Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero
Keyword(s):  
Acoustic Emission ◽  
Finite Length ◽  
Transfer Functions ◽  
Linear Equations ◽  
Combustion Noise ◽  
Navier Stokes ◽  
Subcritical Case ◽  
Compactness Criterion ◽  
Temporal Space ◽  
Euler Solver

This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase for indirect combustion noise is rederived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble and Candel for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D nonlinear Euler solver in temporal space) and CEDRE (3D Navier–Stokes flow solver). Excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*∫0Ldζ/u(ζ)<1 where L is the axial length of the nozzle. Finally, the entropy wave generator (EWG) experimental setup is considered. Analytical results are compared to the results reported by Howe. Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism is not alone responsible for the acoustic emission in the subcritical case.

Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles

2012 ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero
Keyword(s):  
Acoustic Emission ◽  
Finite Length ◽  
Transfer Functions ◽  
Linear Equations ◽  
Combustion Noise ◽  
Navier Stokes ◽  
Subcritical Case ◽  
Compactness Criterion ◽  
Temporal Space ◽  
Euler Solver

This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase et al. (JFM 2007) for indirect combustion noise is red-erived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble & Candel (JSV 1977) for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D non linear Euler solver in temporal space) and CEDRE (3D Navier-Stokes flow solver). An excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*∫0Ldζ/uζ<1 where L is the axial length of the nozzle. Finally, the EWG experimental setup of Bake et al. (JSV 2009) is considered. Analytical results are compared to the results reported by Howe (JFM 2010). Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet provided by Bake et al. (JSV 2009) and Leyko et al. (JSV 2011) are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism cannot be held responsible alone for the acoustic emission in the subcritical case.

Thermoacoustic Shape Optimization of a Subsonic Nozzle

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero ◽  
Sébastien Ducruix ◽  
Franck Richecoeur
Keyword(s):  
Acoustic Emission ◽  
Cross Section ◽  
Source Term ◽  
Combustion Noise ◽  
Noise Emission ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
Nozzle Flows ◽  
Subsonic Nozzle

Indirect combustion noise originates from the acceleration of nonuniform temperature or high vorticity regions when convected through a nozzle or a turbine. In a recent contribution (Giauque et al., 2012, “Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbies Power, 134(11), p. 111202) the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrarily shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in detail. The evolution of the cross-section changes are introduced using Bezier's splines, which provide the necessary freedom to actually achieve arbitrary shapes. Bezier's polar coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (Bloy, 1979, “The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows,” J. Fluid Mech., 94(3), pp. 465–475), the results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections, leading to a square evolution of the cross-section area. Providing insight into the underlying physical reason leading to the difference in the noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an acoustic emission factor, which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This acoustic emission factor, which is much faster to compute, only involves the knowledge of the evolution of the cross-section area and the inlet thermodynamic and velocity characteristics to be computed.

scholarly journals Flow Inhomogeneities in a Realistic Aeronautical Gas-Turbine Combustor: Formation, Evolution and Indirect Noise

2018 ◽  
Author(s):  
Andrea Giusti ◽  
Luca Magri ◽  
Marco Zedda
Keyword(s):  
Gas Turbines ◽  
Transfer Functions ◽  
Guide Vane ◽  
Flame Structure ◽  
Combustion Noise ◽  
Moment Closure ◽  
Combustion Model ◽  
Conditional Moment ◽  
Eddy Simulation ◽  
Nozzle Guide

Indirect noise generated by the acceleration of combustion inhomogeneities is an important aspect in the design of aeroengines because of its impact on the overall noise emitted by an aircraft and the possible contribution to combustion instabilities. In this study, a realistic rich-quench-lean combustor is numerically investigated, with the objective of quantitatively analyzing the formation and evolution of flow inhomogeneities and determine the level of indirect combustion noise in the nozzle guide vane (NGV). Both entropy and compositional noise are calculated in this work. A high-fidelity numerical simulation of the combustion chamber, based on the Large-Eddy Simulation (LES) approach with the Conditional Moment Closure (CMC) combustion model, is performed. The contributions of the different air streams to the formation of flow inhomogeneities are pinned down and separated with seven dedicated passive scalars. LES-CMC results are then used to determine the acoustic sources to feed an NGV aeroacoustic model, which outputs the noise generated by entropy and compositional inhomogeneities. Results show that non-negligible fluctuations of temperature and composition reach the combustor’s exit. Combustion inhomogeneities originate both from finite-rate chemistry effects and incomplete mixing. In particular, the role of mixing with dilution and liner air flows on the level of combustion inhomogeneities at the combustor’s exit is highlighted. The species that most contribute to indirect noise are identified and the transfer functions of a realistic NGV are computed. The noise level indicates that indirect noise generated by temperature fluctuations is larger that the indirect noise generated by compositional inhomogeneities, although the latter is not negligible and is expected to become louder in supersonic nozzles. It is also shown that relatively small fluctuations of the local flame structure can lead to significant variations of the nozzle transfer function, whose gain increases with the Mach number. This highlights the necessity of an on-line solution of the local flame structure, which is performed in this paper by CMC, for an accurate prediction of the level of compositional noise. This study opens new possibilities for the identification, separation and calculation of the sources of indirect combustion noise in realistic aeronautical gas turbines.

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

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Luca Magri ◽  
Jeffrey O'Brien ◽  
Matthias Ihme
Keyword(s):  
Velocity Profile ◽  
Combustion Chamber ◽  
Transfer Functions ◽  
Mixture Fraction ◽  
Supersonic Nozzle ◽  
Noise Pollution ◽  
Combustion Noise ◽  
Dipole Source ◽  
Multicomponent Gas ◽  
Thermoacoustic Oscillations

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.

scholarly journals Fast solvers for finite difference approximations for the stokes and navier-stokes equations

1996 ◽  
Vol 38 (2) ◽  
pp. 274-290 ◽  
Author(s):  
Dongho Shin ◽  
John C. Strikwerda
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Linear Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Fast Solvers ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Grid Points ◽  
First Time

AbstractWe consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.

scholarly journals Flow Inhomogeneities in a Realistic Aeronautical Gas-Turbine Combustor: Formation, Evolution, and Indirect Noise

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Andrea Giusti ◽  
Luca Magri ◽  
Marco Zedda
Keyword(s):  
Gas Turbines ◽  
Transfer Functions ◽  
Guide Vane ◽  
Flame Structure ◽  
Combustion Noise ◽  
Moment Closure ◽  
Combustion Model ◽  
Conditional Moment ◽  
Eddy Simulation ◽  
Aero Engines

Indirect noise generated by the acceleration of combustion inhomogeneities is an important aspect in the design of aero-engines because of its impact on the overall noise emitted by an aircraft and the possible contribution to combustion instabilities. In this study, a realistic rich-quench-lean (RQL) combustor is numerically investigated, with the objective of quantitatively analyzing the formation and evolution of flow inhomogeneities and determining the level of indirect combustion noise in the nozzle guide vane (NGV). Both entropy and compositional noise are calculated in this work. A high-fidelity numerical simulation of the combustion chamber, based on the large-eddy simulation (LES) approach with the conditional moment closure (CMC) combustion model, is performed. The contributions of the different air streams to the formation of flow inhomogeneities are pinned down and separated with seven dedicated passive scalars. LES-CMC results are then used to determine the acoustic sources to feed an NGV aeroacoustic model, which outputs the noise generated by entropy and compositional inhomogeneities. Results show that non-negligible fluctuations of temperature and composition reach the combustor's exit. Combustion inhomogeneities originate both from finite-rate chemistry effects and incomplete mixing. In particular, the role of mixing with dilution and liner air flows on the level of combustion inhomogeneities at the combustor's exit is highlighted. The species that most contribute to indirect noise are identified and the transfer functions of a realistic NGV are computed. The noise level indicates that indirect noise generated by temperature fluctuations is larger than the indirect noise generated by compositional inhomogeneities, although the latter is not negligible and is expected to become louder in supersonic nozzles. It is also shown that relatively small fluctuations of the local flame structure can lead to significant variations of the nozzle transfer function, whose gain increases with the Mach number. This highlights the necessity of an on-line solution of the local flame structure, which is performed in this paper by CMC, for an accurate prediction of the level of compositional noise. This study opens new possibilities for the identification, separation, and calculation of the sources of indirect combustion noise in realistic aeronautical gas turbines.

Thermoacoustic Shape Optimization of a Subsonic Nozzle

2013 ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero ◽  
Sébastien Ducruix ◽  
Franck Richecoeur
Keyword(s):  
Acoustic Emission ◽  
Shape Optimization ◽  
Cross Section ◽  
Emission Factor ◽  
Source Term ◽  
Combustion Noise ◽  
Noise Emission ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross

Indirect combustion noise originates from the acceleration of non-uniform temperature or high vorticity regions when convected through a nozzle or a turbine. In an recent contribution (Giauque et al., JEGTP, 2012), the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrary shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in details. The evolution of the cross-section changes are introduced using Beziers splines which provide the necessary freedom to actually achieve arbitrary shapes. Beziers poles coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (JFM, 1979), results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections leading to a square evolution of the cross-section area. Providing insight in the underlying physical reason leading to the difference in noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an Acoustic Emission Factor which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This Acoustic Emission Factor, much faster to compute, only involves the knowledge of the evolution of the cross-section area as well as the inlet thermodynamic and velocity characteristics to be computed.

scholarly journals Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

2013 ◽  
Vol 13 (2) ◽  
pp. 386-410 ◽  
Author(s):  
Björn Sjögreen ◽  
Jeffrey W. Banks
Keyword(s):  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Linear Equations ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Computational Domain ◽  
Interface Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

AbstractWe consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjögreen in [8] as a special case.

Shock Spectrum Ratios Applied to the Comparison of Pulse Signatures

1980 ◽  
Vol 102 (1) ◽  
pp. 64-76
Author(s):  
J. R. Houghton
Keyword(s):  
Acoustic Emission ◽  
Transfer Functions ◽  
Time Window ◽  
Relative Size ◽  
Emission Data ◽  
Relative Damage ◽  
New Type ◽  
Ratio Approach ◽  
Spectrum Ratio ◽  
The Fourier Transform

Two extensions of the shock spectrum technique are developed for use in pulse signature analysis. A shock spectrum ratio is proposed and compared to the Fourier transfer function for the detection of small perturbations on a larger pulse shape. The shock spectrum ratio is shown to have good sensitivity to the relative size of the perturbation. The shock spectrum ratio approach is extended to a new type of spectrum named “slot transform.” This specialized transform is shown to have several advantages with respect to the Fourier transform in the development of magnitude transfer functions. The transform was developed for analysis of digitized acoustic emission pulses where a rectangular time window is preferred. These two extensions of shock spectrum methods are tested on experimental data from high g shock tests and acoustic emission measurements from damaged and undamaged ball bearings. Deconvolution of the acoustic emission data was necessary before the shork spectrum, ratio was capable of indicating the relative damage of the bearings.

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