Jet Propulsion. Lecture-2. Ujjwal K Saha, Ph.D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1

Transcription

1 Lecture-2 Prepared under QIP-CD Cell Project Jet Propulsion Ujjwal K Saha, Ph.D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1

2 Simple Gas Turbine Cycle 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. 2

3 An Open-Cycle Gas-Turbine Engine 3

4 A Closed-Cycle Gas-Turbine Engine 4

5 The Ideal Brayton Cycle 5

6 Thermal Efficiency of the Ideal Brayton Cycle as a Function of the Pressure Ratio 6

7 The Net Work of the Brayton Cycle For fixed values of T min and T max, the net work of the Brayton cycle first increases with the pressure ratio, then reaches a maximum at r p =(T max /T min ) k/[2(k-1)], and finally decreases 7

8 The Back-Work Ratio is the Fraction of Turbine Work Used to Drive the Compressor 8

9 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 9

10 Regeneration 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. 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. 10

11 Intercooling 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. 11

12 Reheat 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. 12

13 A Gas-Turbine Engine With Regenerator 13

14 T-s Diagram of a Brayton Cycle with Regeneration 14

15 Thermal Efficiency of the ideal Brayton cycle with and without regeneration 15

16 A Gas-Turbine Engine A gas-turbine engine with two-stage compression with intercooling, two-stage expansion with reheating, and regeneration 16

17 T-s Diagram of Ideal Gas-Turbine Cycle with Intercooling, Reheating, and Regeneration 17

18 Turbojet Engine Basic Components and T-s Diagram for Ideal Turbojet Cycle 18

19 Schematic of A Turbofan Engine 19

20 Schematic of a Turboprop Engine 20

21 Schematic of a Ramjet Engine 21

22 Summary 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 coldair-standard assumptions if, in addition, air is assumed to have constant specific heats at room temperature. 22

23 Summary 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. 23

24 Summary Under cold-air-standard assumptions, the Brayton cycle thermal efficiency is where r p = P max /P min is the pressure ratio and k is the specific heat ratio. The thermal efficiency of the simple Brayton cycle increases with the pressure ratio. 24

25 8-43 Summary 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. 25

26 8-44 Summary 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 highpressure 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. The extent to which a regenerator approaches an ideal regenerator is called the effectiveness e and is defined as 26

27 Summary Under cold-air-standard assumptions, the thermal efficiency of an ideal Brayton cycle with regeneration becomes where T 1 and T 3 are the minimum and maximum temperatures, respectively, in the cycle. 27

28 Summary 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. 28

29 8-48 Summary 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. 29

30 8-49 Summary The net thrust developed by the turbojet engine is where m is the mass flow rate of gases, V exit is the exit velocity of the exhaust gases, and V inlet is the inlet velocity of the air, both relative to the aircraft 30

31 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. 31

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