Engine Efficiencies
Factors Affecting Engine Thrust and Efficiency
Analyze the factors affecting engine thrust and efficiency.
Describe thrust specific fuel consumption.
Understand the factors that affect propulsive & thermal efficiency.
Thrust Equation
Basis of thrust: change in momentum of air flowing through the engine.
F = \dot{m} \Delta V
To increase thrust, we must increase:
Mass of air into the engine
Density (using compressor)
Ram effect (using divergent inlet)
Increase the change in velocity between the inlet and exhaust outlet
International Standard Atmosphere
Atmospheric air temperature, density, and pressure at sea level:
Temperature: 15°C
Pressure: 14.7 psi or 101 kPa
Density: 1.225 \frac{kg}{m^3}
Factors Affecting Engine Thrust
Air Temperature
Air Pressure
Altitude
Humidity
Airspeed (Aircraft Forward Speed)
Engine Speed (RPM compressors)
Effect of Temperature on Thrust
As temperature increases, the density of air decreases.
The mass of air entering the compressor decreases for a given engine speed.
Thus, thrust decreases.
Effect of Pressure on Thrust
As air pressure increases, the density of air increases.
The mass of air entering the compressor increases for a given engine speed.
Thus, thrust increases.
Effect of Altitude on Thrust
As altitude increases, both air temperature & pressure decreases
Pressure decreases faster than temperature, so density of air decreases with increasing altitude.
Thrust is proportional to the density of air.
Thus, thrust decreases as altitude increases.
Effect of Airspeed on Thrust
V_o is the aircraft forward speed.
When aircraft picks up speed, Vo increases, but Ve does not increase proportionally to V_o as the exhaust is choked at high power.
Therefore, when V_o increases, the thrust, F, will decrease.
F = \dot{m}e Ve - \dot{m}o Vo
Ram Effect
As aircraft speed increases, a divergent inlet duct causes inlet pressure and air density to increase (pile up of air molecules at the inlet).
As air density increases, thrust increases.
Effect of Airspeed on Thrust - Ram Recovery
Net Thrust is the resultant effect of Ram Effect and Momentum drag.
Effect of Engine Speed on Thrust
Engine speed is measured in %RPM.
Thrust increases in proportion to power lever setting.
Movement of the power lever increases fuel flow to the engine and increases engine RPM.
At low RPM, thrust increase slightly
At high RPM, even small increase in RPM produces a large increase in thrust
Effect of Humidity on Thrust
Increase in humidity means an increase in moisture, and a decrease in air density.
GTE takes in great amount of air and thus, effect of humidity is negligible
Thrust Augmentation
Thrust Augmentation: Increase the amount of thrust a jet engine can produce
Methods:
Afterburners
Water Injection
Effect of Afterburning on Thrust
Increase in thrust as high as 50%.
A large percentage of engine air is not used in combustion
Introduce more fuel and burn the air in the afterburner pipe to increase exhaust gas velocity.
Improve the aircraft take-off, climb, and combat performance.
Afterburner in the Tail Pipe
Flame is concentrated around the center of the burner. Cooling flow helps keep the afterburner well below 1700 °C
Variable nozzle opens for the increase in the volume of the gas stream
The flame stabilizers are blunt-nosed V-section annular rings located downstream of the fuel burners that create a recirculation of the gas flow to ensure proper combustion.
Water Injection
Maximum engine thrust depends on the density (weight) of the airflow through the engine
Power output can be boosted by cooling airflow with:
Water
Water/Methanol mixture or coolant (anti-freezing properties and additional source of fuel)
Can be sprayed directly at the inlet of the compressor or combustion chamber
Effect of Water Injection on Thrust
During hot weather, increase in temperature results in loss of thrust
Cools air mass and maintains constant pressure.
90% Recovery
Compressor Inlet Injection System
If water only was injected, it would reduce the turbine inlet temperature, but with the addition of methanol, the turbine inlet temperature is restored by the burning of methanol in the combustion chamber.
Thus, the power is restored without having to adjust the fuel flow.
Combustion Chamber Injection System
The injection of coolant into the combustion chamber inlet increases the mass flow through the turbine, relative to that through the compressor.
The temperature drop across the turbine is thus reduced, and this results in an increased jet pipe pressure, which in turn gives additional thrust.
Performance Indicators of Turbofan/Turbojet
Thrust specific fuel consumption
\dot{m}_f – fuel flow rate
F – thrust generated
The more thrust obtained per kg of fuel, the more efficient the engine is.
tsfc = \frac{\dot{m}_f}{F}
Propulsive Efficiency
V_0 – Inlet air velocity
V_j – Exit air velocity
Propulsive efficiency: Percentage of the total energy made available by the engine (exhaust jet) which is effective in propelling the engine (aircraft speed)
\eta{Pr} = \frac{2V0}{Vj + V0}
Propulsive Efficiency Comparison of Gas Turbine Engines
Turbojet gives a large acceleration to a small weight of air
Propulsive efficiency is high for a propeller and low for a turbojet.
Turbojet spends a large amount of fuel energy on accelerating the air i.e. injecting large K.E (\frac{1}{2}mv^2) into the air (less fuel efficient)
Turboprop gives small acceleration to a large weight of air
Propulsive Efficiency Example
If an aircraft is traveling at a speed (V0) of 644 km/h and its jet velocity (Vj) is 1851 km/h, what is the propulsive efficiency of the engine?
\eta_{Pr} = \frac{2 \times 644}{1851 + 644} = 0.52 = 52\%
Propulsive Efficiency Comparison of Gas Turbine Engines
Illustrates propulsive efficiency percentages for pure turbojet, by-pass turbojet (low and high by-pass ratios), and turbo-prop engines at different airspeeds.
Thermal Efficiency
Ratio of the actual power an engine produces (after deducting the work used by the compressor) divided by the thermal energy in the fuel consumed.
At cruise, a GTE with 30:1 compression ratio can have a thermal efficiency as high as 50%.
Factors affecting thermal efficiency: turbine inlet temperature (TIT), compression ratio, and efficiencies of turbine and compressor.
Higher TIT and compressor ratio contribute to higher thermal efficiency.
Overall Engine Efficiency
Engine Efficiency = Thermal efficiency x Propulsive Efficiency
At higher airspeed, V_0 increases:
Propulsive efficiency increases
Thermal efficiency decreases slightly
Engine efficiency increases as airspeed increases due to the increase in propulsive efficiency higher than the decrease in thermal efficiency.