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Research Papers

Guiding Actuator Designs for Active Flow Control of the Precessing Vortex Core by Adjoint Linear Stability Analysis

[+] Author and Article Information
Jens S. Müller

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Müller-Breslau-Str. 8,
Berlin 10623, Germany
e-mail: jens.mueller@tu-berlin.de

Finn Lückoff, Kilian Oberleithner

Institut für Strömungsmechanik und
Technische Akustik,
Technische Universität Berlin,
Müller-Breslau-Str. 8,
Berlin 10623, Germany

1Corresponding author.

Manuscript received June 22, 2018; final manuscript received July 5, 2018; published online December 7, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 041028 (Dec 07, 2018) (9 pages) Paper No: GTP-18-1312; doi: 10.1115/1.4040862 History: Received June 22, 2018; Revised July 05, 2018

The fundamental impact of the precessing vortex core (PVC) as a dominant coherent flow structure in the flow field of swirl-stabilized gas turbine combustors has still not been investigated in depth. In order to do so, the PVC needs to be actively controlled to be able to set its parameters independently to any other of the combustion system. In this work, open-loop actuation is applied in the mixing section between the swirler and the generic combustion chamber of a nonreacting swirling jet setup to investigate the receptivity of the PVC with regard to its lock-in behavior at different streamwise positions. The mean flow in the mixing section as well as in the combustion chamber is measured by stereoscopic particle image velocimetry (SPIV), and the PVC is extracted from the snapshots using proper orthogonal decomposition (POD). The lock-in experiments reveal the axial position in the mixing section that is most suitable for actuation. Furthermore, a global linear stability analysis (LSA) is conducted to determine the adjoint mode of the PVC which reveals the regions of highest receptivity to periodic actuation based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity data, and the applicability of the adjoint-based model for the prediction of optimal actuator designs is discussed.

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References

Syred, N. , and Beer, J. , 1974, “ Combustion in Swirling Flows: A Review,” Combust. Flame, 23(2), pp. 143–201. [CrossRef]
Oberleithner, K. , Paschereit, C. , and Wygnanski, I. , 2014, “ On the Impact of Swirl on the Growth of Coherent Structures,” J. Fluid Mech., 741, pp. 156–199. [CrossRef]
Moeck, J. P. , Bourgouin, J.-F. , Durox, D. , Schuller, T. , and Candel, S. , 2012, “ Nonlinear Interaction Between a Precessing Vortex Core and Acoustic Oscillations in a Turbulent Swirling Flame,” Combust. Flame, 159(8), pp. 2650–2668. [CrossRef]
Terhaar, S. , Ćosić, B. , Paschereit, C. , and Oberleithner, K. , 2016, “ Suppression and Excitation of the Precessing Vortex Core by Acoustic Velocity Fluctuations: An Experimental and Analytical Study,” Combust. Flame, 172, pp. 234–251. [CrossRef]
Ghani, A. , Poinsot, T. , Gicquel, L. , and Müller, J.-D. , 2016, “ Les Study of Transverse Acoustic Instabilities in a Swirled Kerosene/Air Combustion Chamber,” Flow, Turbul. Combust., 96(1), pp. 207–226. [CrossRef]
Stöhr, M. , Arndt, C. M. , and Meier, W. , 2015, “ Transient Effects of Fuel–Air Mixing in a Partially-Premixed Turbulent Swirl Flame,” Proc. Combust. Inst., 35(3), pp. 3327–3335. [CrossRef]
Terhaar, S. , Krüger, O. , and Paschereit, C. O. , 2015, “ Flow Field and Flame Dynamics of Swirling Methane and Hydrogen Flames at Dry and Steam Diluted Conditions,” ASME J. Eng. Gas Turbines Power, 137(4), p. 041503. [CrossRef]
Oberleithner, K. , Sieber, M. , Nayeri, C. , Paschereit, C. , Petz, C. , Hege, H.-C. , Noack, B. , and Wygnanski, I. , 2011, “ Three-Dimensional Coherent Structures in a Swirling Jet Undergoing Vortex Breakdown: Stability Analysis and Empirical Mode Construction,” J. Fluid Mech., 679, pp. 383–414. [CrossRef]
Paredes, P. , Terhaar, S. , Oberleithner, K. , Theofilis, V. , and Paschereit, C. O. , 2016, “ Global and Local Hydrodynamic Stability Analysis as a Tool for Combustor Dynamics Modeling,” ASME J. Eng. Gas Turbines Power, 138(2), p. 021504. [CrossRef]
Tammisola, O. , and Juniper, M. , 2016, “ Coherent Structures in a Swirl Injector at Re= 4800 by Nonlinear Simulations and Linear Global Modes,” J. Fluid Mech., 792, pp. 620–657. [CrossRef]
Kaiser, T. L. , Poinsot, T. , and Oberleithner, K. , 2018, “ Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems,” ASME J. Eng. Gas Turbines Power, 140(5), p. 051506. [CrossRef]
Giannetti, F. , and Luchini, P. , 2007, “ Structural Sensitivity of the First Instability of the Cylinder Wake,” J. Fluid Mech., 581, pp. 167–197. [CrossRef]
Marquet, O. , Sipp, D. , and Jacquin, L. , 2008, “ Sensitivity Analysis and Passive Control of Cylinder Flow,” J. Fluid Mech., 615, pp. 221–252. [CrossRef]
Meliga, P. , Pujals, G. , and Serre, E. , 2012, “ Sensitivity of 2D Turbulent Flow past a d-Shaped Cylinder Using Global Stability,” Phys. Fluids, 24(6), p. 061701. [CrossRef]
Meliga, P. , Boujo, E. , and Gallaire, F. , 2016, “ A Self-Consistent Formulation for the Sensitivity Analysis of Finite-Amplitude Vortex Shedding in the Cylinder Wake,” J. Fluid Mech., 800, pp. 327–357. [CrossRef]
Magri, L. , and Juniper, M. P. , 2014, “ Global Modes, Receptivity, and Sensitivity Analysis of Diffusion Flames Coupled With Duct Acoustics,” J. Fluid Mech., 752, pp. 237–265. [CrossRef]
Kuhn, P. , Moeck, J. P. , Paschereit, C. O. , and Oberleithner, K. , 2016, “ Control of the Precessing Vortex Core by Open and Closed-Loop Forcing in the Jet Core,” ASME Paper No. GT2016-57686.
Reynolds, W. , and 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), pp. 263–288. [CrossRef]
Berkooz, G. , Holmes, P. , and Lumley, J. L. , 1993, “ The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows,” Annu. Rev. Fluid Mech., 25(1), pp. 539–575. [CrossRef]
Rukes, L. , Paschereit, C. O. , and Oberleithner, K. , 2016, “ An Assessment of Turbulence Models for Linear Hydrodynamic Stability Analysis of Strongly Swirling Jets,” Eur. J. Mech.-B/Fluids, 59, pp. 205–218. [CrossRef]
Ivanova, E. M. , Noll, B. E. , and Aigner, M. , 2013, “ A Numerical Study on the Turbulent Schmidt Numbers in a Jet in Crossflow,” ASME J. Eng. Gas Turbines Power, 135(1), p. 011505. [CrossRef]
Barkley, D. , 2006, “ Linear Analysis of the Cylinder Wake Mean Flow,” Europhys. Lett, 75(5), pp. 750–756. [CrossRef]
Paredes, P. , 2014, “ Advances in Global Instability Computations: From Incompressible to Hypersonic Flow,” Ph.D. thesis, Technical University of Madrid, Madrid, Spain.
Meliga, P. , Gallaire, F. , and Chomaz, J.-M. , 2012, “ A Weakly Nonlinear Mechanism for Mode Selection in Swirling Jets,” J. Fluid Mech., 699, pp. 216–262. [CrossRef]
Magri, L. , and Juniper, M. P. , 2014, “ Adjoint-Based Linear Analysis in Reduced-Order Thermo-Acoustic Models,” Int. J. Spray Combust. Dyn., 6(3), pp. 225–246. [CrossRef]
Balanov, A. , Janson, N. , Postnov, D. , and Sosnovtseva, O. , 2008, Synchronization: From Simple to Complex, Springer Science & Business Media, Berlin.
Oberleithner, K. , 2012, “ On Turbulent Swirling Jets: Vortex Breakdown, Coherent Structures, and Their Control,” Ph.D. thesis, Universitätsbibliothek der Technischen Universität Berlin, Berlin.
Lückoff, F. , Sieber, M. , Paschereit, C. O. , and Oberleithner, K. , 2018, “ Characterization of Different Actuator Designs for the Control of the Precessing Vortex Core in a Swirl-Stabilized Combustor,” ASME J. Eng. Gas Turbines Power, 140(4), p. 041503. [CrossRef]

Figures

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Fig. 1

Experimental setup: (a) sectional view, with SPIV domains and actuator position xa/D=−2 and (b) top view, with pressure tap positions, laser sheet and camera arrangement

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Fig. 2

Normalized mean flow, normalized POD mode and normalized LSA mode: (a) mean flow, axial, (b) POD mode, transverse, and (c) LSA mode, transverse

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Fig. 3

Eigenvalue spectrum with frequency ℜ(f) and growth rate ℑ(f) of the eigenvalues, selected PVC mode (filled circle •) and measured experimental frequency (vertical solid line)

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Fig. 4

Normalized absolute value of the adjoint LSA modes (left: axial, center: transverse/radial, right: out-of-plane/azimuthal)

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Fig. 5

Forcing modes and their external feedback in lock-in state inside the tube for xa/D=−2, ff/fn=0.95: (a) normalized absolute value of forcing modes (left: axial, center: transverse/radial, right: out-of-plane/azimuthal) and (b) normalized external feedback for each forcing component (left: axial, center: transverse/radial, right: out-of-plane/azimuthal)

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Fig. 6

Normalized theoretical receptivity and experimental receptivity for varied actuator positions xa/D

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Fig. 7

Lock-in diagram with linear fits for varied actuator positions xa/D

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