Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T17:14:06.731Z Has data issue: false hasContentIssue false
  • English
  • Français

Entrainment in a compressible turbulent shear layer

Published online by Cambridge University Press:  24 May 2016

Reza Jahanbakhshi Open the ORCID record for Reza Jahanbakhshi [Opens in a new window]  and
Cyrus K. Madnia
Reza Jahanbakhshi
Affiliation:
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260-4400, USA
Cyrus K. Madnia*
Affiliation:
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260-4400, USA
*
†Email address for correspondence: madnia@buffalo.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of temporally evolving shear layers have been performed to study the entrainment of irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). Four cases with convective Mach number from 0.2 to 1.8 are used. Entrainment is studied via two mechanisms; nibbling, considered as vorticity diffusion across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. The mass flow rate due to nibbling is calculated as the product of the entrained mass flux with the surface area of the TNTI. It is found that increasing the convective Mach number results in a decrease of the average entrained mass flux and the surface area of the TNTI. For the incompressible shear layer the local entrained mass flux is shown to be highly correlated with the viscous terms. However, as the convective Mach number increases, the mass fluxes due to the baroclinic and the dilatation terms play a more important role in the local entrainment process. It is observed that the entrained mass flux is dependent on the local dilatation and geometrical shape of the TNTI. For a compressible shear layer, most of the entrainment of the irrotational flow into the turbulent region due to nibbling is associated with the compressed regions on the TNTI. As the convective Mach number increases, the percentage of the compressed regions on the TNTI decreases, resulting in a reduction of the average entrained mass flux. It is also shown that the local shape of the interface, looking from the turbulent region, is dominated by concave shaped surfaces with radii of curvature of the order of the Taylor length scale. The average entrained mass flux is found to be larger on highly curved concave shaped surfaces regardless of the level of dilatation. The mass fluxes due to vortex stretching, baroclinic torque and the shear stress/density gradient terms are weak functions of the local curvatures on the TNTI, whereas the mass fluxes due to dilatation and viscous diffusion plus the viscous dissipation terms have a stronger dependency on the local curvatures. As the convective Mach number increases, the probability of finding highly curved concave shaped surfaces on the TNTI decreases, whereas the probability of finding flatter concave and convex shaped surfaces increases. This results in a decrease of the average entrained mass flux across the TNTI. Similar to the previous works on jets, the results show that the contribution of the engulfment to the total entrainment is small for both incompressible and compressible mixing layers. It is also shown that increasing the convective Mach number decreases the velocities associated with the entrainment, i.e. induced velocity, boundary entrainment velocity and local entrainment velocity.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 564 - 603
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

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106 (17), 174502.Google Scholar
Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247 (1), 54–65.CrossRefGoogle Scholar
Anand, R. K., Boersma, B. J. & Agrawal, A. 2009 Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion. Exp. Fluids 47 (6), 995–1007.CrossRefGoogle Scholar
Attili, A. & Bisetti, F. 2012 Statistics and scaling of turbulence in a spatially developing mixing layer at Re 𝜆 = 250. Phys. Fluids 24 (3), 035109.CrossRefGoogle Scholar
Attili, A., Cristancho, J. C. & Bisetti, F. 2014 Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer. J. Turbul. 15 (9), 555–568.Google Scholar
Ayachit, U.2015 The Paraview Guide: A Parallel Visualization Application. Kitware Inc.Google Scholar
Babu, P. C. & Mahesh, K. 2004 Upstream entrainment in numerical simulations of spatially evolving round jets. Phys. Fluids 16 (10), 3699–3705.Google Scholar
Bermejo-Moreno, I. & Pullin, D. I. 2008 On the non-local geometry of turbulence. J. Fluid Mech. 603, 101–135.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Brown, G. & Roshko, A.1971 The effect of density differences on the turbulent mixing layer. Tech. Rep. 23. DTIC Document.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (04), 775–816.Google Scholar
Chauhan, K., Philip, J. & Marusic, I. 2014a Scaling of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 751, 298–328.Google Scholar
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014b The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.CrossRefGoogle Scholar
Corrsin, S. & Kistler, A.1955 Free-stream boundaries of turbulent flows. Tech. Rep. TN-1244. NACA, Washington, DC.Google Scholar
Dahm, W. J. A. & Dimotakis, P. E. 1987 Measurements of entrainment and mixing in turbulent jets. AIAA J. 25 (9), 1216–1223.Google Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.Google Scholar
Dimotakis, P. E. & Brown, G. L. 1976 The mixing layer at high reynolds number: large-structure dynamics and entrainment. J. Fluid Mech. 78 (03), 535–560.Google Scholar
Dopazo, C., Martín, J. & Hierro, J. 2007 Local geometry of isoscalar surfaces. Phys. Rev. E 76 (5), 1–11.Google Scholar
Eisma, J., Westerweel, J., Ooms, G. & Elsinga, G. E. 2015 Interfaces and internal layers in a turbulent boundary layer. Phys. Fluids 27 (5), 055103.Google Scholar
Ferré, J. A., Mumford, J. C., Savill, A. M. & Giralt, F. 1990 Three-dimensional large-eddy motions and fine-scale activity in a plane turbulent wake. J. Fluid Mech. 210, 371–414.Google Scholar
Freund, J. B., Lele, S. K. & Moin, P. 2000 Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229–267.Google Scholar
Gampert, M., Narayanaswamy, V., Schaefer, P. & Peters, N. 2013 Conditional statistics of the turbulent/non-turbulent interface in a jet flow. J. Fluid Mech. 731, 615–638.Google Scholar
Gottlieb, D. & Turkel, E. 1976 Dissipative two-four methods for time-dependent problems. Maths Comput. 30 (136), 703–723.Google Scholar
Hadjadj, A., Yee, H. C. & Sjögreen, B. 2012 Les of temporally evolving mixing layers by an eighth-order filter scheme. Intl J. Numer. Meth. Fluids 70 (11), 1405–1427.Google Scholar
Hazewinkel, M. 2002 Minimal Surface. Encyclopedia of Mathematics. Springer.Google Scholar
Hickey, J.-P., Hussain, F. & Wu, X. 2013 Role of coherent structures in multiple self-similar states of turbulent planar wakes. J. Fluid Mech. 731, 312–363.Google Scholar
Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2007 Small-scale aspects of flows in proximity of the turbulent/non-turbulent interface. Phys. Fluids 19 (7), 071702.Google Scholar
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465–475.Google Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.Google Scholar
Hunt, J. C. R. 1994 Atmospheric jets and plumes. In Recent Research Advances in the Fluid Mechanics of Turbulent Jets and Plumes, pp. 309–334. Springer.Google Scholar
Hunt, J. C. R., Eames, I., da Silva, C. B. & Westerweel, J. 2011 Interfaces and inhomogeneous turbulence. Phil. Trans. R. Soc. Lond. A 369 (1937), 811–832.Google ScholarPubMed
Hunt, J. C. R., Eames, I. & Westerweel, J. 2006 Mechanics of inhomogeneous turbulence and interfacial layers. J. Fluid Mech. 554, 499–519.Google Scholar
Jahanbakhshi, R., Vaghefi, N. S. & Madnia, C. K. 2015 Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer. Phys. Fluids 27 (10), 105105.CrossRefGoogle Scholar
Jiménez, J. & Wray, A. A. 1998 On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
Khashehchi, M., Ooi, A., Soria, J. & Marusic, I. 2013 Evolution of the turbulent/non-turbulent interface of an axisymmetric turbulent jet. Exp. Fluids 54 (1), 1–12.CrossRefGoogle Scholar
Kida, S. & Orszag, S. A. 1990a Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5 (2), 85–125.Google Scholar
Kida, S. & Orszag, S. A. 1990b Enstrophy budget in decaying compressible turbulence. J. Sci. Comput. 5 (1), 1–34.Google Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2), 652–665.Google Scholar
Kritsuk, A. G., Norman, M. L., Padoan, P. & Wagner, R. 2007 The statistics of supersonic isothermal turbulence. Astrophys. J. 665 (1), 416.Google Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2013 Experimental study of entrainment and interface dynamics in a gravity current. Exp. Fluids 54 (5), 1–13.Google Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2015 The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech. 765, 303–324.Google Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.Google Scholar
Livescu, D. & Madnia, C. K. 2004 Small scale structure of homogeneous turbulent shear flow. Phys. Fluids 16 (8), 2864–2876.Google Scholar
Mahle, I., Foysi, H., Sarkar, S. & Friedrich, R. 2007 On the turbulence structure in inert and reacting compressible mixing layers. J. Fluid Mech. 593, 171–180.Google Scholar
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 2065–2072.Google Scholar
Mathew, J., Mahle, I. & Friedrich, R. 2008 Effects of compressibility and heat release on entrainment processes in mixing layers. J. Turbul. 9, N14.Google Scholar
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Mungal, M. G., Karasso, P. S. & Lozano, A. 1991 The visible structure of turbulent jet diffusion flames: large-scale organization and flame tip oscillation. Combust. Sci. Technol. 76 (4–6), 165–185.Google Scholar
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371.Google Scholar
Philip, J., Bermejo-Moreno, I., Chung, D. & Marusic, I. 2015 Characteristics of the entrainment velocity in a developing wake. In International Symposium on Turbulence and Shear Flow Phenomena, TSFP-9, Melbourne, Australia.Google Scholar
Philip, J. & Marusic, I. 2012 Large-scale eddies and their role in entrainment in turbulent jets and wakes. Phys. Fluids 24 (5), 055108.Google Scholar
Philip, J., Meneveau, C., de Silva, C. M. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26 (1), 015105.Google Scholar
Pirozzoli, S., Bernardini, M., Marié, S. & Grasso, F. 2015 Early evolution of the compressible mixing layer issued from two turbulent streams. J. Fluid Mech. 777, 196–218.Google Scholar
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. RT Edwards, Inc.Google Scholar
Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 26 (5), 445–469.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Prasad, R. R. & Sreenivasan, K. R. 1989 Scalar interfaces in digital images of turbulent flows. Exp. Fluids 7 (4), 259–264.Google Scholar
Ragab, S. A. & Wu, J. L. 1989 Linear instabilities in two-dimensional compressible mixing layers. Phys. Fluids A 1 (6), 957–966.Google Scholar
Redford, J. A., Castro, I. P. & Coleman, G. N. 2012 On the universality of turbulent axisymmetric wakes. J. Fluid Mech. 710, 419–452.Google Scholar
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254–275.Google Scholar
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101 (19), 194505.Google Scholar
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014a Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567–590.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 (5), 55101–55101.Google Scholar
da Silva, C. B., dos Reis, R. J. N. & Pereira, J. C. F. 2011 The intense vorticity structures near the turbulent/non-turbulent interface in a jet. J. Fluid Mech. 685, 165–190.Google Scholar
da Silva, C. B., Taveira, R. R. & Borrell, G. 2014b Characteristics of the turbulent/non-turbulent interface in boundary layers, jets and shear-free turbulence. J. Phys. 506, 012015.Google Scholar
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent/non-turbulent interface in high reynolds number boundary layers. Phys. Rev. Lett. 111 (4), 044501.Google Scholar
Slessor, M. D., Zhuang, M. & Dimotakis, P. E. 2000 Turbulent shear-layer mixing: growth-rate compressibility scaling. J. Fluid Mech. 414, 35–45.Google Scholar
Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. (11), N2.Google Scholar
Taveira, R. R., Diogo, J. S., Lopes, D. C. & da Silva, C. B. 2013 Lagrangian statistics across the turbulent/non-turbulent interface in a turbulent plane jet. Phys. Rev. E 88 (4), 043001.Google Scholar
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/non-turbulent interface in jets. Phys. Fluids 25 (1), 015114.Google Scholar
Taveira, R. R. & da Silva, C. B. 2014 Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets. Phys. Fluids 26 (2), 021702.Google Scholar
Thompson, K. W. 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89 (2), 439–461.Google Scholar
Townsend, A. A. 1966 The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26 (04), 689–715.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tritton, D. J. 2012 Physical Fluid Dynamics. Springer Science & Business Media.Google Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. vol. 483. Springer.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar
Vaghefi, N. S.2014 Simulation and modeling of compressible turbulent mixing layer. PhD thesis, State University of New York at Buffalo.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
Vaghefi, N. S., Nik, M. B., Pisciuneri, P. H. & Madnia, C. K. 2013 A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence. J. Turbul. 14 (9), 43–61.Google Scholar
Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258.Google Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. & Chen, S. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110 (21), 214505.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014a Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26 (10), 105103.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014b Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet. J. Fluid Mech. 758, 754–785.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95 (17), 174501.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.Google Scholar
Westerweel, J., Hofmann, T., Fukushima, C. & Hunt, J. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp. Fluids 33 (6), 873–878.Google Scholar
Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A. 2013a Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech. 731, 95–116.Google Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24 (10), 105110.Google Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2013b Erratum: investigations on the local entrainment velocity in a turbulent jet [phys. fluids24, 105110 (2012)]. Phys. Fluids 25 (1), 019901.Google Scholar
Yule, A. J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (03), 413–432.Google Scholar