Skip to main content
SpringerLink
Log in

Reacting, Circular Mixing Layers in Transition to Turbulence

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

The evolution of a reacting, circular mixing layer - a model of round-jet flow - in its transition to turbulence was studied by direct numerical simulation. An economical Fourier pseudospectral method was combined with the third-order Adams-Bashforth scheme to integrate Navier-Stokes and scalar transport equations. The Reynolds number based on initial mixing-layer diameter and velocity difference was 1600. The initially thin mixing layer encloses a cylindrical core of fuel that mixes and reacts with the surrounding oxidizer. Both fast and finite-rate reactions were examined. The stages in transition are characterized by roll-up of the mixing layer into a sequence of vortex rings, pairing of adjacent rings, azimuthal instability, and breakdown to a disordered (turbulent) state. Reaction surfaces in the fast reaction limit become extended, folded and pinched off at various times corresponding to the dynamics of the vortices observed in the simulations. When the equivalence ratio is O(1) or smaller,the progress of reaction is determined by the dynamics of vortex rings. For larger ratios there is a qualitative difference: Initially, the flame is located well outside the rings and is relatively unaffected. Following breakdown to turbulence, there is a steep increase in flame surface area resulting in a noticeable change in fuel consumption rate. At smaller reaction rates (small Damkohler numbers), the reaction zones are diffuse and fill the vortical (mixed) regions. Product accumulates in and its presence raises the temperature of vortex cores, but reaction rates remain low due to low reactant concentrations. Reaction rates are highest in the braids between vortex rings where scalar dissipation rates and compressive strain rates show the highest values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akselvoll, K. and Moin, P., Large-eddy simulation of turbulent confined coannular jets. J. Fluid Mech. 315(1996) 387-411.

    Article  ADS  Google Scholar 

  2. Bernal, L.P. and Roshko, A., Streamwise vortex structures in plane mixing layers. J. Fluid Mech. 170(1986) 499-525.

    Article  ADS  Google Scholar 

  3. Brancher, P., Chomaz, J.M. and Huerre, P., Direct numerical simulations of round jets: vortex induction and side jets. Phys. Fluids 6(5) (1994) 1768-1774.

    Article  MATH  ADS  Google Scholar 

  4. Broadwell, J.E., Dahm, W.J.A. and Mungal, M.G., Blowout of turbulent diffusion flames. In: 20th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1984) pp. 303-310.

    Google Scholar 

  5. Chen, J.H., Lienau, J.J. and Kollman, W., Numerical simulation of low Re-number turbulence in round jets. In: Durst, F., Kasagi, N., Launder, B.E. and Schmidt, F.W. (eds), Proceedings Turbulent Shear Flows IX. Springer-Verlag, Berlin (1993) pp. 123-145.

    Google Scholar 

  6. Chen, J.H. and Im, H.G., Correlation of flame speed with stretch in turbulent premixed methane/ air flames. In: 27th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1998) pp. 819-826.

    Google Scholar 

  7. Dahm, W.J.A. and Dimotakis, P.E., Measurements of entrainment and mixing in turbulent jets. AIAA Paper 85-0056 (1985).

  8. Dimotakis, P.E., Two-dimensional shear-layer entrainment. AIAA J. 24(11) (1986) 1791-1796.

    ADS  Google Scholar 

  9. Givi, P., Jou, W.-H. and Metcalfe, R.W., Flame extinction in a temporally developing mixing layer. In: 21st Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1986) pp. 1251-1261.

    Google Scholar 

  10. Hasselbrink Jr., E.F. and Mungal, M.G. Characteristics of the velocity field near the instantaneous base of lifted non-premixed turbulent jet flames. In: 27th Symposium (International) Combustion. The Combustion Institute, Pittsburgh (1998) pp. 867-873.

    Google Scholar 

  11. Hermannson, J.C., Mungal, M.G. and Dimotakis, P.E., Heat release effects on shear layer growth and entrainment. AIAA Paper 85-0142 (1985).

  12. Liepmann, D. and Gharib, M., The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245(1992) 643-668.

    Article  ADS  Google Scholar 

  13. Lowery, P.S. and Reynolds, W.C., Numerical simulation of a spatially-developing forced, plane mixing-layer. Stanford University Report No. TF-26 (1986).

  14. Mahalingam, S., Cantwell, B.J. and Ferziger, J.H., Full numerical simulation pf coflowing, axisymmetric jet diffusion flames. Phys. Fluids 2(5) (1990) 720-728.

    Article  ADS  Google Scholar 

  15. Martin, J.E. and Meiburg, E., Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations. J. Fluid Mech. 230(1991) 271-318.

    Article  MATH  ADS  Google Scholar 

  16. Mathew, J. and Basu, A.J., Reacting circular mixing layers in transition to turbulence Part 1: Formulation, general results. Report No. 97-FM-6, Department of Aerospace Engineering, Indian Institute Science, Bangalore (1997).

    Google Scholar 

  17. McMurtry, P.A., Jou, W.-H., Riley, J.J. and Metcalfe, R.W., Direct numerical simulation of a reacting mixing layer with chemical heat release. AIAA J. 24(1986) 962-970.

    ADS  Google Scholar 

  18. Melander, M.V., Hussain, F. and Basu, A.J., Breakdown of a circular jet into turbulence. Turbulent Shear Flows VIII, Munich, Paper 15-5 (1991).

  19. Moser, R.D. and Rogers, M.M., The three-dimensional evolution of a plane mixing layer: Pairing and transition to turbulence J. Fluid Mech. 247(1993) 275-320.

    Article  MATH  ADS  Google Scholar 

  20. Muller, C.M., Breitbach, H. and Peters, N., Partially premixed turbulent flame propagation in jet flames. 25th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1994) pp. 1099-1106.

    Google Scholar 

  21. Mungal, M.G. and Dimotakis, P.E., Mixing and combustion with low heat release in a turbulent shear layer. J. Fluid Mech. 148(1984) 349-382.

    Article  ADS  Google Scholar 

  22. Mungal, M.G. and Frieler, C.E., The effects of Damkohler number in a turbulent shear layer Comb. and Flame 71(1988) 23-34.

    Article  ADS  Google Scholar 

  23. Orszag, S.A.,Numerical simulation of incompressible flows within simple boundaries: I. Galerkin (spectral) representations. Studies Appl. Math. 50(4) (1971) 293-327.

    MATH  MathSciNet  Google Scholar 

  24. Peters, N., Local quenching due to flame stretch and non-premixed turbulent combustion. Comb. Sci. Tech. 30(1983) 1-17.

    Google Scholar 

  25. Pitts, W.M., Assessment of theories for the behavior and blowout of lifted turbulent jet diffusion flames. In: 22nd Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1988) pp. 809-816.

    Google Scholar 

  26. Poinsot, T., Using direct numerical simulation to understand premixed turbulent combustion. In: 26th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1996) pp. 219-232.

    Google Scholar 

  27. Reutch, G.R. and Maxey, M.R., The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4(12) (1992) 2747-2760.

    Article  ADS  Google Scholar 

  28. Riley, J.J. and Metcalfe, R.W., Direct numerical simulations of the turbulent wake of an axisymmetric body. In: Bradbury, L.J.S., Durst, F., Launder, B.E., Schmidt, F.W. and Whitelaw, J.H. (eds), Proceedings Turbulent Shear Flows II. Springer-Verlag, Berlin (1980) pp. 78-93.

    Google Scholar 

  29. Riley, J.J., Metcalfe, R.W. and Orszag, S.A., Direct numerical simulations of chemically reacting turbulent mixing layers. Phys. Fluids 29(2) (1986) 406-422.

    Article  ADS  Google Scholar 

  30. Rogers, M.M. and Moin, P., The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176(1987) 33-66.

    Article  ADS  Google Scholar 

  31. Savas, O. and Golahalli, S.R., Flow structure in near-nozzle region of gas jet flames. AIAA J. 24(7) (1986) 1137-1140.

    Article  ADS  Google Scholar 

  32. Tso, J. and Hussain, F., Organized motions in a fully developed turbulent axisymmetric jet. J. Fluid Mech. 203(1989) 425-448.

    Article  ADS  Google Scholar 

  33. Van Kalmthout, E., Veynante, D. and Candel, S., Direct numerical simulation analysis of flame surface density equation in non-premixed turbulent combustion. In: 26th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh(1996) pp. 35-42.

    Google Scholar 

  34. Williams, F.A., Combustion Theory, 2nd edn. Benjamin-Cummings, Menlo Park (1985).

    Google Scholar 

  35. Winant, C.D. and Browand, F.K., Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63(1974) 237-255.

    Article  ADS  Google Scholar 

  36. Yoda, M., Hesselink, L. and Mungal, M.G., Instantaneous three-dimensional concentration measurements in the self-similar region of a round high-Schmidt-number jet. J. Fluid Mech. 279(1994) 313-350.

    Article  ADS  Google Scholar 

  37. Zaman, K.B.M.Q. and Hussain, A.K.M.F., Vortex pairing in a circular jet under controlled excitation: Part 1, General jet response. J. Fluid Mech. 101(1980) 449-491.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560 012, India

    Joseph Mathew

  2. Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, 560 064, India

    Amit J. Basu

Authors
  1. Joseph Mathew
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amit J. Basu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mathew, J., Basu, A.J. Reacting, Circular Mixing Layers in Transition to Turbulence. Flow, Turbulence and Combustion 64, 71–93 (2000). https://doi.org/10.1023/A:1009955824402

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009955824402

Search

Navigation