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An efficient empirical approach was developed to accurately represent the blast shock wave loading resulting from the launch of a missile from a military aircraft to be used in numerical analyses. Based on experimental test series of missile launches in laboratory environment and from a helicopter, equations were derived to predict the time- and position-dependent overpressure. The method was finally applied and validated in a structural analysis of a helicopter tail boom under missile launch shock wave loading.

The launch of a space rocket or military missile generates a shock wave behind the nozzle with high pressure loading on the surrounding structures. If such a missile is launched from a flying military aircraft like a fighter jet or helicopter it has to be assured that the structural loading mainly of the rear part of the aircraft does not exceed design limits. In the past, common means of compliance were mainly based on experimental live fire tests with adequate data acquisition equipment on the aircraft structure being expensive in both time and cost.

Aircraft designers seek for more efficient approaches to analyse the structural loading under missile launch blast shock wave. Most attention was recently paid to computational fluid dynamics (CFD) methods to simulate the missile launch procedure and missile exhaust plume [

Another approach to model the missile exhaust plume, based on molecular gas dynamics, is the direct simulation Monte Carlo (DSMC) method, which was used for the modelling of the plume flow field of a space orbiter by Rault [

Therefore, it is desired to handle the whole structural analysis in the framework of a conventional explicit finite element (FE) simulation with a more efficient method for the complex blast shock wave loading of the aircraft. First of all, this paper presents an assessment of potential methods for this load case in commercial explicit FE software with an evaluation of the representation of the real physical phenomena. A new empirical approach is then derived from an experimental test campaign and finally applied to a helicopter structure for verification and validation. Merits and limits of this new method are discussed and guidelines for the structural engineer are given on how to use it for other missile launch load cases. It has to be pointed out that due to the sensitivity and confidentiality of this topic no quantitative values will be published in this paper.

In order to develop a numerical method for the representation of the shock wave during a missile launch it is necessary to have detailed data on the time- and position-dependent pressure distribution behind a missile during an actual launch. Therefore, an experimental campaign of two different test series was conducted.

The first test series was performed under laboratory conditions with the missile being fixed to a solid test rig and being launched under this condition. Four pressure sensors were mounted behind the missile’s nozzle with different lateral and axial distances to record the shock wave pressure loading (Figure

Illustration (top view) of laboratory test launch of missile with highlighted pressure sensors (a) and qualitative illustration of the pressure-time results (b).

The second test series was performed by launching the missile directly from a helicopter, both on ground and in flight (Figure

Illustration (side view) of missile launch tests from helicopter with highlighted pressure sensors (a) and qualitative illustration of the pressure-time results (b).

Keeping in mind the target of deriving an efficient numerical approach for the simulation of this shock wave loading in commercial explicit FE software, a short assessment of potential numerical strategies will be given.

One promising option, based on conventional blast theory and the Friedlander pressure curve, is the ConWep method, which is available in current releases of LS-Dyna [

Another popular option to model blast shock wave loading with realistic fluid-structure interaction is the coupled Eulerian-Lagrangian approach (abbreviated as CEL or ALE in different FE software). With this technique, a fixed Eulerian mesh is generated that is initially filled with air, normally being modelled as an ideal gas. The shock wave loading results from the detonation modelling of an explosive charge, typically using a Jones-Wilkins-Lee equation of state [

Besides this complex fluid-structure-interaction method, the simplest approach to achieve a time-dependent shock wave pressure loading is to apply the pressure based on tabular input as a function of time, either with a simple triangular pulse or by approximating the Friedlander curve. This method was applied, for example, in [

The method of choice should be not only time-dependent but also position-dependent, as described in [

The major challenge is the development of accurate and physically meaningful analytical equations to calculate this current overpressure value

Typical Friedlander curve to display blast shock wave pressure versus time.

The three fundamental values that are needed for each spatial position are basically

The arrival time of the shock wave

Illustration of experimental values and trend lines for arrival time of shock wave

The duration of the positive pressure phase

As a final step, the orientation of the loaded elements with respect to the shock front needs to be taken into account again, since the current value represents the maximum pressure if the element is oriented perpendicularly to the shock front. For this purpose, the final pressure value is recalculated using the angle between the element’s normal (which is provided by the solver) and the connecting line of element and missile nozzle. Furthermore, the pressure is only applied to an element, if this angle is below 90°. In case of angles larger than 90°, the element would be in the shadow and, for reasons of simplification, would not be loaded.

Finally, this approach was adopted to simulate the missile launch shock wave pressure loading on a helicopter structure. The helicopter model is similar to the one of the live fire test campaign and limited to the tail boom, which was fully clamped at the nodes of the forward edge. The structure consists mainly of lightweight composite and sandwich structures, which were modelled using layered shell elements of type S4 with the Hashin composite damage model and an average size of 15 mm, leading to a total number of 137.000 elements for the whole model. Equation (

The only available values to validate the simulation results are the pressure recordings and strain gauge data. The numerically predicted pressure curves in Figure

Overpressure versus time curves of pressure sensors in test (a) and simulation (b) with similar axes scale.

Test

Simulation

Exemplary contour plot of strain distribution in helicopter tail boom during shock wave loading from missile launch (a) and comparison with test data for strain gauge SG1 in front of horizontal stabiliser (b) and SG2 behind horizontal stabiliser (c).

Illustration of maximum deflection of tail boom during shock wave loading from missile launch from top view (a) and front view (b); deformation scale factor = 2.

The development of an empirical approach to represent the blast shock wave loading resulting from the launch of a missile from an aircraft based on an experimental test campaign was presented. Similarities to the blast shock wave of a conventional singular detonation of an explosive charge were highlighted in terms of the possibility to apply the Friedlander curve to approximate the pressure-time response. However, large differences to such a conventional explosion also occur resulting from the physical flow phenomena of the continuous jet flow from the missile nozzle, making approaches like ConWep or coupled Eulerian-Lagrangian simulations inappropriate. Hence, an empirical equation was developed to represent the overpressure at each time and spatial position in a very efficient way. Although a test series of a pressure sensor-instrumented missile launch is required to determine the necessary parameters for the equation, this loading model can afterwards be applied by the aircraft engineer to various aircraft types or configurations. An enhancement of the equation or different interpolation functions could be assessed if a larger test database compared to this study was available, using more pressure sensors at further positions.

Constant in equation for peak overpressure, Pa

Constant in equation for positive pressure duration, s

Speed of sound, m·s^{−1}

Distance of sensor to nozzle, m

Weighted distance

Constant in equation for positive pressure duration, s·m^{−1}

Constant in equation for peak overpressure

Pressure, Pa

Atmospheric pressure, Pa

Peak overpressure, Pa

Time, s

Duration of positive pressure phase, s

Arrival time of shock front, s

Position coordinates, m

Wave form parameter.

The authors declare that there is no conflict of interests regarding the publication of this paper.