The Deformation of an Elastic Cell in an Inviscid Stream

Yorkston, Adam (2020) The Deformation of an Elastic Cell in an Inviscid Stream. Doctoral thesis, University of East Anglia.

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Abstract

In this thesis we study the deformation of an elastic cell in an inviscid fluid flow. We formulate the system of equations which governs the unsteady interaction between a thin-walled two-dimensional elastic cell and an inviscid fluid flow, allowing for fluids both in the exterior and interior of the cell. We present a conformal mapping method to simplify the exterior flow, and discuss numerical methods to evaluate the interior flow.
We focus on two particular flow configurations: a massless cell in a uniform stream, and a massive cell in a stream with circulation where the weight of the cell is balanced by the lift generated by the flow. We present asymptotic methods to obtain equilibria at low flow speeds, and use numerical methods to perform a detailed analysis of the solution space. For the massless cell we also analyse the linear stability of the equilibria, and study the subsequent nonlinear evolution of the unsteady cells.
We also extend the elastic cell formulation to allow for a fixed angle corner and an inextensible internal support, providing a simple model of an inflatable aerofoil. We present numerical methods based on a conformal mapping and a boundary integral equation which we use to analyse the deformed cell shapes in an inviscid flow, and obtain the parameter values for which the cell takes an aerodynamic shape. We compute the viscous flow past these deformed aerofoils and assess their aerodynamic viability.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Nicola Veasy
Date Deposited: 16 Mar 2021 16:01
Last Modified: 16 Mar 2021 16:09
URI: https://ueaeprints.uea.ac.uk/id/eprint/79476
DOI:

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