59008360-parne-turbine.pdf
TRANSCRIPT
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, :23.02.2011
, 2011.
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1 ...........................................................................................................................................7
1.1 , .................................................................................... 7 1.2 .............................................................................. 8 1.3 .................................................................................................................................. 9
1.3.1 ..................................................................................................................9 1.3.2 ..........................................................9 1.3.3 .............................................................................................. 10
1.4 ....................................................................................... 17 1.4.1 ...................................................................... 17
2. .....................................................................................................20 2.1 ..................................................................................... 20 2.2 ............................................................................................................. 20 2.3 .................................................. 20 2.4 ............................................. 24 2.5 ..................... 27 2.6 ....................................................... 29
2.6.1 , [1] ....................................... 29 2.7 .......................................................................................................... 35 2.8 ........................................................................................................................................................ 39 2.9 ................................................................................................................................................................. 45 2.10 ........................................................................................................................................................ 45 2.11 ................................................ 47 2.12 ( ) ................................................ 50 2.13 .............................................................................................. 50 2.14 [6] .............................. 51 2.15 ............................................................................................................ 53 2.16 ........................................................................... 53
3. ......................................................................................................................56 3.1. .................................................. 56
3.1.1 .......................................................................................................... 56 3.1.2. ............................................................................................................................................................ 59 3.1.3. (. 3.1.3) .............. 61 3.1.4. , ............. 62 3.1.5 - ............................................................................................................................................................ 63 3.1.6 ................... 64 3.1.7 ....................................................................................................... 67 3.1.8 ............................................................................................... 71 3.1.9 ................................................................................... 78
3.2. ........................................................................................................................ 79 4. .....................................................................................................84
4.1 .............................................................................................. 84 4.1 .............................................................................................. 85 4.2. .......................................................................................................... 86 4.3. ............................................................................ 87
4.3.1 .................................................................................................... 87 4.3.2 ..................................................................................................................... 89 4.3.3 ...................................................... 91 4.3.4 ............................................................... 92 4.3.5 .................................................................... 92 4.3.6 ............................................................... 93
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4.3.7 .......................................... 94 4.3.8 .............................................................. 95 4.3.9 t ........ 95 4.3.10 ............................................................................................................. 96 4.3.11 ............................................................................. 97
.................................................................................................................................................98 5. J .............................99
5.1 ...................................................... 99 5.2 ............................................................................... 102 5.3 c ............................................ 105
5.3.1 c ........................ 106 5.3.2 c (. 5.3.3 .
5.3.4)................................................................................................................................................. 109 5.3.3 c (. 5.1.1) ..................................................... 111 5.3.4 c ................................... 113
5.4. .............................................................................................. 113 5.5. ............................................................. 116
5.5.1 ............................................................................................... 116 5.5.2 ................................................................................ 117 5.5.3 ............................................................................................................. 119
5.5.3.1 ......................................................119 5.5.3.1 .................................................120
5.5.4 ................................................................................................ 122 5.6. c ....................................... 123 5.7 c ...... 125
6. .....................................................................128 6.1 .................................................. 129 6.2 .............................................................................................. 130 6.3 ....... 133
6.3.1 1 const = ................................................ 135 6.3.2 .................... 138 6.3.3 .................................................................................................................................... 141 6.3.4 .................................................................................. 142
7. ..............................................................................................144 7.1 ........................................................................ 145 7.2 .................................................................................................................. 149 7.3 ..................................................................................... 151 7.4 ......................................................................................... 152 7.5 .................................................................................................................. 154 7.6 ............................................ 158 7.7 ................................................................................................... 162 7.8 ............................................................................................................................................................... 163 7.9 ....................................................................................... 167 7.10 ....................................................................... 169 7.11 ............................................... 172
8. ..........................................................................................177 8.1 ................................................................................................................ 177
8.1.1 ................................................................................................................................. 177 8.1.2 .............................................................................................................................. 178 8.1.3 ........................................................................................... 181
8.1.3.1 ..........................................................................................................................181 8.1.3.2 ............................................................................................................................182 8.1.3.3 .........................................................................................183 8.1.3.4 ..............................................................................................185
8.1.4 .............................................................................................. 187 8.1.5 ................................................................................... 188
8.2. ........................................................................................................................ 192 8.2.1. ........................................................................................................... 193 8.2.2 , .......................................................... 194
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8.3 ............................................................................................................. 195 8.4 ......................................................................................................................... 196
8.4.1 ............................................................................................................... 200 8.4.2 .................................................................................................................. 200
8.5 .................................................................................................................... 201 8.5.1 .................................................................................................................... 202 8.5.2 ...................................................................................................................... 205
8.6 ........................................................................................................................................ 208 8.6.1. .......................................................................................................... 211
8.7 ......................................................................................................................................... 211 8.7.1 ...................................................................................................... 211 8.7.2. .......................................................................................................... 214 8.7.3 .............................................................................. 215 8.7.4 ......................................................................... 216
8.8 ................................................................................................................... 216 8.8.1 ........................................................................................... 216 8.8.2 , ............................................... 217 8.8.3 ................................. 218 8.8.4 ............................................................................................ 218
8.9 ................................................................................................................................. 218 8.9.1. ......................................................................................................................... 218 8.9.2. ........................................................................................................................... 219
8.9.2.1. ........................................................................................................................219 8.9.2.2. 100% .................................................................................219 8.9.2.3. .....................................................................................................................220 8.9.2.4. ................................................................................................220 8.9.2.5. .....................................................................................................220
8.9.3. ............................................................................................................................ 220 8.9.4. ...................................................................................................... 223 8.9.5. ................................................................................................................. 224 8.9.8. ..................................................................................................... 228 8.9.10. ....................................................................................................................... 231 8.9.11. ................................................................................... 231 8.9.12. ................................................................................................................... 231
9. ..........................................................................232 9.1 ............................................................................. 232
10. ..........................................................................................237 10.1. ............................................... 237 10.2 ................................................................................................................... 239
10.2.1 ........................................................................................................ 239 10.2.2 ................................................................................................ 242 10.2.3 ..... 243 10.2.4. ................. 245 10.2.5 ......................................................................................... 245 10.2.6 ............................................................ 246
10.3. ...................................... 246 10.4. ............ 247 10.5. ............................................... 249 10.6 .................................................................................. 251
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7
1
1.1 ,
, ,
. ( ). -, . , , , .
. . . , . . . , . - . (. - ) , .
. . ( 1 ; ) . . , .
.
. . . .
.
-
1.
8
, . , . . . , . , , ( ). . ( ) .
1.2
120 . . 1629. .
1883. . .
1884. . . 80 % .
, 120 . , 1629.
-
9
1883. , 1884.
1.3
1.3.1 . , , .
. . .
, , , ( ). . . .
- , , , .
. .
1.3.2 , . .
-
1.
10
. () . . . . , . . . .
. . . . . .
. , . . . . . - . . , . .
1.3.3 . , . , .
:
1. 2. , 3. , 4. , 5. .
. , . ,
-
11
. .
. 1. 3. 1 ( DIN 2481 [3]). , , . , . . . . .
. 1.3.1 , , Ts - . 1.3.2 . 3 4, , . ( ) 4 1. , . . - -
1p 2p .
, . 2 3. , , , , .
. 1.3.1 -
12
3
4
ond
G~
-
1.
12
0 1 2 3 4 5 6 7 8 9s [kJ/kgK]
-200
-100
0
100
200
300
400
500
600
T[0
C]
4s
2s
4
3
2
1
0 1 2 3 4 5 6 7 8 9
s [kJ/kgK]
0
500
1000
1500
2000
2500
3000
3500
4000
h[k
J/kg
]
3
4s
1
2
. 1.3.2 s- hs-
( ) . ( ) . , . , , . , . . . , , . - . .
, - - . , , . , . 1.3.3 , . , .
. 1.3.3
-
13
. 1.3.4 -
, , . . .
. 1.3.5. - - . . . , , . , , . , .
. 1.3.5 - -
. 1.3.6 -
-
1.
14
, , . , .
. . . . . . , (. 1.3.7). , . (. 1.3.8). . , . , , (. 1.3.9). . . . .
. . . . , . .
, . , , . . . . 1.3.10 .
- - . - (. 1.3.11).
. . . . . 1.3.7 . . 1.3.8 , . 1.3.8 . 1.3.10 . , . .1.3.11 . , , . , . .
-
15
. 1.3.7 - . 1.3.8 -
. 1.3.9 - 1 - (). 2 - . , 3 - 1. , 4 - . . 5 - 2. , 6 , 7 -
. 1.3.10 - - 1 - (). 2 - 1 . 1 . 3 - 1. 4 - 2. . 5 - 2. 6 - . 7 , 8 - , 9 , 10 .
. 1.3.11 -
1 - (). 2 - 2. . 3 - 2. . 4 - . 5
-
1.
16
. . . , , , . 1.3.12.
: 1. ( 10 bar), 2. ( 88 bar), 3. ( 224 bar) 4. ( 224 bar).
( 88 bar ), ( 224 ).
, [1] : 1. , 2. ( 485), 3. ( 565 ) 4. ( 565).
, 565 .
-, -, - .
(. 1.3.6) .
. 1.3.12 - . 1 - (). 2 - . . 3 - . 4 -
-
17
1.4
. , . . - - . . . .
1.4.1 , .
1.4.1 -
1970. 1980.
53 35
22 13
6 3
4
85
36
87
15 15 13 13
. , . , ( , , ). . . . .
: 5.
( ) , . . , . . .
-
1.
18
6. . . 10 , 10 . ( ) . , , , , . 600 W, 1300 W.
7. ( ) . , . . , . . , , , , .
8. . . . . .
9. , .
10. . . - . .
11. , , . ( ) , .
12. . , 70 - 80 % .
13. . .
.
-
19
BSS132. 30 W 200 W 20,1%, 58 %.
1.4.2 - IEC No. 45 34 42 64 88 105 126 140 165
435 455 485 535 535 565
, . , , :
14. , .
15. , , . .
16. .
-
2.
20
2.
2.1
. . . .
2.2
. . , , , . . , . . , , , , , , . . . . , , .
. . 1.3.1 . . . ( ) , . .
2.3
, , . . , .
1 kg . , . iTL .
-
21
, . , . , sTL . , . .
, . .
iTGViT = LMP
sT GV sTP M L= . . . . :
sT
iTiT L
L=
sT
iTiT P
P=
. .
, :
iThhhL == 43iT ( h ) - - - h - . :
shhL 43sT = . . .
-
2.
22
- , . :
iTiT hL = :
sTsT hL = . . :
iTGViT = hMP sTGVsT = hMP
. , , , , . sh, , . , , , iTL .
sTiTsiT hhhL == )( 43iT . . . . . , . . , , .
(. , , 535-565), . , . .
, . . . (. ) . .
-
23
. :
. = GV.
eTe MLP T
(. ). . :
iT
eTmT L
L=
:
iT
eTmT P
P=
eTiT - PP
. , . . .
, :
sTiTmTsiTmTsTiTmTiTmT hhhLLL ==== )( 43eT 3 4s, . , . :
mTeT GV mT iT sT GV mT iT 3 4 GV iT sT ( ) sP M L M h h M h= = = eT iT/P P . . :
iTmTsT
sTiTmT
LMLM
PP
GV
GV
sT
eTeT ===
. . GbP eTP .
eT Gb - P P
-
2.
24
. , . .
Gb GbG
eT eT
L PL P
= =
. b , . . . sp,TPP , sp,BP . .
. . . .
GiTmTsT
sTGiTmTb
sT
Gb
LL
LL
PP ====
sT
GTA
2.4
. , . , -K . . :
GVp - ,
GVt - ,
PKp - .
1.3.1 sT , 1.3.2 3p , 3t , 4p . , . , .
. . . , , .
:
GbL - . . .
-
25
TPb - . . .
GbL , . :
GsTiTmTGsiTmTGsTiTmTb hhhLL )( 43G === ( ) . :
Gb Gb GV 3 4TPb
dov,TP GV 3 2 GV 3 2 3 2
( ) ( ) ( ) ( )
mT iT G s mT iT G sTP P M h h hQ M h h M h h h h
= = = =
. - :
s
sT
hhh
23RC
=
( 22 hh s ): RCGmTiT TPb
. , , ( 90%) 50%. .
( ) . :
Gb GbBb
GV 3 2dov,B ( )K TPb
K
P PM h hQ
= = =
:
22 hh s -:
RCKGmTiT Bb . - :
-
2.
26
)( 23GVTPn hhM
PP SPTPGb
= -:
KTPnNVPR
SPBGb
hhMPP =
=)( PR
Bn
. a :
TPbm - . , .
TPbq - . , .
. , .
:
GsiTmTGbGb
GV
hhLPMm
)(11
43TPb
===
( ) . :
. .GV GVdov,TP 3 2 3 2 3 2
TPb .Gb Gb GV 3 4
( ) ( ) ( ) 1 ( ) mT iT G sT mT iT G RCmT iT G s
Q M h h M h h h hqP P hM h h
= = = =
TPbTPbq
1= .
( ) . :
.GVdov,B 3 2
BbGb
( ) 1K Gb Bb
Q M h hqP P
= = =
-
27
. d 1 kg 1 kg :
dHhhB u
K
==
)( 23Bb
uH :
u
BbBb H
qb =
GbP :
Bb Gb BbB P b= GbP :
GbTPbGV PmM = .
2.5
, , . . . , . , 1 kg .
, . 1.3.1, :
K
hh
)( 23
1 kg . . iNPL , , .
,
122323
)(
)( hhhhLhh
KiNP
K
+=+
.
-
2.
28
1 kg GbL , . .
14 hh :
)( 23
23 hhhh
K
. , , , . . 1 kg . :
GbiTGbeTeTiT LLLLLL =+ :
14232323 )(
)(
)( hhLLLhhhhLhh GbiTGb
KiNP
K
++++=+
. . , . , . , , . , , .
. :
GbiTGbK
iNPK
PPPhhhhhhMLhhM ++
++=
+ )()(
)(
)(
142323
GV23
GV
. . :
KPKNVGV MMMM === , .
, .
-
29
, . . , .
2.6
, . , . .
2.6.1 , [1] ( ) :
sThe 0= h , s . 0T , ( ) . ( ) 1 2. 1 2. :
)( 20210121max sThsTheeLi == )( 10120212in sThsTheeL mi ==
. - . , . . , . :
max i LLi < 21 eeLi <
min i LLi > 21 eeLi >
. . :
iLsThsThe = )( 202101
-
2.
30
[ ])( 101202 sThsThLe i = . ( ) . ( . ). 1 kg . , , . ( ). :
001010 STHE = 1 , 0 . , . 1 kg 1 kg . 10H . . . :
2022 STHE = :
)( 20210010210 STHSTHEE = . , . :
2002020 STHE = :
)( 2010020102010 SSTHHEE = 2010 HH ( ) ( 1 kg ). :
)( 201002010 SSTHEE u = :
uH
. . , , :
)(
20100u
u
HSSTH =
10S 20S .
-
31
. , , . , . , [2]. , . . . , .
- - . , , . , , , 10S 20S . . . 1 kg - kg , d kg - :
K
u hhdH
23 =
. , - - . . , . , .
, . . , . . Carnot- . q Carnot. . . . . , , , .
2.6.2
-
2.
32
1 kg :
K
uu hhd
Hd
SSTH
)( 2320100 =
. ,
NP 23
iKLhh +
1 kg . .
. . , . 1 kg :
)( 20100 SSTH u 1 kg d kg , 1 kg :
)( 20100d
SSTH u
)( 20100d
SST
( ), . :
K
uu hhd
Hd
SSTH
)( 2320100 =
- .
202 sTh 303 sTh . :
)( 202303 sThsTh - - - . () .
:
[ ])()( 20230320100Kot sThsThdSSTH
e u = :
-
33
[ ] )()(
)()(
)(23023
K
23202303
K
23Kot ssThh
hhsThsThhhe +==
. , , . , , . - . . . . . . . , , , . . . . . .
. , , - - .:
Kot 303202K
23
)(
esThsThhh +=+
.
. :
)( 404303 sThsTh , , 43 hhLiT = . , , . .:
)()( 340404303T ssTLsThsThe iT == , ,
T 404303 esThLsTh iT ++= .
-
2.
34
. , , .
.
eTiT - LL
GbeT - LL
() . :
)( 101404K sThsThe = . ( ) . , . . . :
041 TTT ==
34340 )( hhssT = .
. . . , .
[ ] NP 120101202 )()( essTsTisThLiNP ==+ . , , .
:
TGbeTeTiTKNPKotGbiNPk
eLLLLeeeLLhh 23 +++++++=+
. . . 1 kg . . .
-
35
2.7
, . , .
Rankin-Clausius-a :
,
,
.
, . . , . , . , . .
, , . (. 2.7.5-6). . . ( ) . 12 %. ( ) ( ) . ( ) . . - - 535-565 C. . . 535 . . - 535 - .
-
2.
36
. 2.7.5 -
. 2.7.6 -
. 2.7.7 - ( srT 1srT )
2.7.8
. 2.7.9
-
37
, , . . . - . . , . . . . , , . . . , , .
, , . . , , . . . , . . - - . , , .
535C ( ) . , . sh, . , . , , . . sh, . 2.11.3. , ( ) . , . . . [1].
. , , . , . , , , .
-
2.
38
, , . , , , . , . . 2.7.9 2.7.10. , . , . , (.2.7.10). . . , , . .
. 2.7.7 -
- BBC . 2.7.8 -
-
39
. 2.7.10 -
. 2.7.9 -
. 2.7.11 -
2.8
2.8.1. , .
- . . , :
GVp - ,
-
2.
40
GVt - ,
NVp - ,
NVt - ,
PKp - .
sp
Gb
Gn
MZ
Kontrolna granica parnog turbopostrojenja
Kontrolna granica parnog bloka
P
P
P
G
E
NP
ZVP1ZVP2 ZNP2 ZNP1 HZP HE KP
Kond
PK
TNPTVPGV1
. 2.8.1
. . , iTP , , . ( . 2.7.10 2.8.2):
. . . III TII TI TT +++= iiii PPPP
-
41
. 2.8.2 -
:
I TII T = ii LMP
II TIIII T = ii LMP
III TIIIIII T = ii LMP :
. . . III TIIIII TIII TIT +++= iiii LMLMLMP :
. . . ; ; ; 21GVIII1GVIIGVI OOO MMMMMMMMM === , , :
. . .)-)(--()-)(- )-( 32O2O1GV21O1GV1GVT OOOOOGVi hhMMMhhMMhhMP ++=
-
2.
42
. 2.8.3 - . ct - , m - , :
....11 III GV
O2
GV
O1II
GV
O1I GVT
+
+
+= iTiTiTi hM
MMMh
MMhMP
GVM . , - , , . , , , . . ( ) .
iTh :
. . .11 III GV
O2
GV
O1II
GV
O1I TT +
+
+== iTiTiTieqieq hM
MMMh
MMhhL
.
GV
O1
MM
; GV
O2
MM
; . . .
( 100) . , 1 kg , (
-
43
), .
:
GmTieqGmTieqb hLL TTG == , , , . . ( 30 % 70 % ).
. 2.8.4. -
. 2.8.5 - - BBC
-
2.
44
( ) .
:
Gb GbTPb
dov,TP GV GV NV NV
P P
Q M h M h= =
, , , , :
TGV GbTPb
GV GV NV GV NV
( - ) ( - )
ieq mT GhM LM h h h h
= =
NVGV hh ieqTh , GbL , .
- :
K GV TGb
dov,B GV NV GV NV
K
mT G ieqGbBb
PR NV PR NV
M hP PQ M h M h M h M h
= = =
, . :
K mT G ieqTBb K TPbGV NV
hh h
= = .
:
dov,TP GV NVTPb
Gb Gb
GV NVQ M h M hqP P
= =
:
TGVK
NVGV
K
NVGV
ieqGmT
NVPR
Gb
NVPRBb hM
hMhMP
hMhMq ==
, . :
-
45
KTK TPb
ieqGmT
NVGVBb
qh
hhq =
= .
. :
TPbT
1 1
GV
Gb Gb ieq mT G
MmP L h
= = =
2.9
.
, . . . , . , -.
. . . , . , . ( ) . , , , (. 2.8.3).
2.10
.
:
1GVp - ,
1GVt - ,
2GVp - ,
-
2.
46
2GVt - ,
PKp -
NVp - ,
NVt - . . . :
II TII I TI II TI TT ieqGTieqGTiii LMLMPPP +=+= II TII I TI T ieqGVieqGVi hMhMP +=
ieqTIh , ieqTIIh . 1GVM 2GVM . :
+= II T
1
2 I TG ieq
GV
GVieqGmTb hM
MhL
sp
Gb
Gn
MZ
Kontrolna granica parnog turbopostrojenja
Kontrolna granica parnog bloka
P
P
P
G
E
NP
ZVP1ZVP2 ZNP3 ZNP2 ZNP1 HZP HE KP
Kond
PK
TVP
GV1 GV2TSP TNP
. 2.10.1 -
:
-
47
GV 1 GV1 NV GV 2 GV2 II II
Gb
TPbNV T T
PM h M h M h M h
= +
1GVh , TIIh , 2GVh , NVh ( ).
:
GV 1 I NV GV 2 II II II 1GV NV GV T TTPb
Gb TPb
M h M h M h M hqP
+ = =
- :
Bb K TPbGV I R I NV GV II R II II II
K Gb
P NV P T T
PM h M h M h M h
= +
- :
K
TPb
GbK
TTPNVPBb
qP
hMhMhMhMq
II II II RII GVNVI RI GV +=
PR1h , PR2h .
- - :
Gb
SPB
Bb
SPBGb
TTPNVPBn
PP
qPP
hMhMhMhMq-1)(
K
II II 2 R2 GVNV1 R1 GV +=
Bb
Gb
SPB
BnBn q
PP
q
==
11
.
:
+
==II T
1
2 I T
TPb
11
ieqGV
GVieqGmT
Gb hMMh
Lm
2.11
, - ( 11) . , .
-
2.
48
, . .
, , , , . . , . . . 2.11.1, 2.11.2 2.11.3.
. 2.11.1 -
. 2.11.2 -
. 2.11.3 -
, . Schroeder [3]
-
49
, . 200 W, 250 bar, 520/530/ 540C ( ), 303,6C, 0,024 bar 9
kWhkJqBn /8737= . %2.41=Bb . . .
200 W [3]
% %
100 - - . 100
7,85 - - . 47,89
0,8 - - . 1,28
1,05 - - . 6,89
48,07 - - . 1,71
- 1,03 - . 1,03 41,2 41,2 . , , , 9,88%. . , . 92,15 %, . 47,89 %. . . . :
, . , . 1500 W , . . ( ) .
. .
-
2.
50
, , . .
2.12 ( )
. ( ) , , . .
2.13
, . - - . , ( ) . , . . , , . . , , . . . , .
( ) . . , . . . . . . . ( ) ( ). . .
-
51
.
. . . :
iTpT
pT
LL
=
. . , . . .
. . :
ip
p
dLdL
=
, :
ps
dhdh
= .
2.14 [6]
AC AB (. 2.14.1)
a b e d s s( )h h h h dh h a bh h e dh h . abde Ts -.
s sabdedh dh +
p sdh dh=
-
2.
52
( )p s iT p sT dh dh h h A = = + .
p . .
iTiT
sT
= hh
. 2.14.1 -
iTsT
1p pA
h
= + =
. . - - , . .
sT1 A
h
= +
A B C Ts - .
sTh iTh
-
53
2.15
. sS sTh h > .
sS
sT
hh
=
sS sTz h h = iS iT
iS iT
h hz =
iT iS = . ( ).
2.16
, , . ABC , [6]
2Aaz
=
ABC , a abc , z . Ts -
sS sTz h za h A + = +
( ) 11 1 1z
= + . .
2.17
. cT ( 2.14.1). lokG
-
2.
54
revdL idL . .:
lok rev iG dL dL=
c bh h
c b ch h T ds = cT ds . , , - - . . . Carnot . cT ds cT gp gT .
cT ds :
Carnot cT ds rezG ( ) . :
grez lok Carnot c c c g
c1
TG G T ds T ds T ds T ds
T = = =
. . - - [6]:
; g grez lok lokc c
T TG KG G K
T T= = =
. ( ) . . . .
-
55
(. ) . , . . , , , . 1. Energie und Exergie, VDI, Verlag 1965. 2. TRAUPEL, W.: Der Einfluss des Brenstoffes auf den Wirkungsgrad von Verbrennungsmaschinen,
Allgemeine Wrmetechnik, Nr. 1, 1952. 3. SCHRDER, K.: Wege zum verlustrmsten Wrmekraft-Werk, Svetska energetska konferencija,
1964. 4. , .., , ..: . . .
, , 1960. 5. , ..:
, , 1963. 6. TRAUPEL, W.: Thermische Turbomaschinen, Springer, Berlin 1968. 7. BARTLETT, R.: Steam Turbine Performance and Economics. 8. SALlSBURY J.K.: Steam Turbines and Their Cycles, J. Wiley, 1950. 9. STODOLA, A.: Dampf-und Gasturbinen, Springer, Berlin 1924. 10. SCHRDER, K., Grosse Dampfkraftwerke, Springer, Berlin 1962, Bd I, Bd II, Bd III Teil A i B. 11. WOOD, B.: Alternative Fluids for Power Generation, Proc. 1. Mech. E, Vol. 184, N2 4, 1969-70. 12. BARDGETT, W.E., CLARK, C.L.: Comparative High - Temperature Properties of British and American
Steals, Proc. I. Mech. E., Vol. 168, N2 16, 1954. 13. HORLOCK, J.H.: Approximate Equations for the Properties of Superheated Steam, Proc. I. Mech. E.,
Vol. 173, N2 33, 1959. 14. Contra Flov Heat Exchangers, Proc. I. Mech. E. Vol. 159, N2 44, 1948. 15. SPENCE, J.R.: The Development and production of high pressure fead heaters for modern central
power, Proc. I. Mech. E., Vol. 182, N2 36, 1967-68. 16. BROWN, F.H., DORE, J.W.H.: Reheat Practice in British Power Station, Proc. I. Mech. E., Vol. 172,
N2 16, 1958. 17. BAUMANN, K.: Improments in Thermal Efticiencies with High Steam Pressures and Temperatures in
Non-Reheating Plant, Proc. I. Mech. E., Vol. 155, N2 17, 1946. 18. , .: , , 1960. 19. .., . ., . ., . .:
, , 1963. 20. , .., , ..: , , 1960.
-
3. - - . , . . . . . .
3.1.
3.1.1 1A 2A (. 3.1.1.). 1A 2A . dt , . 1A , 1dx . 1 1A dx
1 1 1A dx . dt 2 2A dx . 2 2 2A dx . . . , , .
1 1 1 2 2 2A dx A dx = :
1 21 1 2 2 2
dx dxA A dxdt dt
=
. 3.1.1 -
-
3.
57
1 1dx cdt
= ( ) 2 2dx cdt = ( ) :
1 1 1 2 2 2c A c A =
1 1 2 2
1 2
c A c Av v
= .
c . . 1 2A A=
1 1 2 2c c const = = . , . . . . . . .
. 1A - 1 1p A 2A 2 2p A . F 1c 1 2c 2 . , .
1 1 1A dx 2 2 2A dx . :
2 11 1 1 2 2 2 2 2 2 2 1 1 1 1cos cos cos cos
dx dxp A F p A A c A cdt dt
+ = :
( ) ( )2 21 1 1 1 1 2 2 2 2 2cos cosp c A F p c A + + = + 2p c+ - - .
-
. 1 2 1 20; ; 0F A A const = = = = = :
2 21 1 1 2 2 2p c p c const + = + =
.
1 2A A= 0F = 1 2p p= . ( F ), 1 2p p= . . , . F . - - . .
, . .
. (
1 kg ) 2
2c
.
pA dx . ( 1 kg ) iL , q . , , 1A 1 1 1A dx dt :
21
1 1 1 12cu A dx +
1 1p A 1 1 1p A dx . 2 2 2A dx
22
2 2 2 22cu A dx +
2 2 2p A dx . dt :
iL A dx qA dx , :
-
3.
59
( )2 21 21 1 1 1 1 1 1 2 2 2 2 2 2 22 2 ic cu A dx p A dx u A dx p A dx L q Adx + + = + + +
( ),
2 21 1 2 2
1 21 22 2
ip c p cu u L q + + = + +
Kako je pu h+ = , :
2 21 2
1 22 2 ic ch h L q+ = +
. ( , , p t , s, uh ) ( ). . .
3.1.2. . .
1. . (. 3.1.2) 0iL = 0q = :
1 21 22 2
c ch h const+ = + = . :
0
2ch h= +
-
. 3.1.2 - hs -
02ch h const= + = .
. . . ( h ) c .
2. .
1 21 22 2 i
c ch h L+ = + :
0 01 2iL h h =
, . . . . . , :
0 0 00e h T s=
-
3.
61
3. .
0 01 2q h h =
. , .
3.1.3. (. 3.1.3) . , . . PPc . PPc , p dp+ , d + , dc . p 0c = . PPc , PPc dc PPc . [17]:
PPM A c= :
Adp Mdc= PPdp c dc=
( )( )PP PPA c A d c dc = = :
PP
d dcc
=
-
3.1.3 -
:
PPdpcd=
, ( ) ,
s const= ( )
PP zvs const
dpc cd =
= =
/p const =
zvc RT= . 3.1.4. , . , . . , . , . ,
-
3.
63
. . " " " " . c zvc :
sin zvcc
=
1sinzv
c Mac = =
( ) .
:
( ) .
.
.
3.1.5 - . . ( ) ( ), , . . ( ) 0 0 0; ; p t 0h 0s 0 0c = . ( 0 0c = ) .
00 0h h=
(. 3.1.2) , ,
0 0 01 2 0 0h h h h const= = = =
:
-
0 00 1 2h h h= = .
- - . . hs -. - - . hs - :
0 00 1 2h h h const= = =
e
2 21 2
0 1 22 2c ch h h= + = +
0-1-2 0 2. 0-10-20 . , . 0 0c = , 0 0h h = . .
( )1 0 12c h h=
( )2 0 22c h h=
( ) 22 1 2 12c h h c= + 1c 2c 1c 2c .
3.1.6 - - ( ) ( ). . . , , . ( ) . . .
-
3.
65
, .
2 21 2
0 1 22 2c ch h h= + = +
,
( ) ( )0 1 0 1 0 2 0 2; p ph h c T T h h c T T = = :
2 21 2
0 1 22 2p p
c cT T Tc c
= + = +
20
2 p
cT Tc
= +
. :
0 01 2 0T T T const= = =
. . , . . hs - . , . 1 . . . - hs -, . . , . .
00T T= T
.
20
2 p
cT Tc
= +
-
20 112 zv
T cT c
= + 0
2112
T MaT
= +
20 112
T MaT
= + - - 0T T Ma . , Ma T 0T . T .
. . . , , . - - hs -
0 02 1 0p p p< <
.
Tds dh vdp= . . . :
0 0 0 0 0T ds dh v dp= 0 0 0
00 0 0
dh T dpds RT p T
=
,
0 0dh =
-
3.
67
00
0dpds Rp
=
( )
( 0ds 0dp . . 1 2 ( ):
01
2 1 02
ln ps s s Rp
= =
. 1 2 . 2 1 0s s = 0 01 2p p= . okolT s . , . , :
0 0 0 01 p T p v
p T p v
= =
p 0p . :
0 1211 2
p Map
= +
. - ( ) .
p 0p . . 0p p Ma .
3.1.7
-
020 11
2TT Ma
T T = = +
0 120 11 2
pp Map p
= = +
10 120 11
2vv Ma
v v = = +
10 120 11
2Ma
= = + , . . , .
2
2cdh d
=
:
dp cdc = ( ) .
p const = .
dp dp
= :
0dA dc dA c
+ + =
, :
-
3.
69
2
21dA dp Ma
A p Ma=
2
21dA d Ma
A Ma
=
( )21dA dc MaA c= 2
1dc dc Ma
=
21dc dp
c pMa= .
. Ma , , ( 1). , . , , . . = 0,1 1% 70% ( ). 1% 100%. , . ( ). . 1Ma = . , , ( ). , .
, .
c ,
dc dc
=
1Ma = . . . ( 1Ma = )
-
.
, , . . ( )
( 2 1Ma > ) , ( ). .
, .
. , , :
0 120 11 , =12k k
p p Ma Map p
= = +
0 10 12k k
p pp p
+ = =
00 1
2k k
T TT T
+= = - 1Ma = - . .
k k kcA c A = :
k k
k
cAA c
=
.
zvpc Mac
RT =
2
0
012
111 2
112
Mapc Ma RTR T
Ma
+=
+
-
3.
71
( )0
0 2 12112
p MacR T
Ma
= +
1Ma =
( )0
0 2 112
k kp Mac
R T
=+
( )1
2 121 2 111 2k
A MaA Ma
+ = + +
k k
k
cAA c
=
. . .
3.1.8 ( ) . ( ) . . . . . . , . .
. . .
-
.
2 21 2
1 22 2c ch h const+ = + =
2 21 1 2 2
1 21 2 1 2p c p c
+ = +
1 1 2 2c c =
2 21 1 1 2 2 2p c p c + = +
1c 2c ( 1 2 ):
( ) 1 2 2 12 11 2 2 1
12 1
p pp p + =
Rankien-Hugoniot- . (. 3.1.4) :
1. . 2 1p p
dp dp
= . ( . )
( dp dp
= ). .
2. . .
:
1 1 2 2c c = 2 2
1 1 1 2 2 2p c p c + = +
-
3.
73
2 21 1 2 2
1 21 2 1 2p c p c
+ = +
. 3.1.4 -
12 1
2
cc
=
2 2
1 1 1 2 1 1 2p c p c c + = + :
22 1 1 1 1 1 2p p c c c = +
2p 2 2 2 21 1 1 1 1 1 1 2 2 2
1 1 12 1 1 2c p p c c c c c
c
+ + = +
( )2 21 2 1 2 2 1 21 1
11 2 1
p c c c c c cc
+ =
( ) ( )1 1 2 1 2 1 2 2 1 21 11 2 1
p c c c c c c c c cc
+ + =
:
-
21 1 1 2
1 211 2 2 1
p c c c c c + + =
11 1
11 1p
p RT c T = = :
2 201 1 1
1 011 2 2
p p pp c cc T c T c T + = + = = .
:
( )0 1 21
1 2 1RT c c
+=
20
21 k
RT c =+ :
21 2 kc c c= .
( 1c kc ) .
1c kc 2c kc . .
:
2 2 2 012
2 2 2 21 11 1 1 1
2/ 11/
k k zv
zv
RTc c ccc RTc c c Ma
+= = =
022
1 1 1
2 11
Tcc T Ma= +
21
22
1 1
112 21
Macc Ma
+= +
22
1 1
2 1 11 1
cc Ma
= ++ +
-
3.
75
22
1 1
2 1 1 1 11 1
cc Ma
+ = ++ +
22
1 1
2 11 11
cc Ma
= +
:
2 12
1 2 1
2 11 11
cc Ma
= = +
1Ma : 2 1
1 2
11
cc
= +
:
21 2 kc c c=
21 2
1 2 1 2
k
zv zv zv zv
cc cc c c c
=
2
1 21 2
k
zv zv
cMa Mac c
=
00 0
1 11 21 2
221
1
RT T TMa MaT TRT RT
+= = +
0 01 2
1 11 2
21
T TMa MaT T= +
2 21 1 1 2
2 1 11 11 2 2
Ma Ma Ma Ma = + ++
( )( )
22 12 2
1
2 12 1
MaMa
Ma
+ =
2Ma 1Ma :
21
2Ma
-
2Ma .
2 21 2 2 2
2 1 1 1 1 1
zv
zv
Ma cc Ma Tc Ma c Ma T
= = =
2Ma :
( ) ( )2 22 1 121 1
1 2 11 1 1 11 1
T Ma MaT Ma
= + + + +
:
( )22 2 1 11 1 2
21 11
p T Map T
= = + +
:
Tds dh vdp= pc dT dpds RT p
= ( )pc pdv vdp dpds R
pv p+=
( )p p p vdv dp dpds c c c cv p p= + p v
dv dpds c cv p
= +
v vdv dpds c cv p
= + 2 2 2
1 1 1v v
dv dpds c cv p
= + 2 1 2 2
1 1
ln lnv
s s pc p
= +
:
( )22 1 1 21
2 2 1ln 1 1 ln 1 11 1v
s s Mac Ma
= + + + +
. , ()
0 0 0 0 0T ds dh v dp=
-
3.
77
0 0dh =
0
00
dpds Rp
=
0ds ds= , :
02
2 1 01
ln ps s Rp
=
( )11
0 112210 2
1 1
2 2 11 1 1 11 1
p Map Ma
= + + + +
-
- . 02p 1Ma .
02p 1p , 1Ma . :
0 02 2 2
1 2 2
p p pp p p
=
0 1222
2
112
p Map
= +
( )22 11
21 11
p Map
= + +
( 2Ma 1Ma )
02p 1p 1Ma :
120 12
11 12
1
112
2 11 1
Mapp
Ma
+ + = + +
1p . , 1p . 1p . ,
-
1p [1].
. - .
2 1 2
1 1
1p p pp p =
.
( )22 11
21 11
p Map
= +
1 1Ma . . .
3.1.9 , , . . ( ), . . :
0 02 21 21 2
1 2
1 11 12 2
T TMa MaT T
= + = +
0 01 12 21 21 2
1 2
1 11 12 2
p pMa Map p
= + = +
:
1 1 1
2 2 2
1c Ac A
=
:
-
3.
79
( )1
2 120 0 1
1 1 2 20 0
22 12 12
112
112
MaA p T MaA Map T Ma
+ + = +
:
. . , . ( Ma ) .
, . .
. 0 01 2p p= 0 0
1 2T T= ( ) .
02p 01p ( 2
1) , .
0 0 0 01 1 2 1 1 2
0 0 0 02 22 1 2 1M
A p T A p TA Ap T p T
=
- .
1 1
2 2M
A AA A
=
3.2.
. . . tc .
-
(. 3.3.1). . , . . .
. 3.3.1 -
.
1 1 2 2n nc c = :
2 21 1 1 2 2 2n np c p c + = +
:
1 1 1 2 2 2n t n tc c c c = :
1 2t tc c= - .
:
2 21 2
1 22 2c ch h+ = +
2 2 2 1 2 n t t tc c c c c= + = :
2 21 2
1 22 2n nc ch h+ = +
nc
-
3.
81
nc . Ma nMa . sinnc c = sinnMa Ma = 1Ma . ( )
1Ma 1Ma . , y . (. 3.3.1):
1 1 2 2n nc c = 1 2t tc c=
( ) 22
n
t
ctgc
=
( ) 1 11 2
tg nt
cc
=
( ) 12
tg tg =
1
2
( 1Ma 1 sinMa ) :
( ) 2 21
2 1tg 1 1 tg1 sinMa
= +
3.3.2
( ). .
:
-
( )2 212 sin 11 Ma + ( 90). . 1Ma . .
, . 0 , , :
1sinMa
= . . . . . (. 3.3.2) [3].
. . .
. :
2 2 2 21 1 2 2 01 2
1 2 01 2 1 2 1n t n tc c c c pp p
+ ++ = + =
0
0
21k
pc = + :
( )2 2 21 1 1 11 12 2k n tp c c c + = + ( )2 2 22 2 2 21 12 2k n tp c c c + = +
2 21 1 1 2 2 2n np c p c + = +
-
3.
83
( ) ( )2 2 2 2 2 21 1 1 2 2 21 1 1 12 2 2 2n k t n k tc c c c c c + + + = +
1 1 2 2 1 2 n n t t tc c c c c = = = :
2 21 2
1 .1n n k t
c c c c= +
1. SHAPIRO A.: Compressible Fluid Flow, The Ronald Press Co., 1953 New York, 1, II 2. FANNO: Diplomarbeit ETH, Zi.irich,1904 3. OSWATITSCH K.: Gasdynamik, Springer, Wien, 1952 4. BUSEMANN A.: Vortrage aus dem Gebiete der Aerodynamik, Aachen 1929 5. PRANDTL L. BUSEMANN A.: Naherungsverfahren zur zeichnerische Ermittlung von ebenen Strmungen
in Uber-schallstroemungen, Stodola Festschrift, Ztirich 1929 6. OSWATITSCH K.: Fortschritte in Gasdynamik, Acta Phisica Austriaka, 1947 7. OSWATITSCH K.: SCHWARZENBURGER R.: Ubungen zur Gasdynamik, Springer Wien 1963 8. DEI M. E.: Tehnieskaja Gazodinamika, Gosenergoizdat, Moskva, 1961 9. ABRAMOVI G. A.: Prikladnaja gazovaja dinamika, Nauka, Moskva 1969 10. EMMONS H. W.: Fundamentals of Gas Dynamics, Princeton, New Jersey 1960 11. TOWNSEND A. A.: The Structure of Turbulent Shear Flow, Cambridge at the University Press, 1956 12. VORONJEC K., OBRADOVIC: N.: Mehanika fluida, Gradevinska knjiga, Beograd, 1960 13. THEODORE VON KARMAN: Aerodynamik, Interavia Genf, 1956 14. PATTERSON G. N.: Molecular Flow of Gases, John Wiley and Sons, New York 15. HAYES W., PROBSTEIN R.: Hypersonic Flow Theory, Academic Press, New York, 1959 16. RICHARD VON MISES, Mathematical Theory of Compressible Fluid Flow, Academic Press, New York, 1957 17. PRANDTL L.: Strmungslehre, F. Vieweg, Braunschweig, 1956 18. Compresibile Fluid Flow Tables and Graphs. 19. SEARS E. R.: General Theory of High Speed Aerodynamics, Princeton, 1954 20. HOWARTH L.: Modern Development in Fluid Dynamics Clarendon Press, Oxford, 1953
-
84
84
4. , . . . , , , . , , . , . . l . , .
. 4.1 -
4.1
, . . (. 4.1.1 . 4.1.2). . , . . (. 4.1.3)
. 4.1.1 -
. 4.1.2 -
-
. 4.1. 3 -
. 4.1.4
4.1
.
:
s - - ,
max
s = - - ,
,max,max
xx
s
= - ,
maxffs
= -
,max,max
ff
xx
s= -
t
-
4.
86
s - , ( )1 2180os s s = + ( )1 0 s s - , . ( )2 1 s s - , ( )1 0 R R - , , ( )2 1 R R - .
. . 0 , 1 2 .
, , . , +. -.
- - . (. l )
tts
= -
( ) t t - . . .
ls
-
lD
-
. .
4.2.
. . :
Re - Ma -
-
- ni -
T - .
4.3.
.
: , .
, . , , . , , .
:
R - ( )2 1 -
Pk - .
4.3.1 , , , , ( ).
2 2 2 21 1 2 2, 2 2 2 2
s sd d
c c w wh h = = . ( ) .
-
4.
88
. 4.3.1 -
. 4.3.2 -
. 4.3.3 -
. 4.3.4 -
C
-
. , 'R ''R :
2 21 2
2 21 2
2 2,
2 2
R Rs s
c w
c w = = .
(. 4.3.1, . 4.3.2 ).
:
2 2 2 2 2 21 1 1 2 2 2
2 2 2 2 2 21 1 1 2 2 2
2 2 2 2 2 21 , 1
2 2 2 2 2 2
s s
d dR R
s s s s s s
c c c w w wh h
c c c w w w
= = = = = =
, :
1 , 1R R R R = = .
( prof ) ( sec,kr ). :
sec,R prof kr = + . , (. ) .
4.3.2 :
.
:
Re ,0prof Ma prof i ii = + +
-
4.
90
:
,0prof - i - ii - .
. :
Re - Re Ma -
.
:
.
. 1 kg . , . (. 4.3.8).
. 4.3.8 - ( ) ( ) ( ) ()
, . .
-
. :
( )1 1 1 0u a u uF c c c tl= 1aMc .
1 0
1 1
u u uOP
a a
F c c kMc c
= = . . - - . OPk . /OP profk . (. 4.3.10) prof .
. 4.1.10. -
4.3.3
. :
() () .
-
4.
92
4.3.4 (. 4.3.11). , Ma , Ma . ( )0.9 1.0Ma > , Ma . , Ma Ma :
1.0, 1.0Ma Ma =
( )21 50.0 1 , 1.0Ma Ma Ma = + > Ma .
Ma
1.0
Ma1.0
) )
. 4.3.11 -
4.3.5 . . .
ii ii . :
2, =
20 sinii ii
ii iiA t
=
A ii :
1.0 0.7 , 3.33.1 0.27 , 3.3
B BAB B
+ = + >
-
Re 0
ii
Ma profB
=
. 4.3.12
4.3.6
0 0n si = . 1 1n si = . . . . , , . . . , . . . . , , . . ( ni+ ) ( ni ) . . , ( ) .
-
4.
94
. 4.3.13
4.3.7 . . . . , . . . . . . . . . . .
. . .
-
. 4.3.14
4.3.8 -
; u uOP OPa a
c wk kc w = =
. 1 , ,
2 . . . .
4.3.9 t . . [8]. . 1 (. 4.3.13)
1 1sinac a c t = . BC DE
-
4.
96
. AB AE . AE AB . :
1 1 1cos sin cosa ac a c t = :
11
cossincos a
a aKt t
= = . .
1sinat
=
. /a t / , tt t s = ( / , tt t s = ).
. 4.3.15 -
4.3.10 . :
Ps
MkM
= . . . .
1 1 1 1 1sins s s sM D l c =
-
1 1D l . . ( 1s ). Pk . . . .
.
4.3.11 . .
1 , , , ,Re, , ,R t nt l lf Ma is s D
=
1 2 , , , ,Re, , ,t nt l lf Ma is s D
=
3 , , , ,Re, , ,P t nt l lk f Ma is s D =
- , . :
1) .
2) .
.
. Re Ma :
( )1R nf i = 1 const =
2(Re, )Pk f Ma= ( ) Re Ma
-
4.
98
R const = 1 2, const const = =
Pk const=
1 2, const const .
. ) , Re Ma , . [9], [12], [13].
[1] FORSTER V. T.: Performance los s of modem stearn-turbine duo to surface roughness, Proc. 1. Mech. E., Vol. 181, Ni!. 17, 1967 [2] SCHLlCHTING H.: Grenzschichittheorie, Braun Verlag, Karlsruhe, 1951 [3] PRANDTL L., SCHLlCHTING H.: Das Widerstandgesetz rauher Platt en, Werft, Reed. Hafen, 1934 [4] SPEIDEL L.: The effect of surface finish on the efficiency of stearn turbines, Siemens Zeit., 1961, Ni! 8, Vol. 35 [5] BAMMERT K., FIEDLER K.: Der Reibungsverlust von rauhen Turbinenschaufelgitter, BWK Vol. 18, Ni! 9, 1966 [6] SPEIDEL L.: Einfluss der OberfHichenrauhigkeitauf die Str5rnungsverluste in ebenen Schaufelgitter, Forsch. Geb. Ing. Wes., Ni! 5 1954, [7] SHAPIRO A.: Cornpressible Flid Flow, Ronald Press Co, New York, 1953 [8] TRAUPEL W.: Therrnische Turbornaschinen, Vol. 1, Springer Berlin, 1966 [9] DEl M. E., EILlPOV G. A., LAZAREV L. A.: Atlas profila reetok os evih turbin, Moskva, [10] HAUSENBLAS H.: Vorausberechnung des Teillastverhaltens von Gasturbinen, Springer, Berlin 1962 [11] HAUSENBLAS H.: Zusammenfassende Uebrsicht liber britische Schaufe1gitterrnessungen, Konstruktion, Vol. 11, Ni! 12 [12] DEIC M, E., TROJANOVSKI B. M.: Islodovanija i raoti stupeni osevih turbin, Mainostrojenije, Moskva 1964 [13] DEle M. E., SAMOILOVIC G. S.: Osnovi aerodinamiki osevih turbomain, Magiz, Moskva 1959 [14] MOROZOV S. G.: Teplovi raoti parovih turbini pri peremenih veimah, Magiz, Moskva 1962 [15] ZRICKI G. S., LOKAl V. 1., MAKSUTOVA M. K. STRUNKIN V. A.: Gazovi turbini aviacionih dvigatelji, Oborongiz, Moskva 1963 [16] [17] TRAUPEL W.: Die Theorie der Strmung durch Radia1maschinen, Braun, Karlsruhe 1962 [18] BETZ A.: EinfUhrung in der Theorie der Stromingsmaschinen, Braun Karlsruhe, 1959. [19] HORLOCK J. H.: Some recent reseJrch in turbo-machinery, Proc. I. Mech. E. Vol. 182, NE 26, 1967-68 [20] HORLOCK J. H.: Reynolds number effects in cascades Bnd axial flow compressors, Trans. Am. Soc. mech, Engrs. 1964, Ser. A [21] VAVRA M. H.: Aerothermodynamics and fluid flow in turbomachines, John Wiley, New York 1960 [22] SWAINSTON M. J.: Development of spanwise profile s trough cascedes and axial flow turbomaschines, Proc. I. Mech. E. Vol. 183, NE 10,1968-69 [23] PARKER B.: Calculation of flow trough cascades of blades having relative motion and the genertion of alternating pressures and forces due to
interacting affects, Proc. I. Mech. E., Vol. 182, NE 11, 1967-68 [24] IMBACH H. E.: Zur Darstel1ung der Ergebnisse systematischer Untersuchungen an Schaufelgittern, BBC Mitt. Band. 53, NE 3, 1966 [25] BALJE O. E.: AxiBl Cascade Technology and Application to Flow Path Designs, Trans. Am. Soc. Mech. Engrs' 1968, Ser. A [26] HEBBEL H. H.: Uber den Einfluss der Machzahl und der Reynoldszahl auf die aerodynamischen Beiwerte von Verdichterschaufel bei
verschiedener Turbulenz der Stromung, Forschg. Ing. - Wes. Bd. 33, 1967, NE 5 [27] DZUNG L. S.: Mittelungverfahren in der Theorie der Schaufelgitter, BBC Mitt. Bd. 54, 1967. NE 1 [28] BELIK L, ZDENEK D: Neue Forschungsmethoden fUr den Durchflussteil von Dampfturbinen, Die schw. Ind. Tschech. NE 2, 1964 [29] BAMMERT K.: Vorlesungen iiber Thermische Turbomaschinen-Inst. T. H Hannover-Teil 1 i Teil 2 [30] HAUSENBLAS B.: Uberschal1stromungen am Austritt von Turbinenschaufel-Kranzen, Ing. Archiv Bd. 26, NE 6, 1958 [31] TRAUPEL W.: Die Strahablenkung in der vol1beaufschagten Turbine, Mitt. inst. Therm. Turbomasch. ETH Ziirich, NE 3, 1956 [32] BAMMERT K.: V. I. K. Berichte Nr. 141/42 1963 [33] TODD K. W.: Flow characteristics in stearn turbines, Trans. Inst. Fluid-Flow Mach. NE 14-16 1963 [34] COTTON K. C., ANGELO J.: Observed effects of deposits on stearn turbine effieciency, ASME Paper NE 57-A-116 [35] SCHLICHTING H., SCHOLZ No: Uber theoretische Berechnung der Stromungsverluste eines ebenen Schaufelgittern Ing. Archiv Bd. 19, 1951 [36] KRAFT H.: Nonsteady flow trough a turbine, IX Congres int. Mech. 1957 [37] PFEIL H.: Optimale Primarverluste an Axialgittern und Axialstufen von Stromungsmaschinen, VDI-Forsch-H. 535, 1969 [38] GEISLER O., MANGE J.: Neue GegendruckdampfturbiJ;}e fUr kleine Leistungen und kleine Volumenstrome, BWK, Vol. 22, NE 2, 1970 [39] FAURY M.: Contibution it etude theorique des turbines, Entropie, NE 20, 1968 [40] DOLLIN F.: Some design problems arising in the development of very large high-speed turbines-Proc. I. Mech. E. Vol. 177 NE 9-1963 [41] LUDEK B.: Aerodynamische Forschung auf dem Gebiet des Darnpfturbinenbaus, Schkoda Revue, NE 1, 1969 [42] MEYER H.: Transonic Flow in the Last Rotor Blade 'Row of a Low Pressure Stearn Turbine, Roy, Soc. Conf. on Int. Aerodyn. Carnbridge 1967 [43] BARSUN K: Influence of the Turbulence Level on the Performance of Two-Dimensional Compressor Cascades, Roy. Soc. Conf. on Int. Aerodyn.
Cabridge 1967 [44] HAWTHORNE W. R: Methods of Treating Three-dimensional Flows in Cascades and Blade Rows, Roy. Soc. Conf. on Int. Aerodyn. Cambridge,
1967 [45] HETHERINGTON R: Computer Calculations of the Flow in Axial Compressors, Roy. Soc. Conf. on Int. Aerodyn.Cambridge1967
-
99
5. J . . ( - ) . . . , . , . . .
. . . ( ) . , . , , .
5.1
- 0 (. 5.1.1) ( ). 0 0, p t . ,h s - . . 0c 0 . ( ) . . :
20 00 0 2
ch h= + , .
, . 0 1 hs - , t 0 1
-
100
, 0 00 1
.
. 5.1.1 - ,
1 1, p t , , 1 1, h s ( hs -). 1c 1 . 1 c , :
( ) ( )0 21 0 1 0 1 02 2c h h h h c= = + c ( 0 0, p t 0c 1p ) . c , c ( c). c ( ). c c . 0 1 , 0 1 c . .
sh
sh
dh dh
-
101
1 . c, - . c c - . . c , . . , c 1R 1 . - c - c .
. c 1 1u , 1c 1w . 1c . 1w 1c 1u . . , 1c 1u 1u , ( ) :
( )1 1 1 1 1
2 2 21 1 11 1 1 1 1
cos / cos 1/cos1 1/ 2cos /1 / 2 / cos
u c cc cu c u c
= =
= +
1c .
. . 2p . , cc . , 1 2, . . c - . c . , c -, . c . ( ). .
-
102
, c . , 1 2, . c . c c
5.2
, c . . ( ) . , . , . , . .
- :
2 2
0 0 0 10 1 0 12 2
c ch h h h const= = + = + = :
2 2
0 0 1 21 1 1 22 2u
c cL h h h h = = + +
. 1 2, 1u 2u , .
2
1
2R
RRdR . c
w . c:
2
1
2 221 2
1 22 2R
R
w wh RdR h+ + = + ,
2 2 2 21 1 2 2
1 22 2 2 2w u w uh h+ = + .
.
-
103
2 2 2 2 2 21 2 2 1 1 2
2 2 2uc c w w u uL = + +
2c 1 2 . 2w 2c . 1 2 . .
2 2 21 1 1 1 1 12 cosw c u c u = + 2 2 22 2 2 2 2 22 cosw c u c u = +
:
1 1 1 2 2 2cos cosuL u c u c =
1 1 1 2 2 2 2 2cos , cos cosu uc c c c c = = = . .
u u u uP ML P M = = :
( ) ( )1 1 2 2 1 1 2 2u u u u
uM u c u c M R c R c
M
= =
. .
. ( ) . , c , , c .
2 2 2 2 2 21 2 2 1 1 2
2 2 2uc c w w u uL = + +
, . . c ,
-
104
. . . ( c ) .
1 2u u= . c - c c . , . .
c . .
2 22 1
2 2 2 2 2 21 2 2 1 1 2
kw wr
c c w w u u= + +
:
( 0,15) 0.15.
. 0,5.
.
c .
s
sS
hrh=
sh sSh , .
20
2sS s sch h h = + + . c
. . c :
s
s s
hrh h
= + .
-
105
5.3 c
s sh h + 20
2c
.
( )2u sS d d cL h h h h = + + dh , dh 2ch . ( ). c c . .
20
2sS s sch h h = + +
:
0 0 0 0
0 22 00 0 2
2
u u uu
sS sS ss s
L h h h hL h c h hh h
= = + +
, .
tsu , ts
.
c, , c . , uL . c :
0 0 00 2
2 2 0 022 0 0 22
2 2 2
tt u uu
ssS s s
L h h hc c h hcL h h
= = + +
c ' ''s sh h + c c
0 00 2
0 2 '
th uu
s s s
L h hh h h h
= + .
-
106
5.3.1 c
(. 5.3.1 5.3.2) 0r = 0thr = 1 2u u u= = .
:
( ) ( )0 1 2 1 1 2 2cos cosu u u uL h u c c u c c = = = + 2 2 2 2cos cosc w u = :
( )0 1 1 2 2cos cos .u uL h u c w u = = + c :
2
'' 222
/2/2R s
ww
= .
2221
1 22 2s
swwh h+ = +
0r = . 1 2sh h= 2 1sw w= . . , . , , , , . c
( )0 1 1 1 2cos cos .u u RL h u c w u = = + 1 1 11
1 1
cos .cos cos
uw c uw = =
:
( )0 21 11
coscos 1 .cosu u R
L h u c u = = +
20
2sS sS s scL h h h = = + +
" 0sh = ( 0r = ) 2 2 20 1 1 .2 2 2
ssS sS s
R
c c cL h h = = + = = c [1]:
-
107
21
1 1 1
cos2 cos 1 .cosu R R
u uc c
= +
. 5.3.1 - ( ) ( )
. 5.3.2 -
c c . c ( 1R R = ) ( 1R R = ). . c. c , - 1 2 . c . c c 1 . , 1cos . ,
1 1 11 2 21 1 1 1 1 1
coscos2 cos
uw c uw c u c u
= =
+
1
11
11 1
coscos
1 2 cos
uc
u uc c
=
+
-
108
1 c 1 1
uc
c. c , ( 1 2; ; ; R R ) c . c c c . .
1
uc
. .
. c . , c c .
1
uc
( 1 2 ) . c
( )0 2u u sS d d cL h L h h h = = + + . : dh - dh - y 2ch - . . c
2 21 1 2 2
sd
c ch =
2 2 2 22 2 1 2 2 2 2 2
sd
w w w wh = =
22
2 2cch =
( 21 2
ssS
ch = )
2 2 2 21 2 2 1
2 2uc c w wL = +
. .
c c u 1/u c ( ) . a
1/u c .
-
109
c. 2c . 1/u c c . ;
( ) 11
1
cos0 da je 2
u
opt
ucu
c
= = c u 1/u c . 5.3.2 c (. 5.3.3 . 5.3.4)
c . . . c
1 2 1 2; c w w c= = 0,5kr = . c c R R = c 1 2 = . :
2 2 2 2 2 201 2 2 1 1 2
2 2 2u uc c w w u uL h = + + =
( )0 2 2 2 2 2 21 1 1 1 1 1 1 12 cos 2 cosu uL h c w c c u c u c u u = = = + =
2221
1 22 2swwh h+ = +
''
1 2s sh h h =
2 2'' 2 1
2 2s
sw wh = .
''1 2s sh h h =
-
110
. 5.3.3 -
. 5.3.4 -
c :
2 20 1
0 12 2s
sc ch h+ = + ' 0 1s sh h h =
2 21 0
2 2s
sc ch = .
: 2 2 2 20 1 2 1
2 2 2 2s s
sS s sc c w wL h h = + + = + +
2 1s sw c= . c :
( )0 2
1 12 2 21 1 1 1
2 cos2 2 cos
u uu
sS sS s
L h c u uL L c c u c u
= = = +
dh sh
sh
dh
00p
02p
-
111
21
1 1
11 1
2 cos
2 2cosu
R
R
u u uc c
u uc c
= +
R c c .
R R R = . c c c R , 1 2 =
1/u c . .
( )1
0 uuc
=
1/u c c.
11
cosopt
uc
= .
1 1/u c ( c ) .
5.3.3 c (. 5.1.1)
c c ( 0r = 0,5r = ). 1 2u u= . c c c - . [3] . :
1 1 2 2u u uL u c u c= . c:
1 1 1 2 2 2cos cosuL u c u c = + . ,
-
112
21 1 2 2 2 1
1
, Ru R u R u uR
= = =
2 21 1 1 1 2 2 1
1 1
cos cosuR RL u c u w uR R
=
2w c :
2 2R sw w= 22 2 221 2 1
1 22 2 2s
sww u uh h+ + = +
''1 2s sh h h =
:
'' 2 2 22 1 2 12s sw h w u u= + +
( )2'' 2 2 22 1 1 1 1 1 1 2 1 12 2 cos /s sw h c u c u u R R u= + + + ( )2'' 22 1 1 1 1 1 2 12 2 cos /s sw h c c u u R R= + +
2sw 2w 2w uL , ( " /s sSr h h= ):
( )20 22 21 1 1 1 2 1 1 1 1 1 2 1 11 1
cos cos 2 2 cos /u u R sSR RL h u c u h r c c u u R R uR R
= = + + + .
:
2 20 1
0 12 2s
sc ch h+ = +
2 2' 0 1
2 2s
sc ch + =
2
' ''0
2sS s sch h h = + + " /s sSr h h= ,
( )2 2' ''0 112 2
ss sS s sS
c ch h h h r + = = =
, (2121
/2/2R s
cc
= )
-
113
( )21
'2 1sS sS R
cL hr= = .
c
( ) 1 2 1 21 21 1 1 1
2 1 cos cosuu R RsS
L u R u Rr aL c R c R
= = +
( )2
1 1 21
1 1 1
1 2 cos1R
r u u Rar c c R
= + +
c c
( 1, R ), ( 2, R ) ( 1 21 1
; ; u Rrc R
). c
c . , . 1 1/u c ( ). 2 1/R R . , c , . c .
5.3.4 c
1 21 21 1
, , , , , , R Ru Rrc R
. c . c c . (. ) c c . , . c c , .
5.4.
c c . c c ( c )