| Summary: | This thesis deals with the application of both stability techniques and Direct Numerical Simulation to the understanding of vortex dynamics around complex geometries of practical engineering interest, specifically in the context of race car aerodynamics. The instability analysis of trailing vortices, of which the Batchelor trailing vortex is the most widespread model, is relevant in the context of Formula One ows where the generation of vortices is an efficient technique to generate downforce. Batchelor vortices were originally motivated by the need to understand the breakdown of aircraft vortices. However, contrary to aircraft wakes which consist of relatively isolated vortices, the flow around the complex geometry of a Formula One car involves multiple vortices, some of which will be subject to fast, dynamically driven external effects, like merging or obstacle interactions. Other vortices however are subject to large scale effects such as strong pressure gradients which may lead to vortex breakdown through stabilityrelated mechanisms. The aim of this work is to develop a coherent set of tools to analyse these two types of flow mechanisms. Initially, a mix of BiGlobal linear stability analysis on axially periodic modes is considered, as well as Parabolised Stability Equations to evaluate non-parallel effects on these modes, when the vortices are suffciently isolated. These stability related tools are complemented with local (embedded) Direct Numerical Simulations when the vortex dynamics and interactions with the surrounding geometry prevails. After a systematic characterisation of the vortices present in a typical race car configuration, these methods are tested on model configurations involving co-rotating and counter-rotating vortex pairs interacting with obstacles. Finally, a Direct Numerical Simulations using a spectral/hp discretisation, albeit at reduced Reynolds numbers, of the under oor region of a Formula One car is undertaken, and the results are compared with Detached Eddy Simulations to identify the relative usefulness of both techniques.
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