# Prediction Method of Blast Wave Impact on Crew Module for Liquid Rocket Explosion on Launch Pad
## 4 Finite ElementModel of Rocket Explosion  
### Computational Models and Algorithms  
The impact on the crew module of blast wave under rocket explosion on launch pad could be studied through LS-DYNA. ANSYS LS-DYNA is an explicit analysis tool for modeling nonlinear dynamics of solids, fluids, gas, and their interaction. The 1:1 finite element analysis model including rocket body (including three stages and boosters), crew module, TNT explosive and air domain is set up by LS-DYNA software. In order to improve accuracy, air domain which is a \(\omega 20\) m \(\times\) 57.4 m cylinder and crew module which is a \(\omega 3\) m \(\times\) 0.1 m cylinder are established. Considering the symmetry of rocket, for the sake of saving computation time, a 1/4 symmetrical geometrical model of rocket is adopted.The liquid propellant in the rocket is equivalent to a cylindrical TNT, whose size varies with the different explosion scenes of the rocket, as shown in Table 6. Rocket 3D finite element model and gauges distribution are shown in Figure 2 the thickness of rocket skin is 0.003 m and other size of rocket can be read in Figure 2[23].  
It is assumed that the radius of TNT is \(r_{0}\) (m) and the height is \(h_{0}\) (m). Therefore, the length-diameter ratio of TNT is \(\varphi=h_{0}/2r_{0}\).Given the mass of TNT, \(\varphi\) of TNT can be calculated by using Equation (5) which is derived from the three equations in the Equation (4). Size parameter settings for different explosion scenarios are showed in Table 6. Unit system of cm-g-ms is adopted in the numerical model. The explosive source is located at the center of mass and a point-detonation-method is used [24].  
\[\left\{\begin{array}{l}M_{T}=\rho\cdot V\\ V=\pi r_{0}^{2}h_{0}\\ \varphi=h_{0}/2r_{0}=1\end{array}\right. \tag{4}\]  
\[r=\sqrt[3]{\frac{M_{T}}{4\pi\rho}} \tag{5}\]  
Figure 1: Main size parameters of a certain rocket.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scenarios**} & **StagesInvolved in** & **Propellant** & **Combined** & **Equivalent** \\  & **Explosion** & **Mass(kg)** & **Explosive Yield** & **TNT(kg)** \\ \hline \multirow{2}{*}{1} & stage-3 & \(1.84\times 10^{4}\) & 0.60 & \(1.11\times 10^{4}\) \\  & stage-1, 2 and boosters & \(4.01\times 10^{5}\) & 0.10 & \(4.01\times 10^{4}\) \\  & stage-2 & \(4.98\times 10^{4}\) & 0.10 & \(4.98\times 10^{3}\) \\  & stage-1, 3 and boosters & \(3.70\times 10^{5}\) & 0.12 & \(4.62\times 10^{4}\) \\  & whole rocket & \(4.19\times 10^{5}\) & 0.12 & \(5.12\times 10^{4}\) \\  & stage-1 & \(1.87\times 10^{5}\) & 0.10 & \(1.87\times 10^{4}\) \\  & stage-2 and boosters & \(2.14\times 10^{5}\) & 0.10 & \(2.14\times 10^{4}\) \\  & stage-3 & \(1.84\times 10^{4}\) & 0.60 & \(1.11\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters for typical scenarios of rocket explosion on launch pad.  
In the finite element model (Figure 2), the eight-node element of SOLID 164 is adopted for the 3D explicit analysis. In order to prevent the element distortion in large deformation and nonlinear structural analyses, an arbitrary Lagrangian-Eulerian (ALE) algorism is used in this paper.TNT and air are modeled with ALE multi-material grids, but the rocket and crew module with Lagrangian grids, while the minimal time step is controlled by the smallest element size in the explicit integral method. The grid is divided by grid gradient method, with the minimum size of 0.05 m and maximum size of 0.30 m. Fluid-solid coupling algorithm is used between two grids [25].  
Furthermore, the transitional displacement of the nodes normal to the symmetry planes is constrained, in order to simulate the propagation effect of blast wave in the symmetric plane. Non-reflecting boundary condition is applied to top, bottom, and lateral surfaces, which allows the fluid medium to flow out in order to simulate the effect of infinite space [26].