This PhD studentship is part of the Marie Curie Network FairCFD.

Flow-MRI (magnetic resonance imaging) is a non-invasive imaging method that visualizes fluid flows in the body in 4D (3 spatial and 1 time dimension) without using ionizing radiation. It holds great promise for comprehensive characterization of blood velocity, particularly in the heart and major blood vessels, but is currently hindered by low signal-to-noise ratio (SNR) and low spatial resolution. Scans typically take 30 to 90 minutes because low SNR images must be averaged to generate high SNR images that can be interpreted. Even then, processed images remain noisy, particularly at the vessel walls. This is where accurate flow velocity information is particularly important because the wall shear stress is thought to be a major contributor to cardiovascular disease.

We have developed and tested a method (adjoint-accelerated Bayesian inference) that, in 3D steady flows, reduces engineering Flow-MRI acquisition times by a factor of 100 whilst simultaneously providing accurate wall shear stress and pressure gradient information. This method is promising, but it needs to be extended to pulsatile (periodic) flows through compliant (flexible) boundaries before it can achieve its potential in clinical Flow-MRI.

The objectives of the proposed study are to (i) extend adjoint-accelerated Bayesian inference of Flow-MRI data to 4D pulsatile flows within compliant boundaries; (ii) implement, test, and validate the results with compliant test objects in MRI machines; (iii) increase the image resolution and the predictive accuracy of derived information such as pressure gradients and wall shear stress, and (iv) assess the clinical relevance of this information by working with clinicians.

Thermo-acoustic instability is one of the most persistent and costly problems facing gas turbine manufacturers. It arises when heat release rate fluctuations from a flame lock into acoustic modes in a combustion chamber. This causes large amplitude oscillations even if the thermo-dynamic efficiency of the conversion from heat to work is small. Although the mechanism has been well understood for over a century and carefully studied through experiments and numerical simulations, engines that have been designed to be thermo-acoustically stable often turn out to be unstable when tested. This is because thermo-acoustic behaviour is highly sensitive to the phase difference between heat release rate and pressure, which in turn is sensitive to small changes in the flame behaviour and the combustor’s shape. On the negative side, this sensitivity causes a modelling and practical challenge. On the positive side, it causes the model parameters to be highly observable from experimental data. This makes thermo-acoustic instability an ideal application for Bayesian inference because (i) the physics is well-known, (ii) model parameters are observable from data, (iii) data is available from laboratory to industrial scale rigs, (iv) we know from experience that thermo-acoustic instability can always been eliminated with small changes. The challenge is to design a quantitatively-accurate model that can predict those changes.

Thermo-acoustic experiments contain some precise measurements, such as pressure and flowrate, and some imprecise measurements, such as temperature. Similarly, thermo-acoustic models contain some components with high prior confidence, such as the behaviour of acoustic waves, and some components with low prior confidence, such as acoustic wave reflection. The most influential component is the flame, for which there is a range of prior models, from cheap low confidence n-tau models to expensive high confidence LES.

In this project we will design experiments to maximize the information content of multi-physics data from an industrial-scale experimental rig. We will start by assessing the information content of data from thermo-acoustics experiments on (i) a laboratory rig and (ii) an industrial rig, working closely with Rolls-Royce Deutschland. Based on this assessment, we will redesign the hardware and experimental procedures in both rigs to maximize information content of the data. We will test this by sub-sampling experiments on the laboratory rig with 100,000 datapoints so that parsimonious experiments on the industrial rig are designed to reveal as much information as possible. We will investigate the information content of experimental diagnostics provided by optical access, helping to inform the trade-off between the costs of different diagnostics. We will frame this as a general procedure with a specific example, so that this can be extended to other disciplines.

The aim of this project is to extract maximum information from data by using models that are appropriate for the data. We will then extrapolate from existing models to predict the information content of future experiments and increase the descriptive power of the models as more informative data becomes available. The ultimate goal is to generate a model of a full engine that is sufficiently accurate that we can predict the small changes that will stabilize the engine over the entire operating regime.