Multiphysics Electrifies Modeling in Many Scales
The world's largest companies are typically involved in many areas of business, and their engineers find that multiphysics modeling can play an important role in many of them. These two examples from the Saab Group—one dealing with the heating of aircraft composite materials after a lightning strike, and the other addressing electromagnetic shielding around a power substation—show the wide variety of such applications and the growing importance of virtual prototyping and simulations to firms of all sizes.
by Göran Eriksson, The Saab Group, Linköping, Sweden
About the author
Dr. Göran Eriksson completed his PhD at Uppsala University, Sweden, where his research concerned the study of fusion plasma physics. Eriksson continued as a researcher and senior lecturer in this field at Uppsala University until he moved to the Saab Group in Linköping, where he now specializes in simulating electromagnetic phenomena and applications.
With sales in 2007 of roughly 2.3 billion Euros, the Saab Group is a leader in many of the diverse areas it covers in its 17 business units, which are split into defense & security, systems & products, and aeronautics. Over the years, our company has taken advantage of the many paradigm shifts that have taken place in engineering analysis, one example being our ability to implement comprehensive engineering methodologies that combine traditional experiments and testing with newer tools such as computer modeling and simulation. In fact, back in the 80's, Saab became one of the pioneers in applying large-scale computer simulations, which we used early on to verify the lightning-protection components in the wings of the famous Gripen fighter aircraft.
Lightning heats aircraft composites
Several years ago, one of the Saab divisions was working with the Swedish Defence Material Administration, and engineers in that division asked my group to perform a conceptual study on what happens to airplane materials when struck by lightning. Because weight is a major consideration in aeronautic design, these wings are made of light-weight yet strong composite materials. These materials are made up of several layers of different composites, and in these layers the materials often have a different orientation to increase strength. But, because these modern composites exhibit strongly anisotropic electrical and thermal conductivities and because they have low conductivity compared to metals, when the high electric currents due to a lightning strike flow through them, they experience a high temperature rise and are vulnerable to heating damage. The heat flowing through the composite structure also has an effect on aircraft parts close to the location of the strike.
© U.S. Air Force photo/Senior Airman James Croxon
The anisotropic, layered nature of these composites demands a 3D analysis. In addition, the underlying physics are strongly coupled because the heating, and thus temperature, depends on the current distribution, which in turn is influenced by the fact that the composites’ electrical conductivity is temperature dependent. Any attempt to analyze the temperature rise becomes a non-trivial multiphysics problem.
In our first attempts at modeling this effect, we tried manipulating our own in-house codes and commercial codes so they would include these multiphysics phenomena. However, this proved extremely difficult because none of the codes were built for simultaneously solving the electromagnetic and temperature fields together.
Then, in 2002, I heard about COMSOL Multiphysics and attended one of the company’s seminars. Here I learned about a simulation tool whose fundamental structure was built around coupling physics and solving them together easily and intuitively. This was, at the time, almost unheard of in codes for electromagnetic simulations, which basically analyzed just the electromagnetic fields; if other physics were to be involved in the modeling application, we had to integrate their effect in an empirical or approximate fashion.
When we discovered COMSOL Multiphysics, it represented the latest paradigm shift in my field. We saw that this software was built around the physics-coupling approach, and it suddenly made the modeling of lightning strikes on an airplane very easy and affordable. In particular, modeling this effect with COMSOL Multiphysics is possible thanks to the software's ability to solve virtually any set of coupled differential equations. In addition, we can easily add other physical effects such as wind cooling and black-body radiation heating that arises from the hot lightning channel, which is the 1-cm thick channel of ionized hot air (10,000-20,000 oC) where the lightning discharge flows onto an airplane wing.
Figure 1 shows the results of one such simulation of the heating caused by a current pulse from lightning injected into the leading edge of a wing that consists of two layers of different anisotropic and homogeneous composite materials (Ref 1). The current is injected across a small circular area in the front.
Figure 1: Model of lightning striking an airplane wing. On the left: the slice plot shows current density and the streamlines show current path. On the right: the slice plot shows the temperature, and the boundary plot shows the electric potential from the lightning strike.
The figure shows the distribution of current density on a number of vertical and horizontal slices through the structure at an instant in time just after the lightning has struck. In the left image, the slice plot shows current density while streamlines indicate the current's path. In the figure on the right, the slice plot describes the temperature, and the boundary plot in the middle of the geometry shows the electric potential.
The figure on the right shows where the temperature distribution reaches the material's melting temperature, 300 oC. It is evident that the outer material layer, which has the lowest electrical conductivity, is severely damaged by the temperature rise while the inner layer is not. Furthermore, it is easy to study how the extent of the damage is influenced by the degree of material anisotropies.
We validated this methodology for simulating lightning strikes against actual test results and found excellent agreement. We also learned that radiative heating from the lightning channel also plays an important role. The findings from these simulations had a major impact on construction techniques and provided useful design rules for the next generation of advanced materials for aircraft structures.
Meanwhile, we have used electromagnetic simulations to analyze a variety of other aircraft-related applications such as antenna diagrams, antenna-to-antenna couplings, radar cross-sections, interference propagation, printed circuit board designs, and test setup optimization.
As I started learning the other advantages of COMSOL Multiphysics, I began using it more and more in other simulation projects. I have found it very easy to use with a short learning curve. Any user can get right into the details of modeling immediately, particularly with the help of its Model Libraries. I also found the company’s support team to be the best I have ever come across.
Tricks for handling conductive layers
Another project where COMSOL Multiphysics played a key role concerned one of our external customers, ABB. In this case we were modeling the electromagnetic effects on the casing (the electromagnetic shielding) surrounding a voltage substation. These electricity-distribution systems are used to transform voltages between different forms and levels and thus provide the link between high-voltage transmission lines and the domestic electricity supply. Substations contain many components such as switches, transformers, and reactor coils that generate electromagnetic fields. The strong fields emanating from the transformers must frequently be shielded so as to protect other equipment and systems in and around the substation. In this process, however, the enclosure or shield walls are subject to eddy currents, which can heat the wall material enough to lead to melting.
In this application we easily modeled the multiphysics coupling between heat and electromagnetics with COMSOL, but in this model a different problem arose. An important parameter in electromagnetic shielding is the ratio of the layer thickness, d, to the penetration (skin) depth, δ. In many situations d ≥ δ, particularly at higher frequencies or for very thick layers.
The finite element method (FEM) is very well suited for modeling arbitrary shapes and coupled phenomena, but it often requires a very fine mesh if it is to resolve the interior of very thin structures such as a metal wall as in the case of these shields. With standard grid shapes, modeling such walls and other, thin conducting layers in three dimensions often leads to an excessive number of mesh elements. One approach to reduce the number of elements is to work with scaled or elongated objects, but in many cases this still leads to a number of elements that is difficult or slow to handle.
Figure 2: COMSOL Multiphysics allows users to implement an expression for a conducting layer so the software treats a 3D structure as a 2D surface but nonetheless simulates the 3D behavior. Such can be useful for simulating thin internal borders, such as possible shielding layers modifying the near-field from a cellular phone.
With the tools in COMSOL Multiphysics I found a far better solution. The software lets me implement an expression for the conducting layer, and while it treats the 3D structure as a 2D surface, it nonetheless simulates the layer’s 3D behavior (Refs 2 and 3). To include the influence of the layer on the electromagnetic fields in the surrounding 3D domain, I applied appropriate boundary conditions across the surface (Figure 2). Thus, while I was able to significantly reduce the amount of memory needed and the solution time by treating the wall layer as a 2D boundary, I could still simulate the substation enclosure’s inductive wall heating and the shielding efficiency. These methods have been applied to simulate such cases within microwave phenomena (Ref 2) and electromagnetic compatibility (Ref 3), where an equation at the boundary replaces the need to model the thin domain. An added advantage is that this system of equations can also simulate internal borders such as shielding layers modifying the near-field in a cellular phone such as between the antenna and other components (Figure 2).
Including these equations in the description of the 2D layer or boundary condition was very intuitive; I simply typed them directly into the graphical user interface. This unique feature of the software eliminates the need for time-consuming low level code programming. The implementation and validation of this boundary-condition formulation for thin conducting layers is reported in Ref. 4.
Figure 3: Model of three current-carrying coils of different phase (left) and the inductive heating in the electromagnetic shield (right).
In our specific application, we developed a model of an enclosed substation with three current-carrying coils designed to reduce reactive power, that is, to minimize the phase shift between current and voltage. In this situation, the currents induced in the wall are very strong, leading to high temperatures. In particular, current density in the regions near openings and slits can become so high that the temperature reaches the metal’s melting point. The model results indeed show that the heating is greatest around the porthole at the front of the electromagnetic shield. Figure 3 (left) shows simulation results for three current-carrying coils of different phases and reveals the size and direction of the magnetic flux. The figure on the right illustrates inductive heating in the electromagnetic shield. The model uses aluminum as the shielding material, and the results confirm that heating is greatest around the porthole at the front of the electromagnetic shield. Adjustments in the design are likely necessary in order to reduce the maximum temperature.
About the Saab Group
The Saab Group provides the global market with world-leading products, services and solutions ranging from aviation aircraft and military defense to civil security and communications. With over 13,600 employees throughout the world and annual sales of EUR 2.6 billion ($US 3.7 billion), research and development corresponds to about 20% of Saab’s annual sales. www.saabgroup.se
State-of-the-future technologies
For more than four decades, Saab has provided qualified, cutting-edge expertise aimed at creating solutions for the future. Modeling has been an integral part of achieving this and has ensured that we can offer our customers solutions utilizing state-of-the-art, or even state-of-the-future, technologies at minimal risk. Finding and then mastering COMSOL Multiphysics has helped me greatly in my work for modeling the future.
References
- Eriksson G., Proc. Intl. Conf. on Lightning and Static Electricity (ICOLSE 2005), Seattle, 2005.
- Horton R., et al., Electron. Lett., Vol. 7, no. 17, pp. 490-491, Aug. 1971.
- Sarto M.S., IEEE Trans. Electromagn. Compat., Vol. 41, no. 4, pp. 298-306, Nov. 1999.
- Eriksson G., Proc. 2007 IEEE Intl Symp. Electromagnetic Compatibility, Honolulu, 2007.