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Experimental study of three-scalar mixing in a turbulent coaxial jet

Published online by Cambridge University Press:  19 September 2011

J. Cai ,
M. J. Dinger ,
W. Li ,
C. D. Carter ,
M. D. Ryan  and
C. Tong
J. Cai
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
M. J. Dinger
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
W. Li
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
C. D. Carter
Affiliation:
Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, OH 45433, USA
M. D. Ryan
Affiliation:
Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, OH 45433, USA
C. Tong*
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
*
†Email address for correspondence: ctong@ces.clemson.edu
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Abstract

In the present study we investigate three-scalar mixing in a turbulent coaxial jet. In this flow a centre jet and an annular flow, consisting of acetone-doped air and ethylene respectively, are mixed with the co-flow air. A unique aspect of this study compared to previous studies of three-scalar mixing is that two of the scalars (the centre jet and air) are separated by the third (annular flow); therefore, this flow better approximates the mixing process in a non-premixed turbulent reactive flow. Planar laser-induced fluorescence and Rayleigh scattering are employed to measure the mass fractions of the acetone-doped air and ethylene. The results show that the most unique aspects of the three-scalar mixing occur in the near field of the flow. The mixing process in this part of the flow are analysed in detail using the scalar means, variances, correlation coefficient, joint probability density function (JPDF), conditional diffusion, conditional dissipation rates and conditional cross-dissipation rate. The diffusion velocity streamlines in scalar space representing the conditional diffusion generally converge quickly to a manifold along which they continue at a lower rate. A widely used mixing model, interaction through exchange with mean, does not exhibit such a trend. The approach to the manifold is generally in the direction of the ethylene mass fraction. The difference in the magnitudes of the diffusion velocity components for the two scalars cannot be accounted for by the difference in their dissipation time scales. The mixing processes during the approach to the manifold, therefore, cannot be modelled by using different dissipation time scales alone. While the three scalars in this flow have similar distances in scalar space, mixing between two of the scalars can occur only through the third, forcing a detour of the manifold (mixing path) in scalar space. This mixing path presents a challenging test for mixing models since most mixing models use only scalar-space variables and do not take into account the spatial (physical-space) scalar structure. The scalar JPDF and the conditional dissipation rates obtained in the present study have similarities to those of mixture fraction and temperature in turbulent flames. The results in the present study provide a basis for understanding and modelling multiscalar mixing in reactive flows.

JFM classification

Wakes/Jets: Jets Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 495 - 531
Copyright
Copyright © Cambridge University Press 2011

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References

1. Antonia, R. A., Teitel, M., Kim, J. & Browne, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579–605.CrossRefGoogle Scholar
2. Antonopoulos-Domis, M. 1981 Large-eddy simulation of a passive scalar in isotropic turbulence. J. Fluid Mech. 104, 55–79.Google Scholar
3. Bailey, S. C. C., Hultmark, M., Schumacher, J., Yakhot, V. & Smits, A. J. 2009 Measurement of local dissipation scales in turbulent pipe flow. Phys. Rev. Lett. 103, 014502.CrossRefGoogle ScholarPubMed
4. Balarac, G., Si-Ameur, M., Lesieur, M. & Métais, O. 2007 Direct numerical simulations of high velocity ratio coaxial jets: mixing properties and influence of upstream conditions. J. Turbul. 8 (22), 1–27.Google Scholar
5. Buresti, G., Petagna, P. & Talamelli, A. 1998 Experimental investigation on the turbulent near-field of coaxial jets. Exp. Therm. Fluid Sci. 17, 18–36.CrossRefGoogle Scholar
6. Cai, J., Barlow, R. S., Karpetis, A. N. & Tong, C. 2010 Noise correction and length scale estimation for scalar dissipation rate measurements in turbulent partially premixed flames. Flow Turbul. Combust. 85, 309–332.CrossRefGoogle Scholar
7. Cai, J. & Tong, C. 2009 A conditional-sampling-based method for noise and resolution corrections for scalar dissipation rate measurements. Phys. Fluids 21, 065104.CrossRefGoogle Scholar
8. Cai, J., Wang, D., Tong, C., Barlow, R. S. & Karpetis, A. N. 2009 Investigation of subgrid-scale mixing of mixture fraction and temperature in turbulent partially premixed flames. Proc. Combust. Inst. 32, 1517–1525.Google Scholar
9. Dahm, W. J. A & Dimotakis, P. E. 1990 Mixing at large Schmidt number in the self-similar far field of turbulent jets. J. Fluid Mech. 217, 299–330.CrossRefGoogle Scholar
10. Dowling, D. R. & Dimotakis, P. E. 1990 Similarity of concentration field of gas-phase turbulent jets. J. Fluid Mech. 218, 109.Google Scholar
11. Drake, M. C., Pitz, R. W. & Shyy, W. 1986 Conserved scalar probability functions on a turbulent jet flame. J. Fluid Mech. 171, 27–51.CrossRefGoogle Scholar
12. Effelsberg, E. & Peters, N. 1983 A composite model for the conserved scalar PDF. Combust. Flame 50, 351–360.Google Scholar
13. Eswaran, V. & Pope, S. B. 1988 Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids 31 (3), 506–520.Google Scholar
14. Gao, F. 1991 An analytical solution for the scalar probability density-function in homogeneous turbulence. Phys. Fluids A 3, 511–513.Google Scholar
15. Hall, P. 1990 Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems. J. Multivariate Anal. 32, 177–203.Google Scholar
16. Holzer, M. & Pumir, A. 1993 Simple models of non-Gaussian statistics for a turbulently advected passive scalar. Phys. Rev. E 47, 202–219.CrossRefGoogle ScholarPubMed
17. Jaberi, F. A., Miller, R. S., Madnia, C. K. & Givi, P. 1996a Non-Gaussian scalar statistics in homogeneous turbulence. J. Fluid Mech. 313, 241–282.CrossRefGoogle Scholar
18. Jaberi, F. A., Miller, R. S. & Givi, P. 1996b Conditional statistics in turbulent scalar mixing and reaction. AIChE J. 42, 1149–1152.Google Scholar
19. Janicka, J. & Kollmann, W. 1979 A two-variables formalism for the treatment of chemical reaction in turbulent H 2-air diffusion flames. In Seventh Symposium (International) on Combustion, pp. 421–430.Google Scholar
20. Jayesh, & Warhaft, Z. 1991 Probability-distribution of a passive scalar in grid-generated turbulence. Phys. Rev. Lett. 67, 3503–3506.Google Scholar
21. Jayesh, & Warhaft, Z. 1992 Probability distribution, conditional dissipation, and transport of passive temperature fluctuations in grid-generated turbulence. Phys. Fluids A 4, 2292–2307.Google Scholar
22. Juneja, A. & Pope, S. B. 1996 A DNS study of turbulent mixing of two passive scalars. Phys. Fluids 8, 2161–2184.Google Scholar
23. Kailasnath, P., Sreenivasan, K. R. & Saylor, J. R. 1993 Conditional scalar dissipation rates in turbulent wakes, jets, and boundary layers. Phys. Fluids 5, 3207–3215.CrossRefGoogle Scholar
24. Kerstein, A. R. & McMurtry, P. A. 1994 Mean-field theories of random advection. Phys. Rev. E 49, 474–482.CrossRefGoogle ScholarPubMed
25. Komori, S., Hunt, J. C. R., Kanzaki, T. & Murakami, Y. 1991 The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows. J. Fluid Mech. 228, 629–659.Google Scholar
26. Lavertu, R. A. & Mydlarski, L. 2005 Scalar mixing from a concentrated source in turbulent channel flow. J. Fluid Mech. 528, 135–172.Google Scholar
27. Leonard, A. D. & Hill, J. C. 1991 Scalar dissipation and mixing in turbulent reacting flows. Phys. Fluids A 3, 1286–1299.Google Scholar
28. Lockwood, F. C. & Moneib, H. A. 1980 Fluctuating temperature measurements in a heated round free jet. Combust. Sci. Technol. 22, 209–224.Google Scholar
29. Lockwood, F. C. & Naguib, A. S. 1975 The prediction of the fluctuations in the properties of free, round-jet, turbulent, diffusion flames. Combust. Flame 24, 109–124.Google Scholar
30. Ma, B. & Warhaft, Z. 1986 Some aspects of the thermal mixing layer in grid turbulence. Phys. Fluids 29, 3114–3120.Google Scholar
31. Mi, J., Antonia, R. A. & Anselmet, F. 1995 Joint statistics between temperature and its dissipation rate components in a round jet. Phys. Fluids 7, 1665–1673.CrossRefGoogle Scholar
32. Miller, R. S., Frankel, S. H., Madnia, C. K. & Givi, P. 1993 Johnson–Edgeworth translation for probability modelling of binary mixing in turbulent flows. Combust. Sci. Technol. 91, 21–52.Google Scholar
33. O’Brien, E. E. & Jiang, T. L. 1991 The conditional dissipation rate of an initially binary scalar in homogeneous turbulence. Phys. Fluids A 3, 3121–3123.Google Scholar
34. Overholt, M. R. & Pope, S. B. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8, 3128–3148.CrossRefGoogle Scholar
35. Pope, S. B. 1985 PDF methods for turbulent reacting flows. Prog. Energy Combust. Sci. 11, 119–192.Google Scholar
36. Pope, S. B. & Ching, E. 1993 Stationary probability density function in turbulence. Phys. Fluids A 5, 1529–1531.CrossRefGoogle Scholar
37. Prausnitz, J. M., Poling, B. E. & O’Connell, J. P. 2001 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
38. Pumir, A., Shraiman, B. & Siggia, E. D. 1991 Exponential tails and random advection. Phys. Rev. Lett. 66, 2984–2987.CrossRefGoogle ScholarPubMed
39. Reid, R. C., Prausnitz, J. M. & Poling, B. E. 1989 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
40. Rhodes, R. P. 1975 Turbulent Mixing in Non-reactive and Reactive Flows. Plenum.Google Scholar
41. Ruppert, D. 1997 Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. J. Am. Stat. Assoc. 92, 1049–1062.Google Scholar
42. Sabel’nikov, V. A. 1998 Asymptotic solution of the equation for the probability distribution of a passive scalar in grid turbulence with a uniform mean scalar gradient. Phys. Fluids 10, 743–755.CrossRefGoogle Scholar
43. Sahay, A. & O’Brien, E. E. 1993 Uniform mean scalar gradient in grid turbulence: conditioned dissipation and production. Phys. Fluids A 5, 1076–1078.CrossRefGoogle Scholar
44. Shraiman, B. I. & Siggia, E. D. 1994 Lagrangian path-integrals and fluctuations in random flow. Phys. Rev. E 49, 2912–2927.CrossRefGoogle ScholarPubMed
45. Sinai, Y. G. & Yahkot, V. 1989 Limiting probability distribution of a passive scalar in a random velocity field. Phys. Rev. Lett. 63, 1962–1964.Google Scholar
46. Sirivat, A. & Warhaft, Z. 1982 The mixing of passive helium and temperature fluctuations in grid turbulence. J. Fluid Mech. 120, 475–504.CrossRefGoogle Scholar
47. Sreenivasan, K. R. & Antonia, R. A. 1978 Joint probability densities and quadrant contributions in a heated turbulent round jet. AIAA J. 16, 867–868.CrossRefGoogle Scholar
48. Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S. 1980 Temperature fluctuations and scales in grid-generated turbulence. J. Fluid Mech. 100, 597–621.Google Scholar
49. Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure. J. Fluid Mech. 104, 349–367.CrossRefGoogle Scholar
50. Taylor, A. M. K. P. 1993 Instrumentation for Flows with Combustion. Academic.Google Scholar
51. Tong, C. & Warhaft, Z. 1995 Scalar dispersion and mixing in a jet. J. Fluid Mech. 292, 1–38.Google Scholar
52. Venkataramani, K. S. & Chevray, R. 1978 Statistical features of heat-transfer in grid-generated turbulence: constant-gradient case. J. Fluid Mech. 86, 513–543.Google Scholar
53. Venkataramani, K. S., Tutu, N. K. & Chevray, R. 1975 Probability distributions in a round turbulent jet. Phys. Fluids 18, 1413–1420.Google Scholar
54. Villermaux, E. & Rehab, H. 2000 Mixing in coaxial jets. J. Fluid Mech. 425, 161–185.Google Scholar
55. Wand, M. P. & Jones, M. C. 1995 Kernel Smoothing. Chapman & Hall.Google Scholar
56. Wang, G. H. & Clemens, N. T. 2004 Effects of imaging system blur on measurements of flow scalars and scalar gradients. Exp. Fluids 37, 194–205.Google Scholar
57. Warhaft, Z. 1981 The use of dual heat injection to infer scalar covariance decay in grid turbulence. J. Fluid Mech. 104, 93–109.Google Scholar
58. Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.Google Scholar
59. Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659–684.Google Scholar
60. Yeung, P. K. 1998 Correlations and conditional statistics in differential diffusion: scalars with uniform mean gradients. Phys. Fluids 10, 2621–2635.CrossRefGoogle Scholar