# Ramjet Nozzle Analysis for Transport Aircraft Configuration for Sustained Hypersonic Flight
## 4 CFD Analysis of Ramjet Nozzles
### Altitude Performance of the Nozzles  
To obtain the change in altitude performance, all three nozzles were run under three different flight altitudes with the expected Mach number set according to the flight mission profile and the operational flight regime expected of the ramjet. An additional lower level of the flight at 10,000 ft was also included to scrutinise the performance of the nozzle in over-expanded conditions (see Table 7, below). Figure 26 depicts the lowest tested altitude for all nozzle configurations with the best thrust performance in their respective categories. The conical nozzle performs the most efficiently, accelerating the flow through the nozzle with the highest exit velocity. Dual bell nozzle gives high overall thrust values due to the considerably higher exit velocity across the exit area plane of the nozzle since the radial gradient zone is substantially smaller. The bell nozzles are only efficient for one design point altitude, rendering them progressively less efficient away from it [20]. This leads to the dual bell nozzle having a higher effective expansion area while producing a higher axial thrust. In addition, the smaller pressure gradients at the radial zone of the dual bell nozzle reduce the likelihood of separation before the nozzle exit. Figure 27 depicts the nozzle performance at 50,000 ft, which is the lower end of the ramjet flight regime. The bell nozzle at this stage performs considerably better than the other two nozzles with minimal radial thrust and higher exit velocity across the exit plane due to a series of expansion fans that form from the point of inflection, accelerating the flow evenly throughout nozzle plane. The conical nozzle, on the other hand, shows signs of over-expansion. The dual bell nozzle performs well, exhibiting significant flow acceleration at the kernel zone and high velocity at the nozzle exit. \begin{table}
\begin{tabular}{c c} \hline
**Altitude (m)** & **Mach Number** \\ \hline
10000 & 1.5 \\
50000 & 2.5 \\
80000 & 4.5 \\ \hline \end{tabular}
\end{table} 
Table 7: Flight speeds at the target altitudes selected. Figure 25: Pressure Mach plot across the base nozzle, extended nozzle, and beyond the exit. Figure 28, below, presents the higher end of the flight altitudes investigated. It is evident that the conical and bell nozzle performance is poor due to the comparatively higher degree of over-expansion present. Since energy released after the gas has exited the nozzle cannot be harnessed and converted into thrust, a higher degree of over-expansion leads to poor performance with inefficient utilisation of the energy stored in the combusted exhaust. The dual bell nozzle produces a much more streamlined jet with slight over-expansion characterised by the smallest shear layer thickness. Figure 27: Pressure contours for conical, bell nozzle, and dual bell nozzle at 50,000 ft and Mach 2.5. Figure 26: Pressure contours for conical, bell nozzle, and dual bell ozzle at 10,000 ft and Mach 1.5. The final geometries considered for application in a combined cycle turboramjet-scramjet configuration are summarised in Table 8, with the dual bell nozzle being proposed as the most appropriate shape for implementation and engine integration. The three-dimensional (3-D) shape of the nozzle put forward with the dimensions and geometry provided in Table 8 is presented in Figure 29, below. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Conical Nozzle**} \\ \hline
**H1** & 3.55 m \\
**V1** & 2 m \\
**Gross Thrust** & \(1.47\times 10^{6}\) N \\ \hline \multicolumn{2}{c}{**Bell Nozzle**} \\ \hline
**H1** & 3.55 m \\
**V1** & 2 m \\
**R1** & 6 m \\
**Gross Thrust** & \(1.58\times 10^{6}\) N \\ \hline \multicolumn{2}{c}{**Dual Bell Nozzle**} \\ \hline
**H1** & 3.55 m \\
**V1** & 1.65 m \\
**V2** & 0.85 m \\
**R1** & 7 m \\
**R2** & 1 m \\
**Gross Thrust** & \(1.89\times 10^{6}\) N \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Principal dimensions and final thrust levels achieved by the three nozzles investigated.