Chapter 9Chapter 9GAS POWER CYCLES

Dr Ali Jawarneh

D f M h i l E i iDepartment of Mechanical Engineering

Hashemite University

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ObjectivesE l t th f f l f hi h th• Evaluate the performance of gas power cycles for which 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• 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

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gas power cycles.

• Perform second-law analysis of gas power cycles.

9-1:BASIC CONSIDERATIONS IN THE ANALYSISOF POWER CYCLES Thermal efficiency of heat enginesMost power-producing devices operate on cycles.Ideal cycle: A cycle that resembles the actual cycle closely but is made up totally of internally reversible

y g

processes.Reversible cycles such as Carnot cycle have the highest thermal efficiency of all heat engines operating between the same temperature levelsoperating between the same temperature levels. Unlike ideal cycles, they are totally reversible, and unsuitable as a realistic model.

The ideal cycles are internally reversible, y ybut, 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

Modeling is a powerful i i t l th t

The analysis of many complex processes can be reduced to a manageable

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 

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engineering tool that provides great insight and simplicity at the expense of some loss in accuracy.

reduced to a manageable level by utilizing some idealizations.

is still considerably higher than thethermal efficiency of an actual cycle because of the idealizations utilized

The idealizations and simplifications in the analysis of power cycles:

1. The cycle does not involve any friction.

On a T-s diagram, the ratio of the area enclosed by the cyclic curve to the area under the heat-addition y y

Therefore, the working fluid does not experience any pressure drop as it flows in pipes or devices such as heat exchangers.

2 All expansion and compression processes

the area under the heat addition process curve represents the thermal efficiency of the cycle. Any modification that increases the ratio of these two areas will also increase 2. All expansion and compression processes

take place in a quasi-equilibrium manner.3. The pipes connecting the various

components of a system are well i l t d d h t t f th h th

of these two areas will also increase the thermal efficiency of the cycle.

insulated, and heat transfer through them is negligible.

Care should be exercised On both P-v and T-s diagrams, the area enclosed

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Care should be exercised in the interpretation of the results from ideal cycles.

gby the process curve represents the net work of the cycle which is also equivalent to the net heat transfer for that cycle.

9-2:THE CARNOT CYCLE AND ITS VALUE IN ENGINEERINGThe Carnot cycle is composed of four totally reversible processes: isothermal heat addition, isentropic expansion, isothermal heat rejection, andisentropic compressionisentropic compression.

For both ideal and actual cycles: Thermal efficiency increases with an increase in the average temperature at which heat is supplied to the systemtemperature at which heat is supplied to the system or with a decrease in the average temperature at which heat is rejected from the system.

The Carnot cycle canThe Carnot cycle can be executed in a closed system (a piston–cylinder device) or a steady‐flow system (utilizing two turbines and two compressors, and either a gas or a

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P-v and T-s diagrams of a Carnot cycle.A steady-flow Carnot engine.

either a gas or a vapor can be utilized as the working fluid.

9-3:AIR-STANDARD ASSUMPTIONSAi t d d tiAir-standard assumptions:1. The working fluid is air, which

continuously circulates in a closed loop and always behaves as an ideal gasand 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 p p ya heat-addition process from an external source.

4. The exhaust process is replaced by a h t j ti th t t th

The combustion process is replaced by a heat-addition process in ideal cycles.

heat-rejection process that restores the working fluid to its initial state.

Cold-air-standard assumptions: When the working fluid is considered to be air with constant specific heats at room temperature (25°C). Air-standard cycle: A cycle for which the air-standard assumptions are

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sta da d cyc e cyc e o c t e a sta da d assu pt o s a eapplicable.

9-4:AN OVERVIEW OF RECIPROCATING ENGINESCompression 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

• 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)

due to its higher thermal efficiency)

8Nomenclature 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 cycle

9-5:OTTO CYCLE: THE IDEAL CYCLE FOR SPARK-IGNITION ENGINES SI engineSPARK IGNITION ENGINES

It is named after Nikolaus A. Otto, who built a successful four‐stroke engine in 1876 in Germany

9Actual and ideal cycles in spark-ignition engines and their P-v diagrams.

Four-stroke cycle1 cycle = 4 stroke = 2 revolutionT o stroke c cle

In most spark‐ignition engines, the piston executes fourTwo-stroke cycle

1 cycle = 2 stroke = 1 revolutioncomplete strokes (two mechanical cycles) within the cylinder, and the crankshaft completes twocompletes two revolutions for each thermodynamic cycle.

T-s diagram of the ideal Otto cycle

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cycle.

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Four stroke b ticombustion

engine

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The two-stroke engines are generally less efficient than th i f t k t t

Four-stroke cycle1 cycle = 4 stroke = 2 revolutionT o stroke c cle their four-stroke counterparts

but they are relatively simple and inexpensive, and they have high power-to-weight

Two-stroke cycle1 cycle = 2 stroke = 1 revolution

In two‐stroke engines, all four functions described above are executed in just two strokes: the power stroke and the compression stroke In g p g

and power-to-volume ratios.in just two strokes: the power stroke and the compression stroke. In 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 as the piston moves upward during the compression strokecompressed as the 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 e p lsion of the e ha st gases and the partial e p lsion of

S h ti f t t k

expulsion of the exhaust gases 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

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Schematic of a two-stroke reciprocating 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

Operating Principles

I: inlet port for crankcase E: exhaust port P: fuel inlet port p g p

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.

D i th h ti h th i t i

p

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 i t th t f t thpiston 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

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pressure on the piston

A two-stroke engine is a combustion engine that completes the thermodynamic cycle in two movements of the piston compared to twice that

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p pnumber 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 intake and exhaust (or scavenging) functions.

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The Otto cycle is executed in a closed system

For Constant Specific Heats

η of the ideal Otto cycle increases with both r and kIn SI engines, the compression ratio is limited by autoignition or

Thermal efficiency of The thermal efficiency of the Otto 

autoignition or engine knock.

η f t l SI i

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the ideal Otto cycle as a function of compression ratio (k = 1.4).

cycle increases with the specific heat ratio k (k=cp/cv) of the working fluid.

η of actual SI engines range from about 25 to 30%

When high compression ratios are used, the temperature of the air–fuel mixture rises above theautoignition temperature of the fuel (the temp at which the fuel ignites without the help of aspark) during the combustion process, causing an early and rapid burn of the fuel at some pointor points ahead of the flame front, followed by almost instantaneous inflammation of the endgas. This premature ignition of the fuel, called autoignition, produces an audible noise, which is

ll d i k k A t i iti i k i iti i t b t l t d b it h tcalled engine knock. Autoignition in spark-ignition engines cannot be tolerated because it hurtsperformance and can cause engine damage. The requirement that autoignition not be allowedplaces an upper limit on the compression ratios that can be used in sparkignition internalcombustion 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 usinggasoline blends that have good antiknock characteristics, such as gasoline mixed with tetraethyllead. Tetraethyl lead posses hazardous to health and pollute the environment.y p p

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Isentropic Processes of Ideal GasesConstant Specific Heats (Approximate Analysis)

Chapter 7

Setting this eq equal to The specific heat Setting this eq. equal to zero, we get

pratio k, ingeneral, varies with temperature, and thus anaverage k value for gthe given temperature range should be used. we should refine the calculations{repeat

The isentropic relations of ideal gases are valid for the isentropic processes of ideal gases only.

E ti 7 42 th h 7 44 l b

{ pthe calculations}

Equations 7–42 through 7–44 can also be expressed in a compact form as

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Isentropic Processes of Ideal GasesVariable Specific Heats (Exact Analysis)

Chapter 7

R l ti P d R l ti S ifi V lRelative Pressure and Relative Specific Volume

( °/R) i

The use of Pr data for calculating the final temperatureexp(s°/R) is

the relative pressure Pr.

final temperature during an isentropic

process.

T/Pr is the relativespecific volume vr.

The use of vr data for calculating the final

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calculating the final temperature during an

isentropic processTable A–17 [Air]

Example:

An ideal Otto cycle has a compression ratio of 8. At thebeginning of the compression process air is at 95 kPa and 27°Cbeginning of the compression process, air is at 95 kPa and 27 C,and 750 kJ/kg of heat is transferred to air during the constant‐volume heat‐addition process. Taking into account the variationf ifi h t ith t t d t i ( ) thof specific heats with temperature, determine (a) the pressure

and temperature at the end of the heat addition process, (b) thenet work output, (c) the thermal efficiency, and (d) the meaneffective pressure for the cycle.

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Solution: R = 0.287 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.

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(b) Process 3-4: isentropic expansion.

P 4 1 t t h t j tiProcess 4-1: v = constant heat rejection.

( )(c)

(d)

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9-6: DIESEL CYCLE: THE IDEAL CYCLEFOR COMPRESSION-IGNITION ENGINES

CI engine

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.

• 1-2 isentropic se op ccompression

• 2-3 constant-pressure heat additionaddition

• 3-4 isentropic expansion

• 4-1 constant-

In diesel engines, the spark plug is replaced

volume heat rejection.

η of actual CI

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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%

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 , g y g p g g (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 p g p ,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 j p g p ppcontinues 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 heat-addition process. In fact, this is the only process where the Otto and the Diesel cycles differ. p y p yThe 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 p y y y p pthe 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

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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 heat‐addition 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.

Diesel cycle is executed in a piston–cylinder device,which forms a closed system,

Cutoff ratio

ffor the same compression ratio

Thermal efficiency of the ideal Dieselthe ideal Diesel cycle as a function of compression

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and cutoff ratios (k=1.4).

Dual cycle: A more realistic ideal cycle model for modern,

QUESTIONS

Diesel engines operate at Approximating the combustion process in internal combustion y

high-speed compression ignition engine.

higher air-fuel ratios than gasoline engines. Why?

Despite higher power to weight ratios two-stroke

internal combustion engines as a constant-volume or a constant pressure heat-addition process is overly weight ratios, two-stroke

engines are not used in automobiles. Why?

The stationary diesel

simplistic and not quite realistic. Probably a better (but slightly more complex) approach would be to model the

engines are among the most efficient power producing devices (about 50%). Why?

be to model the combustion process in both gasoline anddiesel engines as a combination of two heat-t f

What is a turbocharger? Why are they mostly used in diesel engines compared to gasoline engines

transfer processes, one at constant volume and the other at constant pressure. The ideal cycle based on this concept is

P-v diagram of an ideal dual cycle.

to gasoline engines.pcalled the dual cycle.

The relative amounts of heat transferred during each process b dj t d t i t th t l l l l

In Duel Cycle heat is added partly at constant volume and partly at constant pressure, the

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can be adjusted to approximate the actual cycle more closely. Note that both the Otto and the Diesel cycles can be obtained as special cases of the dual cycle.

advantage of which is that more time is available for the fuel to completely combust.

TurbochargerA 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 t rbine hich dra s the e ha stcompresses 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 ATherefore, 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

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g

EXAMPLE:

An ideal diesel engine has a compression ratio of 20 and usesAn ideal diesel engine has a compression ratio of 20 and 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 

i h l i d 2200 K d itemperature 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.

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SOLUTION

The properties of air at room temperature are cp = 1.005 kJ/kg·K, cv = 0.718kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4 (Table A-2).

(a) Process 1-2: isentropic compression(a) Process 1-2: isentropic compression.

Process 2-3: P = constant heat addition.

Process 3-4: isentropic expansion.

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(b)

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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

b ti t t t l Th b i f ki f CI i i th Di l l I thi l thcombustion occurs at a constant 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 highcombustion 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 air-fuel 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 isdepending 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 self-ignite.

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, hence6) 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 = 1800

7) 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.

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- 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.

9-7:STIRLING AND ERICSSON CYCLESStirling cycle• 1-2 T = constant expansion (heat addition from the external source)

2 3 t t ti (i t l h t t f f th ki fl id t th t )• 2-3 v = constant 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 pressurereplaced 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 ( g ) g pcycle and is transferred back to the working fluid during another part of the cycle

A regenerator is a device that borrows

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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.

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 

This system consists of a cylinder with two i t h

g g p gregenerator, 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, pistons on each

side and aregenerator in the middle.Regenerator can be a wire or a

y p ,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 gasbe a wire or a

ceramic mesh or any kind of porous plug with a high thermal mass (mass

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

times specificheat). It is used for the temporary storage of thermal energy.

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

34The execution of the Stirling cyclein a closed system

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 4‐1.

Both the Stirling and Ericsson cycles are totally reversible, as is the Carnot cycle,

The Stirling and Ericsson cycles give a message: Regeneration

and thus:give a message: Regeneration can increase efficiency.

The Ericsson engine can be run open- or closed-cycle. Expansion occurs simultaneously with compression on opposite

The Ericsson cycle is very much like the Stirling cycle, except that the two constant-volume processes are replaced by two

A steady‐flow system operating on an Ericsson cycle is shown in Fig. 9–28.Here the isothermal expansion and

Expansion occurs simultaneously with compression, on opposite sides of the piston.

constant-pressure processes.Here the isothermal expansion and compression processes are executed in acompressor and a turbine, respectively, and a counter‐flow heat exchanger serves as a regenerator. Hot and cold fl d h h hfluid 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.

35A steady-flow Ericsson engine.

counter-flow heat exchanger serves as a regenerator

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 

36

utilized in large gas‐turbine power plants and discussed later in this chapter, closely resembles the Ericsson cycle.

Operation

A Stirling engine is a heat engine that operates by cyclic compression and expansion of air or other gas, the working fluid, g g g p y y p p g , g ,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 h t d ld h t h ft ith t b t th h t d l Th h t h t h i ihot 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

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

Alpha type Stirlingengine. The expansion cylinderand 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

ti thi i t ll i l i l ti h d t th l

expansion cylinder (red) is maintained at a high temperature while the compression cylinder (blue) is cooled. The passage between the two

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.

cylinders contains the regenerator

1 M t f th ki i i3. Almost all the gas is 4. The gas reaches

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

2. The gas is now at its maximum volume. The hot cylinder piston begins to move most of the gas into

now in the cold cylinder and cooling continues. The cold piston, powered by flywheel momentum (or other piston pairs on the same shaft) compresses

its minimum volume, and it will now expand in the hot cylinder where it will be heated once more, driving the hot piston

38

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.

most of the gas into the cold cylinder, where it cools and the pressure drops.

same shaft) compresses the remaining part of the gas.

driving the hot piston in its power stroke.

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 b t th di l d th li d ll t ll t il fl d thbetween 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 , y y y , p p p yto 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

2. The heated gas increases in pressure and pushes the power piston

3. The displacer piston now moves, shunting the gas

4. The cooled gas is now compressed by the flywheel

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gas, the displacer piston (light grey) has moved so that most of the gas is adjacent to the hot heat exchanger.

pushes the power piston to the farthest limit of the power stroke.

shunting the gas to the cold end of the cylinder.

momentum. This takes less energy, since when it is cooled its pressure dropped.

EXAMPLEEXAMPLE:

An ideal Stirling engine using helium as theAn ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and 2000 K and pressure limits of p150 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(c) the work output per cycle.

Assume a constant specific heats at room temperature

40

p p

Assumptions Helium is an ideal gas with constant specific heatsSolution: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 = 2.0769 kJ/kg.K, cv = 3.1156 kJ/kg.K and cp = 5.1926 kJ/k K (T bl A 2)kJ/kg.K (Table A-2).

(a) The thermal efficiency of this totally re ersible c cle is determined fromreversible cycle is determined from

(b) The amount of heat transferred in the regenerator is

41

(c) The net work output is determined from

42

9-8:BRAYTON CYCLE: THE IDEAL CYCLE FOR GAS-TURBINE ENGINES The Brayton cycle was first proposed byFOR GAS-TURBINE ENGINES

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 press re heat rejection process to the ambient air

The Brayton cycle was first proposed by George Brayton around 1870.

constant-pressure heat-rejection process to the ambient air. 1-2 Isentropic compression (in a compressor)2-3 Constant-pressure heat addition3-4 Isentropic expansion (in a turbine)p p ( )4-1 Constant-pressure heat rejection

Gas turbines usually operate on an open cycle. Fresh air at ambient conditions is drawn into the compressor whereinto 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 

A closed-cycle gas-turbine engine.

pressure. The resulting high‐temperature gases then enter the turbine, where they expand to the atmospheric pressure while producing 

Th h tThe Brayton cycle is the only

43

An open-cycle gas-turbine engine.power. The exhaust gases leaving the turbine are thrown out (not recirculated), causing the cycle to be classified as an open cycle.

thermodynamic cycle which can be used in both internal combustion engines (such as jet engines) and for external combustion engines.

Notice that all four processes of the Brayton cycle are executed incycle are executed in steady-flow devices

Pressure ratio

The thermal efficiency

Under constant specific heat ratio

Thermal

increases withboth rp and k

Thermal efficiency of the

ideal Brayton cycle as a

44

T-s and P-v diagrams for the ideal Brayton cycle.

yfunction of the pressure ratio.

The two major application areas of gas-turbine engines are aircraft propulsion

d l t i ti

The highest temperature in the cycle is limited by the maximum temperature that the turbine blades can withstand. This also limits the pressure ratios th t b d i th land electric power generation. that 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 pratio of 50 or above is not uncommon.

In most common designs, the

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, diesel is used designs, the

pressure ratio of gas turbines ranges from about 11 to 16.

co b ed d ese a d gas tu b e syste s, d ese s usedto provide for efficient low-power and cruise operation, and gas turbine is used when high speeds are needed.

For fixed values of Tmin and Tmax, the net work of the Brayton cycle first increases with the pressure ratio then reaches a maximum at r Usually more thanpressure ratio, then reaches a maximum at rp= (Tmax/Tmin)k/[2(k - 1)], and finally decreases.

Usually more than one-half of the turbine work output is used to drive the compressor.

For a fixed turbine inlet temperature T3, the net work outputper cycle increases with the pressure ratio, reaches a maximum and then starts to decrease as shown in Fig 9–

back work ratio

45

The fraction of the turbine work used to drive the compressor is called the back work ratio.

maximum, and then starts to decrease, as shown in Fig. 933. Therefore, there should be a compromise between the pressure ratio (thus the thermal efficiency) and thenet work output.

Development of Gas Turbines1. Increasing the turbine inlet (or firing) temperaturesg ( g) p2. Increasing the efficiencies of turbomachinery components (turbines,

compressors):3. Adding modifications to the basic cycle (intercooling, regeneration or

recuperation and reheating)recuperation, and reheating).

Deviation of Actual Gas-Turbine Cycles from IdealizedTurbine Cycles from Idealized OnesReasons: Irreversibilities in turbine and

d h t lcompressors, pressure drops, heat losses

Isentropic efficiencies of the compressor and turbine

The deviation of an actual gas-turbine cycle from the ideal

and turbine

46

turbine cycle from the ideal Brayton cycle as a result of irreversibilities.

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. p yAssuming 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(a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency.

i ifi husing constant specific heats at room temperature.

47

Solution:The properties of air at room temperature are cp = 1.005 kJ/kg·K and k = 1.4 (Table A-2).

(a) Using the compressor and turbine efficiency relations,

48

(b)

(c)(c)

49

9-9:THE BRAYTON CYCLE WITH REGENERATIONWITH REGENERATIONIn 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.

T di f B t

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 T-s diagram of a Brayton

cycle with regeneration.

The thermal efficiency of the Brayton cycle increases as a result of regeneration since less fuel is used for the same work output.

The thermal efficiency of the Brayton cycle increases as a result of regeneration since the portion of energy of the exhaust gasesthe portion 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 workrequirements 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 will flow in the reverse

50A gas-turbine engine with regenerator.

Otherwise, heat will flow in the reverse direction (to the exhaust gases), decreasing the efficiency. This situation is encountered in gas‐turbine engines operating at very high pressure ratios.

Assuming the regenerator to be well insulated and any changes in kinetic and potential energies to be negligible

Effectiveness of regenerator

Effectiveness under coldEffectiveness under cold-air standard assumptions

Under cold-air standard assumptions

T-s diagram of a Brayton cycle with regeneration.

standard assumptions

Can regeneration be used at high

Thermal

The thermal efficiency depends on the ratio of the minimum to maximum t t ll th

be used at high pressure ratios?

Thermal efficiency of

the ideal Brayton cycle

temperatures as well as the pressure ratio. Regeneration is most effective at lower pressure

51

with and without

regeneration.

effective at lower pressure ratios and low minimum-to-maximum temperature ratios.

Example:Air enters the compressor of a regenerative gas‐turbine engineAir 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 i t th t bi t 1200 K F t bi ffi i f 86air enters the turbine at 1200 K. For a turbine efficiency 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

Solution:The properties of air are given in Table A-17.

(a) The properties at various states are

53

(b)

54

9-10:THE BRAYTON CYCLE WITH INTERCOOLING

For minimizing work input to compressor and maximizingWITH INTERCOOLING,

REHEATING, AND REGENERATION

compressor and maximizing work output from turbine:

REGENERATION

A gas turbine engine with two stage compression with intercooling two stage

55

A gas-turbine engine with two-stage compression with intercooling, two-stage expansion with reheating, and regeneration and its T-s diagram.

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 p g g g p pas 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

Comparison of work inputs

Intercooling and reheating always decreases the thermal efficiency unless they are accompanied by regeneration. Why?

to a single-stage 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

56

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 justified economically.

-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 outthe 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

di th i t d h ti it i b t th t i tili i lti t i ithexpanding the gas in stages and reheating it in between—that is, utilizing multistage 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 to the specific volume of the fluid. Therefore, the specific volume of the working fluid should be p p p , p gas 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 tworeheating 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 alwaysdecreases the thermal efficiency unless they are accompanied by regeneration This is because

57

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. 9–44. Therefore, in gasturbine power plants, intercooling and reheating are always used in conjunction with regeneration.

The efficiency of a Brayton engine can be improved in the following manners:*R h t h i th ki fl id i t i d th h i f*Reheat, wherein the working fluid—in most cases air—expands through 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

t ll i l t i t (Alth h f ft b l b f d tany metallurgical constraints. (Although 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, th l th d t f b f t i th b tithen 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 o erallneeded 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*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.

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Example: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 3ratio 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.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

Assumptions: 1- The air standard assumptions are applicable 2- Air is an idealSOLUTION:

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

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

61

9-11: IDEAL JET-PROPULSION CYCLESGas-turbine engines are widely used to power aircraft because they are light and compact and have a hi h t i ht tihigh 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 auxiliarythe 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

f f ( )by either slightly accelerating a large mass of 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) andAircraft 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 high-temperature and high-

pressure gases leaving the turbine are accelerated in a

62

turbine are accelerated in a nozzle to provide thrust.

Propulsive efficiency

Thrust (propulsive force)

Propulsive power

Propulsive power is the thrust acting on the aircraft through a distance per unit time.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 combustioncompressed 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.

The pressures at the inlet and the exit of a turbojet engine are identical (the g (ambient pressure)

63Basic components of a turbojet engine and the T-s diagram for the ideal turbojet cycle.

- Vexit is the exit velocity of the exhaust gases and Vinlet i s the inlet velocityof the air, both relative to the aircraft. Thus, for an aircraft cruising in stillair Vinlet is the aircraft velocityair, Vinlet 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 thedifference 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 sinceCommercial 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 compressorwork. Also, the processes in the diffuser, the compressor, the turbine, andthe nozzle are assumed to be isentropic. In the analysis of actual cycles,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 byThe 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

Modifications to Turbojet EnginesThe first airplanes built were all propeller-d i ith ll d b idriven, with propellers powered by engines essentially identical to automobile engines.Both propeller-driven engines and jet-propulsion-driven engines have their own

Energy supplied to an aircraft

gstrengths 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

(from the burning of a fuel) manifests itself in various forms.

A turbofan engine

Two such modifications are the propjet engineand the turbofan engine.

The most widely usedA turbofan engine. The most widely used engine in aircraft propulsion is the turbofan (or fanjet) engine wherein a largeengine wherein a large fan driven by the turbine forces a considerable amount of air through a duct

66

of air through a duct (cowl) surrounding the engine.

A modern jet engine used to power Boeingused to power Boeing 777 aircraft. This is a Pratt & Whitney PW4084 turbofan

bl f d icapable 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:Various engine types:Turbofan, Propjet, Ramjet, Sacramjet, Rocket

67A turboprop engine. A ramjet engine.

- 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, as shown in Figs. 9–52 and 9–53. The fan exhaust leaves the duct at a higher velocity, enhancing the total g g y gthrust of the engine significantly. A turbofan engine is based on the principle that for the same power, a large volume of slower moving air produces more thrust than a small volume of fast-moving air.-The turbofan engine on an airplane can be distinguished from the less efficient turbojet engine by its fat cowling covering the large fan. All the thrust of a turbojet engine is due to the exhaust gases leaving the engine at about twice the speed of sound In a turbofan engine the high speed exhaust gases are mixedengine at about twice the speed of sound. In a turbofan engine, the high-speed exhaust gases are mixed with the lower-speed air, which results in a considerable reduction in noise.- As a general rule, propellers are more efficient than jet engines, but they are limited to low-speed andlow-altitude operation since their efficiency decreases at high speeds and altitudes.- The old propjet engines (turboprops) were limited to speeds of about Mach 0.62 and to altitudes of around 9100 m. The new propjet engines ( propfans) are expected to achieve speeds of about Mach 0.82and altitudes of about 12,200 m. Commercial airplanes of medium size and range propelled by propfans are expected to fly as high and as fast as the planes propelled by turbofans, and to do so on less fuel.- A ramjet engine is a properly shaped duct with no compressor or turbine, as shown in Fig. 9–55, and is sometimes used for high-speed propulsion of missiles and aircraft The pressure rise in the engineand is sometimes used for high speed propulsion of missiles and aircraft. The pressure rise in the engine is provided by the ram effect of the incoming high-speed air being rammed against a barrier. Therefore,a ramjet engine needs to be brought to a sufficiently high speed by an external source before it can be fired. The ramjet performs best in aircraft flying above Mach 2 or 3 (two or three times the speed of sound). In a ramjet, the air is slowed down to about Mach 0.2, fuel is added to the air and burned at this l l it d th b ti d d d l t d i llow velocity, and the combustion gases are expended and accelerated in a nozzle.- A scramjet engine is essentially a ramjet in which air flows through at supersonic speeds (above the speed of sound). Ramjets that convert to scramjet configurations at speeds above Mach 6 are successfully tested at speeds of about Mach 8.- A rocket is a device where a solid or liquid fuel and an oxidizer react in the combustion chamber.

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qThe high-pressure combustion gases are then expanded in a nozzle. The gases leave the rocket at very high velocities, producing the thrust to propel the rocket.

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EXAMPLE: A turbojet aircraft is flying with a velocity of 320 m/s at an altitude of 9150 m where the ambient conditions are 32altitude of 9150 m, where the ambient conditions are 32kPa and -32°C. The pressure ratio across the compressor is 12 (compressor efficiency of 80 % ), and th t t t th t bi i l t i 1400 K(t bithe temperature at the turbine inlet is 1400 K(turbine efficiency of 85% ). Air enters the compressor at a rate of 60 kg/s, and the jet fuel has a heating value of 42,700g j gkJ/kg. Assuming constant specific heats for air at room temperature, determine (a) the velocity of the exhaust gases (b) the propulsive power developed and (c) thegases, (b) the propulsive power developed, and (c) the rate of fuel consumption.

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SOLUTION:Assumptions 1 Steady operating conditions exist 2 The air standardAssumptions 1 Steady operating conditions exist. 2 The air standard assumptions are applicable. 3 Air is an ideal gas with constant specific heats at room temperature. 4 Kinetic and potential energies are negligible, except at the diffuser inlet and the nozzle exit.

Properties The properties of air at room temperature are cp = 1.005 kJ/kg.K and k = 1.4 (Table A-2a).

Analysis (a) For convenience we assume the aircraft is stationary and the airAnalysis (a) For convenience, we assume the aircraft is stationary and the air is moving towards the aircraft at a velocity of V 1 = 320 m/s. Ideally, the air will leave the diffuser with a negligible velocity (V 2 0).

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Diffuser:

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Compressor:

Turbine:

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Nozzle:

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9-12: SECOND-LAW ANALYSIS OF GAS POWER CYCLES

Exergy destruction for a closed system

For a steady-flow system

Steady-flow, one-inlet, one-exitSteady flow, one inlet, one exit

Exergy destruction of a cycle

F l i h h f

The exergy destruction of a cycle is the sum of the exergyFor a cycle with heat transfer

only with a source and a sink

Closed system exergy

the exergy destructions of the processes that compose that cycle.

Stream exergy

A second law analysis of these cycles reveals where the largest

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A second-law analysis of these cycles reveals where the largest irreversibilities occur and where to start improvements.

EXAMPLE:EXAMPLE:Determine the total exergy destruction associated with the Otto cycle described in Problem 9–34, assuming a source temperature of 2000 K and a sink temperaturesource temperature of 2000 K and a sink temperature of 300 K. Also, determine the exergy at the end of the power stroke.

9–34: An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process air is at 95 kPa and 27°Cbeginning of the compression process, air is at 95 kPa and 27 C, and 750 kJ/kg of heat is transferred to air during the constant-volume heat-addition process. Taking into account the variation of specific heats with temperature determine (a) the pressure andspecific heats with temperature, determine (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.

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p y

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SOLUTION:

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SummaryB i id ti i th l i f l• Basic considerations in the analysis of power cycles

• The Carnot cycle and its value in engineering• Air-standard sssumptionsAir standard sssumptions• An overview of reciprocating engines• Otto cycle: The ideal cycle for spark-ignition engines• Diesel cycle: The ideal cycle for compression-ignition

engines• Stirling and Ericsson cyclesg y• Brayton cycle: The ideal cycle for gas-turbine engines• The Brayton cycle with regeneration• The Brayton cycle with intercooling, reheating, and

regeneration• Ideal jet-propulsion cycles

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j p p y• Second-law analysis of gas power cycles