Modelling of ice crystal icing in engines

[1] The development of mathematical and computational models for the prediction of Turbofan engine deterioration is of great importance in the aerospace industry. Recently, the industry has noted that ice crystal icing (ICI) is likely responsible for numerous observed instances of power loss and engine damage. In this scenario, ice crystals present at high altitudes enter the hot engine core. Despite the high temperatures in the core, the crystals can accrete on the interior surfaces in a partially melted state, and then shed outwards, damaging key components and causing a power loss. Existing knowledge on the mechanism of ice crystal build-up and shedding is extremely limited; recent experimental work has been done to better understand the initial ice crystal impact, but accurate mathematical and computational models have not yet been developed. In particular, these latter reports have highlighted the pressing need to develop better understanding of the fundamental physics of ICI. The focus of this PhD project will be to develop mathematical models for the analysis of ice-crystal formation in the hot engine core.
[2] In particular, our aim is to formulate low-dimensional discrete or continuum models that contain the essential physics of the process. The models will need to describe the processes of initial impact, attachment and accretion; and separation. These models will be studied in order to derive scaling laws for key quantities such as the accretion rates, melting rates, and separation thresholds. We will also develop theoretical (asymptotic) and computational methods for their study. Once the fundamental models have been formulated and studied, the PhD will consider significant extensions that may include some of the following: (i) generalisations to incorporate additional physics (e.g. variable flow fields and heat transfer conditions, different ice crystal densities) and complex curved geometries; (ii) verification against recent experimental results and data; (iii) the investigation of inverse problems (e.g. given engine diagnostics, can the flight conditions be determined?.

Combining specialised modelling techniques with complex data analysis in order to deliver prediction with quantified uncertainties lies at the heart of many of the major challenges facing UK industry and society over the next decades. Indeed, the recent Government Office for Science report "Computational Modelling, Technological Futures, 2018" specifies putting the UK at the forefront of the data revolution as one of their Grand Challenges.

The beneficiaries of our research portfolio will include a wide range of UK industrial sectors such as the pharmaceutical industry, risk consultancy, telecommunications and advanced materials, as well as government bodies, including the NHS, the Met Office and the Environment Agency.

Examples of current impactful projects pursued by students and in collaboration with stake-holders include:

- Using machine learning techniques to develop automated assessment of psoriatic arthritis from hand X-Rays, freeing up consultants' time (with the NHS).

- Uncertainty quantification for the Neutron Transport Equation improving nuclear reactor safety (co-funded by Wood).

- Optimising the resilience and self-configuration of communication networks with the help of random graph colouring problems (co-funded by BT).

- Risk quantification of failure cascades on oil platforms by using Bayesian networks to improve safety assessment for certification (co-funded by DNV-GL).

- Krylov regularisation in a Bayesian framework for low-resolution Nuclear Magnetic Resonance to assess properties of porous media for real-time exploration (co-funded by Schlumberger).

- Machine learning methods to untangle oceanographic sound data for a variety of goals in including the protection of wildlife in shipping lanes (with the Department of Physics).

Future committed partners for SAMBa 2.0 are: BT, Syngenta, Schlumberger, DNV GL, Wood, ONS, AstraZeneca, Roche, Diamond Light Source, GKN, NHS, NPL, Environment Agency, Novartis, Cytel, Mango, Moogsoft, Willis Towers Watson.

SAMBa's core mission is to train the next generation of academic and industrial researchers with the breadth and depth of skills necessary to address these challenges. SAMBa's most sustained impact will be through the contributions these researchers make over the longer term of their careers. To set the students up with the skills needed to maximise this impact, SAMBa has developed a bespoke training experience in collaboration with industry, at the heart of its activities. Integrative Think Tanks (ITTs) are week-long workshops in which industrial partners present high-level research challenges to students and academics. All participants work collaboratively to formulate mathematical
models and questions that address the challenges. These outputs are meaningful both to the non-academic partner, and as a mechanism for identifying mathematical topics which are suitable for PhD research. Through the co-ownership of collaboratively developed projects, SAMBa has the capacity to lead industry in capitalising on recent advances in mathematics. ITTs occur twice a year and excel in the process of problem distillation and formulation, resulting in an exemplary environment for developing impactful projects.

SAMBa's impact on the student experience will be profound, with training in a broad range of mathematical areas, in team working, in academic-industrial collaborations, and in developing skills in communicating with specialist and generalist audiences about their research. Experience with current SAMBa students has proven that these skills are highly prized: "The SAMBa approach was a great template for setting up a productive, creative and collaborative atmosphere. The commitment of the students in getting involved with unfamiliar areas of research and applying their experience towards producing solutions was very impressive." - Dr Mike Marsh, Space weather researcher, Met Office.