Explosion inside aircraft wing
Analytical Service Pty Ltd
TECHNICAL NOTE 201
The purpose of this analysis Is to demonstrate a specific type of explosion inside a wing; an event which would cause a net downward impulse being applied to the wing. One should remember certain basic principles involved here. The first of them is that if the explosion is entirely confined within the wing volume, i.e. no skin is torn, there will be no net impulse applied to the wing as a result. The second is that if the skin is ruptured from the material exploding inside, with both top and bottom skin blown off, there could also be a near-zero effect, normal to the chord. If the downward impulse is desired, it seems best to place the explosive near the top skin, so that it gets broken and the outward jetting begins. The downward shock wave should preferably not break the bottom skin, but only inflate it.
A simulation of such an event was carried out with a flat charge placed along the top surface of the wing (Fig.1) and detonated. The wing fragment approximates that of Tu-154M aircraft.
The computational model is also shown in Figs. 2 and 3. Apart from the charge and the shell the model also involves an air volume (black mesh), somewhat larger than the wing slice. This facilitates observation of pressure changes and allows interaction between the explosive, air and structure. The lift and drag pressures (Fig.4) are present during simulation, but their effects on stress and deformation of the section are minor.
The wing slice is restrained by two rigid planes, one at each cross-section. They can't be penetrated by structural elements, but a section can slide along its respective plane. Only the nodes of the three longerons are restrained with regard to the sliding movement. The reactions at those points, especially in a vertical direction, give us the magnitude of the vertical explosive force applied to the wing.
It is interesting to compare the impulse applied vertically (Fig.11) with one along the wing, perpendicular to the planes limiting the wing slice (Fig.12). The second impulse is larger, firstly because it is applied to a larger area. It is also less meaningful, because the limiting planes are rigid. To make that component more real, one would have to widen the slice so that it covers one bay between two adjacent ribs. If the explosive is placed in that bay only, the ribs would tend to fly away along the wing axis making the actual reflected impulse considerably weaker. Still, the axial effect could be such that the wing would fly off on one side and that a sudden push could be felt at the fuselage.
One should also add that the simulation was run longer than shown here, to 10ms. There was no essential change, except that the rebound of the bottom skin became visible and the magnitude of the vertical impulse reached almost 1000 N-s. (Please see the animation, the link is below.)
The structure is made from an aluminum alloy 2024-T3 with the exception of stringers (visible only as lines) made of 7075-T6. Considering the way of modeling, stringers do not play a key role here.
The explosive material used was 7.5mm thick, had a density of 800 kg/m3 and specific energy of 1.25 MJ/kg. (Much less than TNT with 4.61 MJ/kg.) If such a material forms a one-sided sandwich with a 4mm skin (as near the rear longeron) one can expect the fly-off velocity of skin of up to 500 m/s. At that location this velocity was nearly attained, but the rest of the top skin was flying off much slower; 40 to 50 m/s was a typical range.
The vertical impulse is of interest by itself, because, if large enough, it can affect the flight trajectory. To confine the slice in the way it was done here suggest that the slice must be a part of a much longer wing segment, a continuum. That, in turn, implies that the charge occupies much more space than was modeled here. But even without getting into the size question one should note that the net vertical impulse (per width of slice) may be similar as calculated here, as long as the top skin can be broken and the bottom skin kept intact much longer.
The question of impulse magnitude arises if we want to draw some conclusions related to the Smolensk air crash of 2010. From the published sources we know the magnitude of the vertical impulse to which the wing was subjected. The impulse calculated here turns out to be miniscule compared with what took place. In other words, a large part of the wing span would have to be loaded with explosive to get a significant vertical impulse. It is not realistic to be expecting that based on the circumstances of the crash.
Fig. 1 A slice of the wing, normal to the leading edge is shown. The charge (in red) is placed under the top skin.
Fig. 2 The outline of the wing slice is shown without the explosive. The skin segments shown in blue are somewhat weaker than the rest.
Fig. 3 The outline of the wing slice embedded in a dense mesh of air cells.
Fig. 4 The wing slice with aerodynamic pressure applied. The drag force is applied to the front longeron. (The magnitude of deformation is exaggerated for visual purposes.)
Fig. 5 Explosion pressure seen at the outer boundary of the air volume, soon after the initiation.
Fig. 6 As in Fig5, but a little later, when the shock wave approaches the bottom skin.
Fig. 7 Beginning of breaking of the top skin
Fig. 8 The top continues to break and the bottom gradually inflates
Fig. 9 Final stage of deformation of the slice
Fig. 10 History of the vertical reaction applied by the wing slice to its supports. (Positive means the supports or the wing as a whole is pushed down.)
Fig. 11 The result of integration, with respect to time, of the force in Fig.10. This is the net impulse applied to the wing as a function of time.
Fig. 12 Impulse along the wing axis
A sheet of explosive (green plate) is placed near top skin and detonated. The top disintegrates while the bottom skin inflates. The objective was to estimate the downward impulse applied to the wing as a result.