Optimization in Fluid Mechanics

Lead Research Organisation: University of Sheffield
Department Name: Mathematics and Statistics


This project aims to realise the full potential of optimisation as a theoretical tool to study fluid mechanics motivated by our need to better understand and control flows around us. As an exemplar, the drag experienced by vehicles as they move through either air or water is a huge consumer of energy and source of carbon emissions which the UK urgently needs to reduce. In the past, optimisation has generally only been used with simplified constraints such as the linearised Navier-Stokes equations to keep problems tractable. Recently, however, two breakthroughs now strongly suggest that the solutions to more sophisticated optimisation problems can be successfully computed and a recent experiment highlights what may be achieved using clever geometry design.

This project will seek to exploit these exciting advances by developing new optimisation-based approaches to treat three key problems in fluid mechanics: 1) how to systematically search for new nonlinear flow solutions to the governing Navier-Stokes equations; 2) how to manipulate nonlinear stability via boundary geometry to design more energy-efficient fluid flows in pipelines; and 3) how to calculate the best rigorous upper estimates of energy consumption (or drag) in fully turbulent shear and convective flows.


10 25 50
Description When turbulence appears, replacing a smooth 'laminar' flow, it is often costly, e.g. dramatically increasing the energy required to pump flow through a pipe at the same flow rate. The appearance of turbulence in simple flow geometries often requires a perturbation for it to occur, for example, in the form of an imperfection of an otherwise smooth wall.

We have shown that by manipulating the form of the flow it is possible to increase the size of perturbation necessary to induce turbulence, hence reducing the risk of turbulence appearing due to ambient disturbances. For the case when turbulence is already present, we have also found that it is possible to apply a localised forcing that causes relaminarisation (breakdown of the turbulence and return to a smooth flow). Using optimisation techniques, we have sought the structure of the minimal damping capable of bringing about this relaminarisation.
Exploitation Route Most important is that we have shown the capability of the optimisation methods for these types of problems in fluid mechanics. There several enhancements that could be made for the relaminarisation case, in particular, further relaxation of the form of forcing may lead to significantly more efficient optimals.
Sectors Energy,Manufacturing, including Industrial Biotechology

Description Experiments have shown that it is possible to cause the sudden laminarisation of turbulence in the flow through a pipe, by introducing localised disturbances that flatten the flow profile. This causes a substantial reduction in the drag associated with the laminar flow, vs that of the turbulent flow, but the localised disturbance introduces a significant drag cost. In this project, through numerical simulations we have shown that laminarisation is possible at much lower cost with optimised localised disturbances. Surprisingly, this disturbance is very different from those introduced in experiments. Research is ongoing to establish why, and the methodology is being pushed to further optimise the localised disturbance, going beyond purely drag-inducing perturbations, relevant to 'active' approaches.
Description IST-Austria 
Organisation Institute of Science and Technology Austria
Country Austria 
Sector Academic/University 
PI Contribution Our aim is to combine numerical modelling and laboratory experiments for the isolation and comprehension of invariant solutions in shear flow, and mechanisms for laminarisation and/or drag reduction. I bring expertise of numerical modelling, in particular, nonlinear optimisation techniques.
Collaborator Contribution Prof. B. Hof leads a team who has constructed shear flow apparatus. We discuss what can be implemented experimentally.
Impact Laboratory flows are not subject to symmetries that in numerical simulations can be imposed for computational convenience. We have searched and identified periodic orbits without the artificial rotational symmetry that is routinely used in simulation. We find that the type of orbits that tend to dominate in these more realistic domains have multiple frequencies, including long period oscillations. These render the standard techniques for identifying orbits, via recurrences, in effective. An approach that alleviates this difficulty has been proposed. Flow conditions that cause laminarisation (elimination of turbulence) have been examined experimentally and have been supported by numerical experiments.
Start Year 2008
Description Da Vinci video https://youtu.be/2v9_PadXBuU 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Undergraduate students
Results and Impact Emailed to all undergraduate applicants to show department's research interests, in particular, da Vinci's interests in Fluid Mechanics. Presented by the RA on this project.

The RA also presented a talk at Sheffield's Millennium Galleries, where da Vinci's most famous paining in fluid dynamics was exhibited.

Video has been embedded on departmental front page for nearly a year.
Year(s) Of Engagement Activity 2019
URL https://youtu.be/2v9_PadXBuU