Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-29T20:28:14.167Z Has data issue: false hasContentIssue false
  • English
  • Français

On the effect of heat release in turbulence spectra of non-premixed reacting shear layers

Published online by Cambridge University Press:  10 May 2009

R. KNAUS  and
C. PANTANO
R. KNAUS*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St, Urbana, IL 61801, USA
C. PANTANO
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St, Urbana, IL 61801, USA
*
†Email address for correspondence: rknaus2@illinois.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Velocity, mixture fraction and temperature spectra obtained from five direct numerical simulations of non-reacting and reacting shear layers, using the infinitely fast chemistry approximation, are analysed. Two different global chemical reactions corresponding to methane and hydrogen combustion with air, respectively, are considered. The effect of heat release, i.e. density variation, on the inertial and dissipation turbulence subrange of the spectra is investigated. Analysis of the database supports the experimentally available measurements of spectra in turbulent reacting flows showing that heat release effects can be scaled out by utilizing Favre-averaged (density-weighted) large-scale turbulence quantities. This is supported by the simulation results for velocity and mixture fraction in our moderate-Reynolds-number flows but it appears to be less supported in the dissipation subrange of the temperature spectra. The departure from universal scaling using Favre-averaged quantities in the temperature spectrum, which is evident in the dissipation subrange, appears to be caused by the strong nonlinearity of the state relationship relating the mixture fraction to the temperature, as has been suggested previously. These effects are less pronounced at intermediate wavenumbers. Analysis suggests that the nonlinear state relationship and the spectra of mixture fraction moments can be used to reconstruct the temperature spectrum across the flow. Moreover, the governing equation for the temperature variance is analysed to identify a possible surrogate for the overall rate of dissipation of temperature fluctuations and their corresponding dissipation length scale. This scaling analysis is then used to separate planes across the shear layer where the temperature dissipation length scale is alike that of the mixture fraction from regions where smaller length scales are present, and are evidenced in the dissipation subrange using Kolmogorov scaling. In our simulations, these regions correspond to the centre of the shear layer and the mean flame location. The new estimate for the temperature dissipation length scale is able to collapse the compensated spectra profiles at all planes across the shear layer for all simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 67 - 109
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Antonia, R. & Mi, J. 1993 Temperature dissipation in a turbulent round jet. J. Fluid Mech. 250, 531–551.CrossRefGoogle Scholar
Barlow, R. & Karpetis, A. 2004 Measurements of scalar variance, scalar dissipation, and length scales in turbulent piloted methane/air jet flames. Flow Turbul. Combust. 72 (2), 427–448.CrossRefGoogle Scholar
Batchelor, G. & Townsend, A. 1949 The nature of turbulent motion at large wavenumbers. Proc. R. Soc. Lond. A 199 (1057), 238–255.Google Scholar
Bilger, R. 1980 Turbulent flows with nonpremixed reactants. In Turbulent Reacting Flows (ed. Libby, P. & Williams, F.), ch. 3, pp. 65–113. Springer.CrossRefGoogle Scholar
Bilger, R. 1988 The structure of turbulent nonpremixed flames. Proc. Combust. Inst. 22, 475–488.CrossRefGoogle Scholar
Bilger, R. 2004 Some aspects of scalar dissipation. Flow Turbul. Combust. 72 (2), 93–114.CrossRefGoogle Scholar
Bilger, R., Saetran, L. & Krishnamoorthy, L. 1991 Reaction in a scalar mixing layer. J. Fluid Mech. 233, 211–242.CrossRefGoogle Scholar
Birch, A., Brown, D., Dodson, M. & Thomas, J. 1978 Turbulent concentration field of a methane jet. J. Fluid Mech. 88, 431–449.CrossRefGoogle Scholar
Bos, W., Touil, H. & Bertoglio, J.-P. 2005 Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient. Phys. Fluids 17, 125108.CrossRefGoogle Scholar
Boyer, L. & Queiroz, M. 1991 Temperature dissipation measurements in a lifted turbulent-diffusion flame. Combust. Sci. Tech. 79 (1–3), 1–34.CrossRefGoogle Scholar
Brown, G. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.CrossRefGoogle Scholar
de Bruyn Kops, S., Riley, J. & Kosály, G. 2001 Direct numerical simulation of reacting scalar mixing layers. Phys. Fluids 13 (5), 1450–1465.CrossRefGoogle Scholar
Buch, K. & Dahm, W. 1998 Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 2. Sc = 1. J. Fluid Mech. 364, 1–29.CrossRefGoogle Scholar
Burke, S. & Schumann, T. 1928 Diffusion flames. Proc. Combust. Inst. 1, 2–11.Google Scholar
Campbell, L. 1964 On a class of polynomials useful in probability calculations. IEEE Trans. Inf. Theory 10 (3), 255–256.CrossRefGoogle Scholar
Carter, C., Donbar, J. & Driscoll, J. 1998 Simultaneous CH planar laser-induced fluorescence and particle imaging velocimetry in turbulent nonpremixed flames. Appl. Phys. B 66 (1), 129–132.CrossRefGoogle Scholar
Chen, Y.-C. & Mansour, M. 1996 Measurements of the detailed flame strucutre in turbulent H2air jet diffusion flames with line-Raman/Rayleigh/LIPF-OH technique. Proc. Combust. Inst. 26, 97–103.CrossRefGoogle Scholar
Clemens, N. & Paul, P. 1995 Effects of heat release on the near field flow structure of hydrogen jet diffusion flames. Combust. Flame 102 (3), 271–284.CrossRefGoogle Scholar
Corrsin, S. 1961 The reactant concentration spectrum in trubulent mixing with a first order reaction. J. Fluid Mech. 11, 407–416.CrossRefGoogle Scholar
Dahm, W. 2005 Effects of heat release on turbulent shear flows. Part 2. Turbulent mixing layers and the equivalence principle. J. Fluid Mech. 540, 1–19.CrossRefGoogle Scholar
Dibble, R., Masri, A. & Bilger, R. 1987 The spontaneous raman-scattering technique applied to nonpremixed flames of methane. Combust. Flame 67 (3), 189–206.CrossRefGoogle Scholar
Dimotakis, P. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–56.CrossRefGoogle Scholar
Donbar, J., Driscoll, J. & Carter, C. 1998 Simultaneous CH planar laser-induced fluorescence and particle imaging velocimetry in turbulent flames. In Thirty-Sixth Aerospace Sciences Meeting and Exhibit, AIAA 98-0151. Reno, NV.Google Scholar
Donbar, J., Driscoll, J. & Carter, C. 1999 Strain rates measured along the wrinkled flame contour within turbulent nonpremixed jet flames. In Joint Meeting of U.S. Section of the Combustion Institute. Washington, DC.Google Scholar
Donzis, D., Sreenivasan, K. & Yeung, P. 2005 Scalar dissipation rate and dissipative anomaly in isotropic turbulence. J. Fluid Mech. 532, 199–216.CrossRefGoogle Scholar
Dowling, D. 1991 The estimated scalar dissipation rate in gas-phase turbulent jets. Phys. Fluids A 3 (9), 2229–2246.CrossRefGoogle Scholar
Dowling, D. & Dimotakis, P. 1990 Similarity of the concentration field of gas-phase turbulent jets. J. Fluid Mech. 218, 109–141.CrossRefGoogle Scholar
Everest, D., Driscoll, J., Dahm, W. & Feikema, D. 1995 Images of the two-dimensional field and temperature gradients to quantify mixing rates within a non-premixed turbulent jet flame. Combust. Flame 101 (1), 58–68.CrossRefGoogle Scholar
Fielding, J., Schaffer, A. & Long, M. 1998 Three-scalar imaging in turbulent non-premixed flames of methane. Proc. Combust. Inst. 27, 1007–1014.CrossRefGoogle Scholar
Frank, J. & Kaiser, S. 2008 High-resolution imaging of dissipative structures in a turbulent jet flame with laser Rayleigh scattering. Exp. Fluids 44, 221–233.CrossRefGoogle Scholar
Gladnick, P., LaRue, J. & Samuelsen, G. 1990 Anisotropy in the near-field of a turbulent diffusion flame. In Heat Transfer in Combustion Systems (ed. Farouk, B., Grosshandler, W., Lilley, D. & Presser, C.), vol. 142, pp. 33–40. ASME.Google Scholar
Han, D. & Mungal, M. 2000 Simultaneous measurement of velocity and CH layer distribution in turbulent non-premixed flames. Proc. Combust. Inst. 28, 261–267.CrossRefGoogle Scholar
Han, D. & Mungal, M. 2003 Simultaneous measurement of velocity and CH distributions. Part 1: jet flames in co-flow. Combust. Flame 132 (3), 565–590.CrossRefGoogle Scholar
Hermanson, J. & Dimotakis, P. 1989 Effects of heat release in a turbulent, reacting shear layer. J. Fluid Mech. 199, 333–375.CrossRefGoogle Scholar
Kaiser, S. & Frank, J. 2007 Imaging of dissipative structures in the near field of a turbulent non-premixed jet flame. Proc. Combust. Inst. 31, 1515–1523.CrossRefGoogle Scholar
Karpetis, A. & Barlow, R. 2002 Measurements of scalar dissipation in a turbulent piloted methane/air jet flame. Proc. Combust. Inst. 29, 1929–1936.CrossRefGoogle Scholar
Kida, S. & Goto, S. 1997 A Lagrangian direct-interaction approximation for homogeneous isotropic turbulence. J. Fluid Mech. 345, 307–345.CrossRefGoogle Scholar
Kolmogorov, A. 1941 a Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 19–21.Google Scholar
Kolmogorov, A. 1941 b The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kolmogorov, A. 1961 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
Kosály, G. 1993 Frequency-spectra of reactant fluctuations in turbulent flows. J. Fluid Mech. 246, 489–502.CrossRefGoogle Scholar
Kounalakis, M., Sivathanu, Y. & Faeth, G. 1991 Infrared radiation statistics of nonluminous turbulent-diffusion flames. J. Heat Transfer-Trans. ASME 113 (2), 437–445.CrossRefGoogle Scholar
Kraichnan, R. 1959 The structure of isotropic turbulence at very high reynolds numbers. J. Fluid Mech. 5, 497–543.CrossRefGoogle Scholar
Lide, D. (ed.) 1999 Handbook of Chemistry and Physics. CRC Press.Google Scholar
Liñán, A. 1974 Asymptotic structure of counterflow diffusion flames for large activation-energies. Acta Astron. 1 (7–8), 1007–1039.CrossRefGoogle Scholar
Lumley, J. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10, 855–858.CrossRefGoogle 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.CrossRefGoogle Scholar
Markides, C. & Mastorakos, E. 2006 Measurements of scalar dissipation in a turbulent plume with planar laser-induced fluorescence of acetone. Chem. Engng Sci. 61 (9), 2835–2842.CrossRefGoogle Scholar
Masri, A., Dibble, R. & Barlow, R. 1996 The structure of turbulent nonpremixed flames revealed by Raman–Rayleigh-LIF measurements. Prog. Energy Combust. Sci. 22 (4), 307–362.CrossRefGoogle Scholar
McMurtry, P., Jou, W., Riley, J. & Metcalfe, R. 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24 (6), 962–70.CrossRefGoogle Scholar
Meier, W., Barlow, R., Chen, Y.-L. & Chen, J.-Y. 2000 Raman/Rayleigh/LIF measurements in a turbulent CH4/H2/N2 jet diffusion flame: experimental techniques and turbulence-chemistry interaction. Combust. Flame 123 (3), 326–343.CrossRefGoogle Scholar
Monin, A. & Yaglom, A. 1971 Statistical Fluid Mechanics, vol. 1. MIT Press.Google Scholar
Muñiz, L. & Mungal, M. 2001 Effects of heat release and buoyancy on flow structure and entrainment in turbulent nonpremixed flames. Combust. Flame 126 (1–2), 1402–20.CrossRefGoogle Scholar
Mydlarski, L. 2003 Mixed velocity-passive scalar statistics in high-reynolds-number turbulence. J. Fluid Mech. 475, 173–203.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.CrossRefGoogle Scholar
Nagel, Z. & Dahm, W. 2007 Inner-scale effects of heat release in reacting turbulent shear flows. In 60th Annual Meeting of the Division of Fluid Dynamics. APS, Salt Lake City, UT.Google Scholar
Namazian, M., Schefer, R. & Kelly, J. 1988 Scalar dissipation measurements in the developing region of a jet. Combust. Flame 74 (2), 147–160.CrossRefGoogle Scholar
Nandula, S., Brown, T. & Pitz, R. 1994 Measurements of scalar dissipation in the reaction zones of turbulent nonpremixed H2 air flames. Combust. Flame 99 (3–4), 775–783.CrossRefGoogle Scholar
Noda, S., Mori, H., Hongo, Y. & Nishioka, M. 2005 Nonpremixed flamelet statistics at flame base of lifted turbulent jet nonpremixed flames. JSME Int. J. Ser.ies B 48 (1), 75–82.CrossRefGoogle Scholar
O'Gorman, P. & Pullin, D. 2003 The velocity-scalar cross spectrum of stretched spiral vortices. Phys. Fluids 15 (2), 280–291.CrossRefGoogle Scholar
Overholt, M. & Pope, S. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8 (11), 3128–48.CrossRefGoogle Scholar
Pantano, C., Sarkar, S. & Williams, F. 2003 Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech. 481, 291–328.CrossRefGoogle Scholar
Peters, N. 1984 Laminar diffusion flamelet models in non-premixed turbulent combustion. Prog. Energy Combust. Sci. 10 (3), 319–339.CrossRefGoogle Scholar
Pickett, L. & Chandhi, J. 2003 Structure of a reacting hydrocarbon-air planar mixing layer. Combust. Flame 132 (1), 138–156.CrossRefGoogle Scholar
Pope, S. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flow. Cambridge University Press.CrossRefGoogle Scholar
Rehm, J. & Clemens, N. 1998 The relationship between vorticity/strain and reaction zone structure in turbulent non-premixed jet flames. Proc. Combust. Inst. 27, 1113–1120.CrossRefGoogle Scholar
Renfro, M., Gore, J., King, G. & Laurendeau, N. 2000 Self-similarity of hydroxyl-concentration temporal statistics in turbulent nonpremixed jet flames. AIAA J. 38 (7), 1230–1236.CrossRefGoogle Scholar
Richardson, L. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Sabini, G., Shieh, G. & Givi, P. 1996 Modeling of the fluctuations and the frequency-spectra of reactants in turbulent scalar mixing layers. Chem. Engng Commun. 154, 147–181.CrossRefGoogle Scholar
Saddoughi, S. & Veeravalli, S. 1994 Local isotropy in turbulent boundary layers at high reynolds numbers. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Schumacher, J., Sreenivasan, K. & Yeung, P. 2005 Very fine structures in scalar mixing. J. Fluid Mech. 531, 113–122.CrossRefGoogle Scholar
Seitzman, J., Ungut, A., Paul, P. & Hanson, R. 1990 Imaging and characterization of OH structures in a turbulent nonpremixed flame. Proc. Combust. Inst. 23, 637–644.CrossRefGoogle Scholar
Seshadri, K. & Peters, N. 1988 Asymptotic structure and extinction of methane–air diffusion flames. Comusti. Flame 73, 23–44.CrossRefGoogle Scholar
Shutterly, H. 1963 General results in the mathematical theory of random signals and noise in nonlinear devices. IEEE Trans. Inf. Theory 9 (2), 74–84.CrossRefGoogle Scholar
Sreenivasan, K. 2004 Possible effects of small-scale intermittency in turbulnt reacting flows. Flow Turbul. Combust. 72 (2), 115–131.CrossRefGoogle Scholar
Su, L. & Clemens, N. 2003 The structure of fine-scale scalar mixing in gas-phase planar turbulent jets. J. Fluid Mech. 488, 1–29.CrossRefGoogle Scholar
Tacina, K. & Dahm, W. 2000 Effects of heat release on turbulent shear flows. Part 1. A general equivalent principle for non-buoyant flows and its application to turbulent jet flames. J. Fluid Mech. 415, 23–44.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Theron, M. & Bellenoue, M. 2006 Experimental investigation of the effects of heat release on mixing processes and flow structure in a high-speed subsonic turbulent h2 jet. Combust. Flame 145 (4), 688–702.CrossRefGoogle Scholar
Thompson, W. 1954 The response of a non-linear system to random noise. Proc. IEEE 102, 46–48.Google Scholar
Tsurikov, M. & Clemens, N. 2002 The structure of dissipative scales in axisymmetric turbulent gas-phase jets. In 40th Aerospace Sciences Meeting and Exhibit, vol. 164. Reno, NV.Google Scholar
Uberoi, M. & Freymuth, P. 1969 Spectra of turbulence in wakes behind circular cylinders. Phys. Fluids 12 (7), 1359–1363.CrossRefGoogle Scholar
Vedula, P., Yeung, P. & Fox, R. 2001 Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study. J. Fluid Mech. 433, 29–60.CrossRefGoogle Scholar
Vervisch, L. & Poinsot, T. 1998 Direct numerical simulation of non-premixed turbulent flames. Annu. Rev. Fluid Mech. 30, 655–91.CrossRefGoogle Scholar
Wallace, A. 1981 Experimental investigation of the effects of chemical heat release in the reacting turbulent plane shear layer. PhD thesis, The University of Adelaide (also AFOSR Rep. TR-84-0650).Google Scholar
Wang, G. & Barlow, R. 2008 Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames. Exp. Fluids 44, 633–645.CrossRefGoogle Scholar
Wang, G., Clemens, N. & Varghese, P. 2005 High-repetition rate measurements of temperature and thermal dissipation in a non-premixed turbulent jet flame. Proc. Combust. Inst. 30, 691–699.CrossRefGoogle Scholar
Wang, G.-H., Clemens, N., Varghese, P. & Barlow, R. 2008 Turbulent time scales in a nonpremixed turbulent jet flame by using high-repetition rate thermometry. Comust. Flame 152, 317–335.CrossRefGoogle Scholar
Wang, G., Karpetis, A. & Barlow, R. 2007 Dissipation length scales in turbulent nonpremixed jet flames. Combust. Flame 148 (1), 62–75.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in trubulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory. Benjamin/Cummings.Google Scholar
Wygnanski, I. & Fielder, H. 1969 Some measurements in self-preserving jet. J. Fluid Mech. 38, 577–612.CrossRefGoogle Scholar
Zhang, H., Wang, D. & Tong, C. 2004 On conditional scalar increment and joint velocity-scalar increment statistics. New J. Phys. 6 (38).CrossRefGoogle Scholar