Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T04:00:44.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex breakdown in premixed reacting flows with swirl in a finite-length circular open pipe

Published online by Cambridge University Press:  22 March 2016

Zvi Rusak ,
Jung J. Choi ,
Nicholas Bourquard  and
Shixiao Wang
Zvi Rusak*
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Jung J. Choi
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Nicholas Bourquard
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Shixiao Wang
Affiliation:
Department of Mathematics, University of Auckland, 38 Princes Street, Auckland 1142, New Zealand
*
†Email address for correspondence: rusakz@rpi.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A global analysis of steady states of low Mach number inviscid premixed reacting swirling flows in a straight circular finite-length open pipe is developed. We focus on modelling the basic interaction between the swirl and heat release of the reaction. For analytic simplicity, a one-step first-order Arrhenious reaction kinetics is considered in the limit of high activation energy and infinite Peclet number. Assuming a complete reaction with chemical equilibrium upstream and downstream of the reaction zone, a nonlinear partial differential equation is derived for the solution of the flow stream function downstream of the reaction zone in terms of the specific total enthalpy, specific entropy and circulation functions prescribed at the inlet. Several types of solutions of the nonlinear ordinary differential equation for the columnar flow case describe the outlet states of the flow in a long pipe. These solutions are used to form the bifurcation diagram of steady reacting flows with swirl as the inlet swirl level is increased at a fixed heat release from the reaction. The approach is applied to two profiles of inlet flows, the solid-body rotation and the Lamb–Oseen vortex, both with constant profiles of the axial velocity, temperature and mixture reactant mass fraction. The computed results provide theoretical predictions of the critical inlet swirl levels for the appearance of vortex breakdown states and for the size of the breakdown zone as a function of the inlet flow swirl level, Mach number and heat release of the reaction. For the inlet solid-body rotation, flow is decelerated to breakdown as the inlet swirl is increased above the critical swirl level, and there is a delay in the appearance of breakdown with the increase of the heat release of the reaction. For the inlet Lamb–Oseen vortex at low values of heat release, the critical swirl for breakdown is decreased with the increase of heat release while, at high values of heat release, the appearance of breakdown is delayed to higher incoming flow swirl levels with the increase of heat release. The analysis sheds light on the global dynamics of low Mach number reacting flows with swirl and vortex breakdown and on the interaction between vortex breakdown and heat release that affects the shape of the reaction zone in the domain.

JFM classification

Reacting Flows: Combustion Reacting Flows: Reacting Flows Vortex Flows: Vortex breakdown
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 749 - 776
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

Althaus, W., Brüecker, Ch. & Weimer, M. 1995 Breakdown of slender vortices. In Fluid Vortices, pp. 373–426. Kluwer Academic.Google Scholar
Beran, P. S. 1994 The time-asymptotic behavior of vortex breakdown in tubes. Comput. Fluids 23 (7), 913–937.Google Scholar
Buckmaster, J. B. & Ludford, G. S. S. 1982 Theory of Laminar Flames. Cambridge University Press.Google Scholar
Candel, S., Durox, D., Schuller, T., Bourgouin, J.-F. & Moeck, J. P. 2014 Dynamics of swirling flames. Annu. Rev. Fluid Mech. 46, 147–173.Google Scholar
Choi, J. J., Rusak, Z. & Kapila, A. K. 2007 Numerical simulation of premixed chemical reactions with swirl. Combust. Theor. Model. 11 (6), 863–887.Google Scholar
Durox, D., Moeck, J. P., Bourgouin, J.-F., Morenton, P., Viallon, M., Schuller, T. & Candel, S. 2013 Flame dynamics of a variable swirl number system and instability control. Combust. Flame 160 (9), 1729–1742.Google Scholar
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25, 189–229.Google Scholar
Franzelli, B. G., Riber, E., Gicquel, L. Y. M. & Poinsot, T. 2012 Large eddy simulation of combustion instabilities in a lean partially premixed swirled flame. Combust. Flame 159, 621–637.Google Scholar
Grinstein, F. F. & Fureby, C. 2005 LES studies of the flow in a swirl gas combustor. Proc. Combust. Inst. 30, 1791–1798; Part 2.Google Scholar
Grinstein, F. F., Liu, N. S. & Oefelein, J. C. 2006 Introduction: combustion modeling and large eddy simulation: development and validation needs for gas turbines. AIAA J. 44, 673.CrossRefGoogle Scholar
Gupta, A. K., Lilley, D. G. & Syred, N. 1984 Swirl Flows. Abacus Press.Google Scholar
Gupta, A. K., Lewis, M. J. & Qi, S. 1998 Effect of swirl on combustion characteristics in premixed flames. Trans. ASME J. Engng Gas Turbines Power 120, 488–494.CrossRefGoogle Scholar
Gutmark, E., Parr, T., Hanson-Parr, D. & Schadow, K. C. 1992 Structure of a controlled ducted flame. Combust. Sci. Technol. 87, 217–239.Google Scholar
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–217.Google Scholar
Huang, Y. & Yang, V. 2005 Effect of swirl on combustion dynamics in a lean-premixed swirl-stabilized combustor. Proc. Combust. Inst. 30, 1775–1782; Part 2.Google Scholar
Huang, Y., Wang, S. W. & Yang, V. 2006 Systematic analysis of lean-premixed swirl-stabilized combustion. AIAA J. 44 (4), 724–740.Google Scholar
Kalis, H., Marinaki, M., Strautins, U. & Lietuvietis, O. 2015 On the numerical simulation of the vortex breakdown in the combustion process with simple chemical reaction and axial magnetic field. Intl J. Diff. Equ. Applics. 14 (3), 235–250.Google Scholar
Kiesewetter, F., Konle, M. & Sattelmayer, T. 2007 Analysis of combustion induced vortex breakdown driven flame flashback in a premix burner with cylindrical mixing zone. Trans. ASME J. Engng Gas Turbines Power 129 (4), 929–936.CrossRefGoogle Scholar
Konle, M. & Sattelmayer, T. 2009 Interaction of heat release and vortex breakdown during flame flashback driven by combustion induced vortex breakdown. Exp. Fluids 47 (45), 627–635.Google Scholar
Kuo, K. K. 1986 Principles of Combustion. Wiley.Google Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221–246.Google Scholar
Leibovich, S. 1984 Vortex stability and breakdown: survey and extension. AIAA J. 22, 1192–1206.CrossRefGoogle Scholar
Lieuwen, T. & Yang, V. 2005 Combustion instabilities in gas turbine engines: operational experience, fundamental mechanisms, and modeling. In Prog. Astronaut. Aeronaut., vol. 210. Am. Inst. Aeronaut.Google Scholar
Lopez, J. M. 1994 On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe. Phys. Fluids 6, 3683–3693.Google Scholar
Lu, X. Y., Wang, S. W., Sung, H. G., Hsieh, S. Y. & Yang, V. 2005 Large-eddy simulations of turbulent swirling flows injected into a dump chamber. J. Fluid Mech. 527, 171–195.Google Scholar
Malkiel, E., Cohen, J., Rusak, Z. & Wang, S.1996 Axisymmetric vortex breakdown in a pipe-theoretical and experimental studies. In Proceedings of the 36th Israel Annual Conference on Aerospace Sciences, Tel Aviv and Haifa, Israel, pp. 24–34.Google Scholar
Mattner, T. W., Joubert, P. N. & Chong, M. S. 2002 Vortical flow. Part 1. Flow through a constant-diameter pipe. J. Fluid Mech. 463, 259–291.Google Scholar
O’Connor, J. & Lieuwen, T. 2012 Recirculation zone dynamics of a transversely excited swirl flow and flame. Phys. Fluids 24 (7), 075107.CrossRefGoogle Scholar
O’Connor, J., Acharya, V. & Lieuwen, T. 2015 Transverse combustion instabilities: acoustic, fluid mechanic, and flame processes. Prog. Energy Combust. Sci. 49, 1–39.Google Scholar
Paschereit, O., Gutmark, E. & Weisenstein, W. 1998 Control of thermoacoustic instabilities and emissions in an industrial type gas-turbine combustor. In 27th Symposium (International) on Combustion, vol. 2, pp. 1817–1824. Combustion Institute.Google Scholar
Paschereit, C. O., Gutmark, E. & Weisenstein, W. 2000 Excitation of thermoacoustic instabilities by interaction of acoustics and unstable swirling flow. AIAA J. 38, 1025–1034.Google Scholar
Rusak, Z. 1998 The interaction of near-critical swirling flows in a pipe with inlet azimuthal vorticity perturbations. Phys. Fluids 10 (7), 1672–1684.Google Scholar
Rusak, Z., Choi, J. J., Bourquard, N. & Wang, S. 2015 Vortex breakdown of compressible subsonic swirling flows in a finite-length straight circular pipe. J. Fluid Mech. 781, 3–27.Google Scholar
Rusak, Z., Kapila, A. K. & Choi, J. J. 2002 Effect of combustion on near-critical swirling flow. Combust. Theor. Model. 6 (4), 625–645.Google Scholar
Rusak, Z. & Lamb, D. 1999 Prediction of vortex breakdown in leading-edge vortices above slender delta wings. J. Aircraft 36 (4), 659–667.Google Scholar
Rusak, Z. & Wang, S. 2014 Wall-separation and vortex-breakdown zones in a solid-body rotation flow in a rotating finite-length straight circular pipe. J. Fluid Mech. 759, 321–359.Google Scholar
Rusak, Z., Wang, S., Xu, L. & Taylor, S. 2012 On the global nonlinear stability of a near-critical swirling flow in a long finite-length pipe and the path to vortex breakdown. J. Fluid Mech. 712, 295–326.CrossRefGoogle Scholar
Rusak, Z., Whiting, C. H. & Wang, S. 1998 Axisymmetric breakdown of a Q-vortex in a pipe. AIAA J. 36 (10), 1848–1853.Google Scholar
Sarpkaya, T.1995 Vortex breakdown and turbulence. AIAA Paper 95-0433.Google Scholar
Sivasegaram, S. & Whitelaw, J. H. 1991 The influence of swirl on oscillations in ducted premixed flames. Combust. Flame 85, 195–205.Google Scholar
Syred, N. 2006 A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems. Prog. Energy Combust. Sci. 32 (2), 93–161.Google Scholar
Umeh, C. O. U., Rusak, Z. & Gutmark, E. 2012 Vortex breakdown in a swirl-stabilized combustor. J. Propul. Power 28 (5), 1037–1051.Google Scholar
Wang, S. & Rusak, Z. 1996 On the stability of an axisymmetric rotating flow in a pipe. Phys. Fluids 8 (4), 1007–1016.Google Scholar
Wang, S. & Rusak, Z. 1997 The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown. J. Fluid Mech. 340, 177–223.Google Scholar