# Numerical Simulation and Design of a High-Temperature, High-Pressure Fluid Transport Pipe
## 2 Methodology and Implementation
### Numerical Method
#### 2.3.2 Gas-Leak Simulation
This implied that a new layer of cells was created when the preceding layer stretched beyond 1.4 times the ideal height and that a layer was removed when the last layer shrunk to less than 0.6 times the ideal height. Table 4 lists the conditions that define the behavior of the projectile and surrounding fluid. The fluid in the chamber behind the projectile was the propellant, and the fluid in front of the projectile was air. However, in the simulation, the propellant properties were applied as the properties of all fluid regions. This was mainly because it reflected the movements determined by the propellant properties. When the propellant burned, its molecular weight (M\({}_{\mathrm{w}}\)) changed. The molecular weight information of the burned propellant was required for the gas leakage analysis. Therefore, the molecular weight of the burned propellant was estimated using a CFD simulation. The molecular weights of the fluid region were set to 26.33, 33.38, and 39.5 g/mol (Table 5), to determine the appropriate molecular weight that could minimize the difference between the simulation data and the empirical interior ballistics code data. Table 6 lists the empirical interior ballistics code data and the CFD simulation results. The empirical interior ballistics code data were used to estimate the events when the propellant was ignited, and the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Dynamic Mesh Zone** & **Six DOF Options** \\ \hline \multirow{2}{*}{Rigid body} & Projectile & On \\ \cline{2-3}  & Moving Fluid Region & On \\ \hline Stationary body & Breech, Outlet\_a & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dynamic mesh zone setting. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **M\({}_{\mathrm{w}}\) [g/mol]** & **Description** \\ \hline Fluid\_1 & 26.33 & Before combustion, propellant M\({}_{\mathrm{w}}\) \\ Fluid\_2 & 33.38 & After combustion, M\({}_{\mathrm{w}}\) of the major components of the propellant \\ Fluid\_3 & 39.5 & 1.5 times M\({}_{\mathrm{w}}\) of Fluid\_1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Molecular weight of the fluid region. projectile accelerated along the barrel. Therefore, Fluid_3 was considered suitable for simulating the gas-leakage phenomenon, because it yielded minimum errors. Thus, the fluid properties of the propellant were employed, as detailed in Table 7. For a compressible flow, the density of the fluid was given by the ideal gas equation (i.e., Equation (20)). \[\rho=\frac{\mathrm{P}}{\left(\frac{\mathrm{R_{u}}}{\mathrm{M_{w}}}\right)\times \mathrm{T}}\, \tag{20}\]  
where P is the pressure, \(\mathrm{R_{u}}\) is the universal gas constant, \(\mathrm{M_{w}}\) is the molecular weight, and T is the temperature. As expressed in Equation (20), the density of the gas in the chamber was proportional to the molecular weight. Thus, the density increased with the molecular weight, and finally, the pressure inside the chamber increased. The pressure applied to the projectile base increased with the molecular weight. As expressed in Equation (19), the acceleration of the projectile increased with the pressure applied to the projectile base, such that the velocity of the projectile at the muzzle increased, and the travel time decreased. Thus, it was important to determine the appropriate molecular weight of the fluid in the CFD simulation, as it affects the chamber pressure, velocity, and travel time.