Academic Division: Energy, Fluid Mechanics and Turbomachinery
Research group: Energy
Thermoacoustic oscillations are a recurring problem in jet and rocket engines: When moments of higher heat release inside the combustion chamber coincide with moments of higher pressure, heat gets converted to acoustic energy -- a thermoacoustic instability arises.
Thermoacoustic instabilities are extremely challenging to predict due to their multi-scale, multi-physics nature. The physical mechanisms include:
- Hydrodynamics effects. Turbulence, shear layers, ...
- Compressible effects. Acoustics, entropy waves, ...
- Combustion. Chemical kinetics, heat transfer, diffusion processes, ...
For industrial applications, fully resolved simulations are not feasible due to their computational costs. Some physical mechanisms as well as their interactions thus require modeling assumptions. The presence of models introduces varying degrees of uncertainty into the design of thermoacoustic systems.
A number of classical techniques have been proposed to study thermoacoustic instabilities:
- Linear methods. A base flow solution is derived from the governing equations. Linear stability analysis determines the onset of thermoacoustic instability. Linear sensitivity analysis determines how the base flow and other parameters affect the growth rate and frequency of the thermoacoustic instability.
- Nonlinear methods. By including higher-order terms, weakly nonlinear analysis attempts to estimate the longer-term behavior of thermoacoustic instabilities. Bifurcation theory helps to classify the qualitative aspects of thermoacoustic oscillations, and offers one possible explanation for the route to chaos. Lyapunov exponents help to characterize the chaotic nature of a thermoacoustic system.
On the one hand, all classical techniques have in common that they attempt to solve the direct problem:
Given a model (governing equations, initial and boundary conditions, ...) as well as its parameters, what is the state of a system at a future time?
Understanding uncertainty on the other hand is an epistemological endeavor. It requires the solution of the inverse problem:
Given (possibly noisy) observations of the state of a system, what can be inferred?
Bayes' rule forms a first principle for a rigorous statistical framework to address real-life concepts such as uncertainty and bias. Physically speaking, the following inference tasks may be performed for a dynamical system such as thermoacoustics:
- Given a model of a system and its parameters as well as noisy observations, can I infer the (true) state of the system?
- Given a model of a system as well as noisy observations, can I infer the parameters of the model?
- Given noisy observations, can I assess the bias of the model?
In summary, my research aims at combining simulations and experimental data from collaborators with reduced-order models in order to conduct physics-informed statistical learning for thermoacoustic systems. The goal is to develop methods which provide insight both on a fundamental level and within large-scale systems.
- Low-order modelling of simple thermoacoustic systems.
- Bayesian regression in low-order thermoacoustic models.
- Data assimilation, parameter estimation and uncertainty quantification in thermoacoustic models.
Collaborations: Dr Nicholas Jamieson, Francesco Garita
2017/18 3A1 Fluid Mechanics I
2018/19 3A1 Fluid Mechanics I
2016 -- University of Cambridge, PhD
2014 -- 2016 RWTH Aachen University, MSc
2010 -- 2014 RWTH Aachen University, BSc