Bypass Transition to Sustained Thermoacoustic Oscillations in a Linearly Stable Rijke Tube

2010 ◽  
Author(s):  
Matthew Juniper ◽  
Iain Waugh
Keyword(s):  
Bypass Transition ◽  
Rijke Tube ◽  
Thermoacoustic Oscillations

scholarly journals Boundary Feedback Control of Unstable thermoacoustic Oscillations in the Rijke Tube

2016 ◽  
Vol 49 (8) ◽  
pp. 48-53 ◽  
Author(s):  
Gustavo A. de Andrade ◽  
Rafael Vazquez ◽  
Daniel J. Pagano
Keyword(s):  
Feedback Control ◽  
Boundary Feedback Control ◽  
Rijke Tube ◽  
Boundary Feedback ◽  
Thermoacoustic Oscillations

A Theoretical Approach for Passive Control of Thermoacoustic Oscillations: Application to Ducted Flames

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Heat Release ◽  
Passive Control ◽  
Local Variation ◽  
Control Device ◽  
Adjoint Equations ◽  
Hot Wire ◽  
Adjoint Sensitivity ◽  
Cross Sectional ◽  
Rijke Tube ◽  
Thermoacoustic Oscillations

In this paper, we develop a linear technique that predicts how the stability of a thermoacoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically heated hot wire, and the second contains a diffusion flame. Both heat sources are assumed to be compact, so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermoacoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermoacoustic system should be changed in order to make it stable.

scholarly journals Assimilation of Experimental Data to Create a Quantitatively-Accurate Reduced Order Thermoacoustic Model

2020 ◽  
Author(s):  
Francesco Garita ◽  
Hans Yu ◽  
Matthew P. Juniper
Keyword(s):  
Bayesian Inference ◽  
Ensemble Kalman Filter ◽  
Decay Rates ◽  
Base Flow ◽  
Thermal Dissipation ◽  
Electric Heater ◽  
Rijke Tube ◽  
Reduced Order ◽  
Physical Phenomena ◽  
Thermoacoustic Oscillations

Abstract We combine a thermoacoustic experiment with a thermoacoustic reduced order model using Bayesian inference to accurately learn the parameters of the model, rendering it predictive. The experiment is a vertical Rijke tube containing an electric heater. The heater drives a base flow via natural convection, and thermoacoustic oscillations via velocity-driven heat release fluctuations. The decay rates and frequencies of these oscillations are measured every few seconds by acoustically forcing the system via a loudspeaker placed at the bottom of the tube. More than 320,000 temperature measurements are used to compute state and parameters of the base flow model using the Ensemble Kalman Filter. A wave-based network model is then used to describe the acoustics inside the tube. We balance momentum and energy at the boundary between two adjacent elements, and model the viscous and thermal dissipation mechanisms in the boundary layer and at the heater and thermocouple locations. Finally, we tune the parameters of two different thermoacoustic models on an experimental dataset that comprises more than 40,000 experiments. This study shows that, with thorough Bayesian inference, a qualitative model can become quantitatively accurate, without overfitting, as long as it contains the most influencial physical phenomena.

scholarly journals Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

2016 ◽  
Vol 805 ◽  
pp. 523-550 ◽  
Author(s):  
Alessandro Orchini ◽  
Georgios Rigas ◽  
Matthew P. Juniper
Keyword(s):  
Dynamical Evolution ◽  
Hopf Bifurcations ◽  
Solvability Conditions ◽  
Rijke Tube ◽  
Nonlinear Dynamical ◽  
Weakly Nonlinear ◽  
The Cost ◽  
Fifth Order ◽  
Thermoacoustic Oscillations ◽  
Good Agreement

In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations’ amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.

scholarly journals Assimilation of Experimental Data to Create a Quantitatively-Accurate Reduced Order Thermoacoustic Model

2020 ◽  
Author(s):  
Francesco Garita ◽  
Hans Yu ◽  
Matthew Juniper
Keyword(s):  
Bayesian Inference ◽  
Ensemble Kalman Filter ◽  
Decay Rates ◽  
Base Flow ◽  
Thermal Dissipation ◽  
Electric Heater ◽  
Rijke Tube ◽  
Reduced Order ◽  
Physical Phenomena ◽  
Thermoacoustic Oscillations

Abstract We combine a thermoacoustic experiment with a thermoacoustic reduced order model using Bayesian inference to accurately learn the parameters of the model, rendering it predictive. The experiment is a vertical Rijke tube containing an electric heater. The heater drives a base flow via natural convection, and thermoacoustic oscillations via velocity-driven heat release fluctuations. The decay rates and frequencies of these oscillations are measured every few seconds by acoustically forcing the system via a loudspeaker placed at the bottom of the tube. More than 320,000 temperature measurements are used to compute state and parameters of the base flow model using the Ensemble Kalman Filter. A wave-based network model is then used to describe the acoustics inside the tube. We balance momentum and energy at the boundary between two adjacent elements, and model the viscous and thermal dissipation mechanisms in the boundary layer and at the heater and thermocouple locations. Finally, we tune the parameters of two different thermoacoustic models on an experimental dataset that comprises more than 40,000 experiments. This study shows that, with thorough Bayesian inference, a qualitative model can become quantitatively accurate, without overfitting, as long as it contains the most influential physical phenomena.

Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

2021 ◽  
Vol 933 ◽  
Author(s):  
Calum S. Skene ◽  
Kunihiko Taira
Keyword(s):  
Optimal Placement ◽  
External Forcing ◽  
Frequency Locking ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Phase Dynamics ◽  
Sustained Oscillations ◽  
Phase Reduction ◽  
Efficient Route ◽  
Thermoacoustic Oscillations

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

scholarly journals Assimilation of Experimental Data to Create a Quantitatively-Accurate Reduced Order Thermoacoustic Model

2020 ◽  
Author(s):  
Francesco Garita ◽  
Hans Yu ◽  
Matthew Juniper
Keyword(s):  
Bayesian Inference ◽  
Ensemble Kalman Filter ◽  
Decay Rates ◽  
Base Flow ◽  
Thermal Dissipation ◽  
Electric Heater ◽  
Rijke Tube ◽  
Reduced Order ◽  
Physical Phenomena ◽  
Thermoacoustic Oscillations

We combine a thermoacoustic experiment with a thermoacoustic reduced order model using Bayesian inference to accurately learn the parameters of the model, rendering it predictive. The experiment is a vertical Rijke tube containing an electric heater. The heater drives a base flow via natural convection, and thermoacoustic oscillations via velocity-driven heat release fluctuations. The decay rates and frequencies of these oscillations are measured every few seconds by acoustically forcing the system via a loudspeaker placed at the bottom of the tube. More than 320,000 temperature measurements are used to compute state and parameters of the base flow model using the Ensemble Kalman Filter. A wave-based network model is then used to describe the acoustics inside the tube. We balance momentum and energy at the boundary between two adjacent elements, and model the viscous and thermal dissipation mechanisms in the boundary layer and at the heater and thermocouple locations. Finally, we tune the parameters of two different thermoacoustic models on an experimental dataset that comprises more than 40,000 experiments. This study shows that, with thorough Bayesian inference, a qualitative model can become quantitatively accurate, without overfitting, as long as it contains the most influencial physical phenomena.

Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition

2010 ◽  
Vol 667 ◽  
pp. 272-308 ◽  
Author(s):  
MATTHEW P. JUNIPER
Keyword(s):  
Periodic Solution ◽  
Simple Model ◽  
Initial Energy ◽  
Bypass Transition ◽  
Transient Growth ◽  
Governing Equations ◽  
Initial State ◽  
Rijke Tube ◽  
Sustained Oscillations ◽  
Sequence Of Events

With a sufficiently large impulse, a thermoacoustic system can reach self-sustained oscillations even when it is linearly stable, a process known as triggering. In this paper, a procedure is developed to find the lowest initial energy that can trigger self-sustained oscillations, as well as the corresponding initial state. This is known as the ‘most dangerous’ initial state. The procedure is based on adjoint looping of the nonlinear governing equations, combined with an optimization routine. It is developed for a simple model of a thermoacoustic system, the horizontal Rijke tube, and can be extended to more sophisticated thermoacoustic models. It is observed that the most dangerous initial state grows transiently towards an unstable periodic solution before growing to a stable periodic solution. The initial energy required to trigger these self-sustained oscillations is much lower than the energy of the oscillations themselves and slightly lower than the lowest energy on the unstable periodic solution. It is shown that this transient growth arises due to non-normality of the governing equations. This is analogous to the sequence of events observed in bypass transition to turbulence in fluid mechanical systems and has the same underlying cause. The most dangerous initial state is calculated as a function of the heat-release parameter. It is found that self-sustained oscillations can be reached over approximately half the linearly stable domain. Transient growth in real thermoacoustic systems is 105–106 times greater than that in this simple model. One practical conclusion is that, even in the linearly stable regime, it may take very little initial energy for a real thermoacoustic system to trigger to high-amplitude self-sustained oscillations through the mechanism described in this paper.

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