The Saab Group has 17 business units, which are split into defense and security, systems and products, and aeronautics. Over the years, the company has taken advantage of the many paradigm shifts that have taken place in engineering analysis. One example is implementing comprehensive engineering methodologies that combine traditional experiments and testing with newer tools such as computer modeling and simulation. In the 1980s, Saab began applying large-scale computer simulations, which were used to verify the lightning-protection components in the wings of the Gripen fighter aircraft.

One of the Saab divisions was working with the Swedish Defense Material Administration, and engineers in that division were asked 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 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.

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 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 initial attempts at modeling this effect, engineers tried manipulating in-house codes and commercial codes to 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.

In 2002, Saab learned of COMSOL Multiphysics, 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, their effect had to be integrated in an empirical or approximate fashion.

The software was built around the physics coupling approach, making the modeling of lightning strikes on an airplane easy and affordable. In particular, modeling this effect with COMSOL Multiphysics is possible because of the software's ability to solve virtually any set of coupled differential equations. In addition, other physical effects can be added, 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°C) 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. The current is injected across a small circular area in the front. 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.

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. This can be useful for simulating thin internal borders, such as possible shielding layers modifying the near-field from a cellular phone.

The figure on the right shows where the temperature distribution reaches the material's melting temperature of 300°C. 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.

This methodology was validated for simulating lightning strikes against actual test results. 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.

Electromagnetic simulations have been used 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.

Saab Group also used the software for an external customer, ABB, in which case they modeled 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.

The multiphysics coupling between heat and electromagnetics was modeled 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.

Figure 3. Model of Three Current-Carrying Coils of different phase (left) and the inductive heating in the electromagnetic shield (right).

The finite element method (FEM) is 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. The software enables implementation of an expression for the conducting layer, and while it treats the 3D structure as a 2D surface, it simulates the layer's 3D behavior. To include the influence of the layer on the electromagnetic fields in the surrounding 3D domain, appropriate boundary conditions were applied across the surface (Figure 2). Thus, while significantly reducing the amount of memory needed and the solution time by treating the wall layer as a 2D boundary, engineers 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 and electromagnetic compatibility, 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).

In this specific application, a model was developed 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 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.

This work was done by Dr. Göran Eriksson of the Saab Group, using software from COMSOL. For more information, Click Here .


Embedded Technology Magazine

This article first appeared in the September, 2008 issue of Embedded Technology Magazine.

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