0
Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

[+] Author and Article Information
Thomas L. Kaiser

Institut de Mécanique des Fluides de Toulouse,
UMR CNRS/INP-UPS 5502,
Toulouse 31400, France
e-mail: tkaiser@imft.fr

Thierry Poinsot

Institut de Mécanique des Fluides de Toulouse,
UMR CNRS/INP-UPS 5502,
Toulouse 31400, France

Kilian Oberleithner

Chair of Fluid Dynamics,
Technische Universität Berlin,
Berlin 10623, Germany

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 28, 2017; final manuscript received August 22, 2017; published online January 10, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(5), 051506 (Jan 10, 2018) (10 pages) Paper No: GTP-17-1409; doi: 10.1115/1.4038283 History: Received July 28, 2017; Revised August 22, 2017

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations (LES) show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core (PVC). Mean flow fields of LES, validated by experimental particle image velocimetry (PIV) measurements, are used as input for both local and global linear stability analysis (LSA). It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local LSA are compared to dynamic mode decomposition (DMD) based on LES snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the PVC.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ghani, A. , Poinsot, T. , Gicquel, L. Y. , 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]
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]
Stöhr, M. , Boxx, I. , Carter, C. D. , and Meier, W. , 2012, “Experimental Study of Vortex-Flame Interaction in a Gas Turbine Model Combustor,” Combust. Flame, 159(8), pp. 2636–2649. [CrossRef]
Lessen, M. , Singh, P. J. , and Paillet, F. , 1974, “The Stability of a Trailing Line Vortex—Part 1: Inviscid Theory,” J. Fluid Mech., 63(4), pp. 753–763. [CrossRef]
Chomaz, J.-M. , Huerre, P. , and Redekopp, L. G. , 1991, “A Frequency Selection Criterion in Spatially Developing Flows,” Stud. Appl. Math., 84(2), pp. 119–144. [CrossRef]
Pier, B. , Huerre, P. , and Chomaz, J.-M. , 2001, “Bifurcation to Fully Nonlinear Synchronized Structures in Slowly Varying Media,” Phys. D, 148(1–2), pp. 49–96. [CrossRef]
Gallaire, F. , Ruith, M. , Meiburg, E. , Chomaz, J.-M. , and Huerre, P. , 2006, “Spiral Vortex Breakdown as a Global Mode,” J. Fluid Mech., 549, pp. 71–80. [CrossRef]
Oberleithner, K. , Sieber, M. , Nayeri, C. , Paschereit, C. , Petz, C. , Hege, H. , 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(7), pp. 383–414. [CrossRef]
Oberleithner, K. , Schimek, S. , and Paschereit, C. O. , 2015, “Shear Flow Instabilities in Swirl-Stabilized Combustors and Their Impact on the Amplitude Dependent Flame Response: A Linear Stability Analysis,” Combust. Flame, 162(1), pp. 86–99. [CrossRef]
Pierrehumbert, R. T. , and Widnall, S. E. , 1982, “The Two- and Three-Dimensional Instabilities of a Spatially Periodic Shear Layer,” J. Fluid Mech., 114, pp. 59–82. [CrossRef]
Barkley, D. , 2006, “Linear Analysis of the Cylinder Wake Mean Flow,” EPL (Europhys. Lett.), 75(5), pp. 750–756. [CrossRef]
Fabre, D. , Bonnefisa, P. , Charru, F. , Russo, S. , Citro, V. , Giannetti, F. , and Luchini, P. , 2014, “Application of Global Stability Approaches to Whistling Jets and Wind Instruments,” International Symposium on Musical Acoustics (ISMA), Le Mans, France, July 7–12, pp. 23–28. https://www.imft.fr/IMG/pdf/H000021.pdf
Juniper, M. P. , and Pier, B. , 2015, “The Structural Sensitivity of Open Shear Flows Calculated With a Local Stability Analysis,” Eur. J. Mech.-B/Fluids, 49(Pt. B), pp. 426–437. [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]
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]
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. , 2012, “A Numerical Study on the Turbulent Schmidt Numbers in a Jet in Crossflow,” ASME J. Eng. Gas Turbines Power, 135(1), p. 011505. [CrossRef]
Theofilis, V. , 2011, “Global Linear Instability,” Annu. Rev. Fluid Mech., 43, pp. 319–352. [CrossRef]
Hecht, F. , 2012, “New Development in FreeFem++,” J. Numer. Math., 20(3–4), pp. 251–265.
Lehoucq, R. , Sorensen, D. , and Yang, C. , 1997, Arpack Users' Guide: Solution of Large Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia, PA.
Paredes, P. , Hermanns, M. , Le Clainche, S. , and Theofilis, V. , 2013, “Order 10 4 Speedup in Global Linear Instability Analysis Using Matrix Formation,” Comput. Methods Appl. Mech. Eng., 253, pp. 287–304. [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]
Orszag, S. A. , 1971, “Accurate Solution of the Orr–Sommerfeld Stability Equation,” J. Fluid Mech., 50(4), pp. 689–703. [CrossRef]
Monkewitz, P. A. , Huerre, P. , and Chomaz, J.-M. , 1993, “Global Linear Stability Analysis of Weakly Non-Parallel Shear Flows,” J. Fluid Mech., 251, pp. 1–20. [CrossRef]
Bers, A. , 1983, “Space-Time Evolution of Plasma Instabilities-Absolute and Convective,” Basic Plasma Phys., 1, pp. 451–517. https://inis.iaea.org/search/search.aspx?orig_q=RN:15068895
Briggs, R. J. , 1964, “Electron-Stream Interaction With Plasmas,” Science, 148(3676), pp. 1453–1454.
Poinsot, T. , 2005, The AVBP Handbook, CERFACS, Toulouse, France.
Colin, O. , and Rudgyard, M. , 2000, “Development of High-Order Taylor-Galerkin Schemes for LES,” J. Comput. Phys., 162(2), pp. 338 –371. [CrossRef]
Nicoud, F. , Toda, H. B. , Cabrit, O. , Bose, S. , and Lee, J. , 2011, “Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations,” Phys. Fluids, 23(8), p. 085106. [CrossRef]
Schmid, P. J. , 2010, “Dynamic Mode Decomposition of Numerical and Experimental Data,” J. Fluid Mech., 656, pp. 5–28. [CrossRef]
Juniper, M. P. , Tammisola, O. , and Lundell, F. , 2011, “The Local and Global Stability of Confined Planar Wakes at Intermediate Reynolds Number,” J. Fluid Mech., 686, pp. 218–238. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic representations of wave packets in flows with different stability properties: (a) stable flow, (b) convectively unstable flow, and (c) absolutely unstable flow

Grahic Jump Location
Fig. 2

Schematic sketch of the experiment: (a) primary vanes, (b) secondary vanes, (c) center body, (d) primary injector exit plane, and (e) dump plane

Grahic Jump Location
Fig. 3

Experimental sound pressure level and dynamic mode decomposition (DMD) spectrum of pressure based on LES snapshots

Grahic Jump Location
Fig. 4

Comparison of experimental and LES mean profiles of axial velocity, u¯x, and radial velocity, u¯r, for varying axial positions

Grahic Jump Location
Fig. 5

Mean flow field inside the injector: (a) axial velocity and (b) 2D line integral convolution

Grahic Jump Location
Fig. 6

PVC modes based on LES/DMD and LSA; right column: global LSA adjoint modes

Grahic Jump Location
Fig. 7

Spectrum of global stability analysis

Grahic Jump Location
Fig. 8

Structural sensitivity, λ: (a) global LSA and (b) local LSA

Grahic Jump Location
Fig. 9

Real and imaginary part of the nondimensional frequency, ω, in the complex α-plane for the velocity profile at the exit of the primary injector

Grahic Jump Location
Fig. 10

Real and imaginary part of the absolute frequency, ω0, over the axial coordinate, x

Grahic Jump Location
Fig. 11

Expansion of the absolute frequency, ω0, into the complex x-plane

Grahic Jump Location
Fig. 12

α+ and α as a function of the axial position

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In