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Next-generation key to solving partial differential equations makes it possible to run far more ‘what-if’ analyses while building fewer physical prototypes. Charles Clarke explains.

When using software tools to analyse and replace diseased bone or predicting friction and flow around a swimsuit in the pursuit of speed, engineers are working with the complex behaviour of matter, where one set of variables depends directly on another.

The key to such calculations is to solve the partial differential equations that describe the situations and the way they react in their environment.

Until now, the finite element method has been used to solve these equations. Now a new method is creating a computational environment where the equations for any physical phenomena can be accessed and fully coupled without limitation, and applied to the geometry of the system’s components.

Called multiphysics simulation, this makes it possible to run more ‘what-if’ analyses while building fewer physical prototypes. This ability to solve the fully coupled set of equations in a single, fast simulation is the real breakthrough.

Tim Morris, chief executive of independent FEA industry body NAFEMS, said: ‘We are witnessing a surge of interest in multiphysics modelling within our membership — it has become one of the hot topics.’

Airbus, for example, used the Multiphysics program from Comsol, the computer solutions expert, to simulate friction stir welding (FSW). In this process, a cylindrical tool made up of a shoulder and a threaded pin is spun and inserted into the joint between two pieces of metal. The rotating shoulder and pin generate heat, but not enough to melt the metal.

Instead, the softened, plasticised metal forms a solid phase made up of a fine-grained material with no entrapped oxides or gas porosity. The crushing, stirring and forging action produces a joint with a finer microstructure than the parent material and with twice the strength. The process can even join dissimilar aluminum alloys.

Airbus funded several investigations into the study of FSW. ‘One of the first results was a research project that created a mathematical model, allowing Airbus engineers to look “inside” a weld to examine temperature distributions and changes in microstructures,’ said Paul Colegrove, a lecturer in welding engineering at Cranfield University.

Comsol’s Multiphysics model couples a 3D thermal analysis for calculating heat flow with a 2D axisymmetric swirl flow simulation. This coupling, in turn, allows both the flow and heat generation to be calculated.

The thermal analysis calculates the 3D temperature field from the heat flux imposed at the tool surface. It captures the effect of the tool movement, the thermal boundary conditions and the thermal properties of the material being welded. The model then projects the temperature distribution near the tool surface from the 3D boundary to the domain in the 2D model.

US researchers at Medrad Innovations Group, led by John Kalafut, used multiphysics modelling to investigate the injection of non-Newtonian fluids (in which viscosity changes with the applied strain strain, such as non-drip paint or blood) with high shear-rates through thin syringes.

This work produced a particularly novel device called the Medrad Vanguard Dx Angiographic Catheter. The diffusion tip’s nozzle design allows for a more uniform distribution of injected contrast materials (fluids that enhance the visibility of bodily objects during medical imaging) compared with a traditional end-hole catheter.

One problem with traditional end-hole catheters is that they tend to cause the contrast material to stream from the exit hole at high velocities, potentially endangering blood vessel walls. The Vanguard catheter reduces the reaction forces associated with contrast material streaming from the nozzle and therefore minimises the likelihood of contact and damage to the blood vessel walls.

A crucial feature of the catheter was the ideal configuration of holes or slits around the tip to optimise fluid delivery while preventing structural deflection. Kalafut’s team used Comsol Multiphysics to couple forces from laminar flow with a stress-strain analysis, then modelled the fluid-structure interaction occurring in the catheters with various hole configurations, geometries and flow patterns.

Altair has also been making strides in biomedical engineering — the Shiley Centre for Orthopaedic Research and Education (SCORE) at Scripps Clinic in La Jolla, California, is using Altair HyperWorks software tools to analyse shoulder implants.

‘We take the surface of the bone as the equivalent of CAD geometry,’ said Dr Darryl D’Lima, director of SCORE’s orthopaedic research laboratory. ‘Then we create a solid mesh using HyperMesh and send it back to the CT scan software Mimics. Based on the scan, Mimics assigns material properties on an element-by-element basis and exports the file back to HyperMesh. We then have a high-fidelity surface with material properties that is unique to the patient.’

Using HyperMesh, the team can remove the diseased bone from the model of the patient’s shoulder and replace it with an implant, including the cement that fixes it in position. ‘As far as I know,’ said D’Lima, ‘HyperMesh is the only program that allows us to mesh complex organic bone surfaces and the CAD surfaces of the implant. HyperMesh does all the pre- and post-processing. It’s the glue between Mimics and our stress-analysis solver.’

Similar techniques were used by Speedo to design its LZR Racer swimsuit. The location of various panels of a special ‘slippery’ material was decided on by using ANSYS Fluent CFD software. The software’s predictions of friction and flow around the swimmer helped Speedo identify ‘drag hot spots’ that could benefit from the panels of the new material.

Speedo’s CFD work and physical testing focused on passive drag — the drag produced by a swimmer’s body while it is held in a streamlined position, which the swimmer typically assumes for up to 15m after the initial dive or turn.

This work is important, and there are opportunities to do even more with CFD in the future to analyse a swimmer throughout a race. Jim Cashman, ANSYS president and chief executive, said the success of examining passive drag sets the stage for more complex multiphysics simulations as the swimsuits continue to evolve. ‘For example, we could look at the hydrodynamic pressure on the swimmer’s body moving through the water in conjunction with the structural aspects of the suit,’ he said.

Similar technology helped students at Sussex County Technical School in Sparta, New Jersey, win first prize for innovation and third place in best overall performance among the 26 human-powered submarines at the 9th International Submarine Races.

Sussex used the CFdesign software from Blue Ridge Numerics to optimise the overall configuration of its hull shape and propeller; the school needed a tool that would assess fluid flow early in the design process, so changes could be made quickly. ‘We were able to use CFdesign to do iterations that helped us determine the amount of twist needed in the propeller blade and reduce overall drag,’ said instructor and project manager Chris Land. ‘Using CFdesign gave us a lot more confidence, especially since we didn’t have the luxury of testing with physical prototypes.’