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State prediction of an entropy wave advecting through a turbulent channel flow

Published online by Cambridge University Press:  06 November 2019

Loizos Christodoulou Open the ORCID record for Loizos Christodoulou [Opens in a new window] ,
Nader Karimi Open the ORCID record for Nader Karimi [Opens in a new window] ,
Andrea Cammarano Open the ORCID record for Andrea Cammarano [Opens in a new window] ,
Manosh Paul Open the ORCID record for Manosh Paul [Opens in a new window]  and
Salvador Navarro-Martinez Open the ORCID record for Salvador Navarro-Martinez [Opens in a new window]
Loizos Christodoulou
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Nader Karimi*
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Andrea Cammarano
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Manosh Paul
Affiliation:
James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Salvador Navarro-Martinez
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 1AL, UK
*
†Email address for correspondence: Nader.Karimi@glasgow.ac.uk
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Abstract

Survival of entropy waves during their advection throughout a combustor is central to the generation of entropic sound and the subsequent effects upon thermoacoustic stability of the system. However, the decay and spatial non-uniformity of entropy waves are largely ignored by the existing models used for the calculation of entropy noise generation. Recent investigations have demonstrated the complex spatio-temporal dynamics of entropy waves and cast doubts on the sufficiency of the one-dimensional approach, conventionally used for the analysis of these waves. Hence, this paper proposes a novel approach to the low-order modelling of entropy wave evolution wherein the wave is described by the two states of position and amplitude in the streamwise direction. A high-order model is first developed through direct numerical simulation of the advection of entropy waves in a fully developed, heat transferring, compressible, turbulent channel flow. The data are then utilised to build and validate a series of nonlinear, low-order models that provide an unsteady two-dimensional representation of the decaying and partially annihilating entropy waves. It is shown that these models need, at most, approximately $12.5\,\%$ of the total trace of entropy wave advection to predict the wave dynamics accurately. The results further reveal that the existing linear low-order models are truly predictive only for the entropy waves with less than $2\,\%$ increase in the gas temperature compared to that of the surrounding flow. Yet, in agreement with the assumption of existing models, it is shown that entropy waves travel with the mean flow speed.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Reacting Flows: Combustion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 882 , 10 January 2020 , A8
Copyright
© 2019 Cambridge University Press 

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References

Akaike, H. 2011 Akaike’s Information Criterion. p. 25. Springer.Google Scholar
Alzwayi, A. S., Paul, M. C. & Navarro-Martinez, S. 2014 Large eddy simulation of transition of free convection flow over an inclined upward facing heated plate. Intl Commun. Heat Mass Transfer 57, 330–340.Google Scholar
Bailey, J. C., Intile, J. J., Fric, T. F., Tolpadi, A. K., Nirmalan, N. V. & Bunker, R. S. 2003 Experimental and numerical study of heat transfer in a gas turbine combustor liner. Trans. ASME J. Engng Gas Turbines Power 125 (4), 994–1002.Google Scholar
Bake, F., Kings, N. & Röhle, I. 2008 Fundamental mechanism of entropy noise in aero-engines: experimental investigation. Trans. ASME J. Engng Gas Turbines Power 130 (1), 011202.Google Scholar
Bake, F., Richter, C., Mühlbauer, B., Kings, N., Röhle, I., Thiele, F. & Noll, B. 2009 The entropy wave generator (EWG): a reference case on entropy noise. J. Sound Vib. 326 (3), 574–598.Google Scholar
Brear, M. J., Carolan, D. C. & Karimi, N. 2010 Dynamic response of the exit nozzle of a premixed combustor to pressure and entropic disturbances. In Proceedings of the 8th Euromech Fluid Mechanics Conference. Euromech.Google Scholar
Candel, S., Durox, D., Ducruix, S., Birbaud, A.-L., Noiray, N. & Schuller, T. 2009 Flame dynamics and combustion noise: progress and challenges. Intl J. Aeroacoust. 8 (1), 1–56.Google Scholar
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16 (1), 31–96.Google Scholar
Cumpsty, N. A. & Marble, F. E. 1977 The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise. Proc. R. Soc. Lond. A 357, 323–344.Google Scholar
Dowling, A. P. 1995 The calculation of thermoacoustic oscillations. J. Sound Vib. 180 (4), 557–581.Google Scholar
Dowling, A. P. & Morgans, A. S. 2005 Feedback control of combustion oscillations. Annu. Rev. Fluid Mech. 37, 151–182.Google Scholar
Dowling, A. P. & Stow, S. R. 2003 Acoustic analysis of gas turbine combustors. J. Propul. Power 19, 751–764.Google Scholar
Dúran, I., Leyko, M., Moreau, S., Nicoud, F. & Poinsot, T. 2013 Computing combustion noise by combining large eddy simulations with analytical models for the propagation of waves through turbine blades. C. R. Méc. 341 (1), 131–140.Google Scholar
Dúran, I. & Moreau, S. 2013 Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion. J. Fluid Mech. 723, 190–231.Google Scholar
Dúran, I., Moreau, S. & Poinsot, T. 2012 Analytical and numerical study of combustion noise through a subsonic nozzle. AIAA J. 51 (1), 42–52.Google Scholar
Eckstein, J., Freitag, E. & Sattelmayer, C. H. T. 2006 Experimental study on the role of entropy waves in low-frequency oscillations in a RQL combustor. Trans. ASME J. Engng Gas Turbines Power 128 (2), 264–270.Google Scholar
Eckstein, J. & Sattelmayer, T. 2006 Low-order modelling of low frequency combustion instabilities in aeroengines. J. Propul. Power 22 (2), 425–432.Google Scholar
Emmanuelli, A., Huet, M., Garrec, T. L. & Ducruix, S. 2017 CAA study of entropy noise in nozzle flow for the validation of a 2D semi-analytical model. ASME Turbo Expo (GT2017-63640).Google Scholar
Emmanuelli, A., Huet, M., Garrec, T. L. & Ducruix, S. 2018 Study of entropy noise through a 2D stator using CAA. In 2018 AIAA/CEAS Aeroacoustics Conference. AIAA.Google Scholar
Fattahi, A., Hosseinalipour, S. M. & Karimi, N. 2017 On the dissipation and dispersion of entropy waves in heat transferring channel flows. Phys. Fluids 29, 087104:1–16.Google Scholar
Fattahi, A., Hosseinalipour, S. M., Karimi, N., Saboohi, Z. & Ommi, F. 2019 On the response of a lean-premixed hydrogen combustor to acoustic and dissipative–dispersive entropy waves. Energy 180, 272–291.Google Scholar
Giauque, A., Huet, M. & Clero, F. 2012 Analytical analysis of indirect combustion noise in subcritical nozzles. Trans. ASME J. Engng Gas Turbines Power 134 (11), 111202.Google Scholar
Giusti, A., Worth, N. A., Mastorakos, E. & Dowling, A. P. 2017 Experimental and numerical investigation into the propagation of entropy waves. AIAA J. 55, 446–458.Google Scholar
Goh, C. S. & Morgans, A. S. 2011 Phase prediction of the response of choked nozzles to entropy and acoustic disturbances. J. Sound Vib. 330, 5184–5198.Google Scholar
Goh, C. S. & Morgans, A. S. 2013 The influence of entropy waves on the thermoacoustic stability of a model combustor. Combust. Sci. Technol. 185, 249–268.Google Scholar
Hield, P. A. & Brear, M. J. 2008 Comparison of open and choked premixed combustor exits during thermoacoustic limit cycle. AIAA J. 46 (2), 517–526.Google Scholar
Hield, P. A., Brear, M. J. & Jin, S. H. 2009 Thermoacoustic limit cycles in a premixed laboratory combustor with open and choked exits. Combust. Flame 156, 1683–1697.Google Scholar
Hosseinalipour, M., Fattahi, A., Afshari, A. & Karimi, N. 2017 On the effects of convecting entropy waves on the combustor hydrodynamics. Appl. Therm. Engng 110, 901–909.Google Scholar
Howe, M. S. 1975 The generation of sound by aerodynamic sources in an inhomogeneous steady flow. J. Fluid Mech. 67 (3), 597–610.Google Scholar
Huet, M. & Giauque, A. 2013 A nonlinear model for indirect combustion noise through a compact nozzle. J. Fluid Mech. 733, 268–301.Google Scholar
Ihme, M. 2017 Combustion and engine-core noise. Annu. Rev. Fluid Mech. 49 (1), 277–310.Google Scholar
Jones, W. P. & Wille, M. 1996 Large-eddy simulation of a plane jet in a cross-flow. Intl J. Heat Fluid Flow 17 (3), 296–306.Google Scholar
Karimi, N., Brear, M. J. & Moase, W. H. 2008 Acoustic and disturbance energy analysis of a flow with heat communication. J. Fluid Mech. 597, 67–89.Google Scholar
Karimi, N., Brear, M. J. & Moase, W. H. 2010 On the interaction of sound with steady heat communicating flows. J. Sound Vib. 329 (22), 4705–4718.Google Scholar
Kershaw, D. S. 1978 The incomplete Cholesky-conjugate gradient method for the iterative solution of systems. J. Comput. Phys. 26, 43–65.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
LeBlanc, D. C. 2004 Statistics: Concepts and Applications for Science, vol. 2. Jones and Bartlett.Google Scholar
Lefebvre, A. H. & Ballal, D. R. 2010 Gas Turbine Combustion: Alternative Fuels and Emissions. CRC Press.Google Scholar
Leyko, M., Moreau, S., Nicoud, F. & Poinsot, T. 2011 Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock. J. Sound Vib. 330 (16), 3944–3958.Google Scholar
Leyko, M., Nicoud, F. & Poinsot, T. 2009 Comparison of direct and indirect combustion noise mechanisms in a model combustor. AIAA J. 47, 2709–2716.Google Scholar
Lieuwen, T. 2012 Unsteady Combustor Physics. Cambridge University Press.Google Scholar
Livebardon, T., Moreau, S., Gicquel, L., Poinsot, T. & Bouty, E. 2016 Combining LES of combustion chamber and an actuator disk theory to predict combustion noise in a helicopter engine. Combust. Flame 165, 272–287.Google Scholar
Magri, L. 2017 On indirect noise in multicomponent nozzle flows. J. Fluid Mech. 828, R2.Google Scholar
Magri, L., O’Brien, J. & Ihme, M. 2016 Compositional inhomogeneities as a source of indirect combustion noise. J. Fluid Mech. 799, R4.Google Scholar
Marble, F. E. & Candel, S. M. 1977 Acoustic disturbance from gas non-uniformities convected through a nozzle. J. Sound Vib. 55 (2), 225–243.Google Scholar
Mare, F. D.2002 Large eddy simulation of reacting and non-reacting turbulent flows in complex geometries. PhD thesis, Imperial College London.Google Scholar
Mare, L. D. & Jones, W. P. 2003 LES of turbulent flow past a swept fence. Intl J. Heat Fluid Flow 24 (4), 606–615.Google Scholar
Moase, W. H., Brear, M. J. & Manzie, C. 2007 The forced response of choked nozzles and supersonic diffusers. J. Fluid Mech. 585, 281–304.Google Scholar
Morgans, A. S. & Dúran, I. 2016 Entropy noise: a review of theory, progress and challenges. Int. J. Spray Comb. Dyn. 8 (4), 285–298.Google Scholar
Morgans, A. S., Goh, C. S. & Dahan, J. A. 2013 The dissipation and dispersion of entropy waves in combustor thermoacoustics. J. Fluid Mech. 733, 1–11.Google Scholar
Morinishi, Y. 1995 Conservation properties of finite difference schemes for incompressible flow. CTR Annu. Res. Briefs 1995, pp. 121–132. Center for Turbulence Research.Google Scholar
Motheau, E., Nicoud, F. & Poinsot, T. 2014 Mixed acoustic – entropy combustion instabilities in gas turbines. J. Fluid Mech. 749, 542–576.Google Scholar
Paul, M. C. & Molla, M. M. 2012 Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations. Appl. Math. Model. 36, 4393–4413.Google Scholar
Poinsot, T. 2017 Prediction and control of combustion instabilities in real engines. Proc. Combust. Inst. 36 (1), 1–28.Google Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21 (11), 1525–1532.Google Scholar
Rolland, E. O., Domenico, F. D. & Hochgreb, S. 2018 Direct and indirect noise generated by entropic and compositional inhomogeneities. Trans. ASME J. Engng Gas Turbines Power 140 (8), 082604.Google Scholar
Sattelmayer, T. 2003 Influence of the combustor aerodynamics on combustion instabilities from equivalence ratio fluctuations. Trans. ASME J. Engng Gas Turbines Power 125, 11–19.Google Scholar
Stow, S. R., Dowling, A. P. & Hynes, T. P. 2002 Reflection of circumferential modes in a choked nozzle. J. Fluid Mech. 467, 215–239.Google Scholar
Vorst, H. A. D. 1992 BI-CGSTAB: a first and smoothly converging variant of BI-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (2), 631–644.Google Scholar
Waßmer, D., Schuermans, B., Paschereit, C. O. & Moeck, J. P. 2016 Measurement and modelling of the generation and the transport of entropy waves in a model gas turbine combustor. Intl J. Spray Combust. 9 (4), 299–309.Google Scholar
Williams, J. E. F. & Howe, M. 1975 The generation of sound by density inhomogeneities in low mach number nozzle flows. J. Fluid Mech. 70, 605–622.Google Scholar
Zheng, J., Huet, M., Giauque, A., Cléro, F. & Ducruix, S. 2015 A 2D-axisymmetric analytical model for the estimation of indirect combustion noise in nozzle flows. In 21st AIAA/CEAS Aeroacoustics Conference, Dallas, Texas. AIAA.Google Scholar