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

湍流在工程和工业科学中无处不在，包括航空、航运和运输、海洋可再生能源、赛车设计和管道运输。投入湍流流体系统的大部分能量用于克服流动边界上的表面摩擦力或粘性湍流阻力，例如管道运输期间的管壁或飞行中的飞机机翼。最近的实验和模拟表明，如果使这些流动边界横向于流动进行侧到侧的振荡，则对于飞机飞行，表面摩擦减少高达7.5%，对于管道运输，表面摩擦减少高达25%。如果在飞机飞行中实现这种表面摩擦减少，那么一次跨大西洋飞行的典型能源节省相当于大约1500个英国家庭的日常能源使用量。虽然已经提出了一些物理解释，这种阻力减少，迄今为止，没有一般的基本数学描述的现象。这个项目将提供这样一个解释，通过识别振荡壁如何影响湍流中的关键低阻力结构。在此过程中，该项目将设计优化的壁振动策略，最好地操纵这些低阻力结构，以提供更大的节能。此外，底层的数学描述将有助于在单个框架下将不同的工业应用联系在一起，以促进关键思想和节能解决方案在应用之间的转移。

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.