Saving energy via drag reduction: a mathematical description of oscillatory flows

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Turbulent fluid flows are ubiquitous in the engineering and industrial sciences, including aviation, shipping and transport, marine renewable energy, race car design, and pipeline transport. Much of the energy put into turbulent fluid systems is used to overcome the skin friction, or viscous turbulent drag force, on the boundaries of the flow, such as a pipe wall during pipeline transport or an aircraft wing in flight. Recent experiments and simulations indicate the potential for a reduction in skin friction of up to 7.5% for aircraft flight and up to 25% in pipeline transport if these flow boundaries are made to oscillate side-to-side transversally to the flow. If such skin friction reductions were realised in aircraft flight, then typical energy savings for one transatlantic flight are equivalent to the daily energy usage of around 1500 UK homes. Although some physical explanations for this drag reduction have been forwarded, to date there is no general underlying mathematical description of the phenomenon. This project will provide such an explanation, by identifying how oscillating walls affect key low-drag structures in the turbulent flow. In doing so, the project will design optimised wall oscillation strategies which best manipulate these low-drag structures in order to provide even greater energy savings. Additionally, the underlying mathematical description will help to relate different industrial applications together under a single framework, in order to facilitate the transfer of key ideas and energy saving solutions between applications.