An Algebraic Volume of Fluid Method for Strongly Coupled Spacecraft Fuel Slosh Modelling - Jones, Bevan W S (Department of Mechanical Engineering, 2023)
The increase in the number of commercial space missions has resulted in the increased need for efficient and effective spacecraft designs. A key contributor to the accuracy of space vehicle simulation is the prediction of fuel slosh loads during in-orbit manoeuvres, particularly due to the large fuel-to-solid mass ratios involved. To this end, this thesis details a high resolution mathematical model capable of predicting the dynamic interaction between fuel slosh and the rigid structure of a spacecraft. The Volume of Fluid (VoF) method provides a framework in which Computational Fluid Dynamics (CFD) can be used to model the fluid dynamics of two phase fuel slosh in a mass conservative manner. To be applicable to industrial geometries, an unstructured finite volume median dual cell methodology is employed for spatial discretisation. This gives rise to the first novel contribution of this work, namely the development of a new volume conservative VoF initialisation method for arbitrary interfaces on unstructured meshes. The scheme, called the Arbitrary Grid Initialiser (AGI), is rigorously validated and proven conservative to machine precision [1]. An algebraic, as opposed to geometric, VoF advection method is used due to being similarly well suited to unstructured grids. Improvements to the algebraic VoF method is therefore the next contribution of this thesis; where the CICSAM [2] and HiRAC [3] VoF methods are improved, and the first conservative HiRAC method presented. The improved CICSAM and HiRAC methods are shown to be competitive with their geometric counterparts on unstructured grids while being mass conservative. Both CICSAM and HiRAC are then coupled (HiRAC for the first time) to a well balanced Continuum Surface Force (CSF) surface tension discretisation. The surface tension implementation, for which standard height functions are used, is shown to be well-balanced with an accuracy that compares favourably to existing methods. In the final part of the thesis, the complete spacecraft model is constructed. A numerical rigid body code is developed for this purpose, which can additionally track its orientation. The rigid body and fluid schemes are finally coupled together in a strong, stable, and partitioned manner using the Aitken's ∆2 method [4]. The model is demonstrated to be numerically stable for large liquid-to-solid ratios via a benchmark test case.