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Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

Published online by Cambridge University Press:  08 January 2016

Benjamin Emerson
Affiliation:
Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Tim Lieuwen
Affiliation:
Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Matthew P. Juniper
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Corresponding
E-mail address:

Abstract

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

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Papers
Copyright
© 2016 Cambridge University Press 

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References

Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750756.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539575.CrossRefGoogle Scholar
Biancofiore, L., Gallaire, F., Laure, P. & Hachem, E. 2014 Direct numerical simulations of two-phase immiscible wakes. Fluid Dyn. Res. 46, 041409.CrossRefGoogle Scholar
Cardell, G. S.1993 Flow past a circular cylinder with a permeable wake splitter plate. PhD thesis, California Institute of Technology.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.CrossRefGoogle Scholar
Cross, C., Fricker, A., Shcherbik, D., Lubarsky, E., Zinn, B. T. & Lovett, J. A. 2010 Dynamics of non-premixed bluff body-stabilized flames in heated air flow. In ASME Turbo Expo 2010: Power for Land, Sea, and Air, October 10, 2010, pp. 875884. American Society of Mechanical Engineers.Google Scholar
Emerson, B.2013 Dynamical characteristics of reacting bluff body wakes. PhD thesis, School of Aerospace Engineering, Georgia Institute of Technology.Google Scholar
Emerson, B., Murphy, K. & Lieuwen, T. 2013 Flame density ratio effects on vortex dynamics of harmonically exrefd bluff body stabilized flames. In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, June 3, 2013, pp. V01AT04A014V01AT04A014. American Society of Mechanical Engineers.Google Scholar
Emerson, B., O’Connor, J., Juniper, M. & Lieuwen, T. 2012 Density ratio effects on reacting bluff-body flow field characteristics. J. Fluid Mech. 706, 219250.CrossRefGoogle Scholar
Erickson, R. R., Soteriou, M. C. & Mehta, P. G. 2006 The influence of temperature ratio on the dynamics of bluff body stabilized flames. In 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2006, pp. 912.Google Scholar
Fincham, A. M. & Spedding, G. R. 1997 Low cost, high resolution DPIV for measurement of turbulent fluid flow. Exp. Fluids 23, 449462.CrossRefGoogle Scholar
Fransson, J. H. M., Konieczny, P. & Alfredsson, P. H. 2004 Flow around a porous cylinder subject to continuous suction or blowing. J. Fluids Struct. 19 (8), 10311048.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 Modal and transient dynamics of jet flows. Phys. Fluids 25, 044103.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167197.CrossRefGoogle Scholar
Gülder, Ö., Smallwood, G., Wong, R., Snelling, D. R., Smith, R., Deschamps, B. M. & Sautet, J.-C. 2000 Flame front surface characteristics in turbulent premixed propane/air combustion. Combust. Flame 120, 407416.CrossRefGoogle Scholar
Hill, D. C.1992 A theoretical approach for analysing the restabilization of wakes. Tech. Rep. 103858, NASA Tech. Memorandum.Google Scholar
Huerre, P. & Monkewitz, P. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffat, H. K. & Worster, M. G.), Cambridge University Press.Google Scholar
Juniper, M. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171195.CrossRefGoogle Scholar
Juniper, M. & Candel, S. 2003 The stability of ducted compound flows and consequences for the geometry of coaxial injectors. J. Fluid Mech. 482, 257269.CrossRefGoogle Scholar
Juniper, M. & Pier, B. 2015 The structural sensitivity of open shear flows calculated with a local stability analysis. Eur. J. Mech. (B/Fluids) 49, 426437.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, June 11, 2012, pp. 189198. American Society of Mechanical Engineers.Google Scholar
Juniper, M. P., Tammisola, O. & Lundell, F. 2011 The local and global stability of confined planar wakes at intermediate Reynolds number. J. Fluid Mech. 686, 218238.CrossRefGoogle Scholar
Kiel, B., Garwick, K., Lynch, A., Gord, J. R. & Meyer, T. 2006 Non-reacting and combusting flow investigation of bluff bodies in cross flow. In 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 2006, vol. 5234.Google Scholar
Konstantinidis, E., Balabani, S. & Yianneskis, M. 2007 Bimodal vortex shedding in a perturbed cylinder wake. Phys. Fluids 19, 011701.CrossRefGoogle Scholar
Landau, L. D. 1944 On the problem of turbulence. C. R. Acad. Sci. URSS 44, 311314.Google Scholar
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19, 024102,1–11.CrossRefGoogle Scholar
Lieuwen, T. 2012 Unsteady Combustor Physics. Cambridge University Press.CrossRefGoogle Scholar
Luchini, P., Giannetti, F. & Pralits, J. 2009 Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder. In IUTAM Symp. on Unsteady Separated Flows and their Control (ed. Braza, M. & Hourigan, K.), IUTAM Bookseries, vol. 14, pp. 151160. Springer.CrossRefGoogle Scholar
Ma, X., Karamanos, G.-S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality of a turbulent near wake. J. Fluid Mech. 410, 2965.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221252.CrossRefGoogle Scholar
Mei, R. 1996 Velocity fidelity of flow tracer particles. Exp. Fluids 22, 113.CrossRefGoogle Scholar
Meliga, P., Pujals, G. & Serre, E. 2012 Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability. Phys. Fluids 24, 061701.CrossRefGoogle Scholar
Meliga, P., Sipp, D. & Chomaz, J.-M. 2008 Absolute instability in axisymmetric wakes: compressible and density variation effects. J. Fluid Mech. 600, 373401.CrossRefGoogle Scholar
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8, 14061416.CrossRefGoogle Scholar
Mettot, C., Sipp, D. & Bezard, H. 2014 Quasi-laminar stability and sensitivity analyses for turbulent flows: prediction of low-frequency unsteadiness and passive control. Phys. Fluids 26, 045112.CrossRefGoogle Scholar
Nogueria, J., Lecuona, A. & Rodriguez, P. A. 1997 Data validation, false vectors correction and derived magnitudes calculation on PIV data. Meas. Sci. Technol. 8, 14931501.CrossRefGoogle Scholar
O’Connor, J. & Lieuwen, T. 2011 Disturbance field characteristics of a transversely exrefd burner. Combust. Sci. Technol. 183, 427443.CrossRefGoogle Scholar
Parezanovic, V. & Cadot, O. 2012 Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake. J. Fluid Mech. 693, 115149.CrossRefGoogle Scholar
Perrin, R., Braza, M., Cid, E., Cazin, S., Barthet, A., Sevrain, A., Mockett, C. & Thiele, F. 2007 Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD. Exp. Fluids 43, 341355.CrossRefGoogle Scholar
Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107132.CrossRefGoogle Scholar
Pier, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 3961.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 1996 Fully nonlinear global modes in spatially developing media. Physica D 97, 206222.CrossRefGoogle Scholar
Poinsot, T. J., Trouve, A. C., Veynante, D. P., Candel, S. M. & Esposito, E. J. 1987 Vortex-driven acoustically coupled combustion instabilities. J. Fluid Mech. 177, 265292.CrossRefGoogle Scholar
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 122.CrossRefGoogle Scholar
Rees, S. J. & Juniper, M. P. 2010 The effect of confinement on the stability of viscous planar jets and wakes. J. Fluid Mech. 656, 309336.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263288.CrossRefGoogle Scholar
Roshko, A.1954 On the development of turbulent wakes from vortex streets. National Advisory Committee for Aeronautics. Tech. Note 2913. California Institute of Technology.Google Scholar
Shanbhogue, S. J., Husain, S. & Lieuwen, T. 2009 Lean blowoff of bluff body stabilized flames: scaling and dynamics. Prog. Energy Combust. Sci. 35, 98120.CrossRefGoogle Scholar
Smith, D. A. & Zukoski, E. E. 1985 Combustion instability sustained by unsteady vortex combustion. In AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit, Monterey, CA, July 8–10, 1985, vol. 5234.Google Scholar
Soria, J. 1996 An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp. Therm. Fluid Sci. 12, 221233.CrossRefGoogle Scholar
Soteriou, M. C. & Ghoniem, A. F. 1994 The vorticity dynamics of an exothermic, spatially developing, forced reacting shear layer. Proc. Combust. Inst. 25, 12651272.CrossRefGoogle Scholar
Strykowski, P. J. & Sreenivasan, K. R. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 71107.CrossRefGoogle Scholar
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 121.CrossRefGoogle Scholar
Willert, C. E. 1991 Digital particle image velocimetry. Exp. Fluids 10, 181193.CrossRefGoogle Scholar
Yu, M.-H. & Monkewitz, P. A. 1990 The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids 2, 11751181.CrossRefGoogle Scholar
Zdravkovich, M. M.1997 Flow around circular cylinders: a comprehensive guide through flow phenomena, experiments, applications, mathematical models, and computer simulations. Oxford University Press.Google Scholar
Zinn, B. T. & Lieuwen, T. 2005 Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling (ed. Lieuwen, T. & Yang, V.), Progress in Astronautics and Aeronautics, vol. 210, pp. 324. American Institute of Aeronautics and Astronautics.Google Scholar

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