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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
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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 =
q«
»
( 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