Modelling of ice crystal icing in engines

发展涡扇发动机劣化预测的数学和计算模型在航空航天工业中具有重要意义。最近，业界注意到，冰晶结冰（ICI）很可能是造成大量断电和发动机损坏的原因。在这种情况下，存在于高海拔地区的冰晶进入了热的发动机核心。尽管核心温度很高，但晶体会以部分熔化的状态积聚在内部表面，然后向外脱落，损坏关键部件并造成功率损失。现有的关于冰晶形成和脱落机制的知识非常有限；最近的实验工作已经完成，以更好地了解最初的冰晶撞击，但精确的数学和计算模型尚未开发出来。特别是，这些报告强调了迫切需要更好地理解ICI的基础物理。这个博士项目的重点将是开发用于分析热机核心中冰晶形成的数学模型。[2]特别是，我们的目标是制定低维离散或连续模型，其中包含了基本的物理过程。这些模型需要描述初始撞击、附着和吸积的过程；和分离。将对这些模型进行研究，以得出关键量的标度定律，如吸积速率、熔化速率和分离阈值。我们也将为他们的研究发展理论（渐近）和计算方法。一旦基本模型被制定和研究，博士学位将考虑重要的扩展，可能包括以下一些内容：(i)普遍化，以纳入额外的物理（例如，可变流场和传热条件，不同的冰晶密度）和复杂的弯曲几何；（ii）对最近的实验结果和数据进行验证；（iii）反问题的研究（例如给定发动机诊断，能否确定飞行条件？）

[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?.