## 2 Simulation of Blast Events
### State of the Art on Blast Load Analyses of Tank Structures
[27] perform a fully coupled CFD analysis using the arbitrary Lagrange-Eulerian approach for shock wave propagation. They derive a fitting formula for overpressure as a function of scaled distance, which shows good agreement with blast equations from general literature for shock waves. Furthermore, they analyze the overpressure acting on a cylindrical concrete tank at three positions along the tank circumference at the height of the explosion source. The maximum value results at the position directly perpendicular to the explosion source, while the peak overpressure decreases to about 50% at the side and rear of the tank. Details about the pressure distribution acting on the roof are not provided or discussed. The authors highlight the time effort required for the fully coupled analysis. Further fully coupled CFD analyses are available in the literature. [PERSON] et al. [42] investigated the three-dimensional shock wave interaction with an oblique cylinder. They found out that the shocked flow around the cylinder is truly three-dimensional with the quantitative parameter differing from a plane and axisymmetric case. [PERSON] et al. [43] investigated the interaction of planar shock wave with multi-dimensional convex and concave bubbles and analyzed physical processes such as the jet or vortex formation. Further research on specific problems is available [44; 45]. However, these works are important to understand the interaction of blast wave with the 3D structure but less suitable for practical engineering applications, as methods other than fully coupled CFD analyses are preferred here. [PERSON] [46] proposes a method based on an experimental background by considering a TNT-caused shock wave. Here, the general pressure time history depends on several values, which in turn vary according to the tank's circumferential angle from the incident wave. The pressure time history rises to the peak reflected overpressure P\({}_{1}\). Vortex formation causes a pressure drop to P\({}_{2}\), which is then followed by a further increase in the so-called stagnation pressure P\({}_{3}\). From then on, the pressure decays with a time-dependent drag coefficient. The pressure values, drag coefficient and duration times depend on the angle of circumference of the tank to the incident wave. When the angle equals zero, i.e., where the blast wave first strikes the tank, the maximal peak overpressure occurs, but for larger  
Figure 3: Blast load profile and distribution for a cylindrical tank used in [31]. angles, its value decreases. In small-scale experiments, the pressure distribution around a tank was measured: based on the experimental results, a cosine-shaped fitting curve was developed to describe the angle-dependent behavior of the pressure values and the drag coefficient. Further diagrams are provided for the times t\({}_{1}\), t\({}_{2}\), and t\({}_{3}\) that describe the points of the pressure time history, at which the peak pressures P\({}_{1}\), P\({}_{2}\), and P\({}_{3}\) are reached. While the latter two are constant, the first shows angle-dependent behavior for an angle \(\theta\) larger than 90\({}^{\circ}\). The approach is quite complex and not easy to apply. Furthermore, since the value t\({}_{1}\) equals zero for circumferential angles from the incident wave of 0\({}^{\circ}\) to 90\({}^{\circ}\), it is obvious that a shock wave approach is considered and not a vapor cloud explosion in slow deflagration scenarios. However, it can be taken as general information about a pressure distribution around a cylinder that the most relevant peak pressure P\({}_{1}\) does not drop below zero even for circumferential angles larger than 90\({}^{\circ}\), i.e., on the side facing away from the tank, but it has always a positive (overpressure) value. The pressure distribution acting on a roof has not been analyzed in [46], but a recommendation is given to consider suction forces on the roof and corresponding damage to the roof and anchorage.