Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

@article{Orchini2016WeaklyNA,
  title={Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube},
  author={Alessandro Orchini and Georgios Rigas and Matthew P. Juniper},
  journal={Journal of Fluid Mechanics},
  year={2016},
  volume={805},
  pages={523 - 550}
}
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… 

Modelling and analysis of nonlinear thermoacoustic systems using frequency and time domain methods

Low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed, in which linear acoustics is combined with a nonlinear heat release model to enable analysis both in the frequency and time domains.

Thermoacoustic analysis of combustion chambers with varying temperature: Numerical solutions and comparison with experiments

In the present work, a numerical and experimental study of the thermoacoustic instabilities of a combustor is performed. The numerical model is represented by the one-dimensional linearised Euler

Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors

A simplified model is introduced to study finite-amplitude thermo-acoustic oscillations in $N$ -periodic annular combustion devices. Such oscillations yield undesirable effects and can be triggered

Weakly nonlinear modelling of a forced turbulent axisymmetric wake

A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and

Adjoint Methods as Design Tools in Thermoacoustics

  • L. Magri
  • Physics
    Applied Mechanics Reviews
  • 2019
In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these

Data assimilation in a nonlinear time-delayed dynamical system

This work numerically estimates the most likely nonlinear state of a Galerkin-discretized time delayed model of a horizontal Rijke tube, which is a prototypical combustor and represents the first application of data assimilation to nonlinear thermoacoustics.

Devil’s staircases in a thermoacoustic system with sinusoidal excitations

The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial

Weakly nonlinear evolution of stochastically driven non-normal systems

Abstract We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may

Bifurcation analysis of combustion instability in a Rijke burner with an improved third-order saturated flame model

The bifurcation analysis of nonlinear combustion instability in a Rijke burner is studied numerically. First, a saturated flame model and a third-order saturated flame model are proposed, and the

References

SHOWING 1-10 OF 53 REFERENCES

Modelling and analysis of nonlinear thermoacoustic systems using frequency and time domain methods

Low-order nonlinear models for the prediction of the nonlinear behaviour of thermoacoustic systems are developed, in which linear acoustics is combined with a nonlinear heat release model to enable analysis both in the frequency and time domains.

Subcritical bifurcation and bistability in thermoacoustic systems

Abstract This paper analyses subcritical transition to instability, also known as triggering in thermoacoustic systems, with an example of a Rijke tube model with an explicit time delay. Linear

Nonlinear self-excited oscillations of a ducted flame

  • A. Dowling
  • Physics, Engineering
    Journal of Fluid Mechanics
  • 1997
Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic

Experimental Investigation of Non-Normality of Thermoacoustic Interaction in an Electrically Heated Rijke Tube

An experimental investigation of the non-normal nature of thermoacoustic interactions in an electrically heated horizontal Rijke tube is performed. Since non-normality and the associated transient

Application of dynamical systems theory to nonlinear combustion instabilities

Two important approximations have been incorporated in much of the work with approximate analysis of unsteady motions in combustion chambers: truncation of the series expansion to a finite number

WEAKLY NONLINEAR ANALYSIS OF THERMOACOUS- TIC OSCILLATIONS

In this theoretical study, a weakly nonlinear analysis is pe rformed on a generic thermoacoustic system. The velocity and heat release are assumed to be periodic. The heat release fluctu- ations are

Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics

Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic

Thermoacoustic instabilities in the Rijke tube: experiments and modeling

Thermoacoustic instability can appear in thermal devices when unsteady heat release is coupled with pressure perturbations. This effect results in excitation of eigen acoustic modes of the system.

Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos

Abstract Thermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized

THE CALCULATION OF THERMOACOUSTIC OSCILLATIONS

Thermoacoustic oscillations occur in a wide variety of practical applications in which heat is supplied to an acoustic resonator. A simple geometry is investigated systematically to determine the
...