How to simulate industrial designs for multi-physics applications

Opera is a suite of multi-physics analysis programs that includes electromagnetics, stress and thermal analysis. To highlight the main points that make it suitable for industrial designs:

Opera includes an easy-to-use 3D Modeller, allowing models to be created or imported -in a wide variety of standard CAD formats; Scripting in the Modeller makes it a simple matter to automate the build of families of products. Once built and prepared for simulation (in the Modeller), Opera offers a range of FE solvers, enabling static, harmonic and transient EM – and incorporating linear and rotational motion for machine design. In recent times, advances in computer hardware and software capability have allowed Opera to successfully solve many challenging multi-physics problems. Coupling of EM simulations to thermal and stress simulations in Opera has now been automated with the introduction of a multi-physics interface and database, in which several simulations are set up in a single model, and the appropriate results data are passed automatically from one simulation to the next.

Opera can couple FE models to its circuit model and perform co­simulation; this allows models to be excited by a circuit comprising voltage and current sources, resistors, capacitors, inductors, switches and diodes. Opera has a built in Optimizer – a software tool which can assist users in achieving the “best” designs. The Post-Processor includes an extensive set of data extraction tools – with flexibility and capability enhanced by an in-built scripting facility – the same facility that is available in the Modeller for model creation and preparation. The recent integration of Python scripting into Opera gives the user access to an even wider range of data manipulation and processing features. There are several application specific environments developed: Machines Environment, Transformers and Quench Multiphysics.

Opera includes both thermal and stress solvers, in addition to its range of EM solvers. In Opera, we can chain any number of stages of analysis – all based on a single model. This model includes all set-up options, material properties, boundary conditions, etc, as appropriate, for each type of simulation: EM, thermal and stress.

Once chained in this way, all relevant data from one stage of an analysis are passed automatically to the next, without user intervention. This includes, if necessary, the deformation of the model due to stresses – allowing the effect of the deformations to be analysed by subsequent stages in the chain.

As we chain several simulations into one model, we create a single database shared by all simulations. Results of thermal and structural analyses are of great importance for designing real systems and investigating effects essential for operation of EM devices (overheating, outgassing, vibrations, etc.).

Coupling different analyses can be performed using either Multiphysics interface from Opera-3d Modeller or look-up tables. Both methods have their own advantages and disadvantages.

Let us consider a very simple example of a Static Thermal analysis coupled with a Static Stress.

Let us consider an example of a copper mask designed to trim proton beam to its useful part.
The Charged Particle analysis assumes that all the beam crossing the body of the mask is absorbed. Would the cooling arrangement be adequate for the heat load? The answer could be given by thermal and structural analyses aimed at checking the body temperature and stresses in copper. The total power absorbed by the mask is 535 W.

Given the properties of the emitters, primary and secondary, the Charged Particle analysis predicts trajectories of the particles, beam current density and power density. By integrating power densities on patches immediately before the mask and after the mask we can get the power absorbed by the mask, i.e. 535 W.

The results of thermal analysis give heat flux, temperature (and temperature gradient).

The results show that the maximum temperature on a surface of the mask is 231OC and the highest temperature in the cooling channels is 206OC. We can conclude therefore that cooling of the copper block is not adequate for the amount of heat absorbed by the mask.

Results of Stress analyses indicate maximum von Mises Stress of 35 MPa and maximum deformation of 7 µm. These are small to worry about. Summarising the results we can conclude that a bigger diameter entrance aperture and possibly a longer mask are needed to avoid overheating of the front face of the mask, i.e. the mask need to be completely redesigned.

In the 2nd example we demonstrate a model of a heating bath where a conducting material is heated by Eddy currents induced by a magnetic field. The multi-physics model has two parts: Harmonic EM and a static Thermal analysis.

A racetrack conductor surrounding the bath with a melt is one of the conductors from the Opera standard library. As expected the current density and hence the temperature are highest near the edge of the melt. The bath is cooled from the outside and for the purpose of thermal analysis we assume its external surface temperature is 20OC. The results show that the melt is heated by Eddy currents to a peak temperature of 261OC.

Induction welding is a commonly used industrial process for joining materials together. In this example we describe how Opera FEA software can be used to simulate the induction welding process by considering an example of joining together two thin plates of CFRP (Carbon Fibre Reinforced Polymers).


An induction coil is placed few millimetres above the CFRP sheets which are heated by Eddy currents. In real manufacturing process the sheets are pressed together and cooled down by a pressure roll to complete the welding process. It is a bonding material like epoxy resin or ceramics rather than a carbon fibre that melts and provides a bond between the sheets.

The model includes Harmonic Electromagnetic and Transient Thermal analyses and uses tables to exchange data between the two solvers. In this model, we assume that there is no heat barrier at the interface between the CFRP plates. In fact, Opera could include a thermal contact conductance, if a suitable value was known. To take into account some heat dissipation from the external surfaces of the plates into surrounding air we apply a small heat transfer coefficient (of 20 W/(m2 K)) to the interface between the air and the sheets.

Several ‘tricks’ were done to improve efficiency and reduce solving time:

As motion of the coil occurs on a much slower time-scale than the variation of the field at 1 MHz, it does not have any significant effect on the electromagnetic analysis. Consequently, it is only necessary to move the power density distribution when the coil moves to a new position at each thermal time-step. This power density distribution is either a newly calculated one or the one calculated at a previous position, if the maximum temperature changed only slightly (by less than 25oC) and hence the electrical conductivity of the CFRP has not changed considerably.

The Figure demonstrates temperature ‘trace’ of the moving coil on the surface of the CFRP when the coil moves along the surface of the sheets at different speeds.

Superconducting magnets must be designed to survive a quench in superconducting coils. Quench may originate from a micro movement in the coils causing small energy release and localized temperature rise above the critical temperature making the superconductor resistive. Heat from the resistive region conducts through the coil and spreads the quench.

The Opera-3d Quench module uses a finite element method to simulate the transient thermal and transient electromagnetic behaviour of superconducting coils and magnets.

The model includes an aluminium former, 4 coils and a protection circuit. Once a heat source is applied to initiate quench, currents in the coils start changing and the quench propagates. As the coil currents start to change, rate dependent losses, ~, in the conductor cause more heating.

Coupled Quench has the necessary communication to pass data between electromagnetic and thermal simulations Temperature: thermal . EM Magnetic and electric field: EM => thermal

Variation of current in the coils is shown in this slide. The arrows correspond to t = 0.1 s, 0.5 s and 1 s.

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