# A Practical Approach to Modeling and Performance Analysis of a Turboshaft Engine Using Matlab
## 3 Results  
The calculation results are presented using data for the PZL-10W engine as an example. This is a Polish-made turboshaft engine, and its schematic is shown in Figure 1. Although we do not have access to the compressor and turbine performance maps for this engine, ample information available in the literature allowed for the verification of the adopted assumptions and calculation results. The parameters characterizing processes within the engine components for DP (design point) calculations were selected to match the manufacturer's data as closely as possible. Information from reference [32] was utilized in this regard. The assumed values are presented in Table 3.  
The results of DP calculation for ambient ISA conditions are presented in Table 4. They indicate that the calculations for specific fuel consumption are approximately 3.5% higher than the values reported by the manufacturer. The compressor map was taken from [15] for a compressor with a similar pressure ratio. The map was rescaled to match the pressure ratio and efficiency values corresponding to the PZL-10W compressor parameters in DP. The compressor map, with DP marked, is shown in Figure 6a. The free power turbine map was adapted from the characteristics of the DGEN 380 engine produced by Price Induction (the stand is at Rzeszow University of Technology, in the Department of Aerospace and Space Engineering (Rzeszow, Poland)) for the low-pressure turbine available from the WESTT CS/BV virtual test bench presented in studies by [33; 34]. The map was rescaled to meet the DP work parameters of PZL-10W. The map with the pointed DP is presented in Figure 6b. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Output Shaft Power [kW]** & **SFC [kg/kW/h]** & **A\_HPT\_min [m\({}^{2}\)]** \\ \hline Calculated value & 671 & 0.377 & 0.0055 \\ Manufacturer data & 671 & 0.364 & - \\ \hline Relative difference & 0 & 0.035 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of PZL-10W performance data calculated for DP with those provided by manufacturer. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Param.** & **CPR** & **Tt4 [K]** & **m0** & **IN\_PL** & **C\_EFF** & **B\_PL** & **B\_EFF** & **HPT\_EFF** & **FPT\_EFF** & **DIF\_PL** & **R\_EFF** \\ \hline value & 7.4 & 1110 & 4.58 & 0.98 & 0.83 & 0.975 & 0.985 & 0.86 & 0.868 & 0.97 & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Assumed parameters for PZL-10W DP calculation. In the next step, the working line for the high-pressure turbine and compressor is determined. As a result, values for the compressor pressure ratio, compressor-corrected flow, compressor efficiency, and turbine inlet temperature to ambient temperature ratio are evaluated for the corrected compressor rotational speed. The results of these calculations are presented in Table 5.  
To validate the obtained results concerning the turbine-compressor working line, the calculated data for the compressor rotor speed under ISA conditions is compared with the data prepared based on a graph from a study [6] showing the relationship between the compressor pressure ratio and the rotational speed of the PZL-10 W engine in Figure 7a. The determined CPR values differ slightly from the data presented in the study by [6]. The maximum difference is below 4% and occurs at lower rotational speeds (Figure 7b). In this range, the model tends to overestimate the compression ratio. For higher compressor rotational speeds, the determined values differ by approximately 1%. These discrepancies arise from the iterative solving of the system of equations describing the interaction between the turbine and the compressor. Another possible reason could be the use of a compressor map that was selected and not originating from the specific compressor of this engine. This might also contribute to the discrepancies observed in the calculations.