Model-based control of a Rijke tube combustion instability

A Rijke tube is used to demonstrate model-based control of a combustion instability, where controller design is based on measurement of the unstable system. The Rijke tube used was of length 0.75m and had a grid-stabilised laminar flame in its lower half. A microphone was used as a sensor and a loudspeaker as an actuator for active control. The open loop transfer function (OLTF) required for controller design was that from the actuator to the sensor. This was measured experimentally by sending a signal with two components to the actuator. The first was a control component from an empirically designed controller, which was used to stabilise the system, thus eliminating the non-linear limit cycle. The second was a high bandwidth signal for identification of the OLTF. This approach to measuring the OLTF is generic and can be applied to large-scale combustors. The measured OLTF showed that only the fundamental mode of the tube was unstable; this was consistent with the OLTF predicted by a mathematical model of the tube, involving 1-D linear acoustic waves and a time delay heat release model. Based on the measured OLTF, a controller to stabilise the instability was designed using Nyquist techniques. This was implemented and was seen to result in an 80dB reduction in the microphone pressure spectrum. A robustness study was performed by adding an additional length to the top of the Rijke tobe. The controller was found to achieve control up to an increase in tube length of 19%. This compared favourably with the empirical controller, which lost control for an increase in tube length of less than 3%.

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Transient growth and triggering in the horizontal Rijke tube Matthew

This theoretical paper examines a non-normal and non-linear model of a horizontal Rijke tube. Linear and non-linear optimal initial states, which maximize acoustic energy growth over a given time from a given energy, are calculated. It is found that non-linearity and non-normality both contribute to transient growth and that, for this model, linear optimal states are only a good predictor of non-linear optimal states for low initial energies. Two types of non-linear optimal initial state are found. The first has strong energy growth during the first period of the fundamental mode but loses energy thereafter. The second has weaker energy growth during the first period but retains high energy for longer. The second type causes triggering to self-sustained oscillations from lower energy than the first and has higher energy in the fundamental mode. This suggests, for instance, that low frequency noise will be more effective at causing triggering than high frequency noise.

The effect of acoustic mode on time-resolved temperature measurements in a Rijke-tube pulse combustor

Radial profiles are reported of average and rms temperature in a propane flame for the first, second, and third acoustic modes at four different axial positions above the burner in a Rijke-tube combustor. Selected plots of the power spectral density (PSD) of temperature fluctuations are also reported. These radial profiles are then compared to similar ones made in the same flame, but in the absence of the acoustic field. Visual observations and photographs of the flame showed a remarkable change in flame height and structure with the onset of acoustic oscillations. This reduction in flame length, caused by the enhanced mixing due to the acoustic velocity fluctuations, gave rise to higher and lower average and rms temperatures near or well above the burner, respectively. In general, the PSD plots had a broad frequency content. The general trend was a decrease in magnitude with an increase in frequency. All cases presented broad-band peaks at around 5 Hz related to the flame flickering phenomenon. Preferred frequencies were observed in the oscillating PSD plots related to the fundamental frequency as well as subharmonics in the tube. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Adaptive control of combustion instabilities for unknown sign of the high frequency gain

A type of adaptive, closed-loop controllers known as self-tuning regulators present a robust method of eliminating thermoacoustic oscillations in modern gas turbines. These controllers are able to adapt to changes in operating conditions, and require very little pre-characterisation of the system. One piece of information that is required, however, is the sign of the system's high frequency gain (or its 'instantaneous gain'). This poses a problem: combustion systems are infinite-dimensional, and so this information is never known a priori. A possible solution is to use a Nussbaum gain, which guarantees closed-loop stability without knowledge of the sign of the high frequency gain. Despite the theory for such a controller having been developed in the 1980s, it has never, to the authors' knowledge, been demonstrated experimentally. In this paper, a Nussbaum gain is used to stabilise thermoacoustic instability in a Rijke tube. The sign of the high frequency gain of the system is not required, and the controller is robust to large changes in operating conditions - demonstrated by varying the length of the Rijke tube with time. Copyright © 2008 by Simon J. Illingworth & Aimee S. Morgans.

Triggering in a thermoacoustic system with stochastic noise

This paper explores the mechanism of triggering in a simple thermoacoustic system, the Rijke tube. It is demonstrated that additive stochastic perturbations can cause triggering before the linear stability limit of a thermoacoustic system. When triggering from low noise amplitudes, the system is seen to evolve to self-sustained oscillations via an unstable periodic solution of the governing equations. Practical stability is introduced as a measure of the stability of a linearly stable state when finite perturbations are present. The concept of a stochastic stability map is used to demonstrate the change in practical stability limits for a system with a subcritical bifurcation, once stochastic terms are included. The practical stability limits are found to be strongly dependent on the strength of noise.

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. © Cambridge University Press 2013.

Obtaining bifurcation diagrams with a thermoacoustic network model

Linear techniques can predict whether the non-oscillating (steady) state of a thermoacoustic system is stable or unstable. With a sufficiently large impulse, however, a thermoacoustic system can reach a stable oscillating state even when the steady state is also stable. A nonlinear analysis is required to predict the existence of this oscillating state. Continuation methods are often used for this but they are computationally expensive. In this paper, an acoustic network code called LOTAN is used to obtain the steady and the oscillating solutions for a horizontal Rijke tube. The heat release is modelled as a nonlinear function of the mass flow rate. Several test cases from the literature are analysed in order to investigate the effect of various nonlinear terms in the flame model. The results agree well with the literature, showing that LOTAN can be used to map the steady and oscillating solutions as a function of the control parameters. Furthermore, the nature of the bifurcation between steady and oscillating states can be predicted directly from the nonlinear terms inside the flame model. Copyright © 2012 by ASME.

A novel theoretical approach to passive control of thermo-acoustic oscillations: Application to ducted heat sources

In this paper, we develop a linear technique that predicts how the stability of a thermo-acoustic 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 thermo-acoustic 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 thermo-acoustic system should be changed in order to make it stable. Copyright © 2013 by ASME.

The Chemical Percolation Devolatilization Model Applied to the Devolatilization of Coal in High Intensity Acoustic Fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Simulation of active control using fuzzy logic applied to a pulse combustor

This work analyzes an active fuzzy logic control system in a Rijke type pulse combustor. During the system development, a study of the existing types of control for pulse combustion was carried out and a simulation model was implemented to be used with the package Matlab and Simulink. Blocks which were not available in the simulator library were developed. A fuzzy controller was developed and its membership functions and inference rules were established. The obtained simulation showed that fuzzy logic is viable in the control of combustion instabilities. The obtained results indicated that the control system responded to pulses in an efficient and desirable way. It was verified that the system needed approximately 0.2 s to increase the tube internal pressure from 30 to 90 mbar, with an assumed total delay of 2 ms. The effects of delay variation were studied. Convergence was always obtained and general performance was not affected by the delay. The controller sends a pressure signal in phase with the Rijke tube internal pressure signal, through the speakers, when an increase the oscillations pressure amplitude is desired. On the other hand, when a decrease of the tube internal pressure amplitude is desired, the controller sends a signal 180° out of phase.

The impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25-hydroxyvitamin D concentrations

Studies have examined the associations between cancers and circulating 25-hydroxyvitamin D [25(OH)D], but little is known about the impact of different laboratory practices on 25(OH)D concentrations. We examined the potential impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25(OH)D concentrations. Blood samples from 20 healthy volunteers underwent alternative laboratory procedures: four centrifuging times (2, 24, 72, and 96 h after blood draw); three types of collection tubes (red top serum tube, two different plasma anticoagulant tubes containing heparin or EDTA); and two types of assays (DiaSorin radioimmunoassay [RIA] and chemiluminescence immunoassay [CLIA/LIAISON®]). Log-transformed 25(OH)D concentrations were analyzed using the generalized estimating equations (GEE) linear regression models. We found no difference in 25(OH)D concentrations by centrifuging times or type of assay. There was some indication of a difference in 25(OH)D concentrations by tube type in CLIA/LIAISON®-assayed samples, with concentrations in heparinized plasma (geometric mean, 16.1 ng ml−1) higher than those in serum (geometric mean, 15.3 ng ml−1) (p = 0.01), but the difference was significant only after substantial centrifuging delays (96 h). Our study suggests no necessity for requiring immediate processing of blood samples after collection or for the choice of a tube type or assay.

Deposition of hydroxyapatite and calcium oxalate dihydrate on a heat exchanger tube

Most studies on the characterisation of deposits on heat exchangers have been based on bulk analysis, neglecting the fine structural features and the compositional profiles of layered deposits. Attempts have been made to fully characterise a fouled stainless steel tube obtained from a quintuple Roberts evaporator of a sugar factory using X-ray diffraction and scanning electron microscopy techniques. The deposit contains three layers at the bottom of the tube and two layers on the other sections and is composed of hydroxyapatite, calcium oxalate dihydrate and an amorphous material. The proportions of these phases varied along the tube height. Energy-dispersive spectroscopy and XRD analysis on the surfaces of the outermost and innermost layers showed that hydroxyapatite was the major phase attached to the tube wall, while calcium oxalate dihydrate (with pits and voids) was the major phase on the juice side. Elemental mapping of the cross-sections of the deposit revealed the presence of a mineral, Si-Mg-Al-Fe-O, which is probably a silicate mineral. Reasons for the defects in the oxalate crystal surfaces, the differences in the crystal size distribution from bottom to the top of the tube and the composite fouling process have been postulated.