## 2 Methodology
### Integrated Analysis Model
#### 2.2.2 Solver Setting  
The solver CFX (v.17.1) from ANSYS, typically utilized for turbomachinery analysis, was selected, and the steady-state analysis was conducted. The \(k\)-\(\omega SST\) turbulence model was chosen for the analysis as it is well-suited for inverse pressure gradient analysis. However, the solver usually overpredicts the recirculation area, which can lead to divergences in the analysis of compressors that are sensitive to the recirculation area. To mitigate this, the reattach modification (RM) option was implemented on the model to prevent the overprediction of recirculation regions.  
For the combustion model, the eddy dissipation model (EDM), which is a reactive gas model, was employed. For the reaction model, the JetA Air WD1 Phase 1 reaction model was adapted, which uses JetA as the reactant.  
The analysis was conducted on a series of specified RPMs, ranging from 30,000 RPM to 104,000 RPM, of the engine to compare the actual engine test data and the analyzed results. As shown in Figure 8 and Table 3, the boundary conditions were applied. Among the boundary conditions, it was assumed that the entry boundary's fluid composition was constituted of O\({}_{2}\) and N\({}_{2}\), with the absence of other substances such as H\({}_{2}\)O and CO\({}_{2}\). For the outlet, complete combustion was assumed, so it was assumed to consist of O\({}_{2}\), N\({}_{2}\), H\({}_{2}\)O, and CO\({}_{2}\), with no other substances present, such as CO or NOx. For the fuel boundary condition, a mass flow rate was applied to the fuel inlet, and a user-defined subroutine was employed to calculate and apply the fuel flow rate in each iteration. A detailed description of this subroutine is presented in the latter part of this section.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Inlet Pressure [kPa]** & **Inlet Temperature [K]** & **Simulating Altitude** \\ \hline
1 & 101.325 & 288.15 & 0.0 km (Sea level) \\
2 & 94.3 & 300.7 & 0.6 km \\
3 & 84 & 298.9 & 1.5 km \\
4 & 69.7 & 298.2 & 3.0 km \\ \hline \hline \end{tabular}
\end{table}
Table 3: Boundary Conditions for Micro Gas Turbine Engine.  
Figure 6: Y+ Contour Plots at Different Engine RPM Conditions: (**a**) 50,000 RPM; (**b**)104,000 RPM.  
Figure 7: Grid Independence Test at 90,000 RPM Condition.  
To implement a fully coupled analysis model, it is necessary to establish an interface between each domain component. In this analysis model, the components of a system are represented as both rotating parts, such as compressors and turbines, and fixed parts, such as combustors and nozzles, which exist simultaneously. Accordingly, a mixing plane (stage) interface was implemented to guarantee that the analysis outcomes remain unaltered regardless of the relative angles between the domains, as illustrated in Figure 8.  
Furthermore, the micro gas turbine engine operates at a high rotational speed, which causes the compressor to operate near the surge region; the small size of the micro gas turbine engine results in a minimal distance between the impeller and diffuser blades, with a value of 0.65 mm, as illustrated in Figure 9. This proximity between the impeller and diffuser presents a challenge to the convergence of the simulation. Considering these, this study employed simulations of mixing plane interfaces between the impeller and diffuser and compared with the previous study [21] case, which adapted the frozen rotor interface at the impeller and diffuser.