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

Effects of Nozzle Helmholtz Number on Indirect Combustion Noise by Compositional Perturbations

[+] Author and Article Information
Luca Magri

Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CB2 1PZ, UK
e-mail: lm547@cam.ac.uk

Jeffrey O'Brien, Matthias Ihme

Center for Turbulence Research,
Stanford University,
488 Escondido Mall,
Stanford, CA 94305

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 June 29, 2017; final manuscript received July 28, 2017; published online October 17, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(3), 031501 (Oct 17, 2017) (9 pages) Paper No: GTP-17-1238; doi: 10.1115/1.4037914 History: Received June 29, 2017; Revised July 28, 2017

By modeling a multicomponent gas, a new source of indirect combustion noise is identified, which is named compositional indirect noise. The advection of mixture inhomogeneities exiting the gas-turbine combustion chamber through subsonic and supersonic nozzles is shown to be an acoustic dipole source of sound. The level of mixture inhomogeneity is described by a difference in composition with the mixture fraction. An n-dodecane mixture, which is a kerosene fuel relevant to aeronautics, is used to evaluate the level of compositional noise. By relaxing the compact-nozzle assumption, the indirect noise is numerically calculated for Helmholtz numbers up to 2 in nozzles with linear velocity profile. The compact-nozzle limit is discussed. Only in this limit, it is possible to derive analytical transfer functions for (i) the noise emitted by the nozzle and (ii) the acoustics traveling back to the combustion chamber generated by accelerated compositional inhomogeneities. The former contributes to noise pollution, whereas the latter has the potential to induce thermoacoustic oscillations. It is shown that the compositional indirect noise can be at least as large as the direct noise and entropy noise in choked nozzles and lean mixtures. As the frequency with which the compositional inhomogeneities enter the nozzle increases, or as the nozzle spatial length increases, the level of compositional noise decreases, with a similar, but not equal, trend to the entropy noise. The noisiest configuration is found to be a compact supersonic nozzle.

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Chang, C. T. , Lee, C.-M. , Herbon, J. T. , and Kramer, S. K. , 2013, “ NASA Environmentally Responsible Aviation Project Develops Next-Generation Low-Emissions Combustor Technologies (Phase I),” J. Aeronaut. Aerosp. Eng., 2(4), p. 116.
Dowling, A. P. , and Mahmoudi, Y. , 2015, “ Combustion Noise,” Proc. Comb. Inst., 35(1), pp. 65–100. [CrossRef]
Ihme, M. , 2017, “ Combustion and Engine-Core Noise,” Annu. Rev. Fluid Mech., 49(1), pp. 277–310. [CrossRef]
Rayleigh, L. , 1878, “ The Explanation of Certain Acoustical Phenomena,” Nature, 18(455), pp. 319–321. [CrossRef]
Lieuwen, T. C. , and Yang, V. , 2005, Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling, American Institute of Aeronautics and Astronautics, Reston, VA.
Culick, F. E. C. , 2006, “ Unsteady Motions in Combustion Chambers for Propulsion Systems,” RTO AGARDograph, North Atlantic Treaty Organization, Neuilly-Sur-Seine, France, Report No. AG-AVT-039. http://www.dtic.mil/docs/citations/ADA466461
Strahle, W. C. , 1978, “ Combustion Noise,” Prog. Energy Combust. Sci., 4(3), pp. 157–176. [CrossRef]
Hurle, I. R. , Price, R. B. , Sugden, T. M. , and Thomas, A. , 1968, “ Sound Emission From Open Turbulent Premixed Flames,” Proc. R. Soc. London A, 303(1475), pp. 409–427. [CrossRef]
Singh, K. K. , Zhang, C. , Gore, J. P. , Mongeau, L. , and Frankel, S. H. , 2005, “ An Experimental Study of Partially Premixed Flame Sound,” Proc. Comb. Inst., 30(2), pp. 1707–1715. [CrossRef]
Rajaram, R. , and Lieuwen, T. , 2003, “ Parametric Studies of Acoustic Radiation From Premixed Flames,” Combust. Sci. Technnol., 175(12), pp. 2269–2298. [CrossRef]
Candel, S. , Durox, D. , Ducruix, S. , Birbaud, A.-L. , Noiray, N. , and Schuller, T. , 2009, “ Flame Dynamics and Combustion Noise: Progress and Challenges,” Int. J. Aeroacoust., 8(1–2), pp. 1–56. [CrossRef]
Zhao, W. , and Frankel, S. H. , 2001, “ Numerical Simulations of Sound Radiated From an Axisymmetric Premixed Reacting Jet,” Phys. Fluids, 13(9), pp. 2671–2681. [CrossRef]
Ihme, M. , Pitsch, H. , and Bodony, D. , 2009, “ Radiation of Noise in Turbulent Non-Premixed Flames,” Proc. Comb. Inst., 32(1), pp. 1545–1553. [CrossRef]
Dowling, A. P. , 1997, “ Nonlinear Self-Excited Oscillations of a Ducted Flame,” J. Fluid Mech., 346, pp. 271–290. [CrossRef]
Marble, F. E. , and Candel, S. M. , 1977, “ Acoustic Disturbance From Gas Non-Uniformities Convected Through a Nozzle,” J. Sound Vib., 55(2), pp. 225–243. [CrossRef]
Morfey, C. L. , 1973, “ Amplification of Aerodynamic Noise by Convective Flow Inhomogeneities,” J. Sound Vib., 31(4), pp. 391–397. [CrossRef]
Cumpsty, N. A. , 1979, “ Jet Engine Combustion Noise: Pressure, Entropy and Vorticity Perturbations Produced by Unsteady Combustion or Heat Addition,” J. Sound Vib., 66(4), pp. 527–544. [CrossRef]
Ffowcs Williams, J. E. , and Howe, M. S. , 1975, “ The Generation of Sound by Density Inhomogeneities in Low Mach Number Nozzle Flows,” J. Fluid Mech., 70(3), pp. 605–622. [CrossRef]
Howe, M. S. , 2010, “ Indirect Combustion Noise,” J. Fluid Mech., 659, pp. 267–288. [CrossRef]
Polifke, W. , Paschereit, C. O. , and Döbbeling, K. , 2001, “ Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor With a Choked Exit,” Int. J. Acoust. Vib., 6(3), pp. 135–146.
Goh, C. S. , and Morgans, A. S. , 2013, “ The Influence of Entropy Waves on the Thermoacoustic Stability of a Model Combustor,” Combust. Sci. Technol., 185(2), pp. 249–268. [CrossRef]
Morgans, A. S. , and Annaswamy, A. M. , 2008, “ Adaptive Control of Combustion Instabilities for Combustion Systems With Right-Half Plane Zeros,” Combust. Sci. Technol., 180(9), pp. 1549–1571. [CrossRef]
De Domenico, F. , Rolland, E. O. , and Hochgreb, S. , 2017, “ Detection of Direct and Indirect Noise Generated by Synthetic Hot Spots in a Duct,” J. Sound Vib., 394, pp. 220–236. [CrossRef]
Stow, S. R. , Dowling, A. P. , and Hynes, T. P. , 2002, “ Reflection of Circumferential Modes in a Choked Nozzle,” J. Fluid Mech., 467, pp. 215–239. [CrossRef]
Goh, C. S. , and Morgans, A. S. , 2011, “ Phase Prediction of the Response of Choked Nozzles to Entropy and Acoustic Disturbances,” J. Sound Vib., 330(21), pp. 5184–5198. [CrossRef]
Moase, W. H. , Brear, M. J. , and Manzie, C. , 2007, “ The Forced Response of Choked Nozzles and Supersonic Diffusers,” J. Fluid Mech., 585, pp. 281–304. [CrossRef]
Giauque, A. , Huet, M. , and Clero, F. , 2012, “ Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbines Power, 134(11), p. 111202. [CrossRef]
Duran, I. , and Moreau, S. , 2013, “ Solution of the Quasi-One-Dimensional Linearized Euler Equations Using Flow Invariants and the Magnus Expansion,” J. Fluid Mech., 723, pp. 190–231. [CrossRef]
Duran, I. , and Morgans, A. S. , 2015, “ On the Reflection and Transmission of Circumferential Waves Through Nozzles,” J. Fluid Mech., 773, pp. 137–153. [CrossRef]
Bake, F. , Richter, C. , Mühlbauer, C. , Kings, N. , Röhle, I. , Thiele, F. , and Noll, B. , 2009, “ The Entropy Wave Generator (EWG): A Reference Case on Entropy Noise,” J. Sound Vib., 326(3–5), pp. 574–598. [CrossRef]
Kings, N. , and Bake, F. , 2010, “ Indirect Combustion Noise: Noise Generation by Accelerated Vorticity in a Nozzle Flow,” Int. J. Spray Combust. Dyn., 2(3), pp. 253–266. [CrossRef]
Morgans, A. S. , Goh, C. S. , and Dahan, J. A. , 2013, “ The Dissipation and Shear Dispersion of Entropy Waves in Combustor Thermoacoustics,” J. Fluid Mech., 733, p. R2. [CrossRef]
Giusti, A. , Worth, N. , Mastorakos, E. , and Dowling, A. , 2017, “ Experimental and Numerical Investigation Into the Propagation of Entropy Waves,” AIAA J., 55(2), pp. 446–458. [CrossRef]
O'Brien, J. , Kim, J. , and Ihme, M. , 2016, “ Investigation of the Mechanisms of Jet-Engine Core Noise Using Large-Eddy Simulation,” AIAA Paper No. AIAA 2016-0761.
Magri, L. , O'Brien, J. , and Ihme, M. , 2016, “ Compositional Inhomogeneities as a Source of Indirect Combustion Noise,” J. Fluid Mech., 799, p. R4. [CrossRef]
Williams, F. A. , 1985, Combustion Theory, Perseus Books, Reading, MA.
Poinsot, T. , and Veynante, D. , 2005, Theoretical and Numerical Combustion, 2nd ed., R. T. Edwards, Philadelphia, PA.
Lieuwen, T. C. , 2012, Unsteady Combustor Physics, Cambridge University Press, Cambridge, UK. [CrossRef]
Goodwin, D. G. , Moffat, H. K. , and Speth, R. L. , 2017, “ Cantera: An Object-Oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes,” Version 2.2.1, Zenodo, Geneva, Switzerland.
Peters, N. , 2000, Turbulent Combustion, Cambridge University Press, Cambridge, UK. [CrossRef] [PubMed] [PubMed]
Vie, A. , Franzelli, B. , Gao, Y. , Lu, T. , Wang, H. , and Ihme, M. , 2015, “ Analysis of Segregation and Bifurcation in Turbulent Spray Flames: A 3d Counterflow Configuration,” Proc. Comb. Inst., 35(2), pp. 1675–1683. [CrossRef]
Dimotakis, P. E. , and Miller, P. L. , 1990, “ Some Consequences of the Boundedness of Scalar Fluctuations,” Phys. Fluids A, 2(11), pp. 1919–1920. [CrossRef]
Rolland, E. O. , De Domenico, F. , and Hochgreb, S. , 2017, “ Direct and Indirect Noise Generated by Injected Entropic and Compositional Inhomogeneities,” ASME Paper No. GT2017-64428.


Grahic Jump Location
Fig. 1

Acoustic wave, π, entropy perturbation, σ, compositional inhomogeneity, ξ, decomposition in a (a) subsonic nozzle and (b) supersonic nozzle. M¯th is the Mach number at the throat. The area variation is pictorial.

Grahic Jump Location
Fig. 2

S-shaped curve of maximum temperature Tmax versus scalar dissipation rate at stoichiometric condition χst for n-dodecane-air flamelet computed at p = 1 bar with boundary conditions Tfuel=Tox=295 K. The “X” marker indicates the χst=1 s−1 condition.

Grahic Jump Location
Fig. 3

(a) Chemical potential function, Ψ, and (b) its gradient with respect to theMach number, ∂Ψ/∂M, for an n-dodecane inhomogeneity isentropically compressed/expanded in a nozzle. The results are presented as a function of the rescaled mixture-fraction coordinate. The stoichiometric condition is at 0.5, with the lean side being <0.5.

Grahic Jump Location
Fig. 4

One-dimensional diffusion flame in the mixture-fraction space. (a) Temperature T (solid-black lines), n -dodecane mass fraction YC12H26 (blue-dashed lines), oxygen mass fraction YO2 (red dotted–dashed lines), and water mass fraction YH2O (magenta-dotted lines). (b) Chemical potential function Ψ at the inlet (black-solid line) and specific Gibbs energy of the mixture (blue-dashed lines).

Grahic Jump Location
Fig. 5

(a) Nozzle cross-sectional area A(η) and (b) mean-flow Mach number M¯ versus spatial coordinate η for linear velocity profile cases. A* is the throat area, where in the supersonic nozzle, M¯=1 at η=0.652.

Grahic Jump Location
Fig. 6

Modulus of (a) downstream propagating acoustic response to entropic forcing πb+ /σa and (b) acoustic response at nozzle exit to entropic forcing πb−/σa versus Helmholtz number, He. The corresponding phases are shown in panels (c,d). The solutions reported in Ref. [28] are denoted by circles and were taken from the online version of their paper.

Grahic Jump Location
Fig. 7

Same as Fig. 6 for acoustic perturbations imposed at the inlet instead of entropy perturbations

Grahic Jump Location
Fig. 8

Same as Fig. 7 for compositional perturbations imposed at the inlet instead of acoustic perturbations

Grahic Jump Location
Fig. 9

Modulus of the ratio between indirect noise generated by accelerated compositional inhomogeneities and (a) direct noise and (b) indirect noise generated by accelerated entropy perturbations

Grahic Jump Location
Fig. 10

Spatial evolution of the response to compositional forcing in a supersonic nozzle with linear-velocity profile, M¯a=0.29, M¯b=1.5. First column shows the downstream acoustic response π+(η)/ξa, and second column shows the compositional response ξ(η)/ξa. Top row shows magnitude of response, and bottom row shows the phase. The five lines overlap each other in panel (b).



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