Using FDTD to Study the Effect of Current Flow and Induced Electrical and Magnetic Fields on Carbon Fiber Reinforced Plastic Box Structures
The commercial airline industry is evolving, and manufacturers are turning their heads toward composite materials to build aircraft. Specifically, carbon fiber reinforced plastic (CFRP) has been generating considerable interest because it possesses several advantages. CFRP is lightweight, can’t be bent or forced out of shape, and has a high chemical stability. These factors add up to make CFRP aircraft more fuel efficient and durable than traditional models.
The electrical properties of CFRP differ from metal aircraft and the material’s electrical conductivity mechanism is more complex. These contrasting properties mean that current design approaches cannot be used to achieve lightning protection in aircraft manufactured using CFRP.
To manufacture a lightning resistant CFRP aircraft, you need to take a closer look at the characteristics of lightning-induced current flow in these structures. Numerical simulation is an excellent tool, including the finite-difference time-domain (FDTD) method.
FDTD Simulation Models
EMA engineers used the FDTD method to analyze lightning-induced current flow in CFRP airplanes. To do this, two CFRP box structure models were constructed. One box structure was a small-sized model called the primitive model. The other box structure was a large-sized model called the periodic model. The two models allowed engineers to gain background knowledge on current flow in CFRP structures as well as the magnetic and electric fields in the box structures.
The primitive model consists of a CFRP box structure with an aluminum rib at the center of the structure, as seen in Figure 1. The dimensions are 1806 (width) x 350 (height) x 1000 (length) mm. The dimensions of the aluminum rib are 1806 (width) x 350 (height) mm with a thickness of three mm. This model is designed to be simple and basic so that it can be used to perform FDTD simulations of aircraft wing structures. Figure 1 also shows where the simulated lightning current is injected into the model.
Figure 1. Geometry of primitive model and lightning attachment point.
The periodic model consists of a CFRP box structure with several aluminum ribs inside. It is a jointed model made of multiple primitive models; it is shown in Figure 2. The dimensions are 1806 (width) x 350 (height) x 13,000 (length) mm. The thickness of the CFRP plates is 10 mm. The dimensions of each aluminum rib are 1806 (width) x 350 (height) mm with a thickness of three mm.
Three lightning attachment points are used in the periodic model, Figure 2 shows where they are located.
Figure 2. Geometry of periodic model and lightning attachment points.
To get results, researchers analyzed the flow of current on the CFRP surface and the aluminum rib. Figure 3 shows the current density on the CFRP surface and Figure 4 shows the current density on the aluminum rib, both at one µs. The data shows that current density concentrically increases from the center of the box structure to the edges. The results also found that a considerable amount of the injected current also flows into the aluminum rib.
Figure 3. Current density on CFRP surface of primitive model.
Figure 4. Current density on aluminum rib of primitive model
The effect of a normal magnetic field on a slice of the primitive model was also examined, the location can be seen in Figure 5. The diagram shows the variation in the normal magnetic field on the slice at one µs. The magnitude of the magnetic field at the bottom region of the rib is consistent with the results of the current flow.
Figure 5. Variation in normal magnetic field on a slice of primitive model.
When looking at the periodic model, engineers studied several factors including magnetic fields at multiple points, transitions of the current flow on the CFRP surface, normal magnetic fields on a specific slice, and tangential electric fields on the specific slice.
Figure 6 (a), (b) and (c) shows the interior magnetic field waveforms for the periodic model when current is injected from one of the three lightning points. The curves in Figure 6 show the magnetic waveform at the tip (1), three-quarters of the way down (2), the halfway point (3) and at the bottom (4) of the rib of the model shown in Figure 2. The curve near the lightning point shows the biggest amplitude in each attachment case in Figure 6. The current flow near the lightning attachment point should be the biggest amplitude, which makes the magnetic field. The models show that the interior magnetic fields of the box structure are consistent with the current flow near the lightning attachment points.
Figure 6 (a). Magnetic field waveforms obtained in periodic model in the case of lightning attachment point 1. The number of wave forms corresponds to the measurement point number in Figure 2.
Figure 6 (b). Magnetic field waveforms obtained in periodic model in the case of lightning attachment point 2. The number of wave forms corresponds to the measurement point number in Figure 2.
Figure 6 (c). Magnetic field waveforms obtained in periodic model in the case of lightning attachment point 3. The number of wave forms corresponds to the measurement point number in Figure 2.
The time-expanded images of the current flow can be seen in Figure 7 (a) and (b). Figure 7 (a) shows the current flow from 10 to 60 µs in the case of lightning attachment at point one. During the early stages, the current flows through the corners of the CFRP box structure from the lightning attachment point before going through the center of the box structure toward the structure root. This implies that this track might be the smallest impedance path to the structure root.
Figure 7 (a). Transitions of current flow on CFRP surface from 10 to 60 µs in the case of lightning attachment point 1.
Figure 7 (b). Transitions of current flow on CFRP surface from 70 to 200 µs in the case of lightning attachment point 1.
Continuing to examine the data, Figure 8 (a), (b) and (c) shows the electric field on the slice in and around the periodic model at six µs. Each figure shows a different attachment point. The figures show that the magnitude of all the tangential electric fields from the lightning attachment points to the structure root are higher than that of the electric fields from the current lightning attachment points to the structure tip. This indicates that the current flows toward the structure root.
Figure 8 (a). Tangential electric field on the slice of periodic model at 6 µs in the case of lightning attachment point 1.
Figure 8 (b). Tangential electric field on the slice of periodic model at 6 µs in the case of lightning attachment point 2.
Figure 8 (c). Tangential electric field on the slice of periodic model at 6 µs in the case of lightning attachment point 3.
Researchers compared the results of the current flow from the CFRP surface to the upper side of the rib in both the models for the case of lightning attachment point three. Figure nine shows the comparison between the current flows at the aluminum rib of the periodic model and the primitive model. The data confirms that the result for the periodic model is almost consistent with the results of the primitive model.
Figure 9. Comparison between current flows at the aluminum ribs of periodic and primitive models.
The analysis from the primitive model reveals that the current injected from the lightning attachment point flows concentrically toward the edges of the box structure and that the magnetic field results are consistent with the current flow results. The data also shows that a considerable amount of the injected current flows into the aluminum rib.
Studying the periodic model, researchers concluded that the injected current flows across the CFRP box structure to the structure root. This analysis shows that this current flow track is likely the smallest impedance path to the structure root.
Since the periodic model can model is considered to be formed by the successive alignment of multiple primitive models, the results provide background knowledge for the development of more complex CFRP models.
Achieving Lightning Protection
With this background knowledge of how currents flow in CFRP aircraft, EMA is able to use its FDTD solver, Ansys EMC Plus (formerly EMA3D® Cable), to predict lightning coupling to equipment interfaces.
Ansys EMC Plus is an electromagnetic simulation tool. The first step is to import the mechanical computer-aided design (CAD). Since Ansys EMC Plus has tools to make the transition as smooth as possible, with the ability to import all major CAD formats. Once material properties are assigned, EMA can mesh the geometry using EMA3D®’s voxel style mesh. Once the project is meshed the user is ready for the EMA3D® solver. EMA3D® also includes automated post processing features that will plot the results in the same way that a user would see the results from an electromagnetic compatibility (EMC) test.
Ansys EMC Plus is well-suited for simulations addressing not only lighting, but also EMC and high-intensity radiated fields (HIRF). It can be used to address certification requirements early in the design phase before physical prototypes are complete. EMA3D® is 10 times faster when it comes to building the model and running it compared to competitive products. Past customers have been quoted to save more than $1 million by using EMA3D®.
Ansys EMC Plus is the right choice for any platform with electromagnetic requirements, including aircraft, spacecraft, automotive, rail, and electronics.
If you’re ready to learn more about Ansys EMC Plus, contact EMA to find out how we can help you get your products off the ground faster.