Abaqus CEL simulation of a blast wave interacting with a half wall in a closed system
When an explosive is detonated, the question of how to best ensure survivability is complex and sometimes counterintuitive. Out in the open, the answer is obvious – put as much distance between the target and detonation centre as possible. However, in the real world, the environment is cluttered with an array of objects such as walls and vehicles. In this case, a blast will interact with the environment such that it becomes far more deadly and also far less obvious how to best protect oneself. This is a fact that has unfortunately been exploited by terrorists with devastating effect, targeting environments such as trains, buildings and buses.
On 21st November 1974, bombs were detonated in two public houses in Birmingham. Proximity to the bomb was an entirely unreliable indicator of injury severity. In one case, two individuals escaped death despite being only 2-3 m from the bomb, while fatalities occurred at up to 11 m elsewhere in the building. The reason why people around the corner, out of the line-of-sight of the bomb, sustained some of the most severe injuries relates to the physics of the blast wave. Broadly, the blast is strongly reflected by obstacles such as walls where the peak pressure will approximately double due to momentum conservation. Therefore, a target near a wall in such a confined environment will experience prolonged loading at a greater amplitude and impulse, significantly increasing lethality. An important caveat to this is that there are, in reality, myriad effects responsible for the clinical outcomes outside of the blast wave dynamics. The human body itself significantly supresses a number of pressure wave and penetrating blast injuries, resulting in greater survivability for those situated behind others along the line-of-sight of the detonation. Further, the threat itself can vary enormously in its deployment, type, and shrapnel mass.
Very useful insight into blast dynamics can be gained from simulations. Two techniques are Computational Fluid Dynamics (CFD) and Coupled Eulerian Lagrangian (CEL) codes. Here, we look at the example of a CEL model of a blast impinging on a half wall. We model the body of air as an Eulerian domain and allow it to propagate into a solid Lagrangian domain. For simplicity, the Lagrangian half wall is rigid in this case. This method utilises a fluid Equation of State (often the ideal gas law) that relates air pressure, density, and specific energy, and combines this with the Navier -Stokes equations. As blast waves are supersonic, we use a code that solves the compressible and inviscid form of the Navier-Stokes equations. In the CEL technique, blast interaction can be simulated by solving the Fluid Structure Interaction (FSI) between the Eulerian fluid and Lagrangian solid simultaneously in each time step. This has the advantage of being less computationally expensive than CFD as it uses one solver. Conversely, in CFD, blast-solid interaction requires co-simulation with two separate solvers for the finite element solid and the fluid domain. This approach can be more susceptible to errors where there are overclosures between the structure and fluid. On the other hand, the CEL technique offers less accuracy at very low and high flow speeds. The correct approach will depend on the phenomenon in question.
The build up of pressure on reflection with the blast-facing side of the wall is clearly visible. There is also initial stagnation behind the wall before subsequent increase as the rear side is impinged by the reflected blast. Such models must be well-validated in the laboratory or field. Our shock tube experiments testing various geometries and utilising a range of pressure measurement diagnostics have shown such CEL simulations to be valid and accurate.
The physics of blast interaction is of great importance to both the civilian and military spheres. In the former case, building and vehicle blast resilience is a highly active area of interest. For instance, in the aftermath of events such as the train bombings in Madrid and London, engineered failure points in the carriage such as the windows have been identified as a means of rapidly venting the blast away from the occupants. In the built environment, we must also consider the risk of building collapse. In the military case, the challenges can be very different. Would combatants be better protected if they were prone and presented a smaller area to the explosion? Could this actually be worse because of constructive blast reflections along the ground? What structures and materials could exacerbate and attenuate blast? Due to the complexity of many blast wave interactions, validated numerical simulations will play an important role in answering these questions.