Design of a Reaction Steam Turbine

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Design of a Reaction Steam Turbine

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DESIGN

OP A REACTION STEAK TURBINE

THESIS Submitted in Partial Fulfilment of the requirements for the degree of MASTER OF MECHANICAL ENGINEERING at the POLYTECHNIC INSTITUTE OF BROOKLYN by Abdul Qayyum Sept.1950

Approved:

esis Adviaer

Head of Den^tment

ProQuest Number: 27591624

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 27591624 Published by ProQuest LLO (2019). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLO. ProQuest LLO. 789 East Eisenhower Parkway P.Q. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

VITA The autnor was born in Kotli Loharan, West Punjab, Pakistan on Dec^nber 15th,1926. He went to school in Nairobi, Kenya Colony, British Bast Africa, completing the London Matriculation deamination in July, 1942 and the Senior Cambridge in December of the same year* He joined the University of Punjab at Lahore (Pakistan) in 1943 and took his B.A. degree in June,1946. The academic year of 1946-47 was spent in graduate work in Physics at the Muslim University of Aligarh,U.P.(India). In August 1947f to pursue higher technical learning,the author travelled to the United States and entered the University of Utah, Salt Lake City completing the requirements for B.S.M.E. in June, 1949.

Since then he has been in the Polytechnic Institute

of Brooklyn and this present thesis represents, in part, his efforts towards Master *s Degree in Mechanical Engineering at the Polytechnic Institute of Brooklyn.

(i )

AGKNGfLEDGMMT The author expresses his sincerest appreciation to Professor Edwin F. Church Jr. for his advice and encouragement throughout the study and regards it with great pride to have worked under his distinguished guidance but for which the pro­ gress of the thesis would have been greatly impeded.

(Ü )

ABSTRACT The design of the 7500 kw ( net Output ) Reaction Turbine the first stage being a two-row velocity stage, was undertaken in parallel with an equivalent Impulse Turbine, which was designed in the course ” Steam Turbines” at Polytechnic Institute of Brooklyn, given by Professor Edwin F. Church in Fall 1949. This parallel study revealed that whereas ninteen stages were necessary for the Impulse Turbine, the Reaction Turbine, be­ cause of comparatively lesser enthalpy drop per stage , required twenty-four individual stages under similiar conditions.

This to­

gether with the apurent higher stage efficiency of the Reaction Turbine resulted in a higher over-all turbine efficiency or engine efficiency.

In consequence a less volume of steam under the same

conditions was required thus resu Iting in a more economic opera­ tion of the Reaction Turbine, and hence justifying the initial greater cost of the Reaction Turbine because of its more numerous stages.

To summarize then Reaction Turbine offers an apparently

distinct advantage over the Impulse Turbine.

Ahmed, Mukhtar , thesis M lo43 , 1950, Spicer Library, Polytechnic Institute of Brooklyn. ( iii )

TABLE OF CONTENTS

I . AGKNCMLEDGEHjENTS II . ABSTRACT i n . SYMBOLS

..........................

ii

.................................... iii ...............

IV . REACTION TURBINE........ ...................... V . OBSERVATIONS.........................

vii 1 5

VI . PROCEDURE IN DESIGN OF REACTION TURBINE.........

S

V H ♦ SAMPLE CALCULATIONS OFINDIVIDUAL STAGES.........

14

VIII # APPENDIX

...................................

IX . BIBLIOGRAPHY.................................

( iv )

92 100

TABLE OF FIGURES AND GRAPHS Page I .

Velocity Diagram ,Stage Z ....................

II . Velocity Diagram, Stage Y

......

19

III . Velocity Diagram , Stage X .................. IV . VelocityDiagram , TwoGrow velocity Stage V .

23

......

27

Velocity Diagram ,Stage 2.,...................

34

VI . Velocity Diagram ,Stage 3 ...................... VII * Rotor Skeleton

36

........ ......................

¥111 • Velocity Diagram, Stage 4

•• 40

IX . Velocity Diagram, Stage 5 ...................... X

15

..Velocity Diagram, Stage 6 ......

XI . Velocity Diagram, Stage 7 ............... XII . Velocity Diagram, Stage 8

42 44 47

......

49

XIII . Velocity Diagram, Stage 9 ..........

52

XIV . Velocity Diagram, Stage 1 0 ..................... XV ..Velocity Diagram, Stage 11 XVI . Velocity Diagram, Stage 12 XVII . Velocity Diagram, Stage 13

..................... ............ .....

XVIII . Velocity Diagram, Stage 1 4 .......... XIX . Velocity Diagram, Stage 1 5 ................... XX . Velocity Diagram, Stage 16 XXI . Velocity Diagram, Stage 17

................... ..................

XXII . Velocity Diagram, Stage 1 8 ................ XXIII . Velocity Diagram, Stage 1 9 .....................

( V)

54 56 59 6l 63 65 68 70 72 75

TABLE OF FIGURES AND GRAPHS Page XXIV

♦ VelocityDiagram, Stage20

XXV

# VelocityDiagram, Stage21

XXVI

.VelocityDiagram, Stage22

XXVII

........

77

.............. ..............

.Ehergy Distribution , Table N o . l .............

80 83 84

XXVIII . Velocity Diagrams data. Table No.2 .............. 88 XXIX • Internal Work Done and Stage Efficiencies, Table No. 3 ..... XXX . Rotor Profile...... XXXI . Reheat Factor for Infinite Stages

89 90

........

93

XXXII . Cumulative Energy Diagram ....................... 94 xXXIII . Comparison of Values of Nozzle and Blading Efficiencies, Table No. 4 ..................

95

XXXIV. • Comparison of Stage Efficiencies, Table No.5..,,* 96 XXXV . Reaction Blading Leakage..............

97

XXXVI • Nozzle Blading Efficiencies, Table Mo. 6 ......... 98 XXXVII « Nozzle and Blading Efficiency Graph

( vi )

......

99

LIST OF SYMBOLS

A

= area, square feet or square inches,

d

» diameter , ft.

e

* internal work done in the stage. = internal work done by a turbine as a \diole per pound of steam.

E

a energy or work per pound of steam , Btu ot foot-pounds according to context.

h

* enthalpy per pound of steam.

( ^ h)^ - ideal available energy per pound of steam. %

- isentropic enthalpy drop in moving blades*

Hg

= isentropic enthalpy drop in fixed blades.

J

= mechanical equivalent of heat « 778 =■ velocity coefficient for flow through a nozzle.

kb

= velocity coefficient for flow through blade passages.

m

» thickness coefficient for blade or nozzle edges.

p

- pressure, pounds per square inch absolute, unless otherwise stated. = reheat, Btu per pound,

r

=

R

= reheat factor.

per cent reaction.

T,t = temperature degrees Farenheit. V

= velocity feet per second.

Vb

• velocity at mean blade ring diameter.

V2

- absolute velocity at entrance.

^2r “ relative velocity at entrance. ( vii )

Symbols - Contd. ^3r* relative velocity at exit. V3 =• absolute velocity at exit. V » absolute exit velocity of the previous stage. 3v V = specific volume, cubic feet per pound, w

= actual weight flow, pounds per second.

X

» percentage dryness or quality of steam.

Greek Letters: oc - angle made by steam velocity^ ) with direction of blade velocity. P = blade entrance angle. X = blade exit angle. S = angle made by absolute exit velocity. « difference

or

increment,

nozzle efficiency. (1^^= blading efficiency, ft = nozzle and blading efficiency, stage efficiency, mgine efficiency, f/ = carry-over coefficient. ^a> 0 = percentage of circumference occupied by active nozzles. 1^

= ratio of blade speed to steam speed.

^ - entropy. Subscripts; 1 - initial conditions. 2 « intermediate conditions. 3 * final conditions. ( viii )

Subscripts - üontd. 0

- at throat#

1 = ideal , without losses.



I

M Q

1-4

I

O z; Q) bC Cj +)

CO

20 Blading Efficiency:

2 2r (i-

*la bi = ^

o

3r ?

2

1300^ -

3 9

c c M Q

I

=>

X

0) hC 5

to

24 1(3 *

( .906 - .096 ) « .010 C 1 -II5 )( A h)^ = •l3Cv2 cv > >

I a 0

O s

t4 i H

g $ CO

1

48 Mean Diameter • AP0.35.AS...

3.14 X 3600 • 2.125

ft.

blade Height : w

» m h TT d

19 X .961

sin Ï

3 .80 X h X 3.14 X 2,125 X 494 x .2585

h

=

0.1185

Ft.

STAGE 8

- 4 1 0 .0

1^ »

Y 2 » 410.0/ 0.82

0.82

= 500.0 fps

^

5.00 Btu

With cC-15.0 and 50% reaction , draw the velocity diagram. Vg* 500.0

^

V2f 150.0 ^

5.00

Btu

0.45

Btu

500.0

V^= 150.0 ^ 0.45 Btu

Carry over * = .74 X .45 Therefore

«0.333 Btu.

enthalpy dropn in a single row; «(5.00/0 .95; - 0.333 = 5.26 - 0.333 «

Total drop « 2 x 4.927 h

s

9.854

5.00 Btu

Btu.

4.927

Btu

49

rv

rH

CCL f—I

r-i

r—I

O S rH

II A

>

O

&

rH

>

>

ir\

rH

g S Q M

I >

6^

to O 2; S en

50 From graph

0.74 A

stage

and

0.82

=0.927

Eff.

X Leakage Eff,

= H

- 0.927 X 0.962 - 0.8915 -( 1 -

Keheat

) Q&h)^

= .1085 X 9.854 = 1282,618

i> -1.6875

S
H EM Q

L = 15.0

stu.

and 50% reaction , draw the velocity diagram

7g= 541.5

5.841 Btu

155.0 ^ Carry over

5.841



541.5

.4825 Btu

V^= 155.0 —

5.841 Btu .4825 Btu

=> 0.76 X 0.4825

= 0.367

Btu.

Enthalpy drop in a single row : = ( 5.841 /.95 t - .367 6.14 - .367

= Total

drop

= 2 x 5.773 * 11.546

(Ah)^ From the graph

= 5$773 Btu.

for

Btu.

^ » 0.76

and

f = O.85

Co

V

°*931 -

*1^ X Leakage

Eff.

» 0.931 X 0.97 » 0.903 Reheat

• (1 -

= .097

X

11.546 » 1.120

Btu.

h^ = 1235.4495

^ =1.694

P^“ 73.5

fahSf» 11.546 ih,= 1223.9035 9r = 1.1200

«1.694

ip-5- 64.5

iTo» 383 iv,= 7.57

Pg“ 64.5

384.5 7^=7.59

= 1225.0235^ “1.696

60

T^- 408

v = 6.86

61

o

o

O

IT\ iH

vO nO

iH

II

I) >«

K

02 rH

iH CO

O

iTN

vO -cf

r—1

fH -jLf\

rH

It

II

II

II

11

CV

CV >

>

O

o

>

r—1

o Lf\

u

U

t> 5 g < M O e HH O q >

Cr\

r-H O Z Q) tiT

«3 -P

CO

62 Mean Diameter =

^

- 2.450

ft.

Blade Height: w

*m

19 X .97 X 7.59

h

IT d V^^Sin ir

» .81 x h x 3.14 x 2.45 x 541.5 x .2585

h

=

0.1592

ft.

STAGE 14 V - 470.0

P = 0.85

V = 470.0 /0/85 = 15.0

With

= 553.0 fps

— - 6.10 Btu.

and 50% reaction draw the velocity diagram .

553.0 ^ V » 157.0 2r

6.10 Btu

^

553.0

.494 Btu

V = 3

157.0

üarry Over from stage 13:

" 3v = 0.78

X

0.4825

= 0.376

Btu.

Enthalpy drop in a single row : = ( 6.10/.95 ) - 0.376 = Total drop « •* Stage

Eff.

-

6.42 - 0.376

= 6/044

2 x 6.044 12.088 M

X Hi.

Btu. Leakage

Eff.

Btu.

63

o

U"\ rH

o

vO II

c>a_

o

LT\

R U

o

LT\ U

m

>

g s M

I

(D b; en

64 From graph

^ » 0.78

and

F = 0.8$

,

Co

M » Kb

0.932 X Leakage

= Reheat

«

q j.

0.932

X 0/971

(1 -



Eff. = 0.90$

11^) (ah)^

.095X 12,088* 1.U7

h^ «122$.0235 ^ =1.696 (Ah)f^ 12.0880 i h^l212.^$$ =1.696 3 qr= 1.1470 hg =1214.082$^=1.6975

Btu

p^= 64.5

384.5

v^»7.59

ip, - $6.6 3

IT « 358.5 3

iv =8.40 3

p^= 56.6

360,5

v^»8,43

Mean Diameter - — x .60— 3.14 X 3600 -

2,490

ft.

»

m h T d

Blade Height w 19 X ,971 X 8,43

Sin y

-.Six h x 3.14 x 2,49 x ,2$8$

h

0,1710

=

ft.

stage 15 ? = 480,0

p = 0,8$

V = 430,0/0.8$

= $65,0 fps r- 6,36

Btu.

C

With

©c - 15.0 V = 2

and $0% reaction , draw the velocity diagram $65,0

^

6.36

Btu

3r

= $65.0

65

o

LT\ r4

vO vO

II

II

i

o

g

CO II t>

o lO vO lO 11

cv >

«

>o

O O Cl r4

II f~i

c\)

o

o

ir\ c lO

c

«

«0 >

o

r4

II CO >

n 1-1

I

o

a> S’ +3

CO

66 0.513

V a 160.0 2r

Carry over from stage 14,

7 « 160.0 3

Btu 2 *\.^3v /

® =

« 0.3952

0.80 X 0.494

Btu

Enthalpy in a single row ; “ ( 6.36 / .95 ) - .3952 6.70

» Total Drop (^h). From graph



- .3952

= 6.305

2 x 6.305

=

12.616

for



o

o

«M

%

CO

O O o -411 x>

>

vO r-

1) cv >

\0 r— 1 11

U

W •>

O \0 rII u

ro !>

O \0

r-i

11 CO >

î g j a t —I Q

S

o

o

to to

u\ \l

I

orH

, a

O 3

M O O

0) b. cj +3 CO

Cr3

71 Reheat

=. ( 1 - *^5 ) (^ h)^ = .089 X 13.656 = 1.215

h]^ «1190.7425

htu

^ = 1.7000

p^- 42.1

T^-310.0

10.7

ip^= 35,5

iT^« 279.0

iv^«12.10

35.5

Î3» 281.5

v^-12.20

(Ahy« 13.6560 ih^-1177.0865 -

-1.7000

1.2150

hg «1178.3015 ^ = 1.7025

Mean Diameter - ---199— 2^_^9-3.14 X 3900 = 2.650 Blade

ft.

Height: -

w h

=

m

h TT

^

0.211 ft

d

V^^Sin ^

BTAGE 18

With

7b

- 510.0

p - 0.85

^2

- 510.0/0.85

*600.0 fps

^

7.2 Btu.

oC = 15.0 and 50^ reaction ,draw the velocity diagram Vg = 600.0

7.2 Btu

73= 600.0

72 Vgy» 170.0

0.58

Btu

V

= 170.0

2 Carry over from stage 17,

»

/ 2g J

- 0.82 X 0.56

- 0.459

JSnthalpy drop in a single row: “ ( 7.2/.95 ) - 0.459 @ Total drop

7.58 - 0.459

=

2

From the grap]^ for 1-

Uh^» 14.2420 ih,=ll64.0595 8r= 1.2100 = 1165.2695

f - 0.85

X Leakage

JSff.

X 0.978

= 0.915

I1 -

=■ .085 hi .U78.3015

and

0.936

= 0.936 “

Btu.

o

0

1g II

CM

>

A

>

o O o

g

R

U s < M Q M

I ■>

?;!

/I !:

(f. I

STAGE 19 525.0

P--0.82

^2= 525.0 /0.Ô2 =. 640 fps a 15.0

With

8.175

^

Btu.

and 50^ reaction, draw the velocity diagram*

Uarry over from stage 18

2

=

= 0.84 X 0 .5a = 0.4865 #ithalpy drop in a single row; = ( 8.175 / .95 ) - 0.4865 8.615

= Total drop (^h)^

=2 x

- 0.4865

8,1285

16.257

»

From the graph for

= 8.1285

Btu

*1^= 0,84

and

^ -0.82

(Kb= 0. 937

(dry)

= =

*1^ X Leakage Eff. 0.937 X 0.9815

Moisture Correction =

1.15 x 1.05

= 0.920 = 1.21 =



»

( 1 -

«

.920

-

.0121

0.9179

=• .0821 X 16.257 - 1.335 .1165.2695

^ “1.7045

P^“ 29.4

T^=250.0

v =14.20

16.2570 ih,-1149.0125

1)^=1.7045

ip.» 23.5

dX^=.9895

iv =17.15

Qr = 1.3350 =1150.3475

=1.7060

Pg= 23.5

x^-.991

7^=17.20

74

75

O r-i vO II

o

ir\ ir\

o ir\

r-i II

«Û-

x>

O

O

o

§

a

s vO

If

If

A

>

y-.

>

s o

O O

r4

CM

|l

o

3 C-

IT\ \0 CM

If

cv

P3 < M Q 1— 1 O

§ >

f—1 CM O s

O- CM IT\ M to C «0 (T\ 11 II II II II k k >C\2 CM > >Cf\

< ■2:1 C5 < M O

CM CM

E-. M CJ

hi' cC

o

:>

Ô