MULTI-PHYSICS SIMULATION IN THE 21st CENTURY.

Email: info@physica.co.uk

[ AERO-ACOUSTICS ]   [ CHEMICALLY REACTING FLOW ]
[ DYNAMIC FLUID-STRUCTURE INTERACTION ]
[ HIGH SPEED IMPACT ]   [ MAGNETOHYDRODYNAMICS ]
[ VARIABLY SATURATED FLOW ]   

Dynamic fluid-structure interaction

Dynamic fluid-structure interaction is a multi-physics problem which arises in the analysis of many complex systems, such as nuclear reactor and turbo-machinery components, naval and aerospace structures, dam reservoir systems, flows in elastic pipes and blood vessels. The dynamics of an elastic structure interacting with a fluid medium differ substantially from those in the absence of the fluid medium. Hydrodynamic pressures are generated by the vibrating structure and these pressures will modify the structural deformation, which in turn will modify the hydrodynamic pressures that caused them. Hence the problem is a tightly coupled elastodynamic problem for which the structure and the fluid form a single system. Analytical solutions for this class of problems are generally either not available or are limited to simple cases with simple geometries, which for many complex, real life situations lead to the necessity for a numerical solution.

A dynamic structural algorithm using the same finite volume unstructured mesh spatial discretisation as fluid flow has been developed, where the fluid flow algorithm is cell centred and the structural algorithm is vertex based. Temporal discretisation of the structure is achieved using the Newmark scheme and a procedure for moving the mesh to take account of the deforming structure has been developed using a static implementation of the structural algorithm. The geometric or space conservation law is enforced and the Navier Stokes equations have been amended to take account of the moving mesh. These algorithms together with the coupling procedure between the fluid and the structure are embedded within PHYSICA.

This procedure is illustrated for a three-dimensional loaded fixed-free cantilever in incompressible fluid flow where the ability to move the the three-dimensional mesh using the solid algorithm and the effect of a moving fluid on the structural response is shown.

Three dimensional cantilever in fluid flow

The fixed free cantilever is subjected to an applied point load on the neutral plane at the tip in the direction of the flow.[ IMAGE ]

The analytical solution for the loaded cantilever in the absence of fluid gives the amplitude of 0.1 metres and the period of oscillation as 20 seconds. The available results for this simulation are:

• The displacement at the tip of the cantilever [ IMAGE ]
• The fluid velocity at three quarters along the cantilever length [ IMAGE ]
• The fluid pressure at three quarters along the cantilever length [ IMAGE ]
• The shear xy stress in the cantilever in the neutral z plane [ IMAGE ]

AGARD 445.6 wing

The results presented here show aspects of the modelling of the interaction between the flow around the AGARD 445.6 wing and the dynamic response of the wing itself. Considerable effort was spent on generating a coincident mesh, using Gridpro, for the solid (wing) and the surrounding gas. The resulting mesh was highly orthogonal but contained very high aspect ratio elements which caused convergence issues.

The mesh [ IMAGE ] on the symmetry plane of the domain with the surface of the mesh in the wing shows the condensing of the mesh around the tip and tail of the wing. It is in this area that the aspect ratio of elements is an issue. In this simulation 100,000 elements were used which leads to a run time of the order of weeks on a single processor for around 70 time steps.

The pressure [ IMAGE ] is obtained from a simulation using a 5 degree angle of attack for 0.3 Mach number fluid flow. The graph [ IMAGE ] contains the displacements of the wing tip in stationary air. It can be seen that the properties of the wing mean that there is no noticeable damping of the amplitude of the dynamic response.