Combustion instability is characterized by large-amplitude pressure fluctuations in combustion chambers, and it presents a major challenge for the designer of high-performance, low-emission energy systems such as gas turbines. The instability arises due to complex interactions among acoustics, heat release and transport, and hydrodynamics, which occur over a huge span of time/length scales. In the past, various aspects of the interaction were modelled in isolation, and often on an empirical basis. Advanced mathematical techniques, matched asymptotic expansion technique and multiple-scale methods, provide a means to tackle this multi-physical phenomenon in a self-consistent and systematical manner. By using this approach, a first-principle flame-acoustic interaction theory, valid in the so-called corrugated flamelet regime, has been derived recently. The reduced system in the theory ratains the key mechanisms of combustions instability but is much more tractable computationally. In the present proposed project, the flame-acoustic interaction theory will be extended first to account for the influence of a general externally imposed perturbation. A more general asymptotic theory will be formulated in the so-called thin-reaction-zone regime. Numerical algorithms to solve the asymptotically reduced systems will be developed. The asymptotic theories and numerical methods provide, in principle, an efficient tool for predicting the onset of combustion instability. The fidelity of this approach will be assessed by accurate direct numerical simulations (DNS). It will be applied to the situations pertaining to important experiments in order to predict a number of remarkable phenomena, such as self-sustained oscillations, flame stabilization by pressure oscillations, parametric instability induced by pressure and/or enthalpy fluctuations and onset of chaotic flames. The theoretical models will be employed to develop effective active control of combustion instability by modulating fuel rate, and the effectiveness and robustness of the controllers designed will be tested by simulations using the asymptotic models as well as the fundamental equations for reacting flows.

Potential Impact:
Combustion instability is a major barrier to further improvement in the performance, energy efficiency and emission reduction of a wide range of combustion devices, in particular, gas turbines for both aircraft and land-based power generation operating near the lean limit. Worldwide, legislation is becoming increasingly stringent on emissions from energy systems. The European vision for Aeronautics is to achieve reduction of 80% in NOx, 50% in CO2 and 50% in perceived noise by 2020. The challenges are enormous from both technological and economic points of view. Companies that cannot achieve such targets would suffer competitive disadvantages. With the cost of developing a new gas turbine system running into billions of pounds, guidance and tools based on fundamental research are needed to reduce the development cost and time. With our industrial partners Rolls-Royce (world leader in gas turbine aeroengines) and Siemens (world leader in gas turbines for power generation), we have identified combustion instability as a major topic for which enhanced understanding and increased capability of prediction and control are urgently needed. Mathematics plays a pivotal role in tackling this intricate multi-scale phenomenon. During this project, advanced mathematical techniques will be used to develop theoretical models, numerical methods and control algorithms for combustion instabilities, and their validity will be established by first-principle based direct numerical simulation (DNS). The aim is to gain new insights and to provide simple but reliable predictive tools, which will be able to help the industry upgrade current tools used in R & D. The proposed research will also shed light on an emerging and urgent problem related to the proposed use of bio-derived or synthetic fuels for gas turbines. The project will not have the scope to study the biofuel blend in detail, but the DNS will examine how details of combustion heat release corresponding to different types of fuels would influence the onset and control of combustion instability, thereby providing guidance regarding what modifications are required for future gas turbines burning new fuels. Due to the importance of gas turbines in the energy and defense sectors, the economic, environmental and social impact of the proposed research is enormous. Worldwide, for example, the value of gas turbine production alone was $40.5 billion, up 13% from 2008. By 2014, it is projected to grow to $50.9 billion, a 28% increase. The stake is particularly high for the UK as it is a world leader in the field. Rolls-Royce gas turbines are one of the most important UK exports to the world. It is vitally important that the UK maintains its leadership using advanced R & D underpinned by fundamental researches. For major global airlines, the cost of fuels accounts for 15% to 40% of their operating costs. It is obvious that fuel efficiency of gas turbines determines the economy and in some cases the survival of the aviation industry. The key beneficiaries will be the energy industry and aviation industry. We will fully engage our industrial partners throughout the project. Representatives from Rolls-Royce and Siemens will be invited to attend the kickoff meeting of the project to keep the project team abreast of the latest industry needs, and to involve in formulating action plans that maximise the relevance of the project to industry. At the end of the project a workshop will be organised to present the final outcomes of the research and discuss further exploitation. During the project, four joint meetings will be held with Rolls-Royce and Siemens, with the venues alternating between the research partners (Imperial, Southampton, Rolls-Royce and Siemens). Finally, the project will train three highly skilled researchers in areas of urgent needs, by a team with considerable complementary expertise, and offers the added value of the professional contact with two leading technology companies