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International Journal of Mechanical Engineering Education Vol 29 No 4

On the thermodynamiccycles of gas turbine powerplantsH. A. HEIKAL , Department of Mechanical Power Engineering,Faculty of Engineering, Helwan University, El-Mataria and M. G.HIGAZY *, Mechanical Engineering Department, Faculty of Engineering, Zagazig University, Shoubra, Cairo, [email protected]

This paper proposes new appropriate thermodynamic analysis for gas turbine cycles used for power plants rather than that commonly known from the traditional thermodynamic

methods. The present analysis is based on using two important design criteria known as the pressure ratio and the temperature ratio. These two criteria are employed to indicate thecharacteristics of the thermal efficiency and the non-dimensional work. Characteristic chartsare established as a function of these two criteria to illustrate the cycles theoretical

performance. Appropriate effects of the cycles regeneration, intercooling and reheat arealso discussed. The obtained charts can be used to indicate possible improvement in thethermodynamics of the gas turbine cycles.

Received 19th October 1998 Revised 11th October 1999

NOTATION

c p specific heat of perfect gas at constant pressure (kJ kg K)c v specific heat of perfect gas at constant volume (kJ kg K)m exponent in equation (5)n exponent in equation (6)

p pressure (kN m2)T absolute temperature on the Kelvin scalev volume (m 3)W work of a cycle (kJ)W * non-dimensional work, equation (4) adiabatic exponent, or index of expansion or compression; equal to 1.4

* Address for correspondence: Professor M. G. Higazy, Mechanical Engineering Department, Facultyof Engineering Shoubra, 108 Shoubra Street, Post Code 11689, Shoubra, Cairo, Egypt.

Key words: efficiency, work, basic cycles, gas turbine regeneration, intgercooling, reheat

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322 H. A. Heikal and M. G. Higazy

efficiency of a cycle pressure ratio, equation (1) temperature ratio, equation (2)

degree of multi-stage intercooling or multi-stage reheat

1,2,3,4 condition of state pointsg regenerationi multi-stage intercoolingmin minimummax maximumr multi-stage reheat

th thermal

Subscripts

1.1 The cycle pressure ratio

This parameter is taken as the ratio between the highest or maximum pressure of the cycle tothe initial or minimum pressure cycle. The pressure ratio , takes the form:

= p p

max

min(1)

1. INTRODUCTION

The design of an effective gas turbine is well known to be the result of sound fundamentalconcepts combined with a series of practical compromises. Carnots brilliant ideas were indeducing many fundamental concepts, in the absence of thermodynamics laws, that are nowtaken for granted. These fundamental concepts, such as a useful work ratio, can only beproduced by a heat engine through a process of controlled heat flow from a high to a low

temperature. Thus, work can be produced out of the heat flow from the hot source to the coldsink. Thus, Horlock [1] uses the ratio of the heat source temperature to the sink temperatureas design criteria. Wilson and Radwan [2] showed the importance of the work ratio in a gasturbine design and its effect on thermal efficiency, since in a gas turbine, over half its totaloutput work is used to drive the compressor, i.e. the work ratio is less than 0.5. Normally it isabout 0.25. The effect of such a low work ratio is a low thermal efficiency. Chen et al . [3],taking into account different practical implications of work ratio, indicated that in manyways the concept of work ratio can be regarded more important than the concept of idealcycle thermal efficiency. Therefore, it is the main aim of this paper to expose a realisticcharacteristic of thermodynamics for gas turbine basic cycles. Thermodynamic characteristics

for both open and closed cycles are usually based on two concepts: the non-dimensionalwork criteria as well as the thermal efficiency criteria. Considering the original five airstandard cycles of Carnot, Stirling, Ericsson, Atkinson and Joule, [4] and [5]; the character-istic equations for the thermal efficiency, th and the non-dimensional work, W

* have beendeveloped. Such characteristic equations are derived as functions of two important non-dimensional design criteria. These are the pressure ratio, , and the temperature ratio, , aswill be shown later.

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On the thermodynamic cycles of gas turbine power plants 323

1.2 The cycle temperature ratio

The temperature ratio , is defined as the ratio between the maximum cycle temperature tothe minimum cycle temperature. In other words, it is the ratio between the source temperatureto the sink temperature. Thus, is given by:

=T T

max

min(2)

1.3 The ideal thermal efficiency

As it is usually known, the efficiency of the cycle is the ratio between the net work of a cycledivided by the net heat added to the air per cycle, where:

thwork done per cycle

net heat added to the air per cycle= (3)

1.4 The non-dimensional work of the cycle, W *

The non-dimensional work is defined as the work done per cycle, divided by C pT 1. Where T 1is the cycle minimum temperature. The work done per cycle, W , is the net area of the cycleon T S or p v diagrams. Thus, the non-dimensional work is defined as:

W W

CpT * =

1 (4)

1.5 The exponent of a process

It is designated as

m =

1(5)

and

n =

1(6)

2. CYCLES EFFICIENCIES AND NON-DIMENSIONAL WORKS

The general analysis of cycles is carried out by employing the perfect gas laws for differentprocesses. The cycle processes are for a perfect gas or air having a constant law index. Theanalysis of the cycles are based on using either the p v or T S planes for the five basiccycles, shown in Fig. 1. The cycle implies sequence of processes taking place in which eithergas or air is eventually returned to its original state. During the processes, heat or work willbe transferred into or out of the air. The cycle s efficiencies and non-dimensional work equations are driven as a function of cycle pressure ratio, , and cycle temperature ratio, . InFigs 2 (a b) comparison among the five cycles areas on T S diagram are drawn for thesame and .

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F i g

. 1

. A i r s t a n

d a r

d c y c l e s

f o r g a s

t u r b

i n e s .

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Fig. 2. Air standard cycles superimposed on T S diagrams for the same and .(a) Carnot, Stirling, Ericsson and ideal regenerative cycles. (b) Stirling, Ericsson,Atkinson, Joule, ideal multi-stage intercooling, multi-stage reheat and ideal regenerative

cycles.

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The well-known Carnot cycle consists of two isothermal processes and two isentropic proc-

esses as shown in Fig. 1(a). The non-dimensional work W *

is calculated according to thebasic principles of thermodynamics for the cycle processes. Therefore, work done is equalto:

Word done per cycle = heat transferred to the air heat transferred out of the air

According to equation (4)

W CpT

RT S S RT S SCpT

* ( ) ( )= =

workdone per cycle

1

3 3 2 1 4 1

1

consequently

* This trend is similar for all figures.


2.1 The Carnot cycle


Consequently

th

= 11

(8)

W m n* ( )(ln ln )= 1 (7)

and according to the cycle ideal thermal efficiency, equation (3), is equal to

the ideal thermal efficiency =

1 1 4 1 1

3 3 2 1

RT S S CpT RT S S CpT

( )( )

The above two equations characterize the Carnot cycle performance as a function of only thepressure ratio , and the temperature ratio . Charts representing the above equations aredrawn in Fig. 3 for , ranges from 2.5 to 5000 and for varies from 1.25 up to 8. In thisfigure, the optimum work corresponding to each pressure ratio and temperature ratio is alsoplotted. The solid lines * represent the constant pressure ratio lines, i.e. constant and dashedlines * represent the constant temperature ratio lines, i.e. constant . The constant lines startfrom zero and they increase up to a certain maximum value, then, they decrease back again.The maximum efficiency occurs with nearly zero work. The efficiency-work ratiorelationship shown in Fig. 3 indicates that work ratio increases as the pressure ratio increase.This occurs while both the efficiency and temperature ratio are both constant, i.e. for fixedvalues, no matter how much the value of the pressure ratio changes. This behaviour isexpected from equation (8). The maximum work is accomplished before the efficiencyreaches its maximum value. The work reaches its maximum value while the efficiencyincreases. Then, the work starts to decrease to nearly zero while the efficiency gets to itsmaximum value. Fig. 3 shows that the Carnot cycle operates between a temperature ratio of 5 and corresponding to a very unrealistic pressure ratio of 5000. This temperature ratio, = 5, would be corresponding to maximum temperature of 1500 k when the minimumtemperature is taken as 300 k. The corresponding non-dimensional work for the previousvalues is less than 3.5 which is a very limited work. It is also demonstrated that the Carnotcycle does not work for every pressure ratio and temperature ratio, e.g. for a pressure ratio ,equal 30, and with a temperature ratio = 6, the cycle does not work. This is demonstrated inFig. 3. Although the Carnot cycle will have the maximum thermodynamic efficiency for agiven source and sink temperatures, the Carnot cycle is severely limited in work per cycle asillustrated in Fig. 3

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Fig. 3. Characteristics charts for the Carnot cycle.



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2.2 The Stirling cycle

In Fig. 1(b), the Stirling cycle is shown on the p v and T S planes. The cycle is composed

of two isothermal processes and two constant volume processes. The importance of thiscycle and the following cycles is in their ability to accept the process of regeneration. Thiswill be discussed later. Following the same principle as in the Carnot cycle, consequently,the non-dimensional work W * takes the form

W m* ( ) (ln ln )= 1 (9)

and the thermal efficiency has the form

th =

+

+

1

1

1

m

m

ln

ln(10)

In Fig. 4 the thermal efficiency and non-dimensional work are plotted for temperature andpressure ratios. The temperature ratio, , ranges from 3 up to 7 and pressure ratio, , rangesfrom 2.5 up to 30. The constant temperature ratio lines start from the origin and they increaseoutwards. However, the constant pressure ratio lines start from the origin representing a ring-shaped curve which closes back to zero. The line of maximum non-dimensional work is alsoshown in Fig. 4 where it occurs with an efficiency equal to about two thirds of its highestefficiency. These charts illustrate that a Stirling cycle has higher efficiency with lowertemperature ratios than with higher temperature ratios. The maximum work is almoststraight-line and slightly increases with the increase of temperature ratios but variesconsiderably with pressure ratios.



2.3 The Ericsson cycle

Fig. 1(c) shows the Ericsson cycle on p v and T S planes. This illustrates that the Ericssoncycle agrees with the Stirling cycle on having two isothermal processes, but with twoconstant pressure processes. The process of regeneration is also possible to apply and tobecome a reversible cycle also. The non-dimensional work W * is calculated with the same

procedure as mentioned before and takes the form

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Fig. 4. Characteristics charts for basic cycles: Stirling, Ericsson, Atkinson and Joule.


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W m* ( ) ln= 1 (11)

and the thermal efficiency has the form

th = + +

11

1

( ) ln

( ) lnm

m (12)

Fig. 4 shows the thermal efficiency drawn corresponding to the non-dimensional work. Foran Ericsson cycle, both the constant temperature ratio and constant pressure ratio lines ejectfrom the origin. The constant pressure ratio lines increase with the increase of work ratio upto a certain thermal efficiency. Then, they remain constant and parallel to the work ratio axis.In spite of constant thermal efficiency, increasing the temperature ratio will result in anincrease of the non-dimensional work ratio. For the same pressure and temperature ratios,the Ericsson cycle possesses thermal efficiency and non-dimensional work higher than that

of the Stirling cycle as shown in Fig. 4. Fig. 2(a) demonstrates also that the Carnot cycle willhave a smaller work ratio than that for Stirling or Ericsson cycles. However, the Ericssoncycle will have the largest work.

2.4 The Atkinson cycle

Fig. 1(d) shows also a representation of an Atkinson cycle on p v and T S planes. Itconsists of two isentropic processes, one a constant pressure process and the other a constantvolume process. Therefore, the non-dimensional work W * is

W m*

( )

=

1 1

1

(13)

Also, the thermal efficiency is

th =

11

1

m

( ) (14)

Equation (13) and (14) are plotted in Fig. 4, for variety of pressure and temperature ratios.High constant pressure ratio lines are almost straight-lines which decrease slightly with theincrease of the temperature ratios. The temperature lines start from zero and have a half elliptic shape reaching its maximum with nearly zero work. The line of maximum non-dimensional work is also shown in Fig. 4. It occurs when the thermal efficiency is equal toabout two thirds of its highest efficiency. An Atkinson cycle has higher thermal efficiencythan that of Stirling and Ericsson cycles, but lower non-dimensional work of all. This agreeswell with the cycles representation on T S in Fig. 2(b), where the Atkinson cycle isrepresented by the area 12 A34 A1.

2.5 The Joule cycle

The Joule cycle consists of two isentropic processes and two constant pressure processes.The whole processes are shown in Fig. 1(e) on p v and T S planes. This cycle is some-times referred to as constant pressure cycle. The non-dimensional work W * is equal to

W m m* = + 1 (15)

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Also, the thermal efficiency has the form

3. EFFECTS OF REGENERATION

One way to increase the thermal efficiency is to employ regenerative processes for a givencycle, i.e. storing and recovering heat on the non-isothermal part of the Stirling and Ericsson

cycles or on the isentropic part of the Atkinson and Joule cycles. Ideal regeneration requiresreversible storage and recovery of heat with no net entropy generation, which in turn, impliesa fixed horizontal distance between the regenerative process lines on the T S diagram asshown in Figs 2(a b). Therefore, an ideal regeneration cycle will have a thermal efficiencyequivalent to that of Carnot, in the case of Stirling and Ericsson cycles. However, the work of Stirling and Ericsson cycles will not change, i.e. will be the same as the original cycleThat means both the Stirling and Ericsson regenerative cycles will have efficiencies equal toCarnot cycle efficiency as in equation (8). Thus, their thermal regenerative efficiency takesthe form

th = 11m (16)

Equations (15) and (16) are plotted in Fig. 4, for a variety of pressure and temperature ratios.The Joule characteristic s chart has a similar shape as the Atkinson chart. However, thepressure lines are horizontal straight-lines. For any pressure ratio, the thermal efficiency isconstant. Its value does not depend on the temperature ratio. This is also shown in equation(16). Also the maximum work is achieved with an efficiency equal to about two-thirds thevalue of maximum efficiency. Of course the Joule cycle, as shown in Fig. 4, has the highestthermal efficiency compared to the Stirling, Ericsson, and Atkinson cycles. Also, the Joulecycle has a non-dimensional work higher than an Atkinson cycle but lower than both theStirling and Ericsson cycles. For comparison the four cycles are drawn on a T S diagram in

Fig. 2(b), where all cycles have the same pressure and temperature ratios. In this figure theEricsson cycle has the larger cycle area, i.e. highest work. The Atkinson cycle has thesmallest area, i.e. smaller work. These remarks do agree with the conclusion drawn from themathematical models with the characteristic charts shown in Fig. 4.

thg = 11

(17)

However, in the case of Atkinson and Joule cycles, their thermal regenerative efficienciesare functions of the temperature of state for point 2, as shown in Fig. 2(b). This means thatthe Joule or Atkinson thermal efficiencies depend on the temperature of point 2 at the end of isentropic compression and the temperature of point 4 at the end of isentropic expansion.

3.1 Stirling and Ericsson cycles with regeneration

In Fig. 5, the non-dimensional work and thermal efficiency relationship for Stirling andEricsson cycles with regeneration is shown. This figure illustrates that the regenerativeStirling cycle has attained the same characteristic behaviour as Carnot cycle characteristiccharts shown in Fig. 3. However, the Ericsson cycle shows an asymptotically trend withregeneration. Both Stirling and Ericsson cycles have a thermal efficiency equal to a Carnotcycle as shown in Fig. 5 or the same pressure and temperature ratios.

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Fig. 5. Characteristics charts for regenerative cycles.


3.3 Atkinson and Joule cycles with regeneration

The regenerative Atkinson cycle will have a non-dimensional work equal to that of Atkinson

cycle as in equation (12) but the regenerative thermal efficiency takes the form

th g

m

m

=

11

1 1 1( ) ( ) (18)

For a Joule cycle also, the non-dimensional work is the same as equation (15) but theregenerative thermal efficiency takes the form

th g

m

m

=

11

(19)

In Fig. 5, the relation between the work and the thermal efficiency of Atkinson and Joulecycles is shown. Atkinson and Joule cycles would have a limitation on the regenerativeprocesses. This limitation would be due to the temperature at the end of the isentropicexpansion which should be higher than the temperature at the end of isentropic compression.Of course this causes regeneration existence. Therefore, these two cycles will have a regen-erative efficiency lower or higher than that of Carnot cycle efficiency depending on thetemperature limitation. Also, an important result is that the Atkinson cycle regenerativeefficiency is higher than Carnot cycle equivalent efficiency, for pressure ratios, rangingfrom 7.5 to 10 and temperature ratios, ranging from 6 to 7. For the Joule cycle a regenera-tive process will not be possible for a pressure ratio equal to 30 or over and the limits of temperature ratio ranging from 3 to 7.

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4. EFFECTS OF MULTI-STAGE INTERCOOLING

Multi-stage intercooling consists of a series of small processes in which each is performed intwo stages. One is isentropic compression of the air and the second is cooling the air to itsinitial temperature and so on. Therefore, a compression with an infinite number of these twostages will produce an isothermal process as shown in Fig. 2(b). Thus, the degree of multi-stage intercooling is defined as the ratio between the isothermal part of the process whichtakes place to the whole isothermal compression process. For the Atkinson cycle, it is equalto the isothermal process 11

over isothermal process 12 S and for a Joule cycle, it is theisothermal process 12

over the isothermal process 12 E as shown in Fig. 2(b). When thedegree of multi-stage intercooling is 1, the two processes in each cycle will be equal. TheAtkinson cycle with complete multi-stage intercooling will be represented by 12 S34A1 whilethe Joule cycle will be represented by 12 E34 J1. Carrying out a process with this feature willpossibly reduce the compression work, i.e. the non-dimensional work will increase. How-ever, it will increase the heat added to the cycle and hence will reduce the thermal efficiency.The multi-stage intercooling process for the Atkinson cycle is shown in Fig. 2(b) on a T Sdiagram, in general, i.e. with any degree of regeneration equal to i with notations11

1

34A1. If the degree of multi-stage intercooling is defined as


Where i is the degree of multi-stage intercooling as defined in equation (21). Only twovalues for i are assumed as 0.1 and 1. These two values are chosen to indicate the effect of the multi-stage intercooling on the thermal efficiency and work. An optimized process canbe used to decide the best value for the degree of multi-stage intercooling, i, or theAtkinson cycle corresponding to the temperature ratio, , and the pressure ratio . The multi-stage intercooling thermal efficiency and non-dimensional work are shown in Fig. 6. ForAtkinson cycles, multi-stage intercooling is not useful for a pressure ratio, , less than 10. Itis expected that the isothermal work between two constant pressure lines is less than theisentropic work between the same lines. However, for the Atkinson cycle, the isentropic

work will be between a constant pressure line and a constant volume line. Therefore, it isdetected that the isentropic work is less than the isothermal work between the same two linesonly for small pressure ratios, i.e. less than about 10. For a pressure ratio equal to 10, thenon-dimensional work increases when the temperature ratio, is greater than 5. Thus, forpressure ratios more than 10, the multi-stage intercooling is useful and the non-dimensionalwork increases with the increases of the temperature ratio.

th i i

m i

m

m=

+

11 ln

( ) (22)

Also, the thermal efficiency is given by

W mm

m i

i*

( )ln=

+

11

(21)

The non-dimensional work W * is given by

iS S

S Ss

= 1 1

1 2(20)


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Fig. 6. Characteristics charts for basic cycles with multi-stage intercooling.


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Fig. 6.



W mmm

ii* ( ) ln= +

1 1 (24)


th i i

m i

m

m=

+

1

1

1

ln

( )(25)

where i is the degree of multi-stage intercooling. Also, two values are taken equal to 0.1and 1, as shown in Fig. 6. For the Joule cycle, the increase in the degree of multi-stageintercooling is proportional to the increase in the non-dimensional work. Fig. 6 demonstratesthat the non-dimensional work increases, hence, the multi-stage intercooling thermal effi-ciency decreases. It is generally postulated that the multi-stage intercooling will result indecreasing the work input but that will consequently increase the work output. However, thisdisadvantage will be overcome when a regenerative process is employed as will be shownlater.

4.2 Joule cycle with multi-stage intercooling

The multi-stage intercooling process for a Joule cycle is also shown in Fig. 2(b) on a T Sdiagram, in general, i.e. for any degree of multi-stage intercooling equal to i with notations11

1

34A1. If the degree of multi-stage intercooling is taken as

iS S

S S E

=

1 2

1 2(23)

Then, the complete multi-stage intercooling will be 12 S34J1. The non-dimensional work W *

is given by

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The multi-stage reheat process is also considered as a series of small processes. Each processis performed in two stages. One is isentropic expansion and the second is reheat to thehighest temperature of the cycle and so on. Thus, the multi-stage reheat will produce aprocess of isothermal expansion with an infinite umber of these two stages. Therefore, anexpansion with infinite number of these two stages will produce an isothermal expansionprocess as shown in Fig. 2(b). The degree of multi-stage reheat is defined as the ratiobetween the isothermal part of the process taking place to the whole isothermal process of expansion. Atkinson cycles degree of multi-stage reheat is equal to the isothermal process3

3

over isothermal process 34 A and for Joule cycles the isothermal process 4

4

over theisothermal process 34 J as shown in Fig. 2(b). When the degree of multi-stage reheat is 1, thetwo processes in each cycle will be equal. The Atkinson cycle with complete multi-stagereheat will be represented by 12

A34

E1 and the Joule cycle will also be represented by

12J34E1. Carrying out a process with this feature, will increase the expansion work and thework of compression is unchanged. Then, the non-dimensional work will increase. But theheat added to the cycle is also increased and hence, the thermal efficiency will be reduced.


5. EFFECTS OF MULTI-STAGE REHEAT

5.1 Atkinson cycle with multi-stage reheat

The multi-stage reheat process for an Atkinson cycle is shown in Fig. 2(b) on a T Sdiagram together with other cycles similar to the multi-stage intercooling, with notations12A3 3

3

1, as a general case, and the complete multi-stage reheat cycle will be 12 A34E1. If

the degree of multi-stage reheat is defined as

r S S

S S=

3 33E

(26)

Consequently, the non-dimensional work W * is given by

W m r m r *

( )

( )ln

( )=

+ +

1

11

1 (27)

Also, the multi-stage reheat thermal efficiency is given by

th r r m

r m

=

+

1

1

1

1

1

( )

( )

ln(28)

where r is the degree of multi-stage reheat. Their values are taken equal to 0.1 and 1 asshown in Fig. 7.

5.2 Joule cycle with multi-stage reheat

The multi-stage reheat process for Joule cycle is shown in Fig. 2(b) on a T S diagramtogether with other cycles similar to the multi-stage intercooling, with notations 12 J3 3

3

1,as a general case, and the complete multi-stage reheat cycle will be 12 J34E1. If the degree of multi-stage reheat is taken as

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Fig. 7. Characteristics charts for basic cycles with multi-stage reheat.

r E

S S

S S=

4 33

(29)

and hence the non-dimensional work W * is given by

W mm r m r *

( )ln= + +

1

1 (30)


th =

+

11

1m

mr

r

m

( )

ln(31)

where r is the degree of multi-stage reheat. In Fig. 7, the degree of multi-stage reheat takes

the values of 0.1 and 1. The non-dimensional work increases and the thermal multi-stagereheat efficiency may be decreased or increased, as shown in Fig. 7. The characteristic chartsfor the multi-stage reheat cycles are shown in Fig. 7. For Atkinson multi-stage reheat cyclethe non-dimensional work and the thermal efficiency are increased with a pressure ratio, ,up to 20 and with temperature ratios, , ranging from 3 to 7. However, in the case of theJoule cycle with multi-stage reheat, the non-dimensional work increases and the thermalefficiency decreases.

6. EFFECTS OF COMPOUND MULTI-STAGE INTERCOOLING AND MULTI-STAGE REHEAT

Of course the compound effect of both processes will cause an increase in the non-dimensional work and a decrease in the thermal efficiency of the whole cycle.

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6.1 Atkinson cycle with multi-stage reheat and multi-stage intercooling

This will result in a non-dimensional work as follows


W m mm

r m i

i

r

*( )

( )ln ln=

+ +

11

1

1

(32)

th=

+

11

1

1

1

m r

m

i

r

r

m

m

( )

( )

ln

ln

(33)


where r and i are as above. Their values are taken equal to 0.5 and 1, as shown in Fig. 8.

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where r and i are as above. Their values are taken equal to 0.5 and 1, as shown in Fig. 8.The non-dimensional work is doubled due to the combined effects of multi-stage reheat andmulti-stage intercooling.

th=

+

+

1

11

1

m i

mr

r

r

m

m

( )

( )

ln

ln(35)

Also, the thermal efficiency is equal to

W m mm r m ii

r

* ( )( )

ln ln= + +

11

1 (34)

This will result in

6.2 Joule cycle with multi-stage reheat and multi-stage intercooling

Fig. 8. Characteristics charts for basic cycles with multi-stage reheat and multi-stageintercooling.

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[4] Howell, J. R. and Buckius, R. O. Fundamentals of Engineering Thermodynamics . McGraw-Hill,International Editions, Mechanical Engineering Series, 1992.

[5] Eastop, T. D. and McConkey, A. Apply Thermodynamics for Engineering Technology, Longman,London and New York, Fourth Edition, 1986.

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290321