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The effect of heat release on the entrainment in a turbulent mixing layer

  • Reza Jahanbakhshi (a1) and Cyrus K. Madnia (a1)

Abstract

Direct numerical simulations of a temporally evolving compressible reacting mixing layer have been performed to study the entrainment of the irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). In order to study the effects of heat release and interaction of the flame with the TNTI on turbulence several cases with different heat release levels, $Q$ , and stoichiometric mixture fractions are chosen for the simulations with the highest opted value for $Q$ corresponding to hydrogen combustion in air. The combustion is mimicked by a one-step irreversible global reaction, and infinitely fast chemistry approximation is used to compute the species mass fractions. Entrainment is studied via two mechanisms: nibbling, considered as the vorticity transport across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. As the level of heat release increases, the total entrained mass flow rate into the mixing layer decreases. In a reacting mixing layer by increasing the heat release rate, the mass flow rate due to nibbling is shown to decrease mostly due to a reduction of the local entrainment velocity, while the surface area of the TNTI does not change significantly. It is also observed that nibbling is a viscous dominated mechanism in non-reacting flows, whereas it is mostly carried out by inviscid terms in reacting flows with high level of heat release. The contribution of the engulfment to entrainment is small for the non-reacting mixing layers, while mass flow rate due to engulfment can constitute close to 40 % of the total entrainment in reacting cases. This increase is primarily related to a decrease of entrained mass flow rate due to nibbling, while the entrained mass flow rate due to engulfment does not change significantly in reacting cases. It is shown that the total entrained mass flow rate in reacting and non-reacting compressible mixing layers can be estimated from an expression containing the convective Mach number and the density change due to heat release.

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Email address for correspondence: madnia@buffalo.edu

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Present address: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218-2682, USA.

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Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247 (1), 5465.10.1016/j.physd.2012.12.009
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), 9951007.10.1007/s00348-009-0695-5
Attili, A. & Bisetti, F. 2012 Statistics and scaling of turbulence in a spatially developing mixing layer at Re 𝜆 = 250. Phys. Fluids 24 (3), 035109.10.1063/1.3696302
Ayachit, U. 2015 The Paraview Guide: A Parallel Visualization Application. Kitware, Inc.
Babu, P. C. & Mahesh, K. 2004 Upstream entrainment in numerical simulations of spatially evolving round jets. Phys. Fluids 16 (10), 36993705.10.1063/1.1780548
Barone, M. F., Oberkampf, W. L. & Blottner, F. G. 2006 Validation case study: prediction of compressible turbulent mixing layer growth rate. AIAA J. 44 (7), 14881497.10.2514/1.19919
Becker, H. A. & Yamazaki, S. 1978 Entrainment, momentum flux and temperature in vertical free turbulent diffusion flames. Combust. Flame 33, 123149.10.1016/0010-2180(78)90055-X
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.10.1017/S002211208600099X
Bilger, R. W. 1976 The structure of diffusion flames. Combust. Sci. Technol. 13 (1–6), 155170.10.1080/00102207608946733
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383410.10.1017/S0022112001006759
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21 (6), 926927.10.2514/3.60135
Borrell, G. & Jiménez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801, 554596.10.1017/jfm.2016.430
Brown, G. L. 1975 The entrainment and large structure in turbulent mixing layers. In 5th Australasian Conference on Hydraulics and Fluid Mechanics, vol. 1, pp. 352359. University of Adelaide.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (04), 775816.10.1017/S002211207400190X
Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Engng Chem. 20 (10), 9981004.10.1021/ie50226a005
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014 The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119151.10.1017/jfm.2013.641
Chinzei, N., Masuya, G., Komuro, T., Murakami, A. & Kudou, K. 1986 Spreading of two-stream supersonic turbulent mixing layers. Phys. Fluids 29 (5), 13451347.10.1063/1.865698
Corrsin, S. & Kistler, A.1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. TN-1244, Washington, DC.
Dahm, W. J. A. 2005 Effects of heat release on turbulent shear flows. Part 2. Turbulent mixing layers and the equivalence principle. J. Fluid Mech. 540, 119.10.1017/S0022112005005793
Dahm, W. J. A. & Dimotakis, P. E. 1987 Measurements of entrainment and mixing in turbulent jets. AIAA J. 25 (9), 12161223.10.2514/3.9770
Debisschop, J. R., Chambers, O. & Bonnet, J. P. 1994 Velocity field characteristics in supersonic mixing layers. Exp. Thermal Fluid Sci. 9 (2), 147155.10.1016/0894-1777(94)90107-4
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24 (11), 17911796.10.2514/3.9525
Dimotakis, P. E. 1991 Turbulent free shear layer mixing and combustion. High Speed Flight Propulsion Systems 137, 265340.
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.10.1017/S0022112099007946
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329356.10.1146/annurev.fluid.36.050802.122015
Dimotakis, P. E. & Brown, G. L. 1976 The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J. Fluid Mech. 78 (03), 535560.10.1017/S0022112076002590
Ern, A. & Giovangigli, V. 1994 Multicomponent Transport Algorithms, vol. 24. Springer.10.1007/978-3-540-48650-3
Faeth, G. M. & Samuelsen, G. S. 1986 Fast reaction nonpremixed combustion. Prog. Energy Combust. Sci. 12 (4), 305372.10.1016/0360-1285(86)90005-5
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, 371414.10.1017/S0022112090001331
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, 615638.10.1017/jfm.2013.327
Gottlieb, D. & Turkel, E. 1976 Dissipative two-four methods for time-dependent problems. Maths. Comput. 30 (136), 703723.10.1090/S0025-5718-1976-0443362-6
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), 14051427.10.1002/fld.2753
Haynes, W. M. 2014 CRC Handbook of Chemistry and Physics. CRC Press.
Hazewinkel, M. 2002 Minimal Surface. Encyclopedia of Mathematics. Springer.
Hermanson, J. C. & Dimotakis, P. E. 1989 Effects of heat release in a turbulent, reacting shear layer. J. Fluid Mech. 199, 333375.10.1017/S0022112089000406
Hickey, J., Hussain, F. & Wu, X. 2013 Role of coherent structures in multiple self-similar states of turbulent planar wakes. J. Fluid Mech. 731, 312363.10.1017/jfm.2013.315
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), 071702.10.1063/1.2746037
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.10.1103/PhysRevLett.106.134503
Holzner, M. & van Reeuwijk, M. 2017 The turbulent/nonturbulent interface in penetrative convection. J. Turbul. 111.
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), 811832.10.1098/rsta.2010.0325
Hunt, J. C. R., Eames, I. & Westerweel, J. 2006 Mechanics of inhomogeneous turbulence and interfacial layers. J. Fluid Mech. 554, 499519.10.1017/S002211200600944X
Jahanbakhshi, R.2016 DNS of compressible reacting turbulent shear layer. PhD thesis, State University of New York at Buffalo.10.1017/jfm.2016.296
Jahanbakhshi, R. & Madnia, C. K. 2016 Entrainment in a compressible turbulent shear layer. J. Fluid Mech. 797, 564603.10.1017/jfm.2016.296
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), 105105.10.1063/1.4933250
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), 112.10.1007/s00348-012-1449-3
Kida, S. & Orszag, S. A. 1990 Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5 (2), 85125.10.1007/BF01065580
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), 652665.10.1016/S0021-9991(03)00090-1
Kritsuk, A. G., Norman, M. L., P., P. & Wagner, R. 2007 The statistics of supersonic isothermal turbulence. Astrophys. J. 665 (1), 416.10.1086/519443
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017 Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222250.10.1017/jfm.2016.786
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, 303324.10.1017/jfm.2014.738
Kundu, P. K., Cohen, I. M. & Dowling, D. R. 2015 Fluid Mechanics, 6th edn. Academic Press.
Kuo, K. K. 2005 Principles of Combustion. John Wiley & Sons.
Lee, J., Sung, H. J. & Zaki, T. A. 2017 Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 819, 165187.10.1017/jfm.2017.170
Lee, J. & Zaki, T. A. 2016 Turbulent/non-turbulent interface in transitional and turbulent boundary layers. In 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada, ICTAM.
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643668.10.1017/S0022112092000612
Livescu, D., Jaberi, F. A. & Madnia, C. K. 2002 The effects of heat release on the energy exchange in reacting turbulent shear flow. J. Fluid Mech. 450, 3566.10.1017/S0022112001006164
Mahle, I.2007 Direct and large-eddy simulation of inert and reacting compressible turbulent shear layers. PhD thesis, Universität München.
Mahle, I., Foysi, H., Sarkar, S. & Friedrich, R. 2007 On the turbulence structure in inert and reacting compressible mixing layers. J. Fluid Mech. 593, 171180.10.1017/S0022112007008919
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 20652072.10.1063/1.1480831
Mathew, J., Mahle, I. & Friedrich, R. 2008 Effects of compressibility and heat release on entrainment processes in mixing layers. J. Turbul. (9), N14.10.1080/14685240802004924
McMurtry, P. A., Riley, J. J. & Metcalfe, R. W. 1989 Effects of heat release on the large-scale structure in turbulent mixing layers. J. Fluid Mech. 199, 297332.10.1017/S002211208900039X
Miller, R. S., Madnia, C. K. & Givi, P. 1995 Numerical simulation of non-circular jets. Comput. Fluids 24 (1), 125.10.1016/0045-7930(94)00019-U
Mistry, D., Philip, J., Dawson, J. R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690725.10.1017/jfm.2016.474
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 123.
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), 165185.10.1080/00102209108951708
Muniz, L. & Mungal, M. G. 2001 Effects of heat release and buoyancy on flow structure and entrainment in turbulent nonpremixed flames. Combust. Flame 126 (1), 14021420.10.1016/S0010-2180(01)00253-X
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, 554584.10.1017/jfm.2014.62
Oevermann, M. 2000 Numerical investigation of turbulent hydrogen combustion in a scramjet using flamelet modeling. Aerosp. Sci. Technol. 4 (7), 463480.10.1016/S1270-9638(00)01070-1
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329371.10.1017/S0022112001006978
Pantano, C., Sarkar, S. & Williams, F. A. 2003 Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech. 481, 291328.10.1017/S0022112003003872
Pantano-Rubino, C. A.2000 Compressibility effects in turbulent nonpremixed reacting shear flows. PhD thesis, University of California San Diego.
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453477.10.1017/S0022112088003325
Philip, J., Bermejo-Moreno, I., Chung, D. & Marusic, I.2015 Characteristics of the entrainment velocity in a developing wake. International Symposium on Turbulence and Shear Flow Phenomena, TSFP-9, Melbourne, Australia. TSFP.
Philip, J. & Marusic, I. 2012 Large-scale eddies and their role in entrainment in turbulent jets and wakes. Phys. Fluids 24 (5), 055108.10.1063/1.4719156
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), 015105.10.1063/1.4861066
Pitsch, H. & Peters, N. 1998 A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combust. Flame 114 (1), 2640.10.1016/S0010-2180(97)00278-2
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. RT Edwards.
Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 26 (5), 445469.10.1016/0020-7225(88)90004-3
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.10.1017/CBO9780511840531
Ragab, S. A. & Wu, J. L. 1989 Linear instabilities in two-dimensional compressible mixing layers. Phys. Fluids A 1 (6), 957966.10.1063/1.857407
Redford, J. A., Castro, I. P. & Coleman, G. N. 2012 On the universality of turbulent axisymmetric wakes. J. Fluid Mech. 710, 419452.10.1017/jfm.2012.371
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254275.10.1017/jfm.2013.613
van Reeuwijk, M., Krug, D. & Holzner, M. 2018 Small-scale entrainment in inclined gravity currents. Environ. Fluid Mech. 18 (1), 225239.10.1007/s10652-017-9514-3
Ricou, F. P. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11 (01), 2132.10.1017/S0022112061000834
Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6 (2), 903923.10.1063/1.868325
Saghafian, A.2014 High-fidelity simulations and modeling of compressible reacting flows. PhD thesis, Stanford University.
Samimy, M. & Elliott, G. S. 1990 Effects of compressibility on the characteristics of free shear layers. AIAA J. 28, 439445.10.2514/3.10412
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101 (19), 194505.10.1103/PhysRevLett.101.194505
Sekar, B. & Mukunda, H. S. 1991 A computational study of direct simulation of high speed mixing layers without and with chemical heat release. In Symposium (International) on Combustion, vol. 23, pp. 707713. Elsevier.
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, 567590.10.1146/annurev-fluid-010313-141357
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), 5510155101.10.1063/1.2912513
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, 165190.10.1017/jfm.2011.296
da Silva, C. B. & Silva, T. S. 2016 High Reynolds numbers scaling of the turbulent/non-turbulent interface. In APS Meeting Abstracts: APS Division of Fluid Dynamics Conference 2016. APS.
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.
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), 20362051.10.1063/1.868451
Sutherland, W. 1893 Lii. the viscosity of gases and molecular force. London Edinburgh Dublin Philos. Mag. J. Sci. 36 (223), 507531.10.1080/14786449308620508
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.
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/non-turbulent interface in jets. Phys. Fluids 25 (1), 015114.10.1063/1.4776780
Thompson, K. W. 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89 (2), 439461.10.1016/0021-9991(90)90152-Q
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tritton, D. J. 2012 Physical Fluid Dynamics. Springer.
Tsinober, A. 2000 Vortex stretching versus production of strain/dissipation. Turbul. Struct. Vortex Dyn. 164191.
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. vol. 483. Springer.10.1007/978-90-481-3174-7
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.10.1017/S0022112086001222
Vaghefi, N. S.2014 Simulation and modeling of compressible turbulent mixing layer. PhD thesis, State University of New York at Buffalo.
Vaghefi, N. S. & Madnia, C. K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 6794.10.1017/jfm.2015.235
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), 4361.10.1080/14685248.2013.854901
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), 214505.10.1103/PhysRevLett.110.214505
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.
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, 199230.10.1017/S0022112009006600
Williams, F. A. 1985 Combustion Theory. Benjamin-Cummings.
Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A. 2013 Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech. 731, 95116.10.1017/jfm.2013.365
Yule, A. J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (03), 413432.10.1017/S0022112078002670
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The effect of heat release on the entrainment in a turbulent mixing layer

  • Reza Jahanbakhshi (a1) and Cyrus K. Madnia (a1)

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