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Combined Nozzle and Blade Efficiency

( ) ( )0.931 0.836 0.778nb n bη η η = = =

Stage Efficiency

Assume an average loss from disk friction and fanning of 4% and from leakage of 1.5 %. Correcting for

tese effects gives!

( )( ) ( ) ( )1 " 0.778 1 0.04 0.015 0.735 st b Friction Fanning Leakage

η η η = − + = − + =

#et 0.73 st η = . $is is a rovisional value. &t 'ill (e modified as te design roceeds and more

recise information (ecomes availa(le.

Number of Stages

Ideal Available Energy to Blade

( )

( ) ( ) ( )

) ))

11406 "

39.5 ") ) 3).) 778

f s s m

m f

ft s Btu slbV h Btu lb

ft ft lblb∆ = = =

/

g g

g g

*se te ental+ at te given inlet conditions to te tur(ine and tat of te inlet to te condenser to get te

total isentroic dro in ental+!

( ) ( )1)93.7 9 0).9 390.8 " s mtotal h Btu lb∆ = − =

1.0465 R∞

= ,-eeat from a(ove gra

Trial Number of Stages, n

( ) ( ) ( )

( )

390.8 " 1.046510.35

39.5 "

m s total

m s

h R Btu lbn

h Btu lb

∞∆

= = =∆

/elect 10 stages ten correct for actual value of reeat!

( )1 1 0.73

1 1.0465 1 1 1.056510 0.)

R − = + − − =

Trial Isentropic Drop er Stage

1

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$e ental+ dro er stage is te total amount of actual ental+ cange in te tur(ine including te

reeat divided (+ te num(er of stages.

( ) ( )

( )

390.8 " 1.056541.3 "

10

m

s m

Btu lbh Btu lb∆ = =

$e trial value is 1.8 2tu"l(m greater tan 39.5 and 'ill cause a sligt increase in V 1 'ic 'ill (e

accounted for later.

Stage !e"eat, qr

ere 'e determine te amount of eat leak at eac stage.

( ) ( )41.3 1 0.73 11.15 "r s s st mq h h Btu lbη = ∆ − ∆ = − =

&f te desired final ressure ,0.491 sia is not reaced a ne' trial ∆h s and corresonding qr are found and

additional iterations run as needed. $o estimate te reuired cange divide te error in ental+ (+ te

num(er of stages and (+ te stage efficienc+ and ten add or su(tract tis uantit+ from ∆h s to get a ne'

trial value. After te correct value for ∆h s is found te final velocit+ triangles can (e constructed and

corresonding values calculated.

$e corrected value for V 1 is given (+!

( ) ( ) ( )1 )

) 41.3 " 778 3).)) 1438.49 "

m f

s s

f

Btu ft ft lb lb lbmV ft sh

Btu lb s

× ×= ∆ = =

× ×

( )11 0.965 1438.49 1387 "n sV ft sk V = = × =

from te velocit+ triangle W 1 is 873 ft"s and te (lade velocit+ coefficient is!

[ ] 916.0873,106,89).0 )"15

=−= − xk b

$is value is close enoug to te reviousl+ calculated value of 0.836. roceeding!

Total Internal #or$ er ound of Steam

mmr si lb Btulb Btuqhnw "5.301"15.113.41,10,, =−⋅=−∆⋅=

Internal Efficiency of t"e Turbine

301.5 " 0.7715390.8 "

mi

m

Btu lb Btu lb

η = =

%ec"anical &osses

Curc states te follo'ing roug rule for total mecanical losses including (earing friction and

gland um and governor resistances!

)

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ecanical loss in er cent at normal rating4 4

1.8"1000 5000 "1000kw

= = =

Assume a radiation loss of a(out 0.) % te com(ined mecanical and radiation losses amount to

a(out ) %.

Engine Efficiency, e

( ) ( )0.7715 0.98 0.756eη = =

Ideal Steam !ate

$e ideal steam rate reresents te mass of steam reuired to roduce a single kilo'att of o'er.

( )

( )

34138.73 "

390.8

mm

Btu lb ISR lb kWh

kWh Btu

/= =/

Bra$e Steam !ate

$e (rake steam rate corrects te ideal steam rate for te inefficiencies of te engine ,tur(ine.

( )8.73 " " 0.756 11.55 "m me BSR ISR lb kWh lb kWhη = = =

Turbine %ass 'lo( !ate

( ) ( )

( )

11.55 500016.04 "

3600

m

m

lb kWhm lb s

kWh s= =&

3

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%ollier Diagram

A ollier cart or an h s diagram offers a uniue descrition of te termod+namic interactions occurring

'itin te tur(ine. $e condition line details te termod+namic state rogression and is usuall+ dra'n

suerimosed on te ollier cart. &n order to construct tis cart it is useful to detail te state at eac ofte various stages. $is is most easil+ acieved (+ constructing a ta(le of te stage roerties.

$o construct te ta(le and from tere te ollier cart one must understand o' te termod+namic state

canges (et'een stages. All te ertinent information as alread+ (een determined. &t is siml+ a uestion

of organiation. $e state ta(le for te eamle in rogress is given on te follo'ing age. *sing a ta(ular

format 'e roceed in turn for eac stage to su(tract ∆h s from te entrance ental+ and ten add (ack te

reeat to determine te stage end oint. $e needed termod+namic state roerties including secific

volume are found as te rocess roceeds. &nitiall+ te state is fied and set (+ te inlet steam ressureand temerature. &t is ossi(le to determine te entro+ of te steam directl+. $en as te steam flo's

troug te first stage nole it goes troug an isentroic eansion. &t is ere tat te ental+ of te

fluid dros. $e amount of ental+ cange at eac stage is considered constant and as alread+ (een

determined. :no'ing te ne' value of te ental+ and assuming isentroic eansion it is ossi(le to

determine te ressure at te end of te nole.

/team ten flo's across te vanes on te 'eel 'ere it is reeated due to friction. $is rocess occurs

under constant ressure or iso(aric conditions. $us te increase in energ+ due to te eating is added tote revious value of te ental+. $e constant ressure assumtion fies te state and te resulting value

of entro+ can (e determined at te entrance to te nole for te net stage. $is rocedure is continued

and te values are ta(ulated until te total num(er of stages as (een comleted.

;nce te values of te ental+ and te entro+ are determined at eac stage it is ossi(le to lot tese

values on te ollier cart. $ese lotted values create te condition line and indicate te state

rogression of te steam troug te various tur(ine stages. $e aroriate ollier cart for tis eamle

is given on age 14. <</ 'ill roduce a roert+ lot automaticall+. $e ta(ulated ental+ and entro+

values can ten (e suerimosed on te lot using te =;verla+ lot> otion in te lot menu.

4

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5

Stage artEnt"alpy)BT*+lbm

Entropy)BT*+lbm-!

ressure)psia

1

?ole1)93.70

41.30 ,∆htrial

1.680 150

@eel1)5).40

11.15 ,qB 100.5

) N

1)63.55

41.30

1.69) B

W 1))).)3

11.15

B 65.0

3

N 1)33.40

41.30

1.705 B

W 119).10

11.15

B 40.9

4

N 1)03.)5

41.30

1.719 B

W 1161.95

11.15

B )4.5

5

N 1173.1041.30

1.734 B

W 1131.80

11.15

B 14.0

6 N

114).95

41.30

1.751 B

W 1101.65

11.15

B 7.8)

7

N 111).8041.30

1.768 B

W 1071.50

11.15

B 4.07

8

N 108).65

41.30

1.786 B

W 1041.3511.15

B ).10

9

N 105).50

41.30

1.806 B

W 1011.)0

11.15

B 1.0)

10 N

10)).35

41.30

1.8)6 B

W 981.0511.15

B 1.00 ,ing

<nd oint B 99).)0 1.847

$ermod+namic state ta(le for te stages of te steam tur(ine.

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ollier cart ,h-s diagram so'ing energ+ distri(ution 'itin te tur(ine.

6

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