Tornado Missile Impact Analysis of Nuclear Power Plant Structures

LS-DYNA Simulation


Figure 2. 16-in exhaust pipe
Figure 2. 16-in exhaust pipe FEA model
Figure 3. Missile FEA models
Figure 3. Missile FEA models
Figure 5. LS-DYNA simulation of tornado missile
Figure 5. LS-DYNA simulation of tornado missile impacts
Figure 6. LS-DYNA model of a roof exhaust pipe
Figure 6. LS-DYNA model of a roof exhaust pipe

The TORMIS computer code was developed to estimate the damage probability (risk) to nuclear power plant (NPP) structures and components (targets) from missile impacts in tornado events. TORMIS includes built-in functions to evaluate perforation or spall of barriers. For more complex failure modes, TORMIS can accept failure missile velocity inputs. Such failure velocity inputs are commonly developed off-line using simple analytical methods. For complex targets and missiles, these simple methods can lead to very conservative failure velocities which can unnecessarily overestimate damage frequencies. This can lead to expensive mitigation projects to reduce the risk to acceptable levels. In addition, determining whether the simple models are in fact conservative can be difficult to prove.

Further, many potential tornado missiles commonly identified at power plants are relatively weak compared to the safety-related targets and yet can cause substantial damage.  Examples include metal siding, steel grating, and wood plank missiles.  The loading applied to a target from these ‘soft’ missiles is more difficult to accurately predict with simple analytical methods. Additionally, real targets can have complex boundary conditions and shapes that are difficult to represent with simple analytical models without significant conservative assumptions. Constraints on a target structure can affect response at significant distance from the localized crimping response. This is especially true for soft impactors that take a relatively long time to impart load allowing the target to move prior to time of maximum crimping.


ARA performs high-fidelity computational modeling of tornado missile impacts to assess power plant safety with a nonlinear dynamic finite element software called LS-DYNA. In this way, complex failure modes and constraints on target structures can be modeled with improved accuracy. Detailed modeling of tornado missiles also captures the large scale deformation and redirection during impact experienced by these soft missiles. ARA has developed a suite of soft tornado missiles for this purpose.

One important failure mode in power plants is crimping of exhaust pipes from diesel generators and steam lines that have minimum required flow rates to function properly. For example, a simple 16-in exhaust pipe (shown in Figure 2) was impacted by a metal siding, steel grating, and wide flange beam and the resulting crimped exhaust pipe was compared. All three missiles are shown in Figure 3. The metal siding and steel grating are soft missiles and the wide flange beam is a hard missile. An animation of the LS-DYNA simulation of the metal siding impact with the 16-in exhaust pipe is shown in Figure 4. Maximum crimping occurs at 8 ms. At 20 ms, the pipe moves away from the missile by forming a plastic hinge at the roof sleeve interface. The missile continues to push the exhaust pipe until the missile slides off the pipe at 76 ms. Figure 5 shows the simulation results for the three missiles. The metal siding and steel grating, both soft missiles, show significant crushing at the interface with the exhaust pipe as well as plastic deformations and buckling away from crush zone of the missile. The top views show how the cross section of the impacting material can change due to these deformations away from the crush zone. The wide flange beam does not exhibit any of these behaviors, showing only localized bending of the flanges at the interface with the pipe and slight bending along the length.

A complex exhaust pipe target is shown in Figure 6. The target is a steel exhaust pipe with an angled exit and cover plate. The exhaust pipe extends above the roof sleeve and has insulation installed within the gap in the roof penetration (concrete roof penetration and roof sleeve shown as semi-transparent). Conservatively modeling the insulation as rigid would provide a stiff constraint that maximizes crimping. However, the insulation is easily crushed to a significant fraction of its original thickness making this a poor representation of the real response. Not including the insulation would allow for less crimping as the pipe would have an air gap within the roof penetration and roof sleeve to sway out of the way during impact. An animation of the LS-DYNA simulation of the metal siding impact with the angle exhaust pipe with a cover plate is shown in Figure 7. Maximum crimping occurs at 20 ms when the front of the exhaust pipe impacts the back of the exhaust pipe. At 34 ms, the missile has buckled significantly and at 82 ms the missile has buckled along its length, well away from the target interface.


Using nonlinear dynamic FEA to explicitly model the target/missile interaction gives a more accurate representation of the impact damage compared to simplistic loading methods. More accurate calculations lead to higher critical missile velocities, lower risk numbers, and thus cost savings to a power plant in avoiding costly and unnecessary retrofits.

Project Manager: 
Jeff Sciaudone
(919) 582-3400

Figure 4: Animation of a metal siding missile impact LS-DYNA simulation on the 16-in exhaust pipe at 540 fps.

Figure 7: Animation of a metal siding missile impact LS-DYNA simulation on the angled exhaust pipe with cover plate at 240 fps.
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