Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T17:17:25.808Z Has data issue: false hasContentIssue false
  • English
  • Français

A weakly nonlinear analysis of the precessing vortex core oscillation in a variable swirl turbulent round jet

Published online by Cambridge University Press:  13 December 2019

Kiran Manoharan ,
Mark Frederick ,
Sean Clees ,
Jacqueline O’Connor  and
Santosh Hemchandra Open the ORCID record for Santosh Hemchandra [Opens in a new window]
Kiran Manoharan
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bengaluru, Karnataka560012, India
Mark Frederick
Affiliation:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA16802, USA
Sean Clees
Affiliation:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA16802, USA
Jacqueline O’Connor
Affiliation:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA16802, USA
Santosh Hemchandra*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bengaluru, Karnataka560012, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the emergence of precessing vortex core (PVC) oscillations in a swirling jet experiment. We vary the swirl intensity while keeping the net mass flow rate fixed using a radial-entry swirler with movable blades upstream of the jet exit. The swirl intensity is quantified in terms of a swirl number $S$. Time-resolved velocity measurements in a radial–axial plane anchored at the jet exit for various $S$ values are obtained using stereoscopic particle image velocimetry. Spectral proper orthogonal decomposition and spatial cross-spectral analysis reveal the simultaneous emergence of a bubble-type vortex breakdown and a strong helical limit-cycle oscillation in the flow for $S>S_{c}$ where $S_{c}=0.61$. The oscillation frequency, $f_{PVC}$, and the square of the flow oscillation amplitudes vary linearly with $S-S_{c}$. A solution for the coherent unsteady field accurate up to $O(\unicode[STIX]{x1D716}^{3})$ ($\unicode[STIX]{x1D716}\sim O((S-S_{c})^{1/2})$) is determined from the nonlinear Navier–Stokes equations, using the method of multiple scales. We show that onset of bubble type vortex breakdown at $S_{c}$, results in a marginally stable, helical linear global hydrodynamic mode. This results in the stable limit-cycle precession of the breakdown bubble. The variation of $f_{LC}$ with $S-S_{c}$ is determined from the Stuart–Landau equation associated with the PVC. Reasonable agreement with the corresponding experimental result is observed, despite the highly turbulent nature of the flow in the present experiment. Further, amplitude saturation results from the time-averaged distortion imposed on the flow by the PVC, suggesting that linear stability analysis may predict PVC characteristics for $S>S_{c}$.

JFM classification

Vortex Flows: Vortex breakdown Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A29
Copyright
© 2019 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

Anacleto, P. M., Fernandes, E. C., Heitor, M. V. & Shtork, S. I. 2003 Swirl flow structure and flame characteristics in a model lean premixed combustor. Combust. Sci. Technol. 175 (8), 1369–1388.CrossRefGoogle Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14 (04), 529–551.CrossRefGoogle Scholar
Bayliss, A., Class, A. & Matkowsky, B. J. 1995 Adaptive approximation of solutions to problems with multiple layers by Chebyshev pseudo-spectral methods. J. Comput. Phys. 116 (1), 160–172.CrossRefGoogle Scholar
Bayliss, A. & Turkel, E. 1992 Mappings and accuracy for Chebyshev pseudo-spectral approximations. J. Comput. Phys. 101 (2), 349–359.CrossRefGoogle Scholar
Beér, J. M. & Chigier, N. A. 1972 Combustion Aerodynamics. Academic.Google Scholar
Bendat, J. S. & Piersol, A. G. 2011 Random Data: Analysis and Measurement Procedures. Wiley.Google Scholar
Benjamin, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14 (4), 593–629.CrossRefGoogle Scholar
Billant, P., Chomaz, J. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183–219.CrossRefGoogle Scholar
Boyd, J. P. 2000 Chebyshev and Fourier Spectral Methods. Dover.Google Scholar
Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84 (2), 119–144.CrossRefGoogle Scholar
Clees, S., Lewalle, J., Frederick, M. & O’Connor, J.2018 Vortex core dynamics in a swirling jet near vortex breakdown. AIAA Paper 2018-0052.CrossRefGoogle Scholar
Douglas, C. M., Smith, T., Emerson, B. L., Manoharan, K., Hemchandra, S. & Lieuwen, T. C.2018 Hydrodynamic receptivity predictions and measurements of an acoustically forced multi-nozzle swirl combustor. AIAA Paper 2018-0587.CrossRefGoogle Scholar
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25 (2), 189–229.CrossRefGoogle Scholar
Escudier, M. P. & Keller, J. 1985 Recirculation in swirling flow – a manifestation of vortex breakdown. AIAA J. 23 (1), 111–116.CrossRefGoogle Scholar
Frederick, M., Manoharan, K., Dudash, J., Brubaker, B., Hemchandra, S. & O’Connor, J. 2018 Impact of precessing vortex core dynamics on shear layer response in a swirling jet. J. Engng Gas Turbin. Power 140 (6), 061503.Google Scholar
Gallaire, F. & Chomaz, J. 2003a Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2003b Instability mechanisms in swirling flows. Phy. Fluids 15 (9), 2622–2639.CrossRefGoogle Scholar
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 71–80.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4 (1), 195–218.CrossRefGoogle Scholar
Hill, D. 1992 A theoretical approach for analyzing the restabilization of wakes. In 30th Aerospace Sciences Meeting and Exhibit, p. 67.Google Scholar
Huang, Y. & Yang, V. 2009 Dynamics and stability of lean-premixed swirl-stabilized combustion. Prog. Energy Combust. Sci. 35 (4), 293–364.CrossRefGoogle Scholar
Juniper, M. P. 2012 Absolute and convective instability in gas turbine fuel injectors. In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, pp. 189–198. American Society of Mechanical Engineers.Google Scholar
Juniper, M. P. & Pier, B. 2015 The structural sensitivity of open shear flows calculated with a local stability analysis. Eur. J. Mech. (B/Fluids) 49, 426–437.CrossRefGoogle Scholar
Laizet, S. & Li, N. 2011 Incompact3d: a powerful tool to tackle turbulence problems with up to O (105) computational cores. Intl J. Numer. Meth. Fluids 67 (11), 1735–1757.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics: Course of Theoretical Physics, vol. 6. Butterworth, Heinemann.Google Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10 (1), 221–246.CrossRefGoogle Scholar
Liang, H. & Maxworthy, T. 2004 Vortex breakdown and mode selection of a swirling jet in stationary or rotating surroundings. In APS Division of Fluid Dynamics Meeting Abstracts, vol. 1.Google Scholar
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115–159.CrossRefGoogle Scholar
Lieuwen, T. C. 2012 Unsteady Combustor Physics. Cambridge University Press.CrossRefGoogle Scholar
Loiseleux, T., Delbende, I. & Huerre, P. 2000 Absolute and convective instabilities of a swirling jet/wake shear layer. Phys. Fluids 12 (2), 375–380.CrossRefGoogle Scholar
Lucca-Negro, O. & O’Doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27 (4), 431–481.CrossRefGoogle Scholar
Manoharan, K.2019 Local and global hydrodynamic instability mechanisms of swirled jets. PhD thesis, Indian Institute of Science.Google Scholar
Manoharan, K., Hansford, S., OConnor, J. & Hemchandra, S.2015 Instability mechanism in a swirl flow combustor: precession of vortex core and influence of density gradient. In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, ASME Paper GT2015-42985.Google Scholar
Manoharan, K., Smith, T., Emerson, B., Douglas, C. M., Lieuwen, T. & Hemchandra, S.2017 Velocity field response of a forced swirl stabilized premixed flame. In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, ASME Paper GT2017-63936.Google Scholar
Meliga, P., Gallaire, F. & Chomaz, J.-M. 2012 A weakly nonlinear mechanism for mode selection in swirling jets. J. Fluid Mech. 699, 216–262.CrossRefGoogle Scholar
Moeck, J. P., Bourgouin, J.-F., Durox, D., Schuller, T. & Candel, S. 2012 Nonlinear interaction between a precessing vortex core and acoustic oscillations in a turbulent swirling flame. Combust. Flame 159 (8), 2650–2668.CrossRefGoogle Scholar
Moise, P. & Mathew, J. 2019 Bubble and conical forms of vortex breakdown in swirling jets. J. Fluid Mech. 873, 322–357.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.CrossRefGoogle Scholar
Muthiah, G. & Samanta, A. 2018 Transient energy growth of a swirling jet with vortex breakdown. J. Fluid Mech. 856, 288–322.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C. N., Paschereit, C. O., Petz, C., Hege, H.-C., Noack, B. R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.CrossRefGoogle Scholar
Oberleithner, K., Stöhr, M., Im, S. H., Arndt, C. M. & Steinberg, A. M. 2015 Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: experiments and linear stability analysis. Combust. Flame 162 (8), 3100–3114.CrossRefGoogle Scholar
Olendraru, C. & Sellier, A. 2002 Viscous effects in the absolute-convective instability of the batchelor vortex. J. Fluid Mech. 459, 371–396.CrossRefGoogle Scholar
Olendraru, C., Sellier, A., Rossi, M. & Huerre, P. 1999 Inviscid instability of the batchelor vortex: absolute-convective transition and spatial branches. Phys. Fluids 11 (7), 1805–1820.CrossRefGoogle Scholar
Pradeep, M.2018 Simulations of bubble and conical forms of vortex breakdown in swirling jets. PhD thesis, Indian Institute of Science.Google Scholar
Qadri, U. A., Mistry, D. & Juniper, M. P. 2013 Structural sensitivity of spiral vortex breakdown. J. Fluid Mech. 720, 558–581.CrossRefGoogle Scholar
Renaud, A., Ducruix, S. & Zimmer, L. 2019 Experimental study of precessing vortex core impact on liquid fuel spray in a gas turbine combustor. In GT2019-91619: ASME Turbo Expo Turbine Technical Conference and Exposition, pp. 1–16. American Society of Mechanical Engineers.Google Scholar
Reynolds, W. C. & Hussain, AKMF. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Rigas, G., Morgans, A. S. & Morrison, J. F. 2017 Weakly nonlinear modelling of a forced turbulent axisymmetric wake. J. Fluid Mech. 814, 570–591.CrossRefGoogle Scholar
Ruith, M. R., Chen, P., Meiburg, E. & Maxworthy, T. 2003 Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation. J. Fluid Mech. 486, 331–378.CrossRefGoogle Scholar
Rukes, L., Paschereit, C. O. & Oberleithner, K. 2016 An assessment of turbulence models for linear hydrodynamic stability analysis of strongly swirling jets. Eur. J. Mech. (B/Fluids) 59, 205–218.CrossRefGoogle Scholar
Sarpkaya, T. 1971a On stationary and travelling vortex breakdowns. J. Fluid Mech. 45 (3), 545–559.CrossRefGoogle Scholar
Sarpkaya, T. 1971b Vortex breakdown in swirling conical flows. AIAA J. 9 (9), 1792–1799.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, vol. 142. Springer.CrossRefGoogle Scholar
Shanbhogue, S. J., Sanusi, Y. S., Taamallah, S., Habib, M. A., Mokheimer, E. M. A. & Ghoniem, A. F. 2016 Flame macrostructures, combustion instability and extinction strain scaling in swirl-stabilized premixed CH4/H2 combustion. Combust. Flame 163, 494–507.CrossRefGoogle Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.CrossRefGoogle Scholar
Smith, T. E., Douglas, C. M., Emerson, B. L. & Lieuwen, T. C. 2018 Axial evolution of forced helical flame and flow disturbances. J. Fluid Mech. 844, 323–356.CrossRefGoogle 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.CrossRefGoogle Scholar
Syred, N., O’Doherty, T. & Froud, D. 1994 The interaction of the precessing vortex core and reverse flow zone in the exhaust of a swirl burner. Proc. Inst. Mech. Engng 208 (1), 27–36.CrossRefGoogle Scholar
Taamallah, S., Shanbhogue, S. J. & Ghoniem, A. F. 2016 Turbulent flame stabilization modes in premixed swirl combustion: physical mechanism and Karlovitz number-based criterion. Combust. Flame 166, 19–33.CrossRefGoogle Scholar
Tammisola, O. & Juniper, M. P. 2016 Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes. J. Fluid Mech. 792, 620–657.CrossRefGoogle Scholar
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar