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Jet Propulsion

Lecture-2

Ujjwal K Saha, Ph.D.Department of Mechanical Engineering

Indian Institute of Technology Guwahati

Prepared underQIP-CD Cell Project

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A gas turbine that is configured and operated to closely follow the Brayton cycle is called a simple cycle gas turbine. Most aircraft gas turbines operate in a simple configuration since attention must be paid to engine weight and frontal area. However, in land or marine applications, additional equipment can be added to the simple cycle gas turbine, leading to increases in efficiency and/or the output of a unit. Three such modifications are regeneration,intercooling and reheating.

Simple Gas Turbine Cycle

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An Open-Cycle Gas-Turbine EngineAn Open-Cycle Gas-Turbine Engine

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A Closed-Cycle Gas-Turbine EngineA Closed-Cycle Gas-Turbine Engine

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The Ideal Brayton CycleThe Ideal Brayton Cycle

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Thermal Efficiency of the Ideal Brayton Cycle as a Function of the Pressure Ratio

Thermal Efficiency of the Ideal Brayton Cycle as a Function of the Pressure Ratio

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The Net Work of the Brayton CycleThe Net Work of the Brayton CycleFor fixed values of Tmin and Tmax, the net work of the Brayton cycle first

increases with the pressure ratio, then reaches a maximum at rp=(Tmax/Tmin)k/[2(k-1)], and finally decreases

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The Back-Work Ratio is the Fraction of Turbine Work Used to Drive the Compressor

The Back-Work Ratio is the Fraction of Turbine Work Used to Drive the Compressor

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Deviation of Actual Gas-Turbine Cycle From Brayton cycle

Deviation of Actual Gas-Turbine Cycle From Brayton cycle

The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities

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Regeneration involves the installation of a heat exchanger (recuperator) through which the turbine exhaust gases pass. The compressed air is then heated in the exhaust gas heat exchanger, before the flow enters the combustor.

Regeneration

If the regenerator is well designed (i.e., the heat exchanger effectiveness is high and the pressure drops are small) the efficiency will be increased over the simple cycle value. However, the relatively high cost of such a regenerator must also be taken into account. Regenerated gas turbines increase efficiency 5-6% and are even more effective in improved part-load applications.

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Intercooling also involves the use of a heat exchanger. An intercooler is a heat exchanger that cools compressor gas during the compression process. For instance, if the compressor consists of a high and a low pressure unit, the intercooler could be mounted between them to cool the flow and decrease the work necessary for compression in the high pressure compressor. The cooling fluid could be atmospheric air or water (e.g., sea water in the case of a marine gas turbine). It can be shown that the output of a gas turbine is increased with a well-designed intercooler.

Intercooling

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Reheating occurs in the turbine and is a way to increase turbine work without changing compressor work or melting the materials from which the turbine is constructed. If a gas turbine has a high pressure and a low pressure turbine at the back end of the machine, a reheater (usually another combustor) can be used to "reheat" the flow between the two turbines. This can increase efficiency by 1-3%. Reheat in a jet engine is accomplished by adding an afterburner at the turbine exhaust, thereby increasing thrust, at the expense of a greatly increased fuel consumption rate.

Reheat

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A Gas-Turbine Engine With RegeneratorA Gas-Turbine Engine With Regenerator

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T-s Diagram of a Brayton Cycle with Regeneration

T-s Diagram of a Brayton Cycle with Regeneration

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Thermal Efficiency of the ideal Brayton cycle with and without regeneration

Thermal Efficiency of the ideal Brayton cycle with and without regeneration

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A Gas-Turbine EngineA Gas-Turbine EngineA gas-turbine engine with two-stage compression with intercooling,

two-stage expansion with reheating, and regeneration

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T-s Diagram of Ideal Gas-Turbine Cycle with Intercooling, Reheating, and Regeneration

T-s Diagram of Ideal Gas-Turbine Cycle with Intercooling, Reheating, and Regeneration

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Turbojet Engine Basic Components and T-s Diagram for Ideal Turbojet Cycle

Turbojet Engine Basic Components and T-s Diagram for Ideal Turbojet Cycle

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Schematic of A Turbofan EngineSchematic of A Turbofan Engine

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Schematic of a Turboprop EngineSchematic of a Turboprop Engine

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Schematic of a Ramjet EngineSchematic of a Ramjet Engine

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SummarySummary• The actual gas cycles are rather complex. The

approximations used to simplify the analysis are known as the air-standard assumptions. Under these assumptions, all the processes are assumed to be internally reversible; the working fluid is assumed to be air, which behaves as an ideal gas; and the combustion and exhaust processes are replaced by heat-addition and heat-rejection processes, respectively.

• The air-standard assumptions are called cold-air-standard assumptions if, in addition, air is assumed to have constant specific heats at room temperature.

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•The ideal cycle for modern gas-turbine engines is the Brayton cycle, which is made up of four internally reversible processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection.

SummarySummary

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SummarySummary

• Under cold-air-standard assumptions, the Brayton cycle thermal efficiency is

where rp = Pmax/Pmin is the pressure ratio and k is the specific heat ratio. The thermal efficiency of the simple Brayton cycle increases with the pressure ratio.

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• The deviation of the actual compressor and the turbine from the idealized isentropic ones can be accurately accounted for by utilizing their adiabatic efficiencies, defined as

and

where states 1 and 3 are the inlet states, 2a and 4a are the actual exit states, and 2s and 4s are the isentropic exit states.

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SummarySummary

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• In gas-turbine engines, the temperature of the exhaust gas leaving the turbine is often considerably higher than the temperature of the air leaving the compressor. Therefore, the high-pressure air leaving the compressor can be heated by transferring heat to it from the hot exhaust gases in a counter-flow heat exchanger, which is also known as a regenerator.

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SummarySummary

• The extent to which a regenerator approaches an ideal regenerator is called the effectiveness e and is defined as

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•Under cold-air-standard assumptions, the thermal efficiency of an ideal Braytoncycle with regeneration becomes

where T1 and T3 are the minimum and maximum temperatures, respectively, in the cycle.

SummarySummary

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• The thermal efficiency of the Brayton cycle can also be increased by utilizing multistage compression with intercooling, regeneration, and multistage expansion with reheating. The work input to the compressor is minimized when equal pressure ratios are maintained across each stage. This procedure also maximizes the turbine work output.

SummarySummary

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•Gas-turbine engines are widely used to power aircraft because they are light and compact and have a high power-to-weight ratio. The ideal jet-propulsion cycle differs from the simple ideal Brayton cycle in that the gases are partially expanded in the turbine. The gases that exit the turbine at a relatively high pressure are subsequently accelerated in a nozzle to provide the thrust needed to propel the aircraft.

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SummarySummary

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• The net thrust developed by the turbojet engine is

where m is the mass flow rate of gases, Vexitis the exit velocity of the exhaust gases, and Vinlet is the inlet velocity of the air, both relative to the aircraft

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SummarySummary

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References

1. Hill, P.G., and Peterson, C.R., (1992), Mechanics and Thermodynamics of Propulsion, Addison Wesley.

2. Saravanamuttoo, H.I.H, Rogers, G.F.C, and. Cohen, H,(2001), Gas Turbine Theory, Pearson Education.

3. Oates, G.C., (1988), Aerothermodynamics of Gas Turbine and Rocket Propulsion, AIAA, New York.

4. Mattingly, J.D., (1996), Elements of Gas Turbine Propulsion, McGraw Hill.

5. Cumpsty, N.A., (2000), Jet Propulsion, Cambridge University Press.

6. Bathie, W.W., (1996), Fundamentals of Gas Turbines, John Wiley.

7. Cengel, Y. A., and Boles, M. A., (2003), Thermodynamics-An Engineering Approach, Tata McGraw Hill

8. Treager, I.E., (1997), Aircraft Gas Turbine Engine Technology, Tata McGraw Hill.

9. Zucrow, M.J., (1958), Aircraft and Missile Propulsion, Vol. II, John Wiley.

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