GAS POWER CYCLES. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

Transcription

1 Chapter 9 GAS POWER CYCLES Dr Ali Jawarneh Department of Mechanical Engineering i Hashemite University

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3 Objectives Evaluate the performance of gas power cycles for which h the working fluid remains a gas throughout the entire cycle. Develop simplifying assumptions applicable to gas power cycles. Review the operation of reciprocating engines. Analyze both closed and open gas power cycles. Solve problems based on the Otto, Diesel, Stirling, and Ericsson cycles. Solve problems based on the Brayton cycle; the Brayton cycle with regeneration; and the Brayton cycle with intercooling, reheating, and regeneration. Analyze jet-propulsion cycles. Identify simplifying assumptions for second-law analysis of gas power cycles. Perform second-law analysis of gas power cycles. 3

4 9-1:BASIC CONSIDERATIONS IN THE ANALYSIS OF POWER CYCLES Thermal efficiency of heat engines Most power-producing devices operate on cycles. Ideal cycle: A cycle that resembles the actual cycle closely but is made up totally of internally reversible processes. Reversible cycles such as Carnot cycle have the highest thermal efficiency of all heat engines operating between the same temperature levels. Unlike ideal cycles, they are totally reversible, and unsuitable as a realistic model. Modeling is a powerful engineering i tool that t provides great insight and simplicity at the expense of some loss in accuracy. The ideal cycles are internally reversible, but, unlike the Carnot cycle, they are not necessarily externally reversible. That is, they may involve irreversibilities external to the system such as heat transfer through a finite temperature difference. Therefore, the thermal efficiency of an ideal cycle, in general, is less than that of a totally reversible cycle operating between the same temperature limits. However, it is still considerably higher than the thermal efficiency of an actual cycle because of the idealizations utilized The analysis of many complex processes can be reduced to a manageable level by utilizing some idealizations. 4

5 On a T-s diagram, the ratio of the The idealizations and simplifications in the area enclosed by the cyclic curve to analysis of power cycles: the area under the heat-addition addition 1. The cycle does not involve any friction. process curve represents the thermal Therefore, the working fluid does not efficiency of the cycle. Any experience any pressure drop as it flows in modification that increases the ratio pipes or devices such as heat exchangers. of these two areas will also increase 2. All expansion and compression processes the thermal efficiency of the cycle. take place in a quasi-equilibrium manner. 3. The pipes connecting the various components of a system are well insulated, and heat transfer through h them is negligible. Care should be exercised in the interpretation of the results from ideal cycles. On both P-v and T-s diagrams, the area enclosed by the process curve represents the net work of the cycle which is also equivalent to the net heat transfer for that cycle. 5

6 9-2:THE CARNOT CYCLE AND ITS VALUE IN ENGINEERING The Carnot cycle is composed of four totally reversible processes: isothermal heat addition, isentropic expansion, isothermal heat rejection, and isentropic compression. For both ideal and actual cycles: Thermal efficiency increases with an increase in the average temperature at which heat is supplied to the system or with a decrease in the average temperature at which heat is rejected from the system. A steady-flow Carnot engine. The Carnot cycle can be executed in a closed system (a piston cylinder device) or a steadyflow system (utilizing two turbines and two compressors, and either a gas ora vapor can be utilized as the working fluid. P-v and T-s diagrams of a Carnot cycle. 6

7 9-3:AIR-STANDARD ASSUMPTIONS Air-standard d assumptions: 1. The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas. 2. All the processes that make up the cycle are internally reversible. 3. The combustion process is replaced by a heat-addition process from an external source. 4. The exhaust process is replaced by a heat-rejection ti process that t restores the working fluid to its initial state. The combustion process is replaced by a heat-addition process in ideal cycles. Cold-air-standard assumptions: When the working fluid is considered to be air with constant specific heats at room temperature (25 C). Air-standard d cycle: A cycle for which the air-standard d assumptions s are applicable. 7

8 9-4:AN OVERVIEW OF RECIPROCATING ENGINES Compression ratio Mean effective pressure Ratio of the volume of its combustion chamber; from its largest capacity to its smallest capacity(a high compression ratio is desirable because it allows an engine to extract more mechanical energy from a given mass of air-fuel mixture due to its higher thermal efficiency) Spark-ignition (SI) engines Compression-ignition (CI) engines :(combustion of the air fuel mixture is initiated by a spark plug) :(air fuel mixture is self ignited as a result of compressing the mixture above its self ignition temperature) Nomenclature for reciprocating engines. MEP: It is a fictitious pressure that, if it acted on the piston during the entire power stroke, would produce the same amount of net work as that produced during the actual 8 cycle

9 9-5:OTTO CYCLE: THE IDEAL CYCLE FOR SPARK-IGNITION ENGINES SI engine It is named after Nikolaus A. Otto, who built a successful four stroke engine in 1876 in Germany Actual and ideal cycles in spark-ignition engines and their P-v diagrams. 9

10 Four-stroke cycle 1 cycle = 4 stroke = 2 revolution Two-stroke cyclecle 1 cycle = 2 stroke = 1 revolution In most spark ignition engines, the piston executes four complete strokes (two mechanical cycles) within the cylinder, and the crankshaft completes two revolutions for each thermodynamic cycle. T-s diagram of the ideal Otto cycle. 10

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12 Four stroke combustion engine 12

13 Four-stroke cycle The two-stroke engines are 1 cycle = 4 stroke = 2 revolution generally less efficient than Two-stroke cyclecle their four-stroke counterparts t 1 cycle = 2 stroke = 1 revolution but they are relatively simple and inexpensive, and they In two stroke engines, all four functions described above are executed in just two strokes: the power stroke and the compression stroke. In have high power-to-weight and power-to-volume ratios. these engines, the crankcase is sealed, and the outward motion of the piston is used to slightly pressurize the air fuel mixture in the crankcase. Also, the intake and exhaust valves are replaced by openings in the lower portion of the cylinder wall. During the latter part of the power stroke, the piston uncovers first the exhaust port, allowing the exhaust gases to be partially expelled, and then the intake port, allowing the fresh air fuel mixture to rush in and drive most of the remaining exhaust gases out of the cylinder. This mixture is then compressed asthe piston moves upward during the compression stroke and is subsequently ignited by a spark plug. The two stroke engines are generally less efficient than their four stroke counterparts because of the incomplete expulsion of the exhaust ehastgases and the partial expulsion of the fresh air fuel mixture with the exhaust gases. For a given weight and displacement, a well designed two stroke engine can provide significantly more power than its four stroke counterpart because two stroke engines produce power on every engine revolution instead of every other one Sh Schematic of a two-stroke t reciprocating engine. 13

14 Operating Principles In the combustion phase an ignited charge exerts pressure on the piston crown whilst a fresh charge is drawn through the carburettor into the crankcase via inlet port I. I: inlet port for crankcase E: exhaust port P: fuel inlet port During the exhausting phase the piston moving down partly uncovers the exhaust port E allow the combustion gases to start to discharge. The downward movement of the piston also compresses the fuel air mixture in the crankcase. At the end of the first stroke the exhaust port are fully open and the fuel inlet port P is now open allow the compressed fuel mixture to enter the cylinder above the piston. The piston crown is so shaped that the mixture is deflected upwards above the residue of the escaping exhaust gases. The fuel mixture helps to sweep out the exhaust gases. During the upward compressing stroke, the piston it covers the transfer ports, compresses the charge and creates a small vacuum in the crankcase. At the end of the upward stroke (inner dead centre) ignition occurs resulting in the ignited charge expanding and exerting pressure on the piston 14

15 A two-stroke engine is a combustion engine that completes the thermodynamic cycle in two movements of the piston compared to twice that number for a four-stroke engine. This increased efficiency is accomplished by using the beginning of the compression stroke and the end of the combustion stroke to perform simultaneously the 15 intake and exhaust (or scavenging) functions.

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17 The Otto cycle is executed in a closed system For Constant Specific Heats η of the ideal Otto cycle increases with both r and k In SI engines, the compression ratio is limited by autoignition or engine knock. Thermal efficiency of the ideal Otto cycle as a function of compression ratio (k = 1.4). η of actual SI engines range from about 25 to 30% The thermal efficiency of the Otto cycle increases with the specific heat ratio k (k=c p /c v ) of the working fluid. 17

18 When high compression ratios are used, the temperature of the air fuel mixture rises above the autoignition temperature of the fuel (the temp at which the fuel ignites without the help of a spark) during the combustion process, causing an early and rapid burn of the fuel at some point or points ahead of the flame front, followed by almost instantaneous inflammation of the end gas. This premature ignition of the fuel, called autoignition, produces an audible noise, which is called engine knock. k Autoignition iti in spark-ignition iti engines cannot be tolerated t because it hurts performance and can cause engine damage. The requirement that autoignition not be allowed places an upper limit on the compression ratios that can be used in sparkignition internal combustion engines. Improvement of the thermal efficiency of gasoline engines by utilizing higher compression ratios (up to about 12) without facing the autoignition problem has been made possible by using gasoline blends that have good antiknock characteristics, such as gasoline mixed with tetraethyl lead. Tetraethyl lead posses hazardous to health and pollute the environment. 18

19 Isentropic Processes of Ideal Gases Constant Specific Heats (Approximate Analysis) Chapter 7 Setting this eq. equal to zero, we get The specific heat ratio k, in general, varies with temperature, and thus an average k value for the given temperature range should be used. we should refine the calculations{repeat the calculations} The isentropic relations of ideal gases are valid for the isentropic processes of ideal gases only. Equations 7 42 through h 7 44 can also be expressed in a compact form as 19

20 Chapter 7 Isentropic Processes of Ideal Gases Variable Specific Heats (Exact Analysis) Relative Pressure and Relative Specific Volume exp(s /R) is the relative pressure P. r The use of P r data for calculating the final temperature during an isentropic process. T/P r is the relative specific volume v r. Table A 17 [Air] The use of v r data for calculating the final temperature during an isentropic process 20

21 Example: An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kpa and 27 C C, and 750 kj/kg of heat is transferred to air during the constantvolume heat addition process. Taking into account the variation of specific heats with temperature, t determine ()th (a) the pressure and temperature at the end of the heat addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. 21

22 Solution: R = kj/kg.k. The properties of air are given in Table A-17. a- Process 1-2: isentropic compression. Process 2-3: v = constant heat addition. 22

23 (b) Process 3-4: isentropic expansion. Process 4-1: v = constant t heat rejection. (c) (d) 23

24 9-6: DIESEL CYCLE: THE IDEAL CYCLE FOR COMPRESSION-IGNITION ENGINES In diesel engines, only air is compressed during the compression stroke, eliminating the possibility of autoignition (engine knock). Therefore, diesel engines can be designed to operate at much higher compression ratios than SI engines, typically between 12 and 24. CI engine 1-2 isentropic compression 2-3 constantpressure heat addition 3-4 isentropic expansion 4-1 constantvolume heat rejection. In diesel engines, the spark plug is replaced by a fuel injector, and only air is compressed during the compression process. η of actual CI engines range from about 35 to 40% 24

25 The Diesel cycle is the ideal cycle for CI reciprocating engines. The CI engine, first proposed by Rudolph Diesel in the 1890s, is very similar to the SI engine discussed in the last section, differing mainly in the method of initiating combustion. In spark-ignition engines (also known as gasoline engines), the air fuel mixture is compressed to a temperature that is below the autoignition temperature of the fuel, and the combustion process is initiated by firing a spark plug. In CI engines (also known as diesel engines), the air is compressed to a temperature that is above the autoignition temperature of the fuel, and combustion starts on contact as the fuel is injected into this hot air. Therefore, the spark plug and carburetor are replaced by a fuel injector in diesel engines. The fuel injection process in diesel engines starts when the piston approaches TDC and continues during the first part of the power stroke. Therefore, the combustion process in these engines takes place over a longer interval. Because of this longer duration, the combustion process in the ideal Diesel cycle is approximated as a constant-pressure heataddition process. In fact, this is the only process where the Otto and the Diesel cycles differ. The remaining three processes are the same for both ideal cycles. Remember, though, that diesel engines operate at much higher compression ratios and thus are usually more efficient than the spark-ignition (gasoline) engines. The diesel engines also burn the fuel more completely since they usually operate at lower revolutions per minute and the air fuel mass ratio is much higher than spark-ignition engines. Thermal efficiencies of large diesel engines range from about 35 to 40 %. The ideal Otto and Diesel cycles discussed in the preceding sections are composed entirely of internally reversible processes and thus are internally reversible cycles. These cycles are not totally reversible, however, since they involve heat transfer through a finite temperature difference during the nonisothermal heataddition and heat rejection processes, which are irreversible. Therefore, the thermal efficiency of an Otto or Diesel engine will be less than that of a Carnot engine operating between the same temperature limits. 25

26 Diesel cycle is executed in a piston cylinder device, which forms a closed system, Cutoff ratio for the same compression ratio Thermal efficiency of the ideal Diesel cycle as a function of compression and cutoff ratios (k=1.4). 26

27 Approximating the combustion process in internal combustion engines as a constantvolume or a constant pressure heat-addition process is overly simplistic and not quite realistic. Probably a better (but slightly more complex) approach would be to model the combustion process in both gasoline and diesel engines as a combination of two heat- transfer processes, one at constant volume and the other at constant pressure. The ideal cycle based on this concept is called the dual cycle. Dual cycle: A more realistic ideal cycle model for modern, high-speed compression ignition engine. P-v diagram of an ideal dual cycle. The relative amounts of heat transferred during each process can be adjusted d to approximate the actual cycle more closely. l Note that both the Otto and the Diesel cycles can be obtained as special cases of the dual cycle. QUESTIONS Diesel engines operate at higher air-fuel ratios than gasoline engines. Why? Despite higher power to weight ratios, two-stroke engines are not used in automobiles. Why? The stationary diesel engines are among the most efficient power producing devices (about 50%). Why? What is a turbocharger? Why are they mostly used in diesel engines compared to gasoline engines. In Duel Cycle heat is added partly at constant volume and partly at constant pressure, the advantage of which is that more time is available for the fuel to completely combust. 27

28 Turbocharger A turbocharger's purpose is to compress the air/oxygen entering a car's engine, increasing the amount of oxygen that enters and thereby increasing the power output The turbocharger is composed of two main parts: the compressor, which compresses the air in the intake; and the turbine, which draws the exhaust gases and uses them to power the compressor (the turbocharger is powered by the car's own exhaust gases). The advantage of compressing the air is that it lets the engine squeeze more air into a cylinder, and more air means that more fuel can be added. Therefore, you get more power from each explosion in each cylinder. A turbocharged engine produces more power overall than the same engine without the charging. This can significantly improve the power-to-weight ratio for the engine 28

29 EXAMPLE: An ideal diesel engine has a compression ratioofof 20and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kpa and 20 C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the thermal efficiency and (b) the mean effective pressure. Assume constant specific heats for air at room temperature. 29

30 SOLUTION The properties of air at room temperature are c p = kj/kg K, c v = kj/kg K, R = kj/kg K, and k = 1.4 (Table A-2). (a) Process 1-2: isentropic compression. Process 2-3: P = constant heat addition. Process 3-4: isentropic expansion. 30

31 (b) 31

32 Comparison of Spark Ignition (SI) and Compression Ignition (CI) Engines 1) Type of cycle used: In the case of SI engines, the Otto cycle is used. In this cycle, addition of heat or fuel combustion occurs at a constant t volume. The basis of working of CI engines is the Diesel cycle. In this cycle the addition of heat or fuel combustion occurs at a constant pressure. 2) Introduction of fuel in the engine: In the case of SI engines, during the piston's suction stroke, a mixture of air and fuel is injected from cylinder head portion of the cylinder. The air-fuel mixture is injected via the carburetor that controls the quantity and the quality of the injected mixture. In the case of CI engines, fuel is injected into the combustion chamber towards the end of the compression stroke. The fuel starts burning instantly due to the high pressure. To inject diesel in SI engines, a fuel pump and injector are required. In CI engines, the quantity of fuel to be injected is controlled but the quantity of air to be injected is not controlled. 3) Ignition of fuel: By nature petrol (gasoline) is a highly volatile liquid, but its self-ignition temperature is high. Hence for the combustion of this fuel a spark is necessary to initiate its burning process. To generate this spark in SI engines, the spark plug is placed in the cylinder head of the engine. The voltage is provided to the spark plug either from the battery or from the magneto. With diesel, the self-ignition temperature is comparatively lower. When diesel fuel is compressed to high pressures, its temperature also increases beyond the self-ignition temperature of the fuel. Hence in the case of CI engines, the ignition of fuel occurs due to compression of the airfuel mixture and there is no need for spark plugs. 4) Compression ratio for the fuel: In the case of SI engines, the compression ratio of the fuel is in the range of 6 to 10 depending on the size of the engine and the power to be produced. In CI engines, the compression ratio for air is 16 to 20. The high compression ratio of air creates high temperatures, which ensures the diesel fuel can selfignite. 5) Weight of the engines: In CI engines the compression ratio is higher, which produces high pressures inside the engine. Hence CI engines are heavier than SI engines. 6) Speed achieved by the engine: Petrol or SI engines are lightweight, and the fuel is homogeneously burned, hence achieving very high speeds. CI engines are heavier and the fuel is burned heterogeneously, hence producing lower speeds. RPM max, Si = 4500, RPM max, CI = ) Thermal efficiency of the engine: In the case of CI engines the value of compression ratio is higher; hence these engines have the potential to achieve higher thermal efficiency. In the case of SI engines the lower compression ratio reduces their potential to achieve higher thermal efficiency. - Engines using the Diesel cycle are usually more efficient, although the Diesel cycle itself is less efficient at equal compression ratios. Since diesel engines use much higher compression ratios. 32

33 Stirling cycle 9-7:STIRLING AND ERICSSON CYCLES 1-2 T = constant expansion (heat addition from the external source) 2-3 v = constant t regeneration (internal heat transfer from the working fluid to the regenerator) 3-4 T = constant compression (heat rejection to the external sink) 4-1 v = constant regeneration (internal heat transfer from the regenerator back to the working fluid) Stirling cycle and Ericsson cycle differ from the Carnot cycle in that the two isentropic processes are replaced by two constant-volume regeneration processes in the Stirling cycle and by two constant-pressure regeneration processes in the Ericsson cycle. Regeneration, a process during which heat is transferred to a thermal energy storage device (called a regenerator) during one part of the cycle and is transferred back to the working fluid during another part of the cycle A regenerator is a device that borrows energy from the working fluid during one part of the cycle and pays it back (without interest) during another part. 33

34 This system consists of a cylinder with two pistons it on each side and a regenerator in the middle. Regenerator can be a wire or a ceramic mesh or any kind of porous plug with a high thermal mass (mass times specific heat). It is used for the temporary storage of thermal energy. The execution of the Stirling cycle in a closed system Initially, the left chamber houses the entire working fluid (a gas), which is at a high temperature and pressure. During process 1 2, heat is transferred to the gas at TH from a source at TH. As the gas expands isothermally, the left piston moves outward, doing work, and the gas pressure drops. During process 2 3, both pistons are moved to the right at the same rate (to keep the volume constant) until the entire gas is forced into the right chamber. As the gas passes through the regenerator, heat is transferred to the regenerator and the gas temperature drops from TH to TL. For this heat transfer process to be reversible, the temperature difference between the gas and the regenerator should not exceed a differential amount dt at any point. Thus, the temperature of the regenerator will be TH at the left end and TL at the right end of the regenerator when state 3 is reached. During process 3 4, the right piston is moved inward, compressing the gas. Heat is transferred from the gas to a sink at temperature TL so that the gas temperature remains constant at TL while the pressure rises. Finally, during process 4 1, both pistons are moved to the left at the same rate (to keep the volume constant), forcing the entire gas into the left chamber. The gas temperature rises from TL to TH as it passes through the regenerator and picks up the thermal energy stored there during process 2 3. This completes the cycle. Notice that the second constant volume process takes place at a smaller volume than the first one, and the net heat transfer to the regenerator during a cycle is zero. That is, the amount of energy stored in the regenerator during process 2 3 is equal to the amount picked up by the gas during process

35 The Stirling and Ericsson cycles give a message: Regeneration can increase efficiency. Both the Stirling and Ericsson cycles are totally reversible, as is the Carnot cycle, and thus: The Ericsson engine can be run open- or closed-cycle. Expansion occurs simultaneously with compression, on opposite sides of the piston. A steady flow system operating on an Ericsson cycle is shown in Fig Here the isothermal expansion and compression processes are executed in a compressor and a turbine, respectively, and a counter flow heat exchanger serves as a regenerator. Hot and cold fluid streams enter the heat exchanger from opposite ends, and heat transfer takes place between the two streams. In the ideal case, the temperature difference between the two fluid streams does not exceed a differential amount at any point, and the cold fluid stream leaves the heat exchanger at the inlet temperature of the hot stream. The Ericsson cycle is very much like the Stirling cycle, except that the two constantvolume processes are replaced by two constant-pressure processes. counter-flow heat exchanger serves as a regenerator A steady-flow Ericsson engine. 35

36 Stirling and Ericsson cycles are difficult to achieve in practice because they involve heat transfer through a differential temperature difference in all components including the regenerator. This would require providing infinitely large surface areas for heat transfer or allowing an infinitely long time for the process. Neither is practical. In reality, all heat transfer processes take place through a finite temperature difference, the regenerator does not have an efficiency of 100 percent, and the pressure losses in the regenerator are considerable. Because of these limitations, both Stirling and Ericsson cycles have long been of only theoretical interest. However, there is renewed interest in engines that operate on these cycles because of their potential for higher efficiency and better emission control. Both the Stirling and the Ericsson engines are external combustion engines. That is, the fuel in these engines is burned outside the cylinder, as opposed to gasoline or diesel engines, where the fuel is burned inside the cylinder. External combustion offers several advantages. First, a variety of fuels can be used as a source of thermal energy. Second, there is more time for combustion, and thus the combustion process is more complete, which means less air pollution and more energy extraction from the fuel. Third, these engines operate on closed cycles, and thus a working fluid that has the most desirable characteristics (stable, chemically inert, high thermal conductivity) can be utilized as the working fluid. Hydrogen and helium are two gases commonly employed in these engines. Despite the physical limitations and impracticalities associated with them, both the Stirling and Ericsson cycles give a strong message to design engineers: Regeneration can increase efficiency. It is no coincidence that modern gas turbine and steam power plants make extensive use of regeneration. In fact, the Brayton cycle with intercooling, reheating, and regeneration, which is utilized in large gas turbine power plants and discussed later in this chapter, closely resembles the Ericsson cycle. 36

37 Operation A Stirling engine is a heat engine that operates by cyclic compression and expansion of air or other gas, the working fluid,, at different temperature levels such that there is a net conversion of heat energy to mechanical work. Since the Stirling engine is a closed cycle, it contains a fixed mass of gas called the "working fluid", most commonly air, hydrogen or helium. In normal operation, the engine is sealed and no gas enters or leaves the engine. No valves are required, unlike other types of piston engines. The Stirling engine, like most heat engines, cycles through four main processes: cooling, compression, heating and expansion. This is accomplished by moving the gas back and forth between hot and cold heat exchangers, often with a regenerator between the heater and cooler. The hot heat exchanger is in thermal contact with an external heat source, such as a fuel burner, and the cold heat exchanger being in thermal contact with an external heat sink, such as air fins. A change in gas temperature will cause a corresponding change in gas pressure, while the motion of the piston causes the gas to be alternately expanded and compressed. 37

38 Types of Stirling engines : 1.The two piston alpha type design has pistons in independent cylinders, and gas is driven between the hot and cold spaces. An alpha Stirling contains two power pistons in separate cylinders, one hot and one cold. The hot cylinder is situated inside the high temperature heat exchanger and the cold cylinder is situated inside the low temperature heat exchanger. This type of engine has a high power-to-volume ratio but has technical problems due to the usually high temperature of the hot piston and the durability of its seals. In practice, this piston usually carries a large insulating head to move the seals away from the hot zone at the expense of some additional dead space. The following diagrams do not show internal heat exchangers in the compression and expansion spaces, which are needed to produce power. A regenerator would be placed in the pipe connecting the two cylinders. The crankshaft has also been omitted. Alpha type Stirling engine. The expansion cylinder (red) is maintained at a high temperature while the compression cylinder (blue) is cooled. The passage between the two cylinders contains the regenerator 1. Most of the working gas is in contact with the hot cylinder walls, it has been heated and expansion has pushed the hot piston to the bottom of its travel in the cylinder. The expansion continues in the cold cylinder, which is 90 behind the hot piston in its cycle, extracting more work from the hot gas. 2. The gas is now at its maximum volume. The hot cylinder piston begins to move most of the gas into the cold cylinder, where it cools and the pressure drops. 3. Almost all the gas is 4. The gas reaches now in the cold cylinder its minimum volume, and cooling continues. and it will now expand The cold piston, powered in the hot cylinder by flywheel momentum (or where it will be other piston pairs on the heated once more, same shaft) compresses the remaining part of the gas. driving the hot piston in its power stroke. 38

39 2. The displacement type Stirling engines, known as beta and gamma types, use an insulated mechanical displacer to push the working gas between the hot and cold sides of the cylinder. The displacer is long enough to thermally insulate the hot and cold sides of the cylinder and displace a large quantity of gas. It must have enough of a gap between the displacer and the cylinder wall to allow gas to easily flow around the displacer. A beta Stirling has a single power piston arranged within the same cylinder on the same shaft as a displacer piston. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha type, the beta type avoids the technical problems of hot moving seals. There is also the rotary Stirling engine which seeks to convert power from the Stirling cycle directly into torque, similar to the rotary combustion engine Again, the following diagrams do not show internal heat exchangers or a regenerator, which would be placed in the gas path around the displacer. Beta type Stirling engine. 1. Power piston (dark grey) has compressed the gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger. 2. The heated gas increases in pressure and pushes the power piston to the farthest limit of the power stroke. 3. The displacer piston now moves, shunting the gas to the cold end of the cylinder. 4. The cooled gas is now compressed by the flywheel momentum. This takes less energy, since when it is cooled its pressure dropped. 39

40 EXAMPLE: An ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and 2000 K and pressure limits of 150 kpa and 3 MPa. Assuming the mass of the helium used in the cycle is 0.12 kg, determine (a) the thermal efficiency of the cycle, (b) the amount of heat transfer in the regenerator, and (c) the work output per cycle. Assume a constant specific heats at room temperature 40

41 Solution: Assumptions Helium is an ideal gas with constant specific heats. Properties: The gas constant and the specific heat of helium at room temperature are R = kj/kg.k, c v = kj/kg.k and c p = kj/kg.k (Table A-2). (a) The thermal efficiency of this totally reversible ersible cycle cle is determined from (b) The amount of heat transferred in the regenerator is 41

42 (c) The net work output is determined from 42

43 9-8:BRAYTON CYCLE: THE IDEAL CYCLE FOR GAS-TURBINE ENGINES The Brayton cycle was first proposed by George Brayton around The combustion process is replaced by a constant-pressure heat-addition process from an external source, and the exhaust process is replaced by a constant-pressure heat-rejection process to the ambient air. 1-2 Isentropic compression (in a compressor) 2-3 Constant-pressure heat addition 3-4 Isentropic expansion (in a turbine) 4-1 Constant-pressure heat rejection Gas turbines usually operate on an open cycle. Fresh air at An open-cycle gas-turbine engine. ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure. The resulting hightemperature gases then enter the turbine, where they expand to the atmospheric pressure while producing power. The exhaust gases leaving the turbine are thrown out (not recirculated), causing the cycle to be classified as an open cycle. A closed-cycle gas-turbine engine. The Brayton cycle is the only thermodynamic cycle which can be used in both internal combustion engines (such as jet engines) and for external combustion engines. 43

44 Notice that all four processes of the Brayton cycle are executed in steady-flow devices Pressure ratio Under constant specific heat ratio The thermal efficiency increases with both r p and k T-s and P-v diagrams for the ideal Brayton cycle. Thermal efficiency of the ideal Brayton cycle as a function of the pressure ratio. 44

45 The two major application areas of gasturbine engines are aircraft propulsion and electric power generation. In most common designs, the pressure ratio of gas turbines ranges from about 11 to 16. The highest temperature in the cycle is limited by the maximum temperature that the turbine blades can withstand. This also limits the pressure ratios that t can be used in the cycle. The air in gas turbines supplies the necessary oxidant for the combustion of the fuel, and it serves as a coolant to keep the temperature of various components within safe limits. An air fuel ratio of 50 or above is not uncommon. Many modern marine propulsion systems use gas turbines together with diesel engines because of the high fuel consumption of simple-cycle gas-turbine engines. In combined diesel and gas-turbine systems, s, diesel is used to provide for efficient low-power and cruise operation, and gas turbine is used when high speeds are needed. 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. For a fixed turbine inlet temperature T3, the net work output per cycle increases with the pressure ratio, reaches a maximum, and then starts to decrease, as shown in Fig Therefore, there should be a compromise between the pressure ratio (thus the thermal efficiency) and the net work output. back work ratio The fraction of the turbine work used to drive the compressor is called the back work ratio. Usually more than one-half of the turbine work output is used to drive the compressor. 45

46 Development of Gas Turbines 1. Increasing the turbine inlet (or firing) temperatures 2. Increasing the efficiencies of turbomachinery components (turbines, compressors): 3. Adding modifications to the basic cycle (intercooling, regeneration or recuperation, and reheating). Deviation of Actual Gas- Turbine Cycles from Idealized Ones Reasons: Irreversibilities in turbine and compressors, pressure drops, heat losses Isentropic efficiencies of the compressor and turbine The deviation of an actual gas- turbine cycle from the ideal Brayton cycle as a result of irreversibilities. 46

47 Example: A simple Brayton cycle using air as the working fluid has a pressure ratio of 8. The minimum and maximum temperatures in the cycle are 310 and 1160 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency. using constant specific heats at room temperature. 47

48 Solution: The properties of air at room temperature are c p = kj/kg K and k = 1.4 (Table A-2). (a) Using the compressor and turbine efficiency relations, 48

49 (b) (c) 49

50 9-9:THE BRAYTON CYCLE WITH REGENERATION 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 the hot exhaust gases in a counter-flow heat exchanger (a regenerator or a recuperator). The thermal efficiency of the Brayton cycle increases as a result of regeneration since less fuel is used for the same work output. A gas-turbine engine with regenerator. T-s diagram of a Brayton cycle with regeneration. The thermal efficiency of the Brayton cycle increases as a result of regeneration since theportion of energy of the exhaust gases that is normally rejected to the surroundings is now used to preheat the air entering the combustion chamber. This, in turn, decreases the heat input (thus fuel) requirements for the same net work output. Note, however, that the use of a regenerator is recommended only when the turbine exhaust temperature is higher than the compressor exit temperature. Otherwise, heat willflow inthereverse direction (to the exhaust gases), decreasing the efficiency. This situation is encountered in gas turbine engines operating at very 50 high pressure ratios.

51 Assuming the regenerator to be well insulated and any changes in kinetic and potential energies to be negligible Effectiveness of regenerator Effectiveness under coldair standard assumptions Under cold-air standard assumptions T-s diagram of a Brayton cycle with regeneration. The thermal efficiency depends on the ratio of the minimum to maximum temperatures t as well as the pressure ratio. Regeneration is most effective at lower pressure ratios and low minimum-tomaximum temperature ratios. Can regeneration be used at high pressure ratios? Thermal efficiency of the ideal Brayton cycle with and without regeneration. 51

52 Example: Air enters the compressor of a regenerative gas turbine engine at 300 K and 100 kpa, where it is compressed to 800 kpa and 580 K. The regenerator has an effectiveness of 72 percent, and the air enters the turbine at 1200 K. For a turbine efficiency i of 86 percent, determine (a) the amount of heat transfer in the regenerator and (b) the thermal efficiency. Assume variable specific heats for air. 52

53 Solution: The properties of air are given in Table A-17. (a) The properties at various states are 53

54 (b) 54

55 9-10:THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND REGENERATION For minimizing work input to compressor and maximizing work output from turbine: A gas-turbine engine with two-stage compression with intercooling, two-stage expansion with reheating, and regeneration and its T-s diagram. 55

56 Multistage compression with intercooling: The work required to compress a gas between two specified pressures can be decreased by carrying out the compression process in stages and cooling the gas in between. This keeps the specific volume as low as possible. Multistage expansion with reheating keeps the specific volume of the working fluid as high as possible during an expansion process, thus maximizing work output. Intercooling and reheating always decreases the thermal efficiency unless they are accompanied by regeneration. Why? Comparison of work inputs to a singlestage compressor (1AC) and a two-stage compressor with intercooling (1ABD).) As the number of compression and expansion stages increases, the gas-turbine cycle with intercooling, reheating, and regeneration approaches the Ericsson cycle and the thermal efficiency approaches the theoretical limit (the Carnot efficiency). However, the contribution of each additional stage to the thermal efficiency is less and less, and the use of more than two or three stages cannot be 56 justified economically.

57 -The net work of a gas-turbine cycle is the difference between the turbine work output and the compressor work input, and it can be increased by either decreasing the compressor work or increasing the turbine work, or both. -the work required to compress a gas between two specified pressures can be decreased by carrying out the compression process in stages and cooling the gas in between (Fig. 9 42) that is, using multistage compression with intercooling. As the number of stages is increased, the compression process becomes nearly isothermal at the compressor inlet temperature, and the compression work decreases. -Likewise, the work output of a turbine operating between two pressure levels can be increased by expanding the gas in stages and reheating it in between that th t is, utilizing i multistage t expansion with reheating. This is accomplished without raising the maximum temperature in the cycle. As the number of stages is increased, the expansion process becomes nearly isothermal. -The foregoing argument is based on a simple principle: The steady-flow compression or expansion work is proportional p to the specific volume of the fluid. Therefore, the specific volume of the working fluid should be as low as possible during a compression process and as high as possible during an expansion process. This is precisely what intercooling and reheating accomplish. -Combustion in gas turbines typically occurs at four times the amount of air needed for complete combustion to avoid excessive temperatures. Therefore, the exhaust gases are rich in oxygen, and reheating can be accomplished by simply spraying additional fuel into the exhaust gases between two expansion states. -The working fluid leaves the compressor at a lower temperature, and the turbine at a higher temperature, when intercooling and reheating are utilized. This makes regeneration more attractive since a greater potential for regeneration exists. Also, the gases leaving the compressor can be heated to a higher temperature before they enter the combustion chamber because of the higher temperature of the turbine exhaust. - The back work ratio of a gas-turbine cycle improves as a result of intercooling and reheating. However, this does not mean that the thermal efficiency also improves. The fact is, intercooling and reheating always decreases the thermal efficiency unless they are accompanied by regeneration. This is because intercooling decreases the average temperature at which heat is added, and reheating increases the average temperature at which heat is rejected. This is also apparent from Fig Therefore, in gasturbine power plants, intercooling and reheating are always used in conjunction with regeneration. 57

58 The efficiency of a Brayton engine can be improved in the following manners: *Reheat, h t wherein the working fluid in i most cases air expands through h a series of turbines, then is passed through a second combustion chamber before expanding to ambient pressure through a final set of turbines. This has the advantage of increasing the power output possible for a given compression ratio without exceeding any metallurgical l constraints. t (Although h use of an afterburner can also be referred to as reheat, it is a different process that increases power while markedly decreasing efficiency.) *Intercooling, wherein the working fluid passes through a first stage of compressors, then a cooler, then a second stage of compressors before entering the combustion chamber. While this requires an increase in the fuel consumption of the combustion chamber, this allows for a reduction in the specific heat of the fluid entering the second stage of compressors, with an attendant decrease in the amount of work needed for the compression stage overall. *Regeneration, wherein the still-warm post-turbine fluid is passed through a heat exchanger to pre-heat the fluid just entering the combustion chamber. This allows for lower fuel consumption and less power lost as waste heat. *A Brayton engine also forms half of the combined cycle system, which combines with a rankine engine to further increase overall efficiency. *Cogeneration systems make use of the waste heat from Brayton engines, typically for hot water production or space heating. 58

59 Example: Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats. Assuming an efficiency of 80 percent for each compressor stage and an efficiency of 85 percent for each turbine stage. 59

60 SOLUTION: Assumptions: 1- The air standard assumptions are applicable. 2- Air is an ideal gas with variable specific heats. 3- Kinetic and potential energy changes are negligible. Properties: The properties of air are given in Table A-17. Analysis (a) The work inputs to each stage of compressor are identical, so are the work outputs of each stage of the turbine. Then, 60

61 (b) When a regenerator is used, r bw remains the same. The thermal efficiency in this case becomes 61

62 9-11: IDEAL JET-PROPULSION CYCLES Gas-turbine engines are widely used to power aircraft because they are light and compact and have a high h power-to-weight ratio. Aircraft gas turbines operate on an open cycle called a jet-propulsion cycle. The ideal jet-propulsion cycle differs from the simple ideal Brayton cycle in that the gases are not expanded to the ambient pressure in the turbine. Instead, they are expanded to a pressure such that the power produced by the turbine is just sufficient to drive the compressor and the auxiliary equipment. The net work output of a jet-propulsion cycle is zero. The gases that exit the turbine at a relatively high pressure are subsequently accelerated in a nozzle to provide the thrust to propel the aircraft. Aircraft are propelled by accelerating a fluid in the opposite direction to motion. This is accomplished by either slightly accelerating a large mass of ff fluid ( (propeller-driven engine) ) or greatly accelerating a small mass of fluid (jet or turbojet engine) or both (turboprop engine{turbofan, Propjet}). Aircraft gas turbines operate at higher pressure ratios (typically between 10 and 25), and the fluid passes through a diffuser first, where it is decelerated and its pressure is increased before it enters the compressor. In jet engines, the hightemperature and highpressure gases leaving the turbine are accelerated in a nozzle to provide thrust. 62

63 Thrust (propulsive force) Propulsive power Propulsive efficiency Propulsive power is the thrust acting on the aircraft through a distance per unit time. The pressures at the inlet and the exit of a turbojet engine are identical (the ambient pressure) The pressure of air rises slightly as it is decelerated in the diffuser. Air is compressed by the compressor. It is mixed with fuel in the combustion chamber, where the mixture is burned at constant pressure. The high-pressure and high-temperature combustion gases partially expand in the turbine, producing enough power to drive the compressor and other equipment. Finally, the gases expand in a nozzle to the ambient pressure and leave the engine at a high velocity. Basic components of a turbojet engine and the T-s diagram for the ideal turbojet cycle. 63

64 -V exit is the exit velocity of the exhaust gases and V inlet i s the inlet velocity of the air, both relative to the aircraft. Thus, for an aircraft cruising in still air, V inlet is the aircraft velocity. - In reality, the mass flow rates of the gases at the engine exit and the inlet are different, the difference being equal to the combustion rate of the fuel. However, the air fuel mass ratio used in jetpropulsion engines is usually very high, making this difference very small.thus, m is taken as the mass flow rate of air through the engine. -For an aircraft cruising at a constant speed, the thrust is used to overcome air drag, and the net force acting on the body of the aircraft is zero. -Commercial airplanes save fuel by flying at higher altitudes during long trips since air at higher altitudes is thinner and exerts a smaller drag force on aircraft. - In the ideal case, the turbine work is assumed to equal the compressor work. Also, the processes in the diffuser, the compressor, the turbine, and the nozzle are assumed to be isentropic. In the analysis of actual cycles, however, the irreversibilities associated with these devices should be considered. The effect of the irreversibilities is to reduce the thrust that can be obtained from a turbojet engine. -The thrust developed in a turbojet engine is the unbalanced force that is caused by the difference in the momentum of the low-velocity air entering the engine and the high-velocity exhaust gases leaving the engine. -The net work developed by a turbojet engine is zero. 64

65 65

66 Modifications to Turbojet Engines The first airplanes built were all propellerdi driven, with propellers powered dby engines essentially identical to automobile engines. Both propeller-driven engines and jetpropulsion-driven engines have their own strengths and limitations, and several attempts have been made to combine the desirable characteristics of both in one engine. Two such modifications are the propjet engine and the turbofan engine. A turbofan engine. Energy supplied to an aircraft (from the burning of a fuel) manifests itself in various forms. The most widely used engine in aircraft propulsion is the turbofan (or fanjet) engine wherein a large fan driven by the turbine forces a considerable amount of air through a duct (cowl) surrounding the engine. 66

67 A modern jet engine used to power Boeing 777 aircraft. This is a Pratt & Whitney PW4084 turbofan capable of producing 374 kn of thrust. It is 4.87 m long, has a 2.84 m diameter fan, and it weighs 6800 kg. Various engine types: Turbofan, Propjet, Ramjet, Sacramjet, Rocket A turboprop engine. A ramjet engine. 67