# A Practical Approach to Modeling and Performance Analysis of a Turboshaft Engine Using Matlab
## 2 Modeling the Performance of a Turboshaft Engine with a Free Power Turbine  
Figure 1 presents a schematic of the PZL-10W turboshaft engine with a free power turbine. This engine was chosen because it is of Polish construction and a lot of information about this engine's performance is available. Figure 1 highlights the control cross-sections of the engine and its main components. The engine structure incorporates the following elements: an intake, a compressor, a diffuser connecting the compressor to the combustion chamber, a combustion chamber, a high-pressure turbine (HPT), a free power turbine (FPT), and an exhaust diffuser.  
The engine data available on the manufacturer's website [28] and in publications prepared by the company staff [6;7] are compiled in Table 1.  
The classical approach to modeling the performance of aircraft engines [1;15] requires calculations at the Design Point (DP), where the basic operational parameters of the engine and its characteristic dimensions are determined--particularly the minimum cross-section of the high-pressure turbine. Operational engine characteristics are calculated during OFF-DESIGN computation. To do this, an engine components performance map is needed as well as the results of the ON-DESIGN calculation. While some engine operating parameters at the Design Point (DP) are published by the producer, such as engine power, rotor speed, compressor pressure ratio, air mass flow, etc., component performance characteristics are not available, as they constitute company trade secrets. This presents a challenge in accurate modeling of engine performance, which can be addressed by adapting component characteristics from the literature or the internet for a specific component type (e.g., fan, axial compressor, radial compressor, high- or low-pressure turbine) and rescaling these maps to match the parameters of the engine being modeled.  
This study proposes the following approach for developing the computational model of the engine:  
* Design Point calculations based on On-design analysis, determining key operating parameters of the engine, including the minimum cross-section of the high-pressure turbine and the expansion across the turbine.
* Implementation of the compressor map in the Off-Design model to establish the turbine-compressor working line, using information on turbine expansion and the minimum turbine cross-sectional area, followed by representation in corrected parameters.
* Implementation of the free power turbine map and its integration into engine performance calculations, including output shaft power.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Engine Parameter** & **Value** \\ \hline Take-off power & 900 KM/671 kW \\ Max take-off power & 1150 KM/857 kW \\ Fuel consumption (900 KM) & 268 g/KM/h/364 g/kW/h \\ Maximum flight altitude & 6000 m \\ Engine weight & 144 kg \\ Compressor pressure ratio & 7.4 \\ Air mass flow & 4.58 [kg/s] \\ \hline \hline \end{tabular}
\end{table}
Table 1: PZL-10W data adapted with permission from [6;28].  
Figure 1: PZL-10W turboshaft engine scheme with numbered control cross-sections adapted with permission from [27].