scholarly journals Stability and Limit Cycles of a Nonlinear Damper Acting on a Linearly Unstable Thermoacoustic Mode

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Claire Bourquard ◽  
Nicolas Noiray
Keyword(s):  
Growth Rate ◽  
Combustion Chamber ◽  
Limit Cycle ◽  
Nonlinear Effects ◽  
Coupled System ◽  
High Amplitude ◽  
Van Der Pol Oscillator ◽  
Mean Velocity ◽  
Thermoacoustic Instability ◽  
Numerical Predictions

The resonant coupling between flames and acoustics is a growing issue for gas turbine manufacturers, which can be reduced by adding acoustic dampers on the combustion chamber walls. Nonetheless, if the engine is operated out of the stable window, the damper is exposed to high-amplitude acoustic levels, which trigger unwanted nonlinear effects. This work provides an overview of the dynamics of this coupled system using a simple analytical model, where a perfectly tuned damper is coupled to the combustion chamber. The damper, crossed by a purge flow in order to prevent hot gas ingestion, is modeled as a nonlinearly damped harmonic oscillator. The combustion chamber featuring a linearly unstable thermoacoustic mode is modeled as a Van der Pol oscillator. Analyzing the averaged amplitude equations gives the limit cycle amplitudes as function of the growth rate of the unstable mode and the mean velocity through the damper neck. Experiments are also performed on a simple rectangular cavity, where the thermoacoustic instability is mimicked by an electro-acoustic instability. A feedback loop is built, through which the growth rate of the instability can be controlled. A Helmholtz damper is added to the cavity and tuned to the mode of interest. The stabilization capabilities of the damper and the amplitude of the limit cycle in the unstable cases are in good agreement between the experiments and the analytical and numerical predictions, underlining the potentially dangerous behavior of the system, which should be taken into account for real engine cases.

scholarly journals Stability and Limit Cycles of a Nonlinear Damper Acting on a Linearly Unstable Thermoacoustic Mode

2018 ◽  
Author(s):  
Claire Bourquard ◽  
Nicolas Noiray
Keyword(s):  
Growth Rate ◽  
Combustion Chamber ◽  
Limit Cycles ◽  
Feedback Loop ◽  
Unstable Mode ◽  
Rectangular Cavity ◽  
Van Der Pol Oscillator ◽  
Mean Velocity ◽  
Thermoacoustic Instability ◽  
Numerical Predictions

The resonant coupling between flames and acoustics is a growing issue for gas turbine manufacturers. They can be reduced by adding acoustic dampers on the combustion chamber walls. Nonetheless, if the engine is operated out of the stable window, the damper may be exposed to high-amplitude acoustic levels, which may trigger unwanted nonlinear effects. This work aims at providing an overview of the dynamics associated with those limit cycles using a simple analytical model, where a perfectly tuned damper is coupled to the combustion chamber. The damper, crossed by a purge flow in order to prevent hot gas ingestion, is modeled as a non-linearly damped harmonic oscillator, with vortex shedding as the main dissipation mechanism. The combustion chamber featuring a linearly unstable thermoacoustic mode is modelled as a Van der Pol oscillator. The fixed points of the coupled system and their stability can be determined by analyzing the averaged amplitude equations. This allows the computation of a fixed point topology map as function of the growth rate of the unstable mode and the mean velocity through the damper neck. Simulink simulations are also performed and compared to the analytical predictions. Finally, experiments are performed on a simple rectangular cavity, where the thermoacoustic instability resulting from the interaction between heat release and acoustic pressure is mimicked by an electro-acoustic instability. A feedback loop is built, where the signal from a microphone is filtered, delayed, and amplified before being sent to a loudspeaker placed inside the rectangular cavity. The delay and gain of the feedback loop can be modified to change the growth rate of the instability. One Helmholtz damper can be added to the cavity and tuned to the unstable mode of interest. The growth rate reduction capabilities of the damper and the amplitude of the limit cycle in the unstable cases are in good agreement with the analytical and numerical predictions, underlining the potentially dangerous behavior of the limit cycles which should be taken into account for real engine cases.

Influence of Nonlinear Effects on the Limit Cycle in a Combustion Chamber Equipped With Helmholtz Resonator

2014 ◽  
Author(s):  
Giovanni Campa ◽  
Sergio Mario Camporeale
Keyword(s):  
Combustion Chamber ◽  
Gas Turbine ◽  
Limit Cycle ◽  
Helmholtz Resonator ◽  
Nonlinear Effects ◽  
Bifurcation Diagrams ◽  
Passive Damper ◽  
Gas Turbine Combustion ◽  
The Stability ◽  
Stable Zone

The influence of the introduction of a Helmholtz resonator as a passive damper in a gas turbine combustion chamber on the bifurcation mechanism that characterizes the transition to instability is investigated. Bifurcation diagrams are tracked in order to identify the conditions for which the machine works in a stable zone and which are the operative parameters that bring the machine to unstable conditions. This work shows that a properly designed passive damper system increases the stable zone, moving the unstable zone and the bistable zone (in the case of a subcritical bifurcation) to higher values of the operative parameters, while have a limited influence on the amplitude of limit cycle. In order to examine the effect of the damper, a gas turbine combustion chamber is first modeled as a simple cylindrical duct, where the flame is concentrated in a narrow area at around one quarter of the duct. Heat release fluctuations are coupled to the velocity fluctuations at the entrance of the combustion chamber by means of a nonlinear correlation. This correlation is a polynomial function in which each term is an odd-powered term. The corresponding bifurcation diagrams are tracked and the passive damper is designed in order to increase the stability zone, so reducing the risk to have an unstable condition. Then both plenum and combustion chamber are modeled with annular shape and the influence of Helmholtz resonators on the bifurcation is examined.

Self-Excited High-Frequency Transverse Limit-Cycle Oscillations and Associated Flame Dynamics in a Gas Turbine Reheat Combustor Experiment

2021 ◽  
Author(s):  
Jonathan McClure ◽  
Frederik M. Berger ◽  
Michael Bertsch ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Dynamic Pressure ◽  
High Amplitude ◽  
Limit Cycle Oscillations ◽  
Flame Dynamics ◽  
Auto Ignition

Abstract This paper presents the investigation of high-frequency thermoacoustic limit-cycle oscillations in a novel experimental gas turbine reheat combustor featuring both auto-ignition and propagation stabilised flame zones at atmospheric pressure. Dynamic pressure measurements at the faceplate of the reheat combustion chamber reveal high-amplitude periodic pressure pulsations at 3 kHz in the transverse direction of the rectangular cross-section combustion chamber. Further analysis of the acoustic signal shows that this is a thermoacoustically unstable condition undergoing limit-cycle oscillations. A sensitivity study is presented which indicates that these high-amplitude limit-cycle oscillations only occur under certain conditions: namely high power settings with propane addition to increase auto-ignition propensity. The spatially-resolved flame dynamics are then investigated using CH* chemiluminescence, phase-locked to the dynamic pressure, captured from all lateral sides of the reheat combustion chamber. This reveals strong heat release oscillations close to the chamber walls at the instability frequency, as well as axial movement of the flame tips in these regions and an overall transverse displacement of the flame. Both the heat release oscillations and the flame motion occur in phase with the acoustic mode. From these observations, likely thermoacoustic driving mechanisms which lead to the limit-cycle oscillations are inferred. In this case, the overall flame-acoustics interaction is assumed to be a superposition of several effects, with the observations suggesting strong influences from autoignition-pressure coupling as well as flame displacement and deformation due to the acoustic velocity field. These findings provide a foundation for the overall objective of developing predictive approaches to mitigate the impact of high-frequency thermoacoustic instabilities in future generations of gas turbines with sequential combustion systems.

Adjoint Sensitivity Analysis of Hydrodynamic Stability in a Gas Turbine Fuel Injector

2015 ◽  
Author(s):  
Outi Tammisola ◽  
Matthew P. Juniper
Keyword(s):  
Growth Rate ◽  
Sensitivity Analysis ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Local Stability ◽  
Recirculation Zone ◽  
Base Flow ◽  
Fuel Injector ◽  
Mean Flow ◽  
Thermoacoustic Instability

Hydrodynamic oscillations in gas turbine fuel injectors help to mix the fuel and air but can also contribute to thermoacoustic instability. Small changes to some parts of a fuel injector greatly affect the frequency and amplitude of these oscillations. These regions can be identified efficiently with adjoint-based sensitivity analysis. This is a linear technique that identifies the region of the flow that causes the oscillation, the regions of the flow that are most sensitive to external forcing, and the regions of the flow that, when altered, have most influence on the oscillation. In this paper, we extend this to the flow from a gas turbine’s single stream radial swirler, which has been extensively studied experimentally (GT2008-50278) [8]. The swirling annular flow enters the combustion chamber and expands to the chamber walls, forming a conical recirculation zone along the centreline and an annular recirculation zone in the upstream corner. In this study, the steady base flow and the stability analysis are calculated at Re 200–3800 based on the mean flow velocity and inlet diameter. The velocity field is similar to that found from experiments and LES, and the local stability results are close to those at higher Re (GT2012-68253) [11]. All the analyses (experiments, LES, uRANS, local stability, and the global stability in this paper) show that a helical motion develops around the central recirculation zone. This develops into a precessing vortex core. The adjoint-based sensitivity analysis reveals that the frequency and growth rate of the oscillation is dictated by conditions just upstream of the central recirculation zone (the wavemaker region). It also reveals that this oscillation is very receptive to forcing at the sharp edges of the injector. In practical situations, this forcing could arise from an impinging acoustic wave, showing that these edges could be influential in the feedback mechanism that causes thermoacoustic instability. The analysis also shows how the growth rate and frequency of the oscillation change with either small shape changes of the nozzle, or additional suction or blowing at the walls of the injector. It reveals that the oscillations originate in a very localized region at the entry to the combustion chamber, which lies near the separation point at the outer inlet, and extends to the outlet of the inner pipe. Any scheme designed to control the frequency and amplitude of the oscillation only needs to change the flow in this localized region.

Laser Velocimeter Measurements in Highly Turbulent Recirculating Flows

1984 ◽  
Vol 106 (2) ◽  
pp. 173-180 ◽  
Author(s):  
W. H. Stevenson ◽  
H. D. Thompson ◽  
R. R. Craig
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Quantitative Description ◽  
Sudden Expansion ◽  
Laser Doppler Velocimeter ◽  
Bias Error ◽  
Mean Velocity ◽  
One Dimensional ◽  
Numerical Predictions ◽  
Velocity Bias

This paper presents the results of an extensive study of subsonic separated flows using a laser Doppler velocimeter. Both a rectangular rearward facing step and cylindrical (axisymmetric) sudden expansion geometry were studied. The basic objectives were to resolve the question of whether a velocity bias error does, in fact, occur in LDV measurements in highly turbulent flows of this type and, if so, how it may be eliminated; map the velocity field (mean velocity, turbulence intensity, Reynolds stress, etc.) including the entire recirculation zone; and compare experimental results with numerical predictions based on the k-ε turbulence model. Measurements were carried out using a one-dimensional LDV operating in forward scatter with signal processing by means of a commercial counter-type processor. Results obtained show that velocity bias does occur in turbulent flows and that it can be overcome by proper data acquisition procedures. The results also indicate that the important mean velocity and turbulence quantities can be obtained with reasonable accuracy using a one-dimensional LDV system. Although the k-ε turbulence model provides a good qualitative picture of the flow field, it does not yield a completely adequate quantitative description. Results obtained here illustrate the discrepancies to be expected and provide a basis for further model development.

Nonlinear Effects of Surface Texturing on the Performance of Journal Bearings in Flexible Rotordynamic Systems

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Jocelyn Rebufa ◽  
Fabrice Thouverez ◽  
Erick Le Guyadec ◽  
Denis Mazuyer
Keyword(s):  
Harmonic Balance ◽  
Vibration Amplitude ◽  
Surface Texturing ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Coupled System ◽  
Journal Bearings ◽  
Internal Damping ◽  
Rotating Shaft ◽  
Mean Pressure

A dynamic model of a rotating shaft on two textured hydrodynamic journal bearings is presented. The hydrodynamic mean pressure is computed using multiscale periodic homogenization and is projected on a flexible shaft with internal damping. Harmonic balance method (HBM) is used to study the limit cycles of unbalance response of the coupled system discretized by finite element method (FEM). Stability is analyzed with Floquet multipliers computation. An example of an isotropic texturing pattern representing laser dimples on a lightweight rotor is analyzed. Vibration amplitude and stability zone are compared with plain bearing lubrication. It is shown in an example that full surface texturing leads to relatively higher vibration amplitude compared to plain bearings.

Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour

2021 ◽  
Author(s):  
Induja Pavithran ◽  
Vishnu R. Unni ◽  
Abhishek Saha ◽  
Alan J. Varghese ◽  
R. I. Sujith ◽  
...  
Keyword(s):  
Amplitude Spectrum ◽  
High Amplitude ◽  
Dominant Mode ◽  
Turbine Engines ◽  
Stable Operation ◽  
Scaling Relation ◽  
Thermoacoustic Instability ◽  
Universal Scaling ◽  
Engine Components ◽  
Accuracy Of Prediction

Abstract The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using ‘spectral measures’ which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.

Large-Eddy Simulation of an Integrated High-Pressure Compressor and Combustion Chamber of a Typical Turbine Engine Architecture

2020 ◽  
Author(s):  
Carlos Pérez Arroyo ◽  
Jérôme Dombard ◽  
Florent Duchaine ◽  
Laurent Gicquel ◽  
Nicolas Odier ◽  
...  
Keyword(s):  
High Pressure ◽  
Large Eddy Simulation ◽  
Combustion Chamber ◽  
High Amplitude ◽  
Turbine Engine ◽  
Eddy Simulation ◽  
High Pressure Compressor ◽  
Large Eddy ◽  
Pressure Perturbations ◽  
Pressure Compressor

Abstract The design optimization of aviation propulsion systems by means of computational fluid dynamics is key to increase their efficiency and reduce pollutant and noise emissions. The recurrent increase in available computing power allows nowadays to perform unsteady high-fidelity computations of the different components of a gas turbine. However, these simulations are often made independently of each other and they only share average quantities at interfaces. In this work, the methodology and first results for a sectoral large-eddy simulation of an integrated high-pressure compressor and combustion chamber of a typical turbine engine architecture is proposed. In the simulation, the compressor is composed of one main blade and one splitter blade, two radial diffuser vanes and six axial diffuser vanes. The combustion chamber is composed of the contouring casing, the flame-tube and a T-shaped vaporizer. This integrated computation considers a good trade-off between accuracy of the simulation and affordable CPU cost. Results are compared between the stand-alone combustion chamber simulation and the integrated one in terms of global, integral and average quantities. It is shown that pressure perturbations generated by the interaction of the impeller blades with the diffuser vanes are propagated through the axial diffuser and enter the combustion chamber through the dilution holes and the vaporizer. Due to the high amplitude of the pressure perturbations, several variables are perturbed at the blade-passing frequency and multiples. This is also reflected on combustion where two broadband peaks appear for the global heat release.

Effect of biodiesel oxidation on deposit growth rate in the combustion chamber

2020 ◽  
Author(s):  
Bambang Sugiarto ◽  
J. A. Hidayat ◽  
M. T. Suryantoro ◽  
H. Setiapraja ◽  
S. Yubaidah ◽  
...  
Keyword(s):  
Growth Rate ◽  
Combustion Chamber

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

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