Maria A. Heckl

ANALYSIS AND CONTROL OF AN UNSTABLE MODE IN A COMBUSTOR WITH TUNEABLE END CONDITION

A major problem in the development of low-pollution combustion systems are thermo-acoustic instabilities, i.e. large-amplitude oscillations generated by a feedback between the unsteady heat release and acoustic waves. In order to develop robust control strategies, it is necessary to have a predictive model that captures the physics of the phenomenon. The aim of this paper is to present such a model for a dump combustor with a generic heat release law, and fitted at the inlet end with a perforated plate backed by a tuneable cavity. Our model leads to a simple governing equation for one acoustic mode in the combustor, and from this equation stability predictions can be made with a minimum of numerical effort. We will use it to examine the effect of various system parameters.

Oblique sound transmission through tube bundles and tube gratings

Abstract Tube bundles, which are commonly found in heat exchangers of industrial plant, can be monitored by transmission of ultrasonic signals. This paper presents a model for oblique sound transmission through tube bundles; it extends existing two-dimensional models to three dimensions. The tubes are modelled as flexible cylindrical shells which are filled with a fluid and immersed in another fluid. They are arranged periodically and this leads to grating effects (scattering of a plane wave in discrete directions) and to passing and stopping bands (frequency bands with high and low transmission). Two new effects, not found for perpendicular sound transmission, are discovered. The ‘projection effect’ shifts features in the transmission spectrum to higher frequencies. The ‘coincidence effect’ occurs if the free bending wavelength of the tubes matches the trace wavelength in the outer fluid and can lead to a dramatic reduction of the transmission. Comparison of theoretical predictions and experimental results is given. The model makes useful predictions for the design and operation of ultrasonic monitoring systems for tube bundles; it can, for example, recommend optimal transmission angles and frequency ranges.

A New Perspective on the Flame Describing Function of a Matrix Flame

This paper considers a fundamental thermoacoustic test rig developed by Noiray (“Linear and nonlinear analysis of combustion instabilities, application to multipoint injection systems and control strategies”, PhD thesis, École Centrale Paris, 2007) and models it with an entirely analytical approach. The test rig is treated as a system of two coupled elements: an acoustic resonator and a flame with oscillating rate of heat release. We describe the acoustics of the combustion rig in terms of modes, and derive a governing equation for one such mode. This turns out to be the equation for a damped harmonic oscillator, forced by the heat release rate from the flame. In order to model the heat release rate, and in particular its nonlinear aspects, we develop a generalised nτ-law with amplitude-dependent coefficients and multiple time-lag. The coefficients are determined from Noirays measured flame describing function. Stability predictions are made by evaluating the sign of the damping coefficient in the governing equation. These predictions are in excellent qualitative agreement with the measured stability behaviour. Finally, the physical mechanisms of the amplitude-dependence are explored.

Passive instability control by a heat exchanger in a combustor with nonuniform temperature

Thermoacoustic instabilities, caused by the feedback between unsteady heat release and acoustic pressure perturbations, are characterised by large-amplitude pressure oscillations. These oscillations, if uncontrolled, pose a threat to the integrity of combustion systems. One strategy to mitigate them is by installing cavity-backed perforated plates with bias flow into the combustion chamber. In this study, we consider a generic combustor configuration: a one-dimentional tube (with open and/or closed ends) containing a compact heat source and a heat exchanger tube row. The idea is to use the heat exchanger tube row as a device (analogously to a cavity-backed perforated plate) to manipulate the downstream end condition. We simulate the row of heat exchanger tubes by a slit-plate with bias flow. We derive the characteristic equation for the complex eigenfrequencies of this set-up. From the growth rates (imaginary parts of the eigenfrequencies), we construct stability maps for various system parameter combinations. The results, obtained for the first two modes of the system, show that by varying the cavity length or the bias flow velocity through the slits, we can stabilise a previously unstable combustion system.

Passive control of instabilities in combustion systems with heat exchanger

One of the major concerns in the operability of power generation systems is their susceptibility to combustion instabilities. In this work, we explore whether a heat exchanger, an integral component of a domestic boiler, can be made to act as a passive controller that suppresses combustion instabilities. The combustor is modelled as a quarter-wave resonator (1-D, open at one end, closed at the other) with a compact heat source inside, which is modelled by a time-lag law. The heat exchanger is modelled as an array of tubes with bias flow and is placed near the closed end of the resonator, causing it to behave like a cavity-backed slit plate: an effective acoustic absorber. For simplicity and ease of analysis, we treat the physical processes of heat transfer and acoustic scattering occurring at the heat exchanger as two individual processes separated by an infinitesimal distance. The aeroacoustic response of the tube array is modelled using a quasi-steady approach and the heat transfer across the heat exchanger is modelled by assuming it to be a heat sink. Unsteady numerical simulations were carried out to obtain the heat exchanger transfer function, which is the response of the heat transfer at heat exchanger to upstream velocity perturbations. Combining the aeroacoustic response and the heat exchanger transfer function, in the limit of the distance between these processes tending to zero, gives the net influence of the heat exchanger. Other parameters of interest are the heat source location and the cavity length (the distance between the tube array and the closed end). We then construct stability maps for the first resonant mode of the aforementioned combustor configuration, for various parameter combinations. Our model predicts that stability can be achieved for a wide range of parameters.

Nonlinear analytical flame models with amplitude-dependent time-lag distributions

In the present work, we formulate a new method to represent a given Flame Describing Function by analytical expressions. The underlying idea is motivated by the observation that different types of perturbations in a burner travel with different speeds and that the arrival of a perturbation at the flame is spread out over time. We develop an analytical model for the Flame Describing Function, which consists of a superposition of several Gaussians, each characterised by three amplitude-dependent quantities: central time-lag, peak value and standard deviation. These quantities are treated as fitting parameters, and they are deduced from the original Flame Describing Function by using error minimisation and nonlinear optimisation techniques. The amplitude-dependence of the fitting parameters is also represented analytically (by linear or quadratic functions). We test our method by using it to make stability predictions for a burner with well-documented stability behaviour (Noirays matrix burner). This is done in the time-domain with a tailored Greens function approach.