Experimental sensitivity analysis and control of thermoacoustic systems

Abstract

In this paper, we report the results of an experimental sensitivity analysis on a thermoacoustic system -an electrically heated Rijke tube. We measure the change of the linear stability characteristics of the system, quantified as shifts in the growth rate and oscillation frequency, that is caused by the introduction of a passive control device. The control device is a mesh, which causes drag in the system. The rate of growth is slow, so the growth rate and frequency can be measured very accurately over many hundreds of cycles in the linear regime with and without control. These measurements agree qualitatively well with the theoretical predictions from adjoint-based methods of Magri & Juniper (J. Fluid Mech., vol. 719, 2013, pp. 183-202). This agreement supports the use of adjoint methods for the development and implementation of control strategies for more complex thermoacoustic systems.

Experimental sensitivity analysis via a secondary heat source in an oscillating thermoacoustic system

“…3 This does not support the predictions of Magri and Juniper, 17 because they do not take into account base flow modifications caused by an increase in mean flow temperature.…”

“…This type of feedback could be physically implemented in the form of a mesh, which forces the momentum equation in the opposite direction to the velocity by inducing a drag force. Magri A study by Rigas et al 3 provided the first comparison of experimental sensitivity analysis with adjointbased sensitivity analysis in thermoacoustics. Linear growth rates and decay rates were obtained for a range of different primary heater powers and axial locations of a passive drag device, x c =L.…”

“…The secondary heat source is traversed through a range of axial locations inside the tube. The main novelty is that we extend the work of Rigas et al 3 to carefully measure and compare experimental results with theoretical predictions from adjoint-based sensitivity analysis.…”

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

“…Adjoint eigenvalue sensitivity analysis of thermo-acoustic systems was proposed by Magri and Juniper [28]. The analysis was applied to simplified models of combustors to find optimal passive mechanisms and sensitivity to base-state changes in a Rijke tube [28,29,30,31], a ducted diffusion flame [32] and, more recently, to a ducted premixed-flame [33]. However, these studies dealt with linear eigenvalue problems in which the eigenvalue appears under a linear term.…”

Multiple-scale thermo-acoustic stability analysis of a coaxial jet combustor

“…If at least one eigenvalue has positive growth rate, the system is unstable. The sensitivity of the stability to external feedback mechanisms or passive control has been calculated with adjoint-based methods [7][8][9] , which were recently experimentally validated [10] . However, these versatile methods were applied only to simplified thermo-acoustic models with uniform mean flows.…”