification mechanism is found to be fairly independent of the Mach and Reynolds numbers. Non-focal topologies (the so called unstable-node/saddle/saddle and stable-node/saddle/saddle) are found to be associated with more intense mixing than the focal topologies at almost all dilatation levels. Alignment tendencies (jointly conditioned upon topology and dilatation) between the scalar-gradient vector and the strain-rate eigenvectors are shown to play a key role in shaping the observed behaviour in compressible turbulence. Finally, some modelling implications of these findings are discussed.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 633 - 655
Check for updates
Copyright
© 2016 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

Antonia, R. A. & Orlandi, P. 2003 Effect of Schmidt number on small-scale passive scalar turbulence. Appl. Mech. Rev. 56, 615–632.CrossRefGoogle Scholar
Ashurst, Wm. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343–2353.CrossRefGoogle Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.Google Scholar
Boratav, O. N. & Pelz, R. B. 1995 On the local topology evolution of a high-symmetry flow. Phys. Fluids 7, 1712–1731.CrossRefGoogle Scholar
Boschung, J., Schaefer, P., Peters, N. & Meneveau, C. 2014 The local topology of stream- and vortex lines in turbulent flows. Phys. Fluids 26, 045107,1–14.CrossRefGoogle Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782–792.CrossRefGoogle Scholar
Cantwell, B. J. 1993 On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. Phys. Fluids A 5, 2008–2013.Google Scholar
Cantwell, B. J., Lewis, G. & Chen, J. 1989 Topology of 3-D variable density flows. In Tenth Aust. Fluid Mech. Conf., University of Melbourne, 1989.Google Scholar
Chacin, J. M., Cantwell, B. J. & Kline, S. J. 1996 Study of turbulent boundary layer structure using the invariants of the velocity gradient tensor. Exp. Therm. Fluid Sci. 13, 308–317.CrossRefGoogle Scholar
Chen, J. H., Cantwell, B. J. & Mansour, N. N. 1989 The topology and vorticity dynamics of a 3-D plane compressible wake. In Tenth Aust. Fluid Mech. Conf., University of Melbourne, 1989.Google Scholar
Chen, J. H., Chong, M. S., Soria, J., Sondergaard, R., Perry, A. E., Rogers, M., Moser, R. & Cantwell, B. J. 1990 A study of the topology of dissipating motions in direct numerical simulations of time-developing compressible and incompressible mixing layers. In Center for Turbulence Research, Proc. Summ. Prog., pp. 139–161. Stanford University.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777.Google Scholar
Chu, Y. B. & Lu, X. Y. 2013 Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438.CrossRefGoogle Scholar
Cifuentes, L., Dopazo, C., Martin, J. & Jimenez, C. 2014 Local flow topologies and scalar structures in a turbulent premixed flame. Phys. Fluids 26, 065108,1–24.Google Scholar
Donzis, D. A., Sreenivasan, K. R. & Yeung, P. K. 2005 Scalar dissipation rate and dissipative anomaly in isotropic turbulence. J. Fluid Mech. 532, 199–216.Google Scholar
Donzis, D. A., Sreenivasan, K. R. & Yeung, P. K. 2010 The Batchelor spectrum for mixing of passive scalars in isotropic turbulence. Flow Turbul. Combust. 85, 549–566.Google Scholar
Fox, R. O. 1997 The Lagrangian spectral relaxation model of the scalar dissipation in homogeneous turbulence. Phys. Fluids 9, 2364–2386.Google Scholar
Fox, R. O. 1999 The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence. Phys. Fluids 11, 1550–1571.Google Scholar
Girimaji, S. S. 1992 A mapping closure for turbulent scalar mixing using a time-evolving reference field. Phys. Fluids A 4, 2875–2886.Google Scholar
Girimaji, S. S. 1994 Modeling turbulent scalar mixing as enhanced diffusion. Combust. Sci. Technol. 97, 85–98.Google Scholar
Girimaji, S. S. 1996 A study of turbulent combustion and its modeling using a diffusion reaction equation model. Intl J. Engng Sci. 34, 47–58.CrossRefGoogle Scholar
Girimaji, S. S. & Speziale, C. G. 1995 A modified restricted Euler equation for turbulent flows with mean velocity gradients. Phys. Fluids 7, 1438–1446.Google Scholar
Hill, J. C. 1976 Homogeneous turbulent mixing with chemical reaction. Annu. Rev. Fluid Mech. 8, 135–161.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research, Proc. Summ. Prog. Rep. CTR-S88, p. 193. Stanford University.Google Scholar
Kumar, G., Girimaji, S. S. & Kerimo, J. 2013 WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence. J. Comput. Phys. 234, 499–523.CrossRefGoogle Scholar
Maekawa, H., Hiyama, T. & Matsuo, Y. 1999 Study of the geometry of flow patterns in compressible isotropic turbulence. JSME Intl J. 42, 336–343.CrossRefGoogle Scholar
O’Neill, P. & Soria, J. 2005 The relationship between the topological structures in turbulent flow and the distribution of a passive scalar with an imposed mean gradient. Fluid Dyn. Res. 36, 107–120.Google Scholar
Orlandi, P. & Antonia, R. A. 2004 Dependence of a passive scalar in decaying isotropic turbulence on the Reynolds and Schmidt numbers using the EDQNM model. J. Turbul. 5, 1–13.Google Scholar
Orlandi, P., Pirozzoli, S., Bernardini, M. & Carnevale, G. F. 2014 A minimal flow unit for the study of turbulence with passive scalars. J. Turbul. 15, 731–751.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motion and flow patterns using critical point concepts. Annu. Rev. Fluid Mech. 19, 125–155.Google Scholar
Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16, 4386–4407.Google Scholar
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/non-turbulent interface in jets. Phys. Fluids 20, 055101,1–18.Google Scholar
Soria, J., Ooi, A. & Chong, M. S. 1997 Volume integrals of the Q–R invariants of the velocity gradient tensor in incompressible flows. Fluid Dyn. Res. 19, 219–233.Google Scholar
Soria, J., Sondergaard, R., Cantwell, B. J., Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6, 871–884.Google Scholar
Sreenivasan, K. R. 1996 The passive scalar spectrum and the Obukhov–Corrsin constant. Phys. Fluids 8, 189–196.Google Scholar
Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. 11, 1–24.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence, Cambridge University Press.Google Scholar
Vaghefi, N. S. & Madnia, C. K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 67–94.Google Scholar
Vedula, P., Yeung, P. K. & Fox, R. O. 2001 Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study. J. Fluid Mech. 433, 29–60.CrossRefGoogle Scholar
Wang, L. & Lu, X. Y. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.Google Scholar
Xu, K. 1998 Gas Kinetic Schemes for Unsteady Compressible Flow Simulations, VKI Lecture Series, pp. 1998–2003.Google Scholar
Yeung, P. K. 2002 Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142.Google Scholar
Yeung, P. K., Donzis, D. A. & Sreenivasan, K. R. 2005 High-Reynolds-number simulation of turbulent mixing. Phys. Fluids 17, 081703,1–4.Google Scholar