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%.

Numerical simulation of the growth of ZnO nanostructures in a tube furnace by physical vapour deposition

Zinc oxide is a versatile II-VI naturally n-type semiconductor that exhibits piezoelectric properties. By controlling the growth kinetics during a simple carbothermal reduction process a wide range of 1D nanostructures such as nanowires, nanobelts, and nanotetrapods have been synthesized. The driving force: for the nanostructure growth is the Zn vapour supersaturation and supply rate which, if known, can be used to predict and explain the type of crystal structure that results. A model which attempts to determine the Zn vapour concentration as a function of position in the growth furnace is described. A numerical simulation package, COMSOL, was used to simultaneously model the effects of fluid flow, diffusion and heat transfer in a tube furnace made specifically for ZnO nanostructure growth. Parameters such as the temperature, pressure, and flow rate are used as inputs to the model to show the effect that each one has on the Zn concentration profile. An experimental parametric study of ZnO nanostructure growth was also conducted and compared to the model predictions for the Zn concentration in the tube. © 2008 Materials Research Society.

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.