A novel computational approach could improve understanding of how fluids interact with solid structures such as turbine blades or aeroplanes. This would help engineers eliminate catastrophic mechanical failure caused by unstable contact.
Fluid-solid interfaces are difficult to model mathematically because they comprise two separate phases that constantly interact with one another. ‘The fluid is flowing over a solid that is constantly changing its geometry,’ says Wulf Dettmer, a lecturer at Swansea University’s School of Engineering in the UK. ‘Dealing with this is a computational challenge.’
Such systems are often modelled separately – using computational fluid dynamics for fluids, and finite element analysis for solids – then combined using a third program. Many research groups – including Dettmer’s – prefer to use a single ‘combined’ program, and this can be implemented in different ways.
One is to use a ‘monolithic’ approach – in which all relevant equations are solved simultaneously; the other is to use a‘partitioned’ approach, which solves them separately. In a partitioned approach, a solution is derived for the fluid, and passed to the solid. The resulting answer is then passed back to the fluid, and so on, until a final answer is reached.
The team at Swansea has applied a computational method called exact linearisation, which allows the use of Newton’s procedure – a mathematical technique that quickly improves on estimated values to edge towards an accurate answer.
‘With each iteration you get an improved value, but it’s hard to write a program to do this,’ he explains. ‘We’ve tried to develop something robust and accurate, that can be applied to different fluid-structure problems. Usually, the method you use is very dependant on the problem.’
He has so far modelled a range of general fluid-structure interactions – such as galloping and flutter – in order to demonstrate the algorithm. ‘Later, I intend to develop a specific application to look at wind turbines.’
As well as helping to solve many engineering problems, the technique would be useful in medicine – to improve understanding of blood flow in the vascular system and airflow into the lungs.
Although still far from commercialisation, Dettmer has begun to use the software in one of his teaching modules. ‘The students will be solving 2D problems in fluid-structure interactions using this software,’ he says.