## 3 Computational Modeling and Simulation  
This section covers the problem setup and boundary conditions used for CFD simulations. All CFD simulations were carried out in ANSYS Fluent software using the k-e model to solve steady RANS equations, and data analysis was carried out using in-house developed performance codes. A non-premixed combustion model was utilized for modeling secondary combustion due to its capability of simulating high-speed reactions and turbulent diffusion flame. Additionally, the combustion model also allowed species prediction, the study of dissociation effects, and turbulence chemistry coupling [14].  
For the current research, unstructured dense mesh generation was preferred over structured, since unstructured mesh reduces the overall complexity of the mesh generation and reduces computation time. The unstructured mesh was made using ANSYS ICEM with high grid resolution to capture the flow physics accurately, especially the combustion flame near injectors and oblique shock waves inside the nozzle. In the first instance, mesh sensitivity analysis was conducted using three mesh sizes, namely coarse-mesh A (approx. three million cells), medium-mesh B (approx. six million cells), and fine-mesh C (approx. 10 million cells), respectively. Mesh sensitivity was analyzed using three mesh sizes as given in Table 4.  
These meshes were very fine and were made up of hexahedral elements, which were tightly packed and clustered near the throat and divergent wall to capture flow properties near the wall. The mesh resolution is kept fine where large flow gradients are expected, such as at the wall and throat, whereas y+ was kept below 5.  
To capture the secondary injection effect and its interaction with the flow, the grid was further refined in areas where the secondary injectors were located, as shown in Figure 4  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Mesh Type** & **Mesh Size (Million)** & **Element Type** \\ \hline A & Coarse & 3.0 & Hexahedral \\ B & Medium & 6.0 & Hexahedral \\ C & Fine & 10.0 & Hexahedral \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mesh details.  
Figure 3: Gas generator configurations: (**a**) normal injectors; (**b**) tangent injectors.  
below. To eliminate the near-wall effects, an inflation with a 1.5 mm thickness and five inflation layers was also applied. Some important mesh parameters are given in Table 5.  
Figure 5 presents the grid independence study in which the nozzle axial velocity is plotted against nozzle length for the three meshes. The grid independence study shows that there is a minor variation between all three meshes while the medium-mesh B trend almost gives the same result as the fine-mesh C. Thus, medium-mesh B was selected for further study. The outlet boundary was set as a pressure outlet at standard atmospheric conditions, whereas both the nozzle main inlet and secondary injection inlets were set as pressure inlets with the properties defined in Table 6.  
Combusted species mass fraction from RP1 and LOX in the combustion chamber was used to model the reacting flow. The rocket propulsion analysis tool was utilized to acquire combusted species and their mass fractions. A total of nine species were obtained by combusting RP1 and LOX at standard atmospheric conditions. All the primary combusted species are mentioned in Table 7 and their mass fractions were used in the non-premixed combustion model. Adiabatic heat transfers and no-slip conditions were assumed at the nozzle wall [15; 16; 17].  
Initially, flow separation analysis was performed, and then GOX was injected into the divergent section. Upon stabilization of residuals and flow variables, post-processing was performed. Normal and tangential secondary injection techniques are then studied in comparison for the first time in GG for thrust regulation.