Optimization of heat engines project report

Department of Mechanical and Indutrial Engineering Technology

Project

OPTIMIZATION OF HEAT ENGINES

By

NGOYI PRESTON BR.

(201103088)

A mini-project report submitted

In partial fulfillment of the requirements for the module

Thermodynamics IV (IMT 441)

FOR THE DEGREE OF BACHELOR OF

MECHANICAL ENGINEERING TECHNOLOGY

Submitted to

Supervisor – Mr. K. BAKAYA

DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING

TECHNOLOGY

FACULTY OF ENGINEERING AND THE BUILT ENVIRONEMNT

UNIVERSITY OF JOHANNESBURG

Submitted: Thursday 13th

May, 2014

Performance of heat engines / Preston Ngoyi / 201103088 Page 2

1 Declaration

I NGOYI Preston BR. hereby declare that this mini-project report is wholly my own work

and has not been submitted anywhere else for academic credit, either by myself or another

person.

I understand what plagiarism implies and declare that this report embodies my own ideas,

words, phrases, arguments, graphics, figures, results and organization except where reference

is explicitly made to another work.

I understand further that any unethical academic behavior, which includes plagiarism, is seen

in a serious light by the University of Johannesburg and is punishable by disciplinary action

as stipulated by the university rules and regulations.

Name: ………………………..……………

Student No: ………………………. …….

Signature: ..................................................

Date: ………..............................................


2 Abstract

Regenerative gas turbine with reheat and intercooling, have high performance expectations

over the simple ideal Brayton cycle. Gas turbines are very sensitive to changes in design

parameters such as the pressure ratio and the components in the turbine. The performance of a

gas turbine for marine vessel operating between an ambient temperature of 300k and 1800k is

evaluated in this project. A single shaft turbine was considered. The study was based on an

ideal Brayton cycle and means of improving the performance of this cycle were added

progressively. Given the limits in turbine materials, a pressure ratio of 14:1 was deduced from

the results. The investigations further revealed that reheat and intercooling, limited to two

stage, were not efficient enough unless combined with regeneration, through this

configuration the gas turbine could achieve a thermal efficiency of 89%.


3 Content

1 Declaration ................................................................................................................................ 2

2 Abstract ...................................................................................................................................... 3

3 Content ........................................................................................................................................ 4

4 Nomenclature .......................................................................................................................... 5

5 List of contents ....................................................................................................................... 5

6 Problem definition ................................................................................................................. 6

7 Background ............................................................................................................................... 6

8 Literature review ................................................................................................................... 6

8.1 Composition of gas turbines ........................................................................................ 6

8.2 Performance of gas turbines ........................................................................................ 6

8.3 Examples of gas turbines for marine vessel ................................................................ 7

8.4 Ways of improving the performance of gas turbines .................................................. 8

9 Approach ................................................................................................................................ 9

10 Assumptions ......................................................................................................................... 9

11 Analysis ................................................................................................................................ 10

11.1 The effect of pressure ratio on the net work of an ideal Brayton cycle. ................ 10

11.2 The effect of irreversibility on the net work of the ideal Brayton cycle. ............... 12

11.3 The effect of heat exchanger effectiveness on the thermal efficiency. .................. 13

11.4 Optimum pressure ratio for intercooling ................................................................ 15

11.5 Effect of multistage compression and expansion ................................................... 17

11.6 Effect of turbine inlet temperature on the net work and thermal efficiency .......... 19

11.7 The effects of improvements to the ideal Brayton Cycle. ..................................... 20

12 Discussion & recommendations .............................................................................. 24

13 Conclusion ........................................................................................................................... 26

14 Appendices ......................................................................................................................... 27

15 References .......................................................................................................................... 28


4 Nomenclature

P : Pressure

T : Temperature

n : Isothermal expansion/compression index

Cpa : specific gas constant at constant pressure

Cpg : Measurement While Drilling

Wnet : Net work

Wc : Compressor work

Wt : Turbine work

Q : Heat supply in combustion chamber or reheater

Hx : Heat exchanger effectiveness

Eff. : Thermal efficiency

5 List of contents

Figure 1: Ideal brayton cycle .................................................................................................... 10

Figure 2: Ideal Brayton cycle with irreversibility .................................................................... 12

Figure 3: Plant diagram of intercooled ideal cycle. ................................................................. 15

Figure 4: T-S diagram of a multistage compression and expansion. ....................................... 17

Table 1: Calculations of net work of ideal brayton cycle ........................................................ 10 Table 2: Net work calculations at different isentropic efficiencies .......................................... 12

Table 3: Calculations of thermal efficiency at various regenerator effectiveness. .................. 14 Table 4: Calculation of optimum intercooling pressure ratio. ................................................. 16 Table 5: Calculations: net work and efficiency of multistage compression and expansion. .. 18

Graph 1: effect of pressure ratio on the net work of an ideal brayton cycle ............................ 11 Graph 2: effect of irreversibilities on net work ........................................................................ 13 Graph 3: Effect of regenerator effectiveness on thermal efficiency. ....................................... 14 Graph 4: Optimum pressure ration for two stage intercooling. ................................................ 16 Graph 5: Effect of multistage compression and expansion on thermal efficiency. .................. 18

Graph 6: Effect of turbine temperature on net work. .............................................................. 19

Graph 7: Effect of turbine temperature on cycle efficiency ..................................................... 20

Graph 8: Effect of turbine temperature on cycle efficiency ..................................................... 23 Graph 9: Effect of improvements of cycle Net work ............................................................... 23


6 Problem definition

Alstom South Africa, a large gas turbine manufacturer, is considering an intercooled, reheat

and regenerative gas turbine for propulsion of a marine combat vessel. The unit will use large

axial compressors and large axial turbine expanders. The unit will be working with

compressor inlet conditions of 300K and 100 Kpa and turbine firing temperature of 1400K.

7 Background

A gas turbine delivers mechanical power. It achieves this by expanding hot gases through

turbine’s blade creating rotational motion of the turbine output shaft. The power generated

can be used by industrial devices, electric power generation, aircraft, marine applications and

more.

A gas turbine works on the Brayton cycle. In this cycle a working fluid, preferably air, is

initially compressed in a compressor. The fluid is then mixed with a fuel and heated into a

combustion chamber. Finally it expands through the turbine.

There are two types of gas turbines, Jet engines gas turbines and industrial gas turbines.

Industrial turbines knew a slow development in their early days because a high initial

compression was required. The first gas turbine was only made in 1905 by the Frenchman

Rateau. Gas turbines for power generation came into operation in 1939 in Switzerland.

Although they low efficiencies, they were still useful because they could start quickly. In the

1980’s gas turbines became more popular as natural gas brought about new fuels.

The first proposition of using gas turbine as jet engines came in 1929 by an English man

named Frank Whittle. His idea could not be developed because of funds. The first actual jet

aircraft was built in 1939 by the German Von Ohain. Over the year following its

development, new research on high temperature materials, new cooling techniques and

aerodynamics improved the efficiency of the jet engine. (aerostudents.com)

8 Literature review

8.1 Composition of gas turbines

Gas turbines are mainly made of three sections: the compressor, the combustion chamber

(CC) and the turbine; the turbine drives the compressor. Axial compressors are often preferred

because of their high flow rates and efficiencies. They are made of multiple stages of rotating

blades and fixed guide vanes which continuously compresses the air as it passes through.

8.2 Performance of gas turbines

The performance of gas turbines is dictated by two main parameters, the pressure ratio and the

turbine inlet temperature. Today cooled gas turbines have gas exiting the combustion chamber


with temperatures between 1500k and 1700k, and through advanced technology turbines

metals can withstand temperatures of 1200k to 1400k. (E.D.Brandt, 1987)

Pressure ratios for industrial turbines today are up to 18:1, in jet propulsion applications they

are up to 30:1. Gas turbines efficiencies can be increased with higher turbine inlet

temperatures. However this temperature is limited by the metallurgical properties of the

turbine blades materials available. Typical turbine temperatures ranges from 1200°C

to1400°C, however blade coating and cooling can allow temperatures as high as 1600°C.

The efficiency of an ideal Brayton cycle is relatively low, around 30 percent. This is due

primarily to the fact that about 55% - 65% of the turbine work is used to drive the

compressor. Moreover a large portion of the heat is rejected into the air during the expansion

process. (wartsila)

Irreversibility, this are the losses of energy during the compression and expansion stages,

affect the efficiency of the gas turbines. Isentropic efficiency is defined as the ratio of the

ideal compression work to the actual compression work for the compression process and for

the expansion process; it is the ratio of the actual expansion work to the ideal expansion work.

8.3 Examples of gas turbines for marine vessel

Most shaft power gas turbine engines including those in marine propulsion are based on

existing jet-engines derivatives. The LM2500 built by General Electric is a derivative of the

aircraft CF6 engine. Similarly the Rolls Royce Avon, the Pratt & Whitney FT-4 and FT-12

engines are designed based on jet-engines. (Harmon, 1990).

GE produces highly efficient marine gas turbines. The LM2500 (appendix 1) is a 16 stage,

18:1 pressure ratio compressor and a two stage air cooled high pressure turbine which drives

the compressor and a six stage low pressure power turbine. It delivers 25 MW of power with a

gas flow of 70.5 kg/sec and exhaust turbine temperature of 566 C; the specific fuel

consumption is 227 g/kw-hr. (General electric).

The LM500 marine gas turbine is a simple cycle, two shaft gas turbine with an

aerodynamically coupled power turbine. It is fitted with a 14.5:1 pressure ratio compressor

with variable guide vanes and stator vanes. Rated at 4.57 MW, the exhaust gas leaves the

turbine at 565 C at a rate of 16.4 kg/s. Specific fuel consumption of 269.5 g/kw-hr. (General

electric).


8.4 Ways of improving the performance of gas turbines

Many ways of improving the performance of gas turbines exist and this include the use of

intercooler between compressors (Intercooling); the use of heat regenerator to collect

turbine’s rejected heat and preheat the air delivered to the CC, this is known as regeneration;

the last way of improving turbine performances is by reheat with multistage turbines

expansions. (wartsila)

Intercooling: The net work output of a gas turbine can be increased by reducing the

compressor work input. This can be accomplished by means of multistage compression with

intercooling. Although compressing the gas reduces the work, a heat transfer rate high enough

to reduce considerably the work is difficult to achieve in practice. A practical approach is to

separate the compression process in stages with heat exchangers, called intercoolers. (Shapiro,

2010) Although the net work is improved with intercooling, the heat to be supplied increased

causing a decrease in thermal efficiency. (Rajput, 1994)

Regeneration: Regeneration reduces the amount of fuel input to the combustion chamber.

The exhaust gas from the turbine carries a large amount of heat with them. Because their

temperatures are well above the ambient temperature, they can be used to heat the air coming

from the compressor in a regenerator thereby reducing the mass fuel supplied in the

combustion chamber therefore increasing the efficiency. Regenerators are rated by their

effectiveness; which is the ratio of the heat gained by the air before entering the CC to the

maximum available heat. (Rajput, 1994).

Reheat: The net work of a gas turbine can be amply improved by expanding the gases in two

stages with a reheater between the two. The high pressure turbine drives the compressor and

the low pressure turbine delivers useful power output. This has the same negative impact on

the thermal efficiency of the turbine because more heat is required in the combustion

chamber. (Rajput, 1994)

Regenerative gas turbines with intercooling and reheat: Reheat and intercooling alone

were proved to reduce the thermal efficiency of the turbine, however the plant performance

can be improved by combining these tow means with regeneration. Several stages in both

compressor and turbine can be used in larger gas turbines. (Merle & Kenneth, 2015)


9 Approach

A research on practical marine gas turbines in use was conducted to understand their power

requirement and performance parameters. Then an investigation was carried out to evaluate

the effect of the different parameters of gas turbines. This was conduct in the following

sequence:

a) The effect of pressure ratio on net work, thus find the pressure ratio yielding to

maximum work.

b) The effect of irreversibility on the net work and thermal efficiency.

c) The effect of intercooling on the ideal Brayton cycle

d) The effect of multistage and compression and expansion on the thermal efficiency.

e) The effect of turbine inlet temperature on the net work and thermal efficiency.

f) The effect of improvements to the ideal cycle.

10 Assumptions

The compression and expansion process are isentropic and follow the relation PVn =

C.s

The index n is constant, for compression n=1.4 and for expansion n=4/3.

The specific heat ratios at constant pressure are taken as constant,

Cpair=1.005KJ/KgK and Cpgas=1.15 KJ/KgK.

The heat transfer to the surrounding is ignored.

There are no pressure drops through the gas turbine

Kinetic and potential effects are negligible.


11 Analysis

11.1 The effect of pressure ratio on the net work of an ideal Brayton cycle.

An ideal Brayton cycle was considered; operating between an ambient temperature of 300k

and turbine maximum temperature of 1800k. with varying values of pressure ratio, the net

work of the gas turbine was calculated and the results plotted into a graph.

Figure 1: Ideal Brayton cycle

Compressor:

Turbine:

Net work:

Table 1: Calculations of net work of ideal Brayton cycle

r T2 T4 Wnet

5 475,146 1203,733 509,686

6 500,553 1150,098 545,832

7 523,092 1106,619 573,181

8 543,434 1070,286 594,519

9 562,033 1039,230 611,542

10 579,209 1012,214 625,348

11 595,199 988,381 636,687

12 610,181 967,113 646,088

13 624,296 947,953 653,937

14 637,656 930,552 660,521

15 650,350 914,639 666,063

16 662,454 900,000 670,734

17 674,028 886,462 674,670

18 685,126 873,885 677,980

19 695,792 862,153 680,754

20 706,064 851,167 683,063

21 715,976 840,848 684,969

22 725,555 831,126 686,522

23 734,829 821,941 687,765

24 743,819 813,242 688,734


Graph 1: effect of pressure ratio on the net work of an ideal Brayton cycle

Graph 1 showed that the net work increased with the pressure ratio until it reached a

maximum value where additional increase in pressure ratio would not change it. From the

calculated results, the pressure ratio yielding to the maximum work is 25.

Increasing the pressure ratio requires higher turbine inlet temperatures. However the extent to

which we can increase the pressure ratio depends on the turbine blades material. (Shapiro,

p.395). Practical gas turbines for marine applications have pressure ratio up to 18:1.

From the graph it was found that the net work increased at a lesser rate between pressure

ratios of 10:1 to 14:1. 14:1 was therefore found reasonable for this design.

The pressure ratio resulting in maximum work could be derived mathematically by

differentiating the net work with respect to the pressure ratio and equating the result to zero as

follow:

This equation showed how the pressure ratio providing the maximum net work is limited by

the turbine inlet temperature as well as the atmospheric conditions.

500

550

600

650

700

750

800

850

5 10 15 20 25 30

Ne

t W

ork

Pressure ratio

Wnet/pressure ratio

Wnet

Log. (Wnet)


11.2 The effect of irreversibility on the net work of the ideal Brayton cycle.

Because of friction in the turbine and the compressor, the temperature of the working fluid

would increase at the exit of both units.

Figure 2: Ideal Brayton cycle with irreversibility

Compressor analysis:

Turbine analysis:

r Wnet 60% Wnet 70% Wnet 80% Wnet 90% Wnet 100%

5 118,055188 228,535852 328,53904 421,557243 509,685957

6 112,506168 235,234445 345,965347 448,697999 545,831876

7 104,754499 237,876011 357,651858 468,530595 573,181355

8 95,750099 237,917489 365,522297 483,418717 594,519266

9 86,0253534 236,214649 370,728745 494,792707 611,541575

10 75,8964653 233,302612 374,006059 503,574372 625,348092

11 65,5592629 229,53231 375,846145 510,387171 636,687233

12 55,1387249 225,142644 376,591086 515,66921 646,088112

13 44,7162806 220,3012 376,486249 519,738052 653,936583

14 34,3456479 215,128447 375,712186 522,829884 660,521354

15 24,0624149 209,712752 374,404635 525,124216 666,063184

16 13,8900388 204,120033 372,667529 526,760026 670,734023

17 3,84371345 198,400161 370,581706 527,846648 674,669969

18 -6,067076 192,591312 368,210904 528,471299 677,980255

19 -15,8368304 186,722999 365,605986 528,704411 680,753643

20 -25,4628533 180,818221 362,807962 528,603482 683,063046

21 -34,9444265 174,89502 359,850215 528,215909 684,968951

22 -44,2822281 168,967623 356,76014 527,581102 686,521974

23 -53,4779161 163,047284 353,560385 526,732088 687,764811

24 -62,5338301 157,142932 350,269802 525,696743 688,733735

25 -71,4527736 151,261653 346,90417 524,498746 689,459765 Table 2: Net work calculations at different isentropic efficiencies


Graph 2: effect of irreversibility on net work

Graph 2 revealed that for a given pressure ratio, the net work generated with lower isentropic

efficiencies. Each trends showed a peak in network followed by a decrease. For units

operating at higher isentropic efficiencies, the peak in net work occurred at higher pressure

ratio. By comparing the net work of the ideal cycle, proved that irreversibility within the

system significantly reduces the net work. High turbine and compressor isentropic efficiencies

would be recommended for better net work

11.3 The effect of heat exchanger effectiveness on the thermal efficiency.

Here the exhaust gas from turbine was used in a regenerator to preheat the air entering the

combustion chamber. Considering irreversibility, the effect of varying the regenerator

effectiveness on the thermal efficiency was investigated.

The compressor and turbine analysis are done in the same way as part 7.2. the isentropic and

heat exchanger effectiveness were varied from 0.6 to 1 with increment of 1.

Heat exchanger analysis:

Air inlet temperature to the CC:

The Heat added

0,6

0,7

0,8

0,9

1

-200

-100

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30

Ne

t w

ork

pressure ratio

Wnet / pressure ratio

60% 70% 80% 90% 100%


r T5 0,6 T5 0,7 T5 0,8 T5 0,9 T5 1 T.eff 0,6 T.eff 0,7 T.eff 0,8 T.eff 0,9 T.eff 1

5 1102,11 1132,89 1162,18 1186,48 1203,73 14,710 29,789 44,791 59,749 74,330

6 1099,74 1117,50 1134,20 1145,86 1150,10 13,971 29,971 45,185 59,647 73,032

7 1099,11 1105,85 1112,01 1113,15 1106,62 12,996 29,799 45,204 59,317 71,882

8 1099,59 1096,77 1093,84 1085,98 1070,29 11,888 29,419 45,011 58,873 70,846

9 1100,81 1089,52 1078,62 1062,89 1039,23 10,699 28,911 44,688 58,371 69,900

10 1102,54 1083,65 1065,62 1042,92 1012,21 9,462 28,320 44,285 57,839 69,027

11 1104,62 1078,82 1054,36 1025,39 988,38 8,198 27,676 43,831 57,295 68,214

12 1106,95 1074,82 1044,50 1009,83 967,11 6,918 26,997 43,345 56,748 67,454

13 1109,46 1071,48 1035,76 995,87 947,95 5,631 26,295 42,837 56,203 66,738

14 1112,10 1068,68 1027,97 983,26 930,55 4,342 25,580 42,318 55,665 66,061

15 1114,84 1066,32 1020,96 971,79 914,64 3,054 24,855 41,791 55,134 65,418

16 1117,64 1064,34 1014,61 961,27 900,00 1,770 24,127 41,261 54,613 64,805

17 1120,48 1062,66 1008,84 951,59 886,46 0,492 23,398 40,731 54,101 64,220

18 1123,35 1061,26 1003,57 942,64 873,89 -0,780 22,670 40,202 53,599 63,658

19 1126,24 1060,08 998,73 934,32 862,15 -2,044 21,944 39,677 53,108 63,119

20 1129,13 1059,10 994,26 926,56 851,17 -3,300 21,222 39,155 52,626 62,600

21 1132,02 1058,29 990,14 919,31 840,85 -4,549 20,504 38,638 52,154 62,099

22 1134,91 1057,63 986,31 912,50 831,13 -5,790 19,792 38,126 51,692 61,615

23 1137,78 1057,11 982,75 906,09 821,94 -7,022 19,085 37,619 51,238 61,147

24 1140,65 1056,70 979,43 900,04 813,24 -8,247 18,384 37,118 50,794 60,694

25 1143,49 1056,39 976,33 894,32 804,98 -9,464 17,688 36,623 50,358 60,253Table 3: Calculations of thermal efficiency at various regenerator effectiveness.

Graph 3: Effect of regenerator effectiveness on thermal efficiency.

When a heat exchanger is used, the graphs showed that the thermal efficiency decreased as

the pressure ratio increased. It was also observed that for a given pressure ratio, higher

effectiveness values gave higher thermal efficiency. For a given regenerator effectiveness and

-20

-10

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30

the

rmal

eff

.

pressure ratio

Thermal eff. Vs pressure ratio

The.eff 60% The.eff 70% The.eff 80% The.eff 90% The.eff 100%


isentropic efficiency, the graph showed that the thermal efficiency decreased as the pressure

ratio increased.

11.4 Optimum pressure ratio for intercooling

The analysis comprised an ideal two stage compression with intercooling. It was intended to

find the optimum pressure ratio for intercooling.

Figure 3: Plant diagram of intercooled ideal cycle.

Turbine analysis:

From section 7.1, an overall pressure ratio of 14 was recommended. In this analysis P4/P1 is

the overall pressure ratio.

Overall pressure ratio

Intermediate pressure ratio (1st stage):

2nd

stage pressure ratio:


rp P2/P1 P4/P3 Wc1 WC2 WC1+WC2

5 2,236 6,26099 77,9374 207,713 285,65059

6 2,449 5,71548 87,9501 194,621 282,57152

7 2,646 5,2915 96,6215 183,816 280,437

8 2,828 4,94975 104,289 174,645 278,93433

9 3 4,66667 111,175 166,701 277,8753

10 3,162 4,42719 117,433 159,706 277,13929

11 3,317 4,22116 123,176 153,469 276,64528

12 3,464 4,04145 128,488 147,849 276,33667

13 3,606 3,8829 133,433 142,74 276,17277

14 3,742 3,74166 138,062 138,062 276,1235

15 3,873 3,61478 142,416 133,751 276,1662

16 4 3,5 146,527 129,756 276,28346

17 4,123 3,3955 150,424 126,037 276,46168

18 4,243 3,29983 154,13 122,561 276,69014

19 4,359 3,21182 157,662 119,298 276,96022

20 4,472 3,1305 161,039 116,226 277,26496

21 4,583 3,05505 164,275 113,324 277,5987

22 4,69 2,98481 167,38 110,576 277,95675

23 4,796 2,9192 170,367 107,968 278,33524

24 4,899 2,85774 173,245 105,486 278,73091

25 5 2,8 176,022 103,119 279,14106 Table 4: Calculation of optimum intercooling pressure ratio.

Graph 4: Optimum pressure ration for two stage intercooling.

3,605551275; 276,1727657

274

276

278

280

282

284

286

288

0 1 2 3 4 5 6

WC

1+W

C2

P2/P1

P2/P1 vs WC's

Total compressor work

Minimum compressor work obtained when rpi is the square root of the overall pressure ratio.


Graph 4 above shows the variation of compressor work with the intermediate pressure ratio. It

revealed that the compressor work increases with the intermediate pressure ratio. The least

amount of compressor work was found to be at the square root of the overall pressure ratio.

The best intermediate pressure is the one that gives equal pressure ratio in each stage of

compression. From the calculations table, we can see that,

when the overall pressure

ratio is 14 (i.e rpi = 3.742). When performing compression in two stages the work required to

drive the compressor is significantly reduced. However the amount of heat to be supplied

increases, reducing the thermal efficiency (McKonkey, 1993).

11.5 Effect of multistage compression and expansion

Figure 4: T-S diagram of a multistage compression and expansion.

The T-S diagram of figure 4 was used to simplify the analysis.

Compressor analysis:

Pressure ratio

Compressor work

Turbine analysis:

Pressure ratio

Turbine work

CC analysis:

The net work and thermal efficiency as before.


N rpi Tcomp in Tc 2 Wc Tturbine in Tturb out Wturb Qin Wnet Eff

2 2,236 300 377,550 155,875 1800 1471,978 754,451 754,451 598,576 79,339

4 1,495 300 336,549 146,925 1800 1627,747 792,364 792,364 645,439 81,457

6 1,308 300 323,896 144,093 1800 1683,251 805,571 805,571 661,479 82,113

8 1,223 300 317,749 142,704 1800 1711,708 812,286 812,286 669,582 82,432

10 1,175 300 314,117 141,879 1800 1729,013 816,351 816,351 674,472 82,620

12 1,144 300 311,719 141,332 1800 1740,647 819,076 819,076 677,743 82,745

14 1,122 300 310,017 140,944 1800 1749,004 821,029 821,029 680,086 82,833

16 1,106 300 308,747 140,653 1800 1755,299 822,499 822,499 681,846 82,899

18 1,094 300 307,763 140,428 1800 1760,210 823,644 823,644 683,217 82,950

20 1,084 300 306,977 140,248 1800 1764,149 824,562 824,562 684,314 82,991

22 1,076 300 306,337 140,101 1800 1767,379 825,314 825,314 685,213 83,025 Table 5: Calculations for net work and efficiency of multistage compression and expansion.

Graph 5: Effect of multistage compression and expansion on thermal efficiency.

Graph 5 illustrates the effect of having a heat engine with multiple stage compression and

expansion. It was found that the thermal efficiency increased, with the number of stages, to a

maximum fixed value of 83% with 22 stages. The minimum efficiency achieved was 79%

with 2 stages. Going from 2 to 22 stages only improved the efficiency by 4%, the use of more

than 2 stages would not therefore be justified economically.

As the number of stages approach infinity, the contribution each compressor and turbine

became less and less. The resulting T-S diagram would be similar to the Ericsson cycle. The

efficiency of the Ericsson approaches the Rankine cycle and can be computed as follow:

Computing this with Tmax=1800 k and Tmin= 300 K, resulted in an Ericsson efficiency of

83.3%. This value corresponded to the maximum thermal efficiency on graph 4.

79

80

81

82

83

84

0 5 10 15 20 25

Eff

N

Number of stages vs Thermal Efficiency

Thermal efficiency


11.6 Effect of turbine inlet temperature on the net work and thermal efficiency

The T-S diagram used to analyze this part is the same as the one in part 7.5, except that here

regeneration was not considered, an ideal Brayton cycle was assumed. Two stages were

proven reasonably economic and therefore were used. The combustion and turbine analysis

were the same as 7.5, only the heat supplied was analyzed since the exhaust gases are no

longer used to pre-heat the air, an increase in heat supplied was expected.

CC analysis:

Graph 6: Effect of turbine temperature on net work.

Graph 6 described the relationship between the net work and turbine inlet temperatures at

different pressure ratio. It showed that, the net work increases with the pressure ratio. For a

given pressure ratio, increasing the inlet temperature from 1200K to 1800K resulted in a

significant increase in net work.

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30

Wn

et

Pressure ratio

Net work vs Pressure ratio

1800

1700

1600

1500

1400

1300

1200


Graph 7: Effect of turbine temperature on cycle efficiency

Graph 5(b) shows the relation between pressure ratio and the cycle efficiency of the plant at

different turbine inlet temperatures. It can be seen that the efficiency increases rapidly at

lower pressure ratio. The inlet temperature had an opposite effect on the efficiency of the

cycle as compared to the net work. The graph illustrated that the efficiency decreased as the

temperature increased.

11.7 The effects of improvements to the ideal Brayton Cycle.

The effect of improving the ideal Brayton cycle was investigated in this part. For each

configuration, the net work and cycle efficiency was calculated and graphs showing the

variations of net work and thermal efficiencies against the pressure ratio were plotted.

An ideal cycle was first considered; then reheat was added; then intercooling alone (without

reheat); the regeneration and last we combined reheat, intercooling and regenerations.

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30

Effi

cie

ncy

pressure ratio

Thermal Eff. Vs pressure ratio

1800 1700 1600 1500 1400 1300 1300


Below are tables obtained from the calculations:

r rpi Wc Wt Net work Qin Th. Eff.

5 2,236 1,552 685,708 509,686 1523,582 33,4531307

6 2,449 1,778 747,388 545,832 1494,364 36,5260347

7 2,646 1,977 797,389 573,181 1468,445 39,0332315

8 2,828 2,158 839,171 594,519 1445,051 41,1417591

9 3,000 2,322 874,885 611,542 1423,662 42,9555367

10 3,162 2,475 905,953 625,348 1403,909 44,5433404

11 3,317 2,616 933,362 636,687 1385,521 45,9528971

12 3,464 2,749 957,820 646,088 1368,292 47,2185936

13 3,606 2,874 979,854 653,937 1352,059 48,365972

14 3,742 2,993 999,866 660,521 1336,696 49,4144904

15 3,873 3,105 1018,165 666,063 1322,097 50,3792908

16 4,000 3,213 1035,000 670,734 1308,178 51,2723729

17 4,123 3,315 1050,568 674,670 1294,868 52,1033969

18 4,243 3,413 1065,032 677,980 1282,105 52,8802471

19 4,359 3,508 1078,525 680,754 1269,839 53,6094364

20 4,472 3,599 1091,157 683,063 1258,026 54,2964034

21 4,583 3,687 1103,024 684,969 1246,628 54,9457329

22 4,690 3,772 1114,205 686,522 1235,611 55,5613237

23 4,796 3,854 1124,768 687,765 1224,947 56,1465171

24 4,899 3,934 1134,772 688,734 1214,608 56,7041969

ideal cycle

Wc Wt Wnet Qin Th. Eff

176,022 754,451 578,429 1900,80779 30,4307198

201,556 830,736 629,180 1909,73182 32,9459845

224,207 893,891 669,684 1915,39008 34,963318

244,651 947,624 702,972 1918,86247 36,6348414

263,343 994,280 730,937 1920,80195 38,0537355

280,605 1035,438 754,833 1921,62827 39,2808859

296,675 1072,206 775,531 1921,6242 40,3580889

311,732 1105,391 793,659 1920,98743 41,3151785

325,918 1135,602 809,684 1919,86036 42,1741337

339,344 1163,305 823,961 1918,34818 42,9515769

352,102 1188,866 836,764 1916,53017 43,6603586

364,266 1212,578 848,312 1914,4672 44,3106024

375,898 1234,678 858,780 1912,20669 44,9104139

387,052 1255,362 868,311 1909,78607 45,4663753

397,771 1274,792 877,021 1907,23526 45,9838994

408,094 1293,104 885,010 1904,57836 46,467486

418,055 1310,414 892,358 1901,83501 46,9209136

427,683 1326,820 899,137 1899,02131 47,3473832

437,003 1342,408 905,405 1896,15058 47,7496281

446,038 1357,252 911,213 1893,23386 48,1299995

Reheat


Wc Wt Wnet Qin Th. Eff

155,874867 685,707569 529,832701 1635,81786 32,3894679

175,90013 747,387774 571,487644 1624,36062 35,1823133

193,242956 797,388523 604,145567 1614,43811 37,4214139

208,577816 839,170636 630,59282 1605,66443 39,2730141

222,349078 874,884943 652,535864 1597,78535 40,8400204

234,865783 905,953457 671,087674 1590,62405 42,1902128

246,351965 933,361992 687,010028 1584,05236 43,3704116

256,975466 957,820121 700,844655 1577,97424 44,4142014

266,86544 979,854397 712,988957 1572,31579 45,3464221

276,123498 999,865571 723,742073 1567,01889 46,1859187

284,83109 1018,16521 733,334121 1562,03694 46,947297

293,054556 1035 741,945444 1557,33197 47,6420865

300,848683 1050,56834 749,719662 1552,87264 48,2795331

308,259262 1065,03203 756,77277 1548,63276 48,8671549

315,32498 1078,5246 763,199615 1544,59019 49,4111398

322,078825 1091,15743 769,07861 1540,72605 49,9166359

328,549169 1103,02439 774,475217 1537,02411 50,3879681

334,760598 1114,20517 779,444576 1533,4703 50,8288014

340,734562 1124,76806 784,033502 1530,05237 51,242266

346,489894 1134,77193 788,282032 1526,75951 51,6310542

352,043224 1144,26786 792,224633 1523,58223 51,9974974

Intercooling

Wc Wt Wnet T3 inlet CC Qin Th. Eff

176,021612 685,707569 509,685957 1021,58588 895,176235 56,9369401

201,555898 747,387774 545,831876 987,711474 934,131805 58,4319978

224,207169 797,388523 573,181355 960,736934 965,152526 59,3876449

244,65137 839,170636 594,519266 938,573352 990,640645 60,0136154

263,343367 874,884943 611,541575 919,931164 1012,07916 60,4242829

280,605365 905,953457 625,348092 903,963119 1030,44241 60,6873401

296,67476 933,361992 636,687233 890,085349 1046,40185 60,8453849

311,732008 957,820121 646,088112 877,87998 1060,43802 60,926532

325,917815 979,854397 653,936583 867,038607 1072,9056 60,9500576

339,344217 999,865571 660,521354 857,327742 1084,0731 60,9295957

352,102027 1018,16521 666,063184 848,566779 1094,1482 60,8750425

364,265977 1035 670,734023 840,613427 1103,29456 60,7937398

375,898376 1050,56834 674,669969 833,35379 1111,64314 60,6912366

387,051777 1065,03203 677,980255 826,695428 1119,30026 60,5717948

397,770953 1078,5246 680,753643 820,562392 1126,35325 60,4387339

408,094388 1091,15743 683,063046 814,891603 1132,87466 60,2946709

418,055435 1103,02439 684,968951 809,630159 1138,92532 60,1416916

427,683199 1114,20517 686,521974 804,733307 1144,5567 59,9814738

437,003253 1124,76806 687,764811 800,162887 1149,81268 59,8153789

446,038191 1134,77193 688,733735 795,886126 1154,73095 59,64452

454,808093 1144,26786 689,459765 791,874695 1159,3441 59,4698127

Regeneration


Graph 8: Effect of turbine temperature on cycle efficiency

Graph 8 showed the effect that the improvements made on the ideal Brayton cycle had on the

efficiency. It revealed that when reheat and intercooling were added independently to the

ideal cycle, the thermal efficiency of the plant for both cases were less than the efficiency of

the ideal cycle. Adding regeneration alone to the ideal cycle, proved to be more efficient then

the ideal cycle. The combined effect of reheat, regeneration and intercooling showed a major

improvement on the thermal efficiency of the plant, with efficiency almost double to that of

the ideal cycle at low pressure ratio.

Graph 9: Effect of improvements of cycle Net work

Graph 9 showed how the net work of the cycle varied when making improvement to the ideal

Brayton cycle. Regeneration had no effect on the net work, from the graph the curves for the

ideal cycle and the regeneration followed the same path. Adding intercooling independently

showed a slight increase in net work noticeable only at higher pressure ratio. Reheat alone had

a better net work than intercooling. The combined effect of all the improvement methods

above significantly improved the net work of the plant by over 150%.

0

20

40

60

80

100

0 5 10 15 20 25 30

Eff

rp

Efficiency vs Pressure ratio

ideal brayton Reheat Intercooloing Regeneration Regen-Inter-Reheat

0

500

1000

1500

2000

2500

0 1 2 3 4 5 6

Wn

et

rp

Net Work vs pressure ratio

Ideal cycle Reheat Intercooling

Regeneration Regen-Intercooling-reheat


12 Discussion & recommendations

11.1 The effect of pressure ratio on the net work of an ideal Brayton cycle

It was proven that the net work increased with pressure ratio however they are thermal and

economic limitations to the extent to which the pressure ratio can be increased. Higher

pressure ratio involves higher firing temperatures and bigger equipments size. By

calculations, the optimum pressure ratio, given the atmospheric and firing temperatures, was

found to be 23. However as mentioned before, today’s available turbines have pressure ratios

up to 18:1, because of these reasons the recommended pressure ratio was 14:1. For an ideal

cycle 18:1 yielded to a compressor work of 339 kj/kgk, a net work of 660.5 kj/kgk and

thermal efficiency of 49%.

12.2 The effect of irreversibility on the net work and thermal efficiency.

Irreversibility increased the compressor work and had an opposite effect on the turbine, which

consequently reduces the net work. For the recommended pressure ratio of 14:1, it was found

that the net work of the ideal cycle reduced to 522.3 kj/kgk with 90%, 375.7 kj/kgk with 80%,

210 kj/kgk with 70% and 34.4 kj/kgk with 60% isentropic efficiency. Since irreversibility

cannot be avoided, it would be suitable to seek for a compressor and turbine with the highest

possible isentropic efficiency preferably equal or greater to 90%.

12.3 The effect of heat exchanger effectiveness thermal efficiency.

Using exhaust gases from the turbine reduced the amount of fuel to be supplied to the CC,

giving an economical advantage to the plant. It would be ideal that the air enters the CC with

the exhaust gas temperature (Hx effectiveness of 1) however losses occur during the transfer

of heat. (Rajput, 1994).

The thermal efficiency decreased with increase of pressure ratio for a given regenerator

effectiveness. This can be explained by the fact that as the pressure ratio increases the

temperatures of the gas leaving the turbine decreases which implies less energy to be transfer

in the heat exchanger (decrease in the temperature of the air entering the CC) leading to more

fuel required to be burnt therefore reducing the efficiency of the cycle.

Regeneration should only be considered if the gas leaving the turbine has a higher

temperature than the air leaving the compressor; otherwise it will have a negative impact on

the plant. In practice regenerator effectiveness ranges from 60%-80%, going higher than that

would required an increase in heat transfer area (Bigger regenerator). (Shapiro, 2010, p. 401)

Cost wise going for bigger regenerator might cancel the saving made in fuel.

Because of the cost involved and engineering facts mentioned above, 75% regenerator

effectiveness was recommended for this design.


12.4 The optimum pressure ratio for intercooling.

The condition for minimum compressor work was that the intercooled pressure be the square

root of the overall pressure ratio. This assumption was validated in section 7.4, where the

graph revealed an inverse parabola with minimum work at the square root of the overall

pressure ratio.

In order to achieve this condition, sufficient cooling water has to be provided continuously to

the intercooler and additional means to closely monitor the temperatures have to be included

in the design.

12.5 The effect of multistage compression and expansion.

Multistage compression and expansion with regeneration allowed the turbine to reach a

thermal efficiency of 83%, when an infinite number of stages were used. However the reason

for having multiple stages of compression and turbine cannot be justified economically as the

increase the increase in efficiency was not considerable. It was shown that going from two

stages to twenty two stages only increased the efficiency by 4% (from 79% to 83%). A

minimum of two stages was recommended if multistage compression and expansion was to be

considered.

12.6 The effect of inlet temperature

The investigations revealed that the net work of the ideal cycle increased with the turbine inlet

turbine temperature meanwhile the efficiency was found to be decreasing. The selection of the

turbine should therefore be dictated on what the plant would want to achieve, high efficiency

or high net work.

High efficiency, Low net work

Applying this approach implies going for low turbine firing temperature. The amount of heat

per unit mass of fuel is reduced resulting in high efficiency. In the event where higher net

work would be required, the mass of fuel supplied have to be increased to reach that since the

power generated is the product of the mass of fuel to the net work. This in turn would imply

more cost in fuel an impact to the environment.

Pros.: Low cost turbine, high eff, reduced size.

Cons: Les power generated, high fuel cost, impact on the environment.

High net work, low efficiency

Aiming for high net work, would require higher temperature subsequently a more expensive

turbine. However the size of the turbine allows it to produce a considerable amount of power

with less cost related to fuel consumption. For marine vessel, according to General Electric,

this approach is more favorable because they require a lot of power to be propelled. (General

electric, 2015).


Pros: High power delivery, less fuel related cost.

Cons: Size, expensive turbine.

12.7 The effect of improvements to the ideal Brayton cycle.

With the recommended pressure ratio of 14:1, the ideal cycle had an efficiency of 49% and a

net work of 660.5 kj/kgk. Improving with reheat and intercooling applied independently

decreased the efficiency to 42.9% and 46.1% respectively. On the other hand the net work

showed an improvement to 824 kj/kgk and 723.7 kj/kgk respectively for reheat and

intercooling.

In intercooling, it was discussed previously in section 7.4 that performing the compression in

two stages with equal pressure ratios reduced to input work to the compressor thus increasing

the net work. In reheat the increase in net work was attributed to the fact that the gas were

allowed to expand twice, in a high pressure turbine and a low pressure turbine creating more

turbine work.

The performances read from the graphs when regeneration was added to the ideal cycle

showed no improvement on the net work and a major increase in cycle efficiency.

Regeneration reduces the amount of heat to be supplied in the combustion chamber buy using

the exhaust gas from the turbine after this last had completed its work. Applying this add an

additional cost of installing a regenerator however cuts down the fuel cost and limits the fuel

emission in the atmosphere.

Combining the effect of an intercooler, a reheater and a regenerator showed significant

increase in both net work and thermal efficiency. With an efficiency of 89% and net work of

1723 kj/kgk this was proven to be the most effective way of improvement by far. Appendix 2

showed tables of fuel consumption for different improvement methods for different power

output requirements.

13 Conclusion

The aim of this project was to investigate the performance of the different units of a

regenerative ideal cycle with reheat and intercooling. The main performance parameters used

to evaluate these where, the pressure ratio, the net work and thermal efficiency. It was found

that the net work of a gas turbine increased with pressure ratio. For this design a pressure ratio

of 14:1 was found acceptable given the actual practical gas turbine for marine vessels.

The effect of irreversibility if highly pronounced (isentropic efficiency of 60%) in the

compressor and turbine reduced their performance by 95%. Turbines with isentropic

efficiency higher than 90% should be considered for better performance.

A minimum of two stage compressor and turbine was recommended; however reheat and

intercooling could only be considered if they were combined with regeneration. This

configuration would result in a thermal efficiency of 89,8 % and a net work of 1723,6 kj/kg.k.


14 Appendices

Appendix 1: Fuel consumption based on the current design for different power output need.

Improvement Ideal Reheat Intercooler Regenerative Combined effect

Thermal effi.% 49,9 42,9 46,1 61,89 89,8

Net work Kj/kg/k 620,51 823,9 723,74 660,5 1723,6

Mass of fuel kg/s 96,69 72,82 82,90 90,84 34,81


Thermal effi.% 49,9 42,9 46,1 61,89 89,8

Net work Kj/kg/k 620,51 823,9 723,74 660,5 1723,6

Mass of fuel kg/s 48,35 36,41 41,45 45,42 17,41


Thermal effi.% 49,9 42,9 46,1 61,89 89,8

Net work Kj/kg/k 620,51 823,9 723,74 660,5 1723,6

Mass of fuel kg/s 16,12 12,14 13,82 15,14 5,80

Lowest Highest

Mass fuel comsumption for a 60 MW output




15 References

1. aerostudents.com. (n.d.). Gas Turbines. Retrieved 05 12, 2015, from www.aerostudents.com:

http://www.aerostudents.com/files/gasTurbines/gasTurbinesFullVersion.pdf

2. E.D.Brandt. (1987). Heavy duty turbopower. Mechanica engineering magazine , 28-36.

3. General electric. (n.d.). GE LM2500. Retrieved 04 13, 2015, from www.ge.com:

http://www.geaviation.com/engines/docs/marine/datasheet-lm2500.pdf

4. General electric. (2015, 04 17). Marine Gas Turbine. Retrieved from www.geaviation.com:

http://www.geaviation.com/engines/docs/marine/datasheet-4.5mw.pdf

5. McKonkey, T. E. (1993). Applied thermodynamics for technologists. Delhi: Pearson

education.

6. Merle, C. P., & Kenneth, A. P. (2015). Thermodynamics for engineers. Stamford: Timothy L.

Anderson.

7. Rajput, R. K. (1994). Engineering thermodynamics. LONDON: JONES AND BARTLETT

PUBLISHERS.

8. Shapiro, H. N. (2010). Fundamentas of engineering thermodynamics. New Jersey: Jonn wiley

& sons.

9. wartsilaGas Turbine for Power Generation: Introduction