Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2025-01-04T04:41:32.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Receptivity of the turbulent precessing vortex core: synchronization experiments and global adjoint linear stability analysis

Published online by Cambridge University Press:  06 February 2020

J. S. Müller Open the ORCID record for J. S. Müller [Opens in a new window] ,
F. Lückoff ,
P. Paredes Open the ORCID record for P. Paredes [Opens in a new window] ,
V. Theofilis Open the ORCID record for V. Theofilis [Opens in a new window]  and
K. Oberleithner Open the ORCID record for K. Oberleithner [Opens in a new window]
J. S. Müller*
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Müller-Breslau-Str. 8, 10623Berlin, Germany
F. Lückoff
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Müller-Breslau-Str. 8, 10623Berlin, Germany
P. Paredes
Affiliation:
National Institute of Aerospace, 1100 Exploration Way, Hampton, VA 23666, USA
V. Theofilis
Affiliation:
School of Engineering, University of Liverpool, The Quadrangle, Brownlow Hill, LiverpoolL69 3GH, UK
K. Oberleithner
Affiliation:
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Müller-Breslau-Str. 8, 10623Berlin, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The precessing vortex core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical prediction by global linear stability analysis (LSA) is found. By employing an adjoint LSA, it is found that the PVC is particularly receptive inside the duct upstream of the swirling jet. Open-loop zero-net-mass-flux actuation is applied at different axial positions inside the duct with the goal of frequency synchronization of the PVC. The actuation is shown to have the strongest effect close to the exit of the duct. There, frequency synchronization is reached primarily through direct mode-to-mode interaction. Applying the actuation farther upstream, synchronization is only achieved by a modification of the mean flow that manipulates the swirl number. These experimental observations match qualitatively well with the theoretical receptivity derived from adjoint LSA. Although the process of synchronization is very complex, it is concluded that adjoint LSA based on mean-field theory sufficiently predicts regions of high and low receptivity. Furthermore, the adjoint framework promises to be a valuable tool for finding ideal locations for flow control applications.

JFM classification

Flow Control: Flow Control Instability: Instability Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A3
Copyright
© The Author(s), 2020. Published by 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

Balanov, A., Janson, N., Postnov, D. & Sosnovtseva, O. 2008 Synchronization: From Simple to Complex. Springer Science & Business Media.Google Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750–756.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Chandler, G. J.2011 Sensitivity analysis of low-density jets and flames. PhD thesis, University of Cambridge.Google Scholar
Chigier, N. & Beer, J. 1964 Velocity and static-pressure distributions in swirling air jets issuing from annular and divergent nozzles. Trans. ASME J. Basic Engng 86 (4), 788–796.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Crouch, J., Garbaruk, A. & Magidov, D. 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 (2), 924–940.CrossRefGoogle Scholar
Demaret, P. & Deville, M. O. 1991 Chebyshev collocation solutions of the Navier–Stokes equations using multi-domain finite element preconditioning. J. Comput. Phys. 95 (2), 359–386.CrossRefGoogle Scholar
Dörfler, P., Sick, M. & Coutu, A. 2012 Flow-Induced Pulsation and Vibration in Hydroelectric Machinery. Springer.Google Scholar
Farrell, B. F. & Ioannou, P. J. 1993 Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A 5 (11), 2600–2609.CrossRefGoogle Scholar
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J.-M. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 71–80.CrossRefGoogle Scholar
Ghani, A., Poinsot, T., Gicquel, L. & Müller, J.-D. 2016 LES study of transverse acoustic instabilities in a swirled kerosene/air combustion chamber. Flow Turbul. Combust. 96 (1), 207–226.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
Ivanova, E. M., Noll, B. E. & Aigner, M. 2013 A numerical study on the turbulent schmidt numbers in a jet in crossflow. Trans. ASME J. Engng Gas Turbines Power 135 (1), 011505.CrossRefGoogle Scholar
Juniper, M. P., Li, L. K. & Nichols, J. W. 2009 Forcing of self-excited round jet diffusion flames. Proc. Combust. Inst. 32 (1), 1191–1198.CrossRefGoogle Scholar
Kaiser, T. L., Poinsot, T. & Oberleithner, K. 2018 Stability and sensitivity analysis of hydrodynamic instabilities in industrial swirled injection systems. Trans. ASME J. Engng Gas Turbines Power 140 (5), 051506.CrossRefGoogle Scholar
Khorrami, M. R., Malik, M. R. & Ash, R. L. 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81 (1), 206–229.CrossRefGoogle Scholar
Kirschner, O., Schmidt, H., Ruprecht, A., Mader, R. & Meusburger, P. 2010 Experimental investigation of vortex control with an axial jet in the draft tube of a model pump-turbine. IOP Conf. Ser.: Earth Environ. Sci. 12, 012092.Google Scholar
Kuhn, P., Moeck, J. P., Paschereit, C. O. & Oberleithner, K. 2016 Control of the precessing vortex core by open and closed-loop forcing in the jet core. In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers.Google Scholar
Kurokawa, J., Imamura, H. & Choi, Y.-D. 2010 Effect of J-groove on the suppression of swirl flow in a conical diffuser. Trans. ASME J. Fluids Engng 132 (7), 071101.CrossRefGoogle Scholar
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115–159.CrossRefGoogle Scholar
Luchini, P. & Bottaro, A. 2014 Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46, 493–517.CrossRefGoogle Scholar
Lückoff, F., Sieber, M., Paschereit, C. O. & Oberleithner, K. 2018 Characterization of different actuator designs for the control of the precessing vortex core in a swirl-stabilized combustor. Trans. ASME J. Engng Gas Turbines Power 140 (4), 041503.CrossRefGoogle Scholar
Lückoff, F., Sieber, M., Paschereit, C. O. & Oberleithner, K. 2019 Phase-opposition control of the precessing vortex core in turbulent swirl flames for investigation of mixing and flame stability. J. Engng Gas Turbines Power 141 (11), 111008.CrossRefGoogle Scholar
Magri, L. & Juniper, M. P. 2014 Global modes, receptivity, and sensitivity analysis of diffusion flames coupled with duct acoustics. J. Fluid Mech. 752, 237–265.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.CrossRefGoogle Scholar
Meliga, P., Boujo, E. & Gallaire, F. 2016a A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 800, 327–357.CrossRefGoogle Scholar
Meliga, P., Cadot, O. & Serre, E. 2016b Experimental and theoretical sensitivity analysis of turbulent flow past a square cylinder. Flow Turbul. Combust. 97 (4), 987–1015.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 (6), 061701.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
Nishi, M., Kubota, T., Matsunaga, S. & Senoo, Y. 1980 Study on swirl flow and surge in an elbow type draft tube. In Proceedings of the 10th IAHR Symposium on Hydraulic Machinery and Cavitation, Tokyo, Japan, vol. 1.Google Scholar
Noiray, N. & Schuermans, B. 2013 Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Intl J. Non-Linear Mech. 50, 152–163.CrossRefGoogle Scholar
Oberleithner, K., Paschereit, C. & Wygnanski, I. 2014 On the impact of swirl on the growth of coherent structures. J. Fluid Mech. 741, 156–199.CrossRefGoogle Scholar
Oberleithner, K., Paschereit, C. O., Seele, R. & Wygnanski, I. 2012 Formation of turbulent vortex breakdown: intermittency, criticality, and global instability. AIAA J. 50, 1437–1452.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C., Paschereit, C., Petz, C., Hege, H.-C., Noack, B. & 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
Oden, J. T. & Demkowicz, L. 2017 Applied Functional Analysis. CRC Press.Google Scholar
Paredes, P.2014 Advances in global instability computations: from incompressible to hypersonic flow. PhD thesis, Technical University of Madrid.Google Scholar
Paredes, P., Hermanns, M., Clainche, S. L. & Theofilis, V. 2013 Order 104 speedup in global linear instability analysis using matrix formation. Comput. Meth. Appl. Mech. Engng 253, 287–304.CrossRefGoogle Scholar
Paredes, P., Terhaar, S., Oberleithner, K., Theofilis, V. & Paschereit, C. O. 2016 Global and local hydrodynamic stability analysis as a tool for combustor dynamics modeling. Trans. ASME J. Engng Gas Turbines Power 138 (2), 021504.CrossRefGoogle Scholar
Parezanović, V. & Cadot, O. 2012 Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake. J. Fluid Mech. 693, 115–149.CrossRefGoogle Scholar
Pasche, S., Avellan, F. & Gallaire, F. 2017 Part load vortex rope as a global unstable mode. J. Fluids Engng 139 (5), 051102.CrossRefGoogle Scholar
Pasche, S., Gallaire, F. & Avellan, F. 2018 Predictive control of spiral vortex breakdown. J. Fluid Mech. 842, 58–86.CrossRefGoogle Scholar
Peckham, D. & Atkinson, S.1957 Preliminary results of low speed wind tunnel tests on a gothic wing of aspect ratio, 1.0, aeronaut. Tech. Rep. 508, Royal Aircraft Establishment, Aeronautical Research Council, vol. 18162.Google Scholar
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145–174.CrossRefGoogle Scholar
Qadri, U. A., Mistry, D. & Juniper, M. P. 2013 Structural sensitivity of spiral vortex breakdown. J. Fluid Mech. 720, 558–581.CrossRefGoogle Scholar
Reau, N. & Tumin, A. 2002a Harmonic perturbations in turbulent wakes. AIAA J. 40, 526–530.CrossRefGoogle Scholar
Reau, N. & Tumin, A. 2002b On harmonic perturbations in a turbulent mixing layer. Eur. J. Mech. (B/Fluids) 21, 143–155.CrossRefGoogle Scholar
Reynolds, W. & Hussain, A. 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
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
Rukes, L., Sieber, M., Paschereit, C. O. & Oberleithner, K. 2015 Effect of initial vortex core size on the coherent structures in the swirling jet near field. Exp. Fluids 56 (10), 197.CrossRefGoogle Scholar
Salwen, H. & Grosch, C. E. 1972 The stability of Poiseuille flow in a pipe of circular cross-section. J. Fluid Mech. 54 (1), 93–112.CrossRefGoogle Scholar
Sieber, M., Paschereit, C. O. & Oberleithner, K. 2016 Spectral proper orthogonal decomposition. J. Fluid Mech. 792, 798–828.CrossRefGoogle Scholar
Sieber, M., Paschereit, C. O. & Oberleithner, K. 2017 Advanced identification of coherent structures in swirl-stabilized combustors. Trans. ASME J. Engng Gas Turbines Power 139 (2), 021503.CrossRefGoogle Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.CrossRefGoogle 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 (2), 221–233.CrossRefGoogle Scholar
Stöhr, M., Arndt, C. M. & Meier, W. 2015 Transient effects of fuel–air mixing in a partially-premixed turbulent swirl flame. Proc. Combust. Inst. 35 (3), 3327–3335.CrossRefGoogle Scholar
Stöhr, M., Boxx, I., Carter, C. D. & Meier, W. 2012 Experimental study of vortex-flame interaction in a gas turbine model combustor. Combust. Flame 159, 2636–2649.CrossRefGoogle Scholar
Stöhr, M., Oberleithner, K., Sieber, M., Yin, Z. & Meier, W. 2017 Experimental study of transient mechanisms of bi-stable flame shape transitions in a swirl combustor. In Volume 4B: Combustion, Fuels and Emissions. ASME.Google Scholar
Strykowski, P. & Sreenivasan, K. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 71–107.CrossRefGoogle Scholar
Syred, N. & Beer, J. 1974 Combustion in swirling flows: a review. Combust. Flame 23 (2), 143–201.CrossRefGoogle Scholar
Tammisola, O. & Juniper, M. 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
Terhaar, S., Ćosić, B., Paschereit, C. & Oberleithner, K. 2016 Suppression and excitation of the precessing vortex core by acoustic velocity fluctuations: an experimental and analytical study. Combust. Flame 172, 234–251.CrossRefGoogle Scholar
Terhaar, S., Krüger, O. & Paschereit, C. O. 2015 Flow field and flame dynamics of swirling methane and hydrogen flames at dry and steam diluted conditions. Trans. ASME J. Engng Gas Turbines Power 137 (4), 041503.CrossRefGoogle Scholar
Terhaar, S., Reichel, T. G., Schrödinger, C., Rukes, L., Paschereit, C. O. & Oberleithner, K. 2014 Vortex breakdown and global modes in swirling combustor flows with axial air injection. J. Propul. Power 31 (1), 219–229.CrossRefGoogle Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–315.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Theofilis, V., Duck, P. & Owen, J. 2004 Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249–286.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
Tumin, A. 1996 Receptivity of pipe Poiseuille flow. J. Fluid Mech. 315, 119–137.CrossRefGoogle Scholar
Tumin, A. & Fedorov, A. 1984 Instability wave excitation by a localized vibrator in the boundary layer. J. Appl. Mech. Tech. Phys. 25 (6), 867–873.CrossRefGoogle Scholar
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Wieneke, B. 2005 Stereo-PIV using self-calibration on particle images. Exp. Fluids 39 (2), 267–280.CrossRefGoogle Scholar
Willert, C. 1997 Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8 (12), 1465.CrossRefGoogle Scholar
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exp. Fluids 10 (4), 181–193.CrossRefGoogle Scholar