Luca Magri

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates.

Compositional inhomogeneities as a source of indirect combustion noise

© 2016 Cambridge University Press. The generation of indirect combustion noise by compositional inhomogeneities is examined theoretically. For this, the compact-nozzle theory of Marble & Candel (J.Sound Vib., vol.55 (2), 1977, pp.225-243) is extended to a multi-component gas mixture, and the chemical potential function is introduced as an additional acoustic source mechanism. Transfer functions for subcritical and supercritical nozzle flows are derived, and the contribution of compositional noise is compared to entropy noise and direct noise by considering an idealized nozzle downstream of the combustor exit. It is shown that compositional noise is dependent on the local mixture composition and can exceed entropy noise for fuel-lean conditions and supercritical nozzle flows. This suggests that the compositional indirect noise requires potential consideration with the implementation of low-emission combustors.

Uncertainty quantification of growth rates of thermoacoustic instability by an adjoint Helmholtz solver

Technological foundations for the design of thermally and mechanically highly loaded components of future space transportation systems (SFB TR40), Royal Academy of Engineering Research Fellowships Scheme

Adjoint-based linear analysis in reduced order thermo-acoustic models

This paper presents the linear theory of adjoint equations as applied to thermo-acoustics. The purpose is to describe the mathematical foundations of adjoint equations for linear sensitivity analysis of thermo-acoustic systems, recently developed by Magri and Juniper (J. Fluid Mech. (2013), vol. 719, pp. 183--202). This method is applied pedagogically to a damped oscillator, for which analytical solutions are available, and then for an electrically heated Rijke tube with a mean-flow temperature discontinuity induced by the compact heat source. Passive devices that most affect the growth rate / frequency of the electrical Rijke-tube system are presented, including a discussion about the effect of modelling the mean-flow temperature discontinuity.

Non-normality in combustion-acoustic interaction in diffusion flames: a critical revision†

Perturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important practical consequences for combustion-acoustic oscillations, which are a continual problem in rocket and aircraft engines. Balasubramanian and Sujith (Journal of Fluid Mechanics, 2008, 594, 29-57) modelled an infinite-rate chemistry diffusion flame in an acoustic duct and found that the transient growth in this system can amplify the initial energy by a factor,

Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part II. Uncertainty quantification

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Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity

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

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On the use of the theory of dynamical systems for transient problems

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EXAMPLE OF A NON-SMOOTH HOPF BIFURCATION IN AN AERO- ELASTIC SYSTEM

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