Parametric Cycle Analysis of Real Turbofan

Transcription

1 Parametric Cycle Analysis of Real Turbofan Introduction Parametric cycle analysis of a real turbofan The behaviour of a turbofan operating at optimum bypass ratio

2 Cycle Analysis of Real Turbofan Assumptions : Upstream of main burner: perfect gas with constant properties γ c, R c, c pc, etc. Downstream of main burner: perfect gas with constant properties γ t, R t, c pt, etc. All components are adiabatic (turbine cooling is neglected) Constant polytropic efficiencies e f, e c, e t for fan, compressor, and turbine Source: Real Turbofan Input:,,,,,,,,,,,,,,,,,,,,, Output:,,,,,,, Source:

3 Real Turbofan T-s Diagram for Turbofan Engine with Losses Source: Real Turbofan Equations = 1 = 1 = = = = =1 for 1 = for >1 = Source:

4 Real Turbofan Equations = = = 1 1 = = 1 1 = 1 = = = 1 1 Source: Real Turbofan Equations = = = = = = = Source:

5 Real Turbofan Equations Source: Cycle Analysis of Real Turbofan = K = 0.98 = 0.90 Baseline = 1.4 = 0.98 : 0.91 = 0.9 = kj/(kg. K) = = 0.98 = 0.88 = 24 = 1.35 = 0.99 = 42,800 kj/kg = 2 = kj/(kg. K) = 0.98 = 1670 K Turbofan with Losses: Specific Thrust vs Comp Pressure Ratio Turbofan with Losses: Fuel-air Ratio vs Comp Pressure Ratio Source: Example 7.7

6 Cycle Analysis of Real Turbofan As α increases, difference in S between real engine cycle and ideal engine cycle increases: Due mainly to the much higher f for the "real" engine. Turbofan with Losses: Thrust Specific Fuel Consumption vs Comp Pressure Ratio Source: Example 7.7 Cycle Analysis of Real Turbofan Specific thrust is reduced more than that of ideal engine at high M 0 because of increasing inlet total pressure loss Limiting M 0 is much lower for real engine than for ideal engine. Turbofan with Losses: Specific Thrust vs Mach Number Turbofan with Losses: TSFC vs Mach Number Source: Example 7.7

7 Optimum BPR, a* Turbofan Optimum bypass ratio, in a turbofan with losses, that gives the minimum thrust specific fuel consumption Source: Optimum BPR, a* Turbofan An optimum-bypass-ratio turbofan engine has the following characteristics: π c has very little effect on the specific thrust Increasing theπ f increases the specific thrust α* increases with π c and decreases with π f Specific fuel consumption decreases with increasing π c Specific fuel consumption increases with increasing π f Specific thrust decreases with M 0 up to a critical value before increasing again. Specific fuel consumption increases with increasing M 0 Optimum bypass ratio decreases with increasing M 0 Adapted:

8 Optimum BPR, a* Turbofan = K = 0.98 Baseline = 1.4 = 0.98 = 0.9 = kj/(kg. K) = = 0.98 = 24 = 1.35 = 0.99 = 2 = kj/(kg. K) = 0.98 = 0.90 : 0.91 = 0.88 = 42,800 kj/kg = 1670 K = 1 = 1 π c has very little effect on the specific thrust Optimum Bypass Ratio Turbofan: Specific Thrust and α* vs Comp Pres Ratio Increasing theπ f increases the specific thrust α* increases with π c and decreases with π f Source: Example 7.8 Optimum BPR, a* Turbofan Specific fuel consumption decreases with increasing π c Specific fuel consumption increases with increasing π f Optimum Bypass Ratio Turbofan: Thrust Specific Fuel Consumption vs Comp Pres Ratio Source: Example 7.8

9 Optimum BPR, a* Turbofan Specific thrust decreases with M 0 to a critical value before increasing again. Optimum bypass ratio decreases with increasing M 0 Optimum Bypass Ratio Turbofan: Specific Thrust and a* vs Mach Number Source: Example 7.8 Optimum BPR, a* Turbofan Specific fuel consumption increases with increasing M 0 Optimum Bypass Ratio Turbofan: Thrust Specific Fuel Consumption vs Mach Number Source: Example 7.8

10 Summary Parametric cycle analysis of a real turbofan Consideration for losses More real-world assumptions Comparison with ideal turbofan Evaluating a turbofan operating at optimum bypass ratio Reflection Question What is defined as a turbofan engine with optimum bypass ratio, and what are the characteristics of such an engine?