Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
Renaud Gaudron ◽  
Dong Yang ◽  
Aimee Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Physical Insight ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh's criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Delta and the cycle-to-cycle acoustic energy ratio lambda, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles (rest of the abstract in the article).

Design of Acoustic Liner in Small Gas Turbine Combustor Using One-Dimensional Impedance Models

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Daesik Kim ◽  
Seungchai Jung ◽  
Heeho Park
Keyword(s):  
Gas Turbine ◽  
Side Wall ◽  
Acoustic Energy ◽  
Gas Turbine Combustor ◽  
Design Guideline ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Acoustic Dissipation ◽  
Acoustic Liner ◽  
Bias Flow

The side-wall cooling liner in a gas turbine combustor serves main purposes—heat transfer and emission control. Additionally, it functions as a passive damper to attenuate thermoacoustic instabilities. The perforations in the liner mainly convert acoustic energy into kinetic energy through vortex shedding at the orifice rims. In the previous decades, several analytical and semi-empirical models have been proposed to predict the acoustic damping of the perforated liner. In the current study, a few of the models are considered to embody the transfer matrix method (TMM) for analyzing the acoustic dissipation in a concentric tube resonator with a perforated element and validated against experimental data in the literature. All models are shown to quantitatively appropriately predict the acoustic behavior under high bias flow velocity conditions. Then, the models are applied to maximize the damping performance in a realistic gas turbine combustor, which is under development. It is found that the ratio of the bias flow Mach number to the porosity can be used as a design guideline in choosing the optimal combination of the number and diameter of perforations in terms of acoustic damping.

scholarly journals Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

2016 ◽  
Vol 805 ◽  
pp. 52-87 ◽  
Author(s):  
G. Ghirardo ◽  
M. P. Juniper ◽  
J. P. Moeck
Keyword(s):  
Gas Turbines ◽  
Practical Importance ◽  
Industrial Applications ◽  
Local Pressure ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Rotationally Symmetric ◽  
Flame Response ◽  
Annular Combustor

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in annular combustors, which shows that rotationally symmetric annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

Ranking of Aircraft Fuel-Injectors Regarding Low Frequency Thermoacoustics Based on an Energy Balance Method

2021 ◽  
Author(s):  
André Fischer ◽  
Claus Lahiri
Keyword(s):  
Energy Balance ◽  
Low Frequency ◽  
Network Models ◽  
Operating Conditions ◽  
Balance Method ◽  
Energy Balance Method ◽  
Fuel Injectors ◽  
Thermoacoustic Instabilities ◽  
Aircraft Fuel ◽  
Flame Response

Abstract Many modern low emission combustion systems suffer from thermoacoustic instabilities, which may lead to customer irritation (noise) or engine damages. The prediction of the frequency response of the flame is oftentimes not straightforward, so that it is common practice to measure the flame response in an experiment. The outcome of the measurement is typically a flame transfer-function (FTF), which can be used in low order acoustic network models to represent the flame. This paper applies an alternative criterion to evaluate the potential of the flame to become instable, the flame-amplification factor (FAF). It is based on an energy balance method and can be directly derived from the measured flame-transfer-matrix (FTM). In order to demonstrate this approach two different kerosene-driven aircraft fuel injectors were measured in the Rolls-Royce SCARLET rig in a single-sector RQL-combustor under realistic operating conditions. Here the multi-microphone method has been applied with acoustic forcing from up- and downstream side to determine the FTM. In contrast to the FTF-approach the full FTM data has been post-processed to derive the FAF. The FAF is then successfully used to rank the fuel injectors regarding their low frequency thermo-acoustic behaviour, because it is proportional to amplitudes of self-excited frequencies in FANN-rig (full annular) configuration.

scholarly journals Ligand-induced structural changes analysis of ribose-binding protein as studied by molecular dynamics simulations

2021 ◽  
pp. 1-12
Author(s):  
Haiyan Li ◽  
Zanxia Cao ◽  
Guodong Hu ◽  
Liling Zhao ◽  
Chunling Wang ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Structural Changes ◽  
Binding Protein ◽  
Network Models ◽  
Md Simulations ◽  
Protein Domain ◽  
Opening Angle ◽  
Conformation Changes ◽  
Wide Range ◽  
Ribose Binding Protein

BACKGROUND: The ribose-binding protein (RBP) from Escherichia coli is one of the representative structures of periplasmic binding proteins. Binding of ribose at the cleft between two domains causes a conformational change corresponding to a closure of two domains around the ligand. The RBP has been crystallized in the open and closed conformations. OBJECTIVE: With the complex trajectory as a control, our goal was to study the conformation changes induced by the detachment of the ligand, and the results have been revealed from two computational tools, MD simulations and elastic network models. METHODS: Molecular dynamics (MD) simulations were performed to study the conformation changes of RBP starting from the open-apo, closed-holo and closed-apo conformations. RESULTS: The evolution of the domain opening angle θ clearly indicates large structural changes. The simulations indicate that the closed states in the absence of ribose are inclined to transition to the open states and that ribose-free RBP exists in a wide range of conformations. The first three dominant principal motions derived from the closed-apo trajectories, consisting of rotating, bending and twisting motions, account for the major rearrangement of the domains from the closed to the open conformation. CONCLUSIONS: The motions showed a strong one-to-one correspondence with the slowest modes from our previous study of RBP with the anisotropic network model (ANM). The results obtained for RBP contribute to the generalization of robustness for protein domain motion studies using either the ANM or PCA for trajectories obtained from MD.

scholarly journals Parameter estimation for energy balance models with memory

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140349 ◽  
Author(s):  
Lionel Roques ◽  
Mickaël D. Chekroun ◽  
Michel Cristofol ◽  
Samuel Soubeyrand ◽  
Michael Ghil
Keyword(s):  
Parameter Estimation ◽  
Energy Balance ◽  
Statistical Model ◽  
Ice Cores ◽  
Temperature Measurements ◽  
Age Dating ◽  
Observation Process ◽  
Wide Range ◽  
Energy Balance Models ◽  
With Memory

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE's domain of definition D , using only temperature information in a small subdomain E ⊂ D . This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample's remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.

scholarly journals Flame Dynamics Intermittency in the Bi-Stable Region Near a Subcritical Hopf Bifurcation

2017 ◽  
Author(s):  
D. Ebi ◽  
A. Denisov ◽  
G. Bonciolini ◽  
E. Boujo ◽  
N. Noiray
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Acoustic Pressure ◽  
Oscillation Amplitude ◽  
Stable Region ◽  
Describing Function ◽  
Acoustic Damping ◽  
Intermittent Behavior ◽  
Flame Describing Function

We report experimental evidence of thermoacoustic bi-stability in a lab-scale turbulent combustor over a well-defined range of fuel-air equivalence ratios. Pressure oscillations are characterized by an intermittent behavior with “bursts”, i.e. sudden jumps between low and high amplitudes occurring at random time instants. The corresponding probability density functions of the acoustic pressure signal show clearly separated maxima when the burner is operated in the bi-stable region. A flame describing function, which links acoustic pressure to heat release rate fluctuations, is estimated at the modal frequency from simultaneously recorded flame chemiluminescence and acoustic pressure. The representation of its statistics is new and particularly informative. It shows that this describing function is characterized, in average, by a nearly constant gain and by a significant drift of the phase as function of the oscillation amplitude. This finding suggests that the bi-stability does not result from an amplitude-dependent balance between flame gain and acoustic damping, but rather from the non-constant phase difference between the acoustic pressure and the coherent fluctuations of heat release rate.

Predicting Thermoacoustic Instability in an Industrial Gas Turbine Combustor: Combining a Low Order Network Model With Flame LES

2017 ◽  
Author(s):  
Y. Xia ◽  
A. S. Morgans ◽  
W. P. Jones ◽  
J. Rogerson ◽  
G. Bulat ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Acoustic Waves ◽  
Gas Turbine Combustor ◽  
Network Modelling ◽  
Weakly Nonlinear ◽  
Thermoacoustic Instability ◽  
Reduced Chemistry ◽  
Flame Describing Function ◽  
Industrial Gas Turbine ◽  
Low Order

The thermoacoustic modes of a full scale industrial gas turbine combustor have been predicted numerically. The predictive approach combines low order network modelling of the acoustic waves in a simplified geometry, with a weakly nonlinear flame describing function, obtained from incompressible large eddy simulations of the flame region under upstream forced velocity perturbations, incorporating reduced chemistry mechanisms. Two incompressible solvers, each employing different numbers of reduced chemistry mechanism steps, are used to simulate the turbulent reacting flowfield to predict the flame describing functions. The predictions differ slightly between reduced chemistry approximations, indicating the need for more involved chemistry. These are then incorporated into a low order thermoacoustic solver to predict thermoacoustic modes. For the combustor operating at two different pressures, most thermoacoustic modes are predicted to be stable, in agreement with the experiments. The predicted modal frequencies are in good agreement with the measurements, although some mismatches in the predicted modal growth rates and hence modal stabilities are observed. Overall, these findings lend confidence in this coupled approach for real industrial gas turbine combustors.

scholarly journals Experimental Study of Advanced Helmholtz Resonator Liners with Increased Acoustic Performance by Utilising Material Damping Effects

2018 ◽  
Vol 8 (10) ◽  
pp. 1923
Author(s):  
Martin Dannemann ◽  
Michael Kucher ◽  
Eckart Kunze ◽  
Niels Modler ◽  
Karsten Knobloch ◽  
...  
Keyword(s):  
Polymer Films ◽  
Helmholtz Resonator ◽  
Broadband Noise ◽  
Acoustic Energy ◽  
Acoustic Damping ◽  
Acoustic Performance ◽  
Acoustic Liners ◽  
Flexible Polymer ◽  
Noise Absorption ◽  
Aero Engines

In aero engines, noise absorption is realised by acoustic liners, e.g., Helmholtz resonator (HR) liners, which often absorb sound only in a narrow frequency range. Due to developments of new engine generations, an improvement of overall acoustic damping performance and in particular more broadband noise absorption is required. In this paper, a new approach to increase the bandwidth of noise absorption for HR liners is presented. By replacing rigid cell walls in the liner’s honeycomb core structure by flexible polymer films, additional acoustic energy is dissipated. A manufacturing technology for square honeycomb cores with partially flexible walls is described. Samples with different flexible wall materials were fabricated and tested. The acoustic measurements show more broadband sound absorption compared to a reference liner with rigid walls due to acoustic-structural interaction. Manufacturing-related parameters are found to have a strong influence on the resulting vibration behaviour of the polymer films, and therefore on the acoustic performance. For future use, detailed investigations to ensure the liner segments compliance with technical, environmental, and life-cycle requirements are needed. However, the results of this study show the potential of this novel liner concept for noise reduction in future aero-engines.

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