# A Practical Approach to Modeling and Performance Analysis of a Turboshaft Engine Using Matlab
## 3 Results
### Engine Performance Calculation for Various Ambient Conditions  
This section presents the results of the analysis of the impact of ambient conditions on engine performance. The analysis is limited to demonstrating the effects of changes in ambient temperature, which have a significantly greater influence on engine performance than variations in ambient pressure.  
The analysis is conducted at a high-pressure rotor speed of 100%, with the ISA standard temperature T0 = 288 K (15 \({}^{\circ}\)C) and ambient temperature increased and decreased by 15 K. According to Equations (6) and (8), changes in ambient temperature will affect the corrected speed and mass flow rate, as well as the compressor pressure ratio, as illustrated in Figure 11. For T0 ISA \(-\) 15 K (0 \({}^{\circ}\)C), N\({}_{\rm rel\;cor}\) raises to 1.027; for TO ISA (15 \({}^{\circ}\)C), N\({}_{\rm rel\;cor}\) is equal to the design point; and for T0 ISA + 15 K (30 \({}^{\circ}\)C), N\({}_{\rm rel\;cor}\) decreases to 0.975. In general, it is observed that an increase in ambient temperature reduces the rotor speed, mass flow rate, and compressor pressure ratio, which is consistent with the theory of turbine engine operation, as outlined in [15,35].  
The operation of the free power turbine and the performance of the turbine engine are illustrated in Figures 12 and 13. In Figure 12, the operating parameters for various ambient temperatures are marked on the power turbine map across its entire speed range. It shows that a lower ambient temperature, at the same compressor speed, allows for a greater pressure expansion ratio in the power turbine, thereby achieving higher power output on the engine output shaft (Figure 13 blue lines). Consequently, this results in lower specific fuel consumption (Figure 13, red lines). This is consistent with the operating principle of aircraft engines, which are controlled to maintain constant power output regardless of ambient conditions, up to a critical ambient temperature. Beyond this temperature,  
Figure 11: Compressor map with working points for Nc = 100%, and ambient temperature T0 = 0 \({}^{\circ}\)C (ISA \(-\) 15 K) T0 = 15 \({}^{\circ}\)C (ISA), T0 = 30 \({}^{\circ}\)C (ISA + 15 K).  
either the compressor speed or the turbine inlet temperature would exceed the maximum allowable value.  
The simulation results for maintaining constant output power up to an ambient temperature of +26 \({}^{\circ}\)C, which was assumed as critical, are presented in Figure 14. Figure 14a shows the maximum power at the engine output shaft and the compressor speed as a function of ambient temperature. Figure 14b illustrates the dependence of specific fuel consumption (SFC) on ambient temperature for engine operation conditions as defined in Figure 14a.  
Figure 12: Free power turbine map with working points for Nc = 100%, and ambient temperature T0 = 0 \({}^{\circ}\)C (ISA \(-\) 15 K) T0 = 15 \({}^{\circ}\)C (ISA), T0 = 30 \({}^{\circ}\)C (ISA \(+\) 15 K).  
Figure 13: Output shaft power (blue lines) of turboshaft engine and specific fuel consumption (red lines) for Nc = 100% and T0 = 0 \({}^{\circ}\)C (ISA \(-\) 15 K) T0 = 15 \({}^{\circ}\)C (ISA), T0 = 30 \({}^{\circ}\)C (ISA \(+\) 15 K).  
As the ambient temperature increases, the constant power at the engine output shaft is maintained by increasing the compressor speed, which reaches 100% at an ambient temperature of +15 \({}^{\circ}\)C (ISA condition). When assuming a maximum temperature of +26 \({}^{\circ}\)C, the compressor rotor speed rises to 101.5%. Beyond 26 \({}^{\circ}\)C, the engine power decreases while maintaining constant compressor speed and a constant value of turbine inlet temperature (not presented on the plot). In the ambient temperature range up to 26 \({}^{\circ}\)C, the increase in ambient temperature is accompanied by a slight rise in specific fuel consumption (SFC); however, after exceeding this temperature, the increase in SFC occurs at a significantly higher rate.