## 2 Materials and Methods  
In this study, the injection system is applied to a small size axial flow turbine, part of the gas generator assembly for a microjet engine. At a nominal regime, the turbine generates approximately 274 kW for a mass flow of 1.4 kg/s. The 3D models for the turbine parts and assembly are shown in Figure 1 with the main parameters presented in Table 1.  
To determine the influence of the injection system on the axial turbine flow field, a numerical study was conducted using CFD tools (Computational Fluid Dynamics). For the studies presented in this paper, ANSYS CFX was used to perform numerical simulations and to characterize the flow and resulting performance of the turbine. The numerical model of the turbine, which incorporates the injection system, was constructed based on previously formulated methodology [1], starting with the identification of the critical section of the vanes and its intersection with the suction side, followed by the translation of the intersection curve upstream with predefined values. The injection orifices, with predefined dimensions and similar size and shape, were placed equidistant from the hub and shroud on this translated curve. The numerical model for this study is presented in Figure 2.  
For the second part of the study, the internal flow was considered, thus injection channels were introduced to the numerical model. The injection inlet is moved upstream on the injection path and a cylindrical chamber inside the vane is created, which is connected by a number of small channels to the turbine main flow. This numerical model is presented in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Measurement Unit** & **Value** \\ \hline Vane shroud diameter & mm & 89.8 \\ Rotor shroud diameter & mm & 92.7 \\ Vane maximum height & mm & 19.8 \\ Rotor maximum height & mm & 25.7 \\ Rotor tip clearance & mm & 0.5 \\ Number of vanes & - & 26 \\ Number of rotor blades & - & 37 \\ Nominal rotational speed & rpm & 45,000 \\ Nominal mass flow & Kg/s & 1.427 \\ Nominal power & KW & 274 \\ Pressure ratio & - & 2.1 \\ Isentropic efficiency & \% & 84.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Axial turbine main parameters. Figure 1: (**a**) Axial turbine vane assembly; (**b**) axial turbine rotor part; (**c**) axial turbine assembly. For this model, the numerical grid is unstructured and was generated using ANSYS Mesh. In order to determine the grid influence on the numerical result, a grid analysis was performed using three configurations with the number of elements increased by a total factor of 3.4. The results from the grid analysis are presented in Table 2. The differences between the results from the grid configurations are negligible. For this study, the second configuration was used as the values of y+ for this grid were in the recommended interval for the respective turbulence model and the computational demands were acceptable. The general dimension of the cell is 0.5 mm with smaller values near the walls. For the injection channels, the dimension for the cell is 0.05 mm and 0.1 mm for the internal cylindrical chamber. Numerical grids for both the vane and rotor are presented in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Configuration** & **Number of Elements** & **Generated Power [kW]** & **Isentropic Efficiency** \\ \hline
1 & 699,864 & 176.803 & 0.844 \\ \hline
2 & 1,216,848 & 175.027 & 0.845 \\ \hline
3 & 2,380,918 & 174.812 & 0.845 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical grid analysis results. Figure 3: Turbine vane numerical model with injection system and internal flow channels. Figure 2: Turbine vane numerical model with injection system. The boundary conditions and numerical case are typical for axial turbine simulations, with the total pressure and temperature set at the vane inlet and mass flow set at the rotor outlet. A single vane channel and respective single rotor channel were employed using rotational periodicity conditions in order to lower the computational demands.