# Thermal Modeling

EMA® has a multi-physics platform through which to simulate and quantify the direct effects of lightning. The following content illustrates our analysis applied to a sample problem.

Thermal heating is one of the primary Direct Effects (DE) of lightning.  When large current loads are forced through regions of moderate resistance, energy is deposited into structures and significant heating can occur.  Quantifying the amount of heating that is likely to occur in sensitive regions during a lightning strike is an important factor in a lightning hardening program.  Fasteners, cables, ordnance components and other vulnerable areas should be protected to ensure safety of flight or mission.

EMA® uses numerical simulation as a tool to quantify the potential for damaging thermal effects during a lightning strike. We employ a multi-physics approach to accurately obtain both induced currents and subsequent heating on the vulnerable structures in aerospace vehicles. We demonstrate our thermal simulation capabilities on a sample problem in what follows.

Consider a titanium sheet connected to a carbon fiber sheet by aluminum fasteners with one inch spacing, as seen in the figure below.  The sheets are both 5 mm thick and the fasteners are about one inch long (in the body) and have a 1/8 by 1/8 inch profile.

A 5 mm thick sheet of carbon fiber (blue) is connected to a 5 mm thick sheet of titanium (purple) by six fasteners (orange) with 1 inch spacing. The two images show the geometry at different angles.

This sample geometry is similar to what may be found at the intersection of structures in many aerospace vehicles.  To investigate the potential for heating, we apply a 200 ampere component C lightning waveform to the sheets.  The fasteners have 0.5 Ω resistance and are the primary avenue for heating, since the current is forced through the small region where the fasteners touch the sheets.

The results are seen in the animations below.  The scale shown is temperature change in degrees Kelvin (K) due to the lightning current. The highest gain in temperature is about 93 K and occurs in the region of the fastener that touches the two sheets.  This is most easily viewed in the third animation, which has reduced opacity to allow for internal viewing.  Interestingly, the carbon fiber sheet itself gains about 40 K in the region near the fasteners and the titanium sheet heats up by about 30 K. This is also visible in the animation.

For aluminum to melt it would require a gain of about 640 K, so there is no threat of melting in this case. However, if there were ordnance components in this region, the potential for unintended ignition due to heating would need to be addressed.

Thermal heating due to lightning component C. View is facing the titanium sheet. The fastener bodies are visible.

Thermal heating due to lightning component C. View is facing the carbon fiber sheet. The fastener heads are visible.

Thermal heating due to lightning component C. View is a cross section of the geometry with limited opacity. The part of the fasteners inside of the sheets is visible.