Effect on Efficiency of a Steam Turbine of Variation of Size of a Two-Row Velocity Stage Wheel

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EFFECT ON EFFICIENCY OF A STEAM TURBINE OF VARIATION OF SIZE OF A TWO-RON VELOCITY STAGE

WHEEL

THESIS Submitted in partial fulfilment of the requirement for the degree

MASTER

OF

of

MECHANICAL ENGINEERING at the

/POLYTECHNIC

-INSTITUTE OF BROOKLYN

MUKHTAR

AHMAD

June 1950

Approved;-

Thesi

ead of Depa/Went

ProQuest N um ber: 27591586

All rights reserved INFORMATION TO ALL USERS The q u a lity of this re p ro d u c tio n is d e p e n d e n t u p o n the q u a lity of the co p y su b m itte d . In the unlikely e v e n t that the a u th o r did not send a c o m p le te m a n u scrip t and there are missing p a g e s, these will be n o te d . Also, if m a te ria l had to be re m o v e d , a n o te will in d ic a te the d e le tio n .

uest P roQ uest 27591586 Published by ProQuest LLO (2019). C o p y rig h t of the Dissertation is held by the A uthor. All rights reserved. This work is p ro te cte d a g a in s t u n a u th o rize d co p yin g 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

DEDICATED

to iny /\FATHER

ACKNOWLEDGEMENT

The author expresses his deep appreciation and sincere thanks to Prof. Edwin F, Church Jr. of the Mechanical Engi­ neering department. Polytechnic Institute of Brooklyn , for his encouragement and guidance in the completion of the present thesis.

VITA

The author , î-iuklitar Ahmad , was born on October 1st. 1927 in the town of Azamgarh , U.P, j,India.) ■ . He graduated from Muslim University High School in the year 1941. He joined the Engineering Colle^g , hhislim University , Aligarh in 1945 after completing two years in the University., He took his Bachlor's Degree in Mechanical Engineering in June 1949, During his stty in the College the author compiled a comprehensive design report on "Design of Thermo-electric Power Station". After graduation the author joined the Tata Iron and Steel Works , Jamshedpore, Tatanagçr (India) , as an apprentice in December 1346 and was with them till June 1347, The author aws selected by Government of Pakistan for studies in this country. The author |iad an opportunity

to be a lecturer in Mechanical

Engineering Department of the N.E.D. Engineering College, Karachi (Pakistan) from February 1948 till July 1948, He came to this country in August 1948 and joined the Polytchnic Institute of Brooklyn as a full-time graduate student in the Mechanical Engineering Department, The present investigation ■statted in May 1949 and was completed in January 1350,

TABLE

OF

CONTENT;

Page (l)

Introduction

(2)

Object and Working. procedure

4

(3 )

Discussions

7

(4 )

Results andConclusions----------------

(b)

Sample Calculations

------

—

15 19

USED.

A, Ap

Cross- sectional area of

Drv^

Diameter of rotor wheel at mean blade height

h

Blade height in inches

h^

Nozzle exit height at ex

Ah

Enthalpy difference a^on in BTU per lb

nozzle atexit and throat

actual or irreversible path

Cumulative enthalpy drop in BTU per lb Hpj_

Hors© Power loss due to disc friction Velocity coefficient for flow through a nozzle

kh

Velocity coefficient for flow through blade passage

m

Thickness coefficient for blades or nozzle edges

N

Revolution per minute

P

Absolute

pressure in psia

Mean c ircumfrencial pitch R

Reheat Factor Reheat Factor for infinite no. of stages

r = p/p 2. '

Fressure Ratio

T-fR

Ratio of blade width to radius of blade face

s

Entropy

V^

Absolute

velocity of steam issuing from nozzle

V3

Absolute

velocity of steam at exit from blades

Vgy

Relative

velocity of steam at inlet to blades

V^y

Relative

velocity .of steam at out let from blades

Vb

Mean peripheral velocity of blades

Velocity of whirl V^

Velocity of axial flow

V

(Specific Volume of steam in cu ft per Ih

¥

Weight flow in lb per

X

Quality of steam

o(

Nozzle angle

|3

Blade enterence angle

Y

Blade exit angle

X

Absolute direction of

sec

steam leaving blades

Nozzle efficiency I p

Ratio of blade speed to steam speed

0-

Percentage of circumfrenece occupied by active nozzles Combined nozzle and blading efficiency

nb

Blading or Diagram efficiency Stage efficiency 1 Overall efficiency

INTRODUCTION

With increasing demand from Central Poorer Stations for high­ er efficiency , reliability and comparatively cheap turbines , high­ er rotative speeds were introduced to meet this demand. For a 50cycle generator a two - pole alternator will require a speed of 500u RPM and for 6u - cycle a speed of 5,000 RPH, •Mr» O.B, Warren of the General Electric Company ( reference # has pointed out that the turbine efficiency is increased §.s the des­ igned speed is increased j and that the increase is small in the last stages of the turbine due to high specific volume of steam. But when the volume of steam is small -, which is generally the case when h i ^ pressure and high temperature steam is used , the g- in in efficiency is greater with increasing speed. This fact made it possible to use high pressures and temperatures in the turbines. Another important feetor in using higher pressures and temperatures in turbines is that it is easier to build reliable turbines if the dimensions of t the shell and rotor etc are kept small , and higher pressures and temperatures provide these conditions. Go it becomes a very signifi­ cant point in the design of a turbina to design the e-arly stages of this high pressure,and high temperature turbine with great care. In this country two- row velocity wheels are nearly uni­ versally used as the first stage in large and medium size turbines, The choice of a t'wo-ro^v velocity wheel in the early sU-.ges is usual­ ly the best design for reasons to be stated presently. .Suppose we were to use pressure stages instead of a two-row velocity wheel. The number of pressure stages required for replacing

(2)

a two-row

velocity wheel will be about

to 6 stages, ( in this

case , depending upon the size of the wheels) in order to absorb the energy utilizes in a two - row velocity wheel. This increase in the number of stgaes of the turbine might increase the.overall efficiency of the turbine. But the fact remains that there will be y. .

considerable amount of loss in partial admission in all these

early -pres sure .-.stages as compared to losses in the two-rox velocity wheel. These losses are due to the. fact that the specific volume-is small at high pressures and the flow area required is such that partial admission has to be introduced. If 'we want to avoid .partial admission and cut down the disc friction losses , with the same area available for flow , the nozzle heights and the cor ‘esponding blade heights will be shorter. But using shorter blades ther is a definite decrease in the nozzle efficiency , and the stage efficiency shows a greater trend towards low values • This may be due to t^;fact ; . . that tfie turbulance and other disturbances in the flow passages are q-. ite Hight. Not only this but by using two-row/wiieel the pressures within the shell will be considerably lowered and hence- the ^pressure '

'A,

on high pressure packings and on diaphgram packings will be reduced to a graeter extent. These losses are major items to be taken-care of in low volume flow. The rotational losses in the early stages of the turbine are also reduced considerably^ •

r.'.

'; There is no doubt that a t%m-row:velocity stage is not as efficient as a single pressui'e stage , but the efficiency .ith a two-row velocity stage rems.ins relatively constant over a range of operating loads. We find that use of

wide r

a t o-row velocity

stage is desirable for reasons of efficiency , less cost and greater, reliability in operation.

(5)

Another importance in the use oi tat- two-row velocity stage as 6 our first stage is from the point of view of governing. It is an established fact th: t nozzle - control governing is more economi­ cal and more efficient than throttle governing in the 1st. pres,sure stage of a. turbine , due to the factthat the

total steamconsuin-

ption at no load is much belo\/that in thethrottle

governing. It

has been pointed out in reference (l) page 157 , that if the load carried by üie nozzle controlled stage is increased and appro ches 100 % y the steam flow |)ass through

d

will

at economi­

cal load and will approach c

at the no load end, as

shown in Fig. (l) . If a two-row velocity stage is controlled by cut­ ting out nozzles , the curve of steam per i&J-hr will be given by

ME.

ab. It is evident

that the point

b

on the

most economical load end will be raised because a two-row

Fig. (l) velocity stage is le.^s efficient than

the pressure stages which it replaces. This indicates that such a unit , having a two - row velocity wheel

as the first

wheel gover­

ned by nozzle cut-out , will be more efficient at part load opera­ tion than a straight throttle- governed turbine will be.

(4)

OBJZ.C?

MD

PROCEDURE

This paper is an investigation , from purely theoretical calculations , as to the effect on the efficiency of a steam turbine of variation of the size of the two-row velocity wheel. As the topic .suggests an effort is made to study the variations of such factors as blade efficiency , stage efficiency , the disc friction losses and the blading work , with tir change in the mean blade ring diam­ eter of tlie t. o-row v locity wheel. Also the effect of changing the mean blade ring diameter on the overall efficiency and the total out-put of the turbine is studied. The working procedure for the major design will be outlined at this stage very briefly. .The following main items were calculated: (a) Calculation of Steam Rate

this was based on the assumption

of a trial heat rate of ll,üüü BTU per hr, (B)

(i) Preliminary Calcul tions for Last Stage

this stage

called (Z) stage was designed for a mocimijn leaving loss of 1:: BTU and with axial discharge, (ii) Design of stages (Y) and (X)

these are the stages be­

fore the last stage , the discharges in these were also axial, (C)

Design of T\ro-Rov/ Velocity Stage

the design speid wus limit-

ed to 450 ft per eec. Stage efficiency was o.lcul téd includi­ ng disc losses. (D)

(i) Design Of Pressure Stages: , Stage efficiencies and reheat ' repaired were calculated..

(5)

(ii) Layout of the Rotor Profile

based on assumed spacing bet-

ween stages. Reheat fg^tor and Cumulative Energy were calCulated, (iii) Energy Distribution

Trial error method used to determine

the distribution of enrgy among the stages. (E) Design Of Individual Stages. (E) Calculations of Diaphragm Leakage:,

based on nominal leakage

and assumed no. of labyrinth rings. (G)

"Calculations Of Disc Friction Losses:, based on full periph­ eral admission and volum' with reheat.

(K)

Calculations of the Overall Efficiency.

having finished this me.j or design there now remains theé task of changing the diameter of the two-row velocity wheel and re­ calculating the whole thing again to find the overall efficiency and total power. The diameter of the two-row^ velocity irheel was changed in steps by changing the enthalpy drop in the stage sufficiently r each time. By changing the enthalpy drop in the stage the absolute steam velocity was changed accordingly. If we keep the ratio of blade speed to steam speed constant in all cases , the blade 'speed will change and along with it the diameter of the w&eel. After changing the blade velocity and the me n blade ring diajiieter , the calculations for two-row velocity wheel is carried out to the point where we are again ready to make the energy trial distribution. It was found while carrying out this procedure that minor changes in the last stages of the turbine was required to reach the exhaust poip$

on l.b"Hg line . Calculations for these

(G)

changes were again made and entered in the Tables, Calculations for disc friction and diaphpagiii l^kage is carried out more or less in the same fashion taking care of the new specific volumes found due to changênin the entropy. Finally the overall efficiency was calcu­ lated, Case (l).has been worked out completely to show the method of approach > while Case (ll), (III) and (Ivj are presented in tabular form. An attempt was made to use some of the date which has already been calculated to avoid recalculations.

(7)

DISCUSSIONS The

resiiltG obj:ained

c^.lcTlL,..tiii2 ail the five different

cases with changed mean blade ring diameters, will be checned with the help of tlie Enthalpy - Entropy charts. This is necessaiy in order to visualise the type of results to be expected after tny calculations. r

Referring to

the bnthalpy-entropy diagram

we

sec that if AyC represents the enthalpy drop in the two-row velocity wheel In the major design, then A,C, is the enthalpy drop in case(I) , and AgC^then will be in case (II) and so on. Vie see in case (l) the drop In the enthalpy la great so that the reheat at constant pressure is greater than

C A

so that in

F-■ig i b

(8)

this case the reheat is the increase of enthalpy along entropy at

A

has increased to that at

A,C,. The

A, • Cases (II) ,(ill) are

similar. But in case (IV) since the enthalpy is smaller than

A^C

so we end up with A^C and hence the reheat is srualler and the entr&py is decreased rather than increased. Tracing the condition lines to the exhaust conditions we find that on the exhaust pressure line we end up with greater final enthalpy in cases (I) , (II) ,and (III) but in case (IV) again the entropy is smaller compared to the point E. The effect: of these can be studied separately in the two diffcrent cases.

(1)

TtV' -ROW VELOCITi CT. GBP

tliii'L:

If we again refer to the. enthalpy -entropy chart , we find that when the isontropic enthalpy drop of the stgae is increased from A C

to A^C,, the pressm'e is considerably reduced from P

to

P, , By increasing the enthalpy drop we increase the steam velocity and the appropriate blade velocity increases with it. The disc 3

friction loss , which is a

function of ( Blade velocity ) , increa­

ses rapidly. With this increase in the disc friction loss the stage efficiency is lowered. There is also a drop in the efficiency due b to lowered value of the combined bl de and nozzle efficiency with greater steam velocities. Since the reheat is

A h ( 1 -

)

it u.

also increases with drop in strxge efficiency. So we end up with greater entropy and hence greater specific volume. This greater volume of steam requires , if the nozzle dimensions remain s.-..me a greater nozzle and blade height and hence the windage losses increase. The Figures (Z) and (4) for the ti%o-row velocity wheel show blade

(s)

efficiency , stage efficiency , disc losses and stage work plotted against the mean blade ring diameter.

(2)

WhOLE

TUlBDjZ;

Referring to the enthalpy- entropy diagram again, we find t that

A^X represents the isentropic enthalpy drop for the whole

turbine, But when we increase the enthalpy of the t'. o-row velocity wheel we end up with higher entlialpy in the stage , which means that

A@L,and A^L^ will be less than

A^L

and hence the overall

efficiency of the turbine will decrease with increasing mean blade ring diameter . The overall efficiency is the ratio of

A^L /A^X .

This decrease in the overall efficiency also decreases the tui'binc output. Figure (5) shows these values . It is inheres ting to note that the combined nozzle ahdibladèpg efficiency of the individual stages do not change so rapidly as the combined nozzle and blade efficiency of the two-row velocity stage. Actually , in case of the individual pressure stages , value of

k|, increases with increase

in the steam velocity and hence the combined nozzle and binding efficiency decreases with it. The combined effect of both these decreasing combined nozzle and blading efficiency causes the drop in the overall efficiency of the turbine.

.1 V vO

10

O

OO

in in ro

OO

■T\

00

ro

■o N

UJ f V/)

fvo

Co

'O

U o

C\)

-J LU

> .r

o

DO

< OQ -r OO

'O

Ô

rv)

C\] OO K)

NO 00

cn

00

SÔ CO

ÜJ pq '- O

CO

h

VO

OO

CQ'

00

V NO

^ : U h : ; l | r î i t i : t r i ji: r r b : t V |; K :t% :t -

r-rt

i;-;Vm

o LU

L3 00 Q p-SijHii o o

< (A

L::4

TUJ-.U LLZLi MEAN ' B L A D E

T?1NG D I A M E T E R

IN . nkmes

m

feni %:

Hrm'i :4iIV:

ÎETS! MEAN

BLADE RING DIAMETER IN

INCHES

(IS)

NCo 00

ui OO

w ?

OO

U)

PQ

O' 3 h to

00

UJ -J

O

0_

X

3:

OO

to

OO OO

ro

Oo

N LU — »

PQ




UJ

A

ÙC ul

a ■z UJ V K

M E A N BLADE RING DIAMETER IN .kchm

(15)

5F,SULTS

AND

CONCLTIGIONS

In Figures (3) and (4)

we have curves oi bl:.de efficiency ,

stage efficiency find bl\.de and stage works , all plotted against tx the blade ring mean di n e ter of the tco-ro\; velocity stage. Disc friction los.es are also plotted against the dlmietor. The curve for the disc friction los^ is a curve similar to a cubic curve , because while ue calculated the horsepower lost we found that it varies as a third power of the blade velocity i.e. as the third power of the diametr. The disc friction losses increase rapidly with the change in di'.-jneter of the \hecl. The bi dding work and t the stage work in IfW

are plotted on the same scale against the

diameter, -^he curves are parabolic form indie sting that the energy varies as the squared of the steam velocity and hence with the Squared of the wheel diameter. We may e^lso note thc.t as the diem., eter increases these curves ,-ire separating due to the f ct that the disc losses are increasing rapidly . Thtc &tic I'y Looking into the curves for bl.ding efficiency and the r stage efficiency , we find th t the bl .ding efficiency curve foll­ ows a rapidly changing curve. The values drops off considerably as the diameter of the wheel increases. It is ... peculiur ..curve, with a reversal of curvature at a certain di meter of the two-row velocity is reached. Theoretically such a cliange in slope is not to be found , as the polytropic efficiency of a tui'bine v.ries with a covex (upward) curve filling off slowly. This ch-nge m.y be due to. some unavoidable assumptions made in the calculations. The trend of the blade efficiency cui've is v^'cy similar t.; the

(16)

stage efficiency but a reversal is not obvious. Reffering to fig (5) for the whole turbine we find values of KV7 ouput of turbine ,lovèrdll efficiency .and the percentage of total power developed by the two roar velocity wheel plotted again­ st the me'.n blade ring diameter of the two-ro'v velocity wheel. The output of the turbine decreases slowly with the. increasing value of the diameter. It is a smoother :curve covex upwards • The overall efficiency curve is veiy^ similar to the output power curve of the turbine. The curve of percentage, power developed in the t.ro-roi; velocity wheel is a parabolic curve , values incre sing rapidly in the 1 st case (iien the diameter of the. wheel is maximiva.

In Fig, (g ) percentage power developed by two-row velocity wheel is plotted against the total output of the turbine and the overall efficiency of tha turbine. From this curve it is evident that if we allot greater percentage of the power to the two-row velocity stage , the overall efficiency- end the total output of the turbine both drop+Those conditions occur for the designed point i.e, themost economical loads on the turbinr. At part load operation

as has been pointed out , the nosslc control governing of

two-ro'.r velocity stage is economical. If ;•© increase the pov-.'er in the two-row velocity stage , it means that greater number of nozzle are opened upto a point vrhere the pressure in the wheel is about b5t' of the Intial pressure. If we operate the turbine at part loads the no. of nozzles will be cut and the total steam consumption will be small while

n-

Bum

T1T:

n.Ui -ra S

rtR :ira

;rr.;:ar;

ü i m m m

ïgïæi MriiT :::r a : r r::i :::] :.tr: îi;*

0 125

0-135

b'i45"... OUTPUT

TOTAL

3 OF

2 -Row

OUTPUT

OF

0- 166 WHEEL

TURGffVE

0-175

0 '85

o 195'

O'ZoS

(Ig) the efficiency of the turbine will be or lese constant . So by increasing poi;er in tv.o-ro

velocity wheel un economical operat­

ion of the turbine can be hud if ,.'e operate at part load* This thesis was bused on full load conditions . ^^fect on the efficiency of the turbine con be found for part load operations by redesigning the wln.ie turbine. By doing so we can exact­ ly say how mich percentage of the power we acn give to the two-row velocity wheel in order to operate the turbine for the most econo­ mical conditions.

(19)

&1E

CALCULATIONS

The design is based upon an impulse turbine which is to deliver; 7,500 K¥ ( net electrical output), rating at 5600 RFM , steam being supplied to the first stage nos&les at 450 pound per sq. in absolute and 740 F , the exhaust being at 1.0" Hg abs. The turbine has a tworow velocity -staged wheel , the mean speed of which shall not exceed 450 ft per sec followed by single pressure stages. For this particular initial calculations the mean blade speed on the pressure stages start at 550 ft per sec and gardually increase in the follovdng stages to a maximum value of 900 ft per sec in the last stage, Ttie tip speed should not exceed 1100 ft per sec. The leaving loss shall not exceed an optimum value of 12.0 BTÜ in the last stage. Blade Height ratio should not exceed 0.5 . i.e. to mean blade ring diameter* This turbine is straight condensing with no reheat and no regenerative feed heating. The design procedure followed here is adopted fr - leaving loss x carryover

k

44.86

- 2.0 X 0*7

43*45

BTU per lb

44,85 - total losses — ------ — --------- --------enthalpy drop with carryover

Stage efficiency -

But total losses

=

- nozzleloss + blade loss+ disc loss ^ leaving loss =

3*35

+ 1,30 + 0*9 t 2,85

c 8.10 BTU per lb

stage eff n = fj

44.85 - 8.10 — ----------------- — 45.45

0,850

Stage efficiency corrected for moisture contents of 0*935 Stage

7)

Is

= 0.85 ( 100 - 1.15 z G.5 )

- 0*785.

(52)

(c)

CALCULATION

OF

8ATGE

%$

Enthalpyu of steam leaving stage X - Enthalpy of steam leaving = 1046.75 c

t

1090.20

Keeping the entheter

s

stage Ïstag© drop

in X

43.45 BTU per lb

-

1.026 constant for calculation puroees.

From Ellenvoodts Charts, for enthalpy of 1090.20 BTU per lb ve get ^ - 5*18 psia X

-0.960

V

- 108.4

cu ft per lb

Total volume of steam flowing through this stage

-

19*8 x 108*4

- 2146 Assuming

CU ft per sec

that the volume delivered by similaruwheels vary as the

linear dimension. The ratio of reduction of be

/

flow through stage

X

flow through stage

I

. . Ratio of reduction

sytl46 / 4080

X stage to t stage would

- 0.725

Take this value as 0.75 times diameter. - 0.75 x 4.1

= 5.08 ft

DzTÜMixTT — 60

-

-TTxB

Circumfrenece

_ ~

- 5 . 1 4 z 5.00

- (580 X 396 )/ 775 Blade height

=

P

-

:- 580 ft per sec

= 9.65 ft

- 297 ft per sec ( approz)

(13.8 z 108.4 )/ ( 9.65 Z 297 )

Blade height ratio Assume

5.08 x 5600 % 5.14 — : --- : — 60

- 0.65 / 5.06

0*65 ft

- 0.211

0,45

= 7b/ P ^ 580 / 0*45

% 1290

ft per

sec

For mazimum discharge the exit velocity must b© axial | but since the

(35)

icr 00

to r O O "D

n m X

(c4)

enterence angXeg are now normal we began to draw the velocity diagram* Take 0( - 16

and draw the diagram * From the

^2y Assume

744 ft per sec

TfR

- 0.45 K

kb _ 0.37 -

and

v

diagram weget ,

•* 26.5 -s. 108.4 cu ft per lb

= 0,001382 744

% 0.001582

= 0,950

55

=

0.95 % 744

- 706 ft per sec

Vj - 316 ft per sec

S =

80.4°

The leaving loss corresponding to to S.O BTU

516 ft per sec

velocity is equal

which we took in the calculations.

Nozale losses =

(

- 9% )/ 2gJ

= (

55.65 ~ 55.30 )

^ 2.55 Btu per lb Similarly blade losses

- (

- 9^ )/2gJ

r ( 11 #06 - 3.95) = 1,10 BTU per lb

Leaving loss

= 2.0 Btu per lb

Take disc fricticm loss

tt 0.66

Btu per lb

Enthalpy drop per lb with cariy over = I (hh)^ - leaving loss X carryover =

55*65 - 0*6 % 1,10

= 54,99 BTU

But total losses := Mozsle loss ^ blade loss -f disc loss + leaving load =

2.55 + 1.10 + 0.65 + 2.0

= 6*10 BTU per lb 55.66 - G.IO Stage eff.

-

0.845 34.99

Stage efficiency corrected for moisture contents of 0,968 Stage eff .

=

0.845 ( 100 - 1.15 % 3,2 )

- 0,814

(56)

(6)

DB8I8B OF TWO-RGÜ ŸB&OCITZ GTWIB* (à)

Blade Efficiency t This stage

be design with the foUcwiag data*

=. 450 ft per sec X, = 15*

0.216

-

=

Yk/p = 450 / 0.216

fig

(7 )

_ 0.9GO

/. i?t

=

Yz / b = Nn

= 20e0 ftper @eé

2080/ 0.960

* 2170.0ft per aec 94.10 BTU per lb

Ideal enthalpy for this wheel L

= b,-

- 1581.80 - 94.10& 1287.70

BTU

This corresponds to the following ccnditions ; P

=

193.9 psi

s

1.6456

T

r: 555 F

)

V

= 2.85

cu ft per

lb

Laying out the velocity diagram , from the diagram we get , =. 1650 ft per sec

;

p,

At this shags reduce the exit angle Y, ând for

t* 19.25 to

17. Assume

- 0*55

V - 2.85 cu ft per lb K =

-

0.00588G

0.97 - Vzr

% K

% 0.97 *

1650

% 0.005886

17^ 19-25

= 0.7950 /. V,y ~ bt,x Vj

T~R

=

-

0.7930 X 1650

890 ft per sec

Reduce the angle S' to

20

;

- 94*X ( 1 - 0.92X)

* 7,45 BTU

(40)

Enthalpy at exit from noZzla Volume of sjseam

at

P,

= 1287,7

-.7*45

% 199,9 psia

- 1295,15 BTU

« 2,90 cu ft per lb

Hence the nozzle exit area should be increased

to

0*492 ( 2*90/2,85)

-0,4975 sq, in, , which will give a diameter of 0,706 inches Instead of 0,703 in. This increased

of 0,003 in, is not sufficient to effect

appreciably the blade enterance height adopted, Tne blading loss can also be computed similarly. Actual reheat in blades

- ( 1 - n ) ( Vz / •b) '2JJ

Vj/2gJ^

= (1 - 0*7085)( 86,5 - 1,13)

- 24,90BTU

Enthalpy of steamleaving last row of blading -

1295,15 + 24,90

. . Specific Volume of steam at ^ Hence

(iv)

-

2,15 (

% 199*9 psia

3,040/2,85)

Bisê^Brlction Losses

&

= 1320*05 BTU

- 2,295

-

3*04 cu ft per

lb

in , instead of 2*15 in*

Stage Efficiency:

From reference (l) page 219 , the power lost in Disc friction is given by Kp Take

= m «

m ,u, (

V /iCof , d/v. ( d/2560 + (1 - e ) c *

1,0 0.5

h «

1,45 in.

c = 1,25 0 = 0,268 V - 5,040 cu ft per lb Hp

=

1.0 X U.5 ( 450/100)^. 28.G6 / 5.04

| 26.65/2360

t'S ( 1 - 0.268) . 1.25 X 1.43 -

31.10 H.P.

-

23.20 KW

(41) 2

Useful blading work

-

2

V/2g x ^

x V/550

=

2080 /G4.4 x 0.7083

b

as*

= 1713 HP Disc loss as percentage of total HP '. Stage efficiency

«

n

r 51.1 / 1715

x (1 - losses)

- 1.814 %

- 0.652 x 0.90186

(n b

« 0,641. Rehaet A// = V

(Ah) ( 1 f n ) "

« 94.1 ( 1 - 0*641)

Adding this reheat to 1287,70 BTU at

s = 1.6436 » we get steam enter­

ing the 2nd. stage ( or 1st pressure stage) at P,

-

199,0 pel

h

« 1321.60 BTU

8

« 1,6765

T

= 598"p

V

« 3,04 cu ft per lb.

- 35,80 BTU par lb

(4%)

(D) (a)

Design Of Stage (^) t

For maximum efficiency of a pressure stage ^ *vJieré (y - noszle angle

Cos o( /'

Ü - 15

= 0.429 But we will assise a value

gî

P t: 0,44 i we have V, = 550 ft per sec

= 550 / 0.44 For this velocity of steam ky^ = IV^

-

/|^

-

796

per see

0.966

- 796 / 0.9G5

= 825 ft per aec - 1 3 . 6 7 ETU per lb

Draw the velocity diagram , and wefind \ Assume

y

Tt-H

- 472 ft per sec = 0.4 E

kb

and

;

^

~ 26 = 26*, and for

v = 5.08 cu ft per lb

= 0.00597

_ o^j7 _

X %

- o;:'7 -

472

% 0.00597

^+y = 0.954 Vgy

-

- 0,334 X 472

Vj

= 197 ft per sec ^ Vg - V

=

441ft per sec

2

X

2.

-2. +441 »197

Blade ?

V

bl

796^

' = 0.884 Combined >> tb

=•'0 x d

How with 5600 RRi Circumference Mean Diameter

&

0.331 x C,884

=.0.023

/bl

ana blade ppeed of 350 ft per sec , we =: ( Vyx 60)/ 5600 =

5.83 /"TT

=(350 % 60) /5600 = l,857p = 22.3 in.

= 5,83 ft

(

We h&ve enthalp^ at

43)

t onteranee to nozzle of this stage

= 1321.95 BTU

S = 1.676 . . Enthalpy at exit from nozzle

At

= 1521,^5

- 15.67

= 1368*28 BTU

this enthalpy and entropy we get P,

= IV 5 psi

T

= STO" F

8

= 1.678

V

= 5.4 cu ft per lb y X V X 144

Nozzle exit area

19*3 X 5.4 x 144

A ^ Vz = 1. .18

For full peripheral admission , take

79G

in. m= 0.9 for square nozzles

Area of nozzles Maximum Height

12,18

= Ti X D X 8ino( X n

70 x C,2oB8 x 0,3

- 0.746 in. Nozzle cross-sectional area No. of nozzles use

% ( 0.746)

- 12.18 / 0.555

-

=. Q.v., 5 sq, in. 21.95

22 Nozzles Area of each nozzle

= 12,18 / 22

= 0*554 sq. in*

Area of nozzles Pitch

12.18

= h X 8ino( X No,of Nozzles x m

0.746 x 0.2588 x 22 x 0.9

=.: 3.16 in. Total arc occupied

= 22 x 3,18

Percentage perlpheiy" occupied Breadth of nozzle

. Height of blades

= 70/70

= 1,0

- Pitch X Sin X % m = 0,741

. . Height of Nozzle

= 70,0

=

- 5,18 x 0,2588 x 0*9

in*

0.554 / 0,741

- 0.748 in,

- Height of nozzle + Ove lap ( 0*1) - 0*748 + 0.1

=. 0*85 in*

(V-)

We ci.in now calculate the disc friction losses, Hp

=

m.n. ( :Vb/lOÜ)’ . d/v ,$ d/2560 + ( 1 - s ) c . t

Since we are using full peripheral admission

9

= 1,0.

*

:Hp

-

a . n . ;( Y J

IQO) . d/«- . A 3

= l.G X 0.5 X t

/ 2560

■

■

( 550/100) % 22.5/ 3.4 x 22*5 / 2560

= 1.546HP' Z

Now Work done by blading

-

Vj^/Sg x n x ¥ / 550

- 706 /84 ,4 x 0,884 x 19 9

‘t

55o

= 515.80 HP '• Disc loss as percentage of the total loss Assume average lealtage loss Stage efficiency

%

1.346/ 513,80 = 0.45$

= 1 .5 $

= n x Losses (rib

. . ggeful work delivered

-

- 0.825 % (1 - 0,019s)

n

- OàBOS

x(Ah)^

= 0.805 X 15.67 = 11,0 BTU Reheat

(b)

:

= 15.67 ( 1 ^ 0.805 )

= 2.66 BTU

Design Of Stage (5) : ; At thiB stage we will increase the blade velocity from 550

ft per sec to 560 ft per sec ) and keeping V;>

t: Vb / p

Take X = 15 iV;,

4 Vz/L

= 560/ 0.44 ,

Sathalpy at exit from stage (2)

,¥é get

= 818 ft per sec

From Fig ( ? )

=; 818 / 0.965

=0,44

kn

= 0,965

= 848 ft per sec = 1306,28

+ 2,66

14,4

= 1510 ,94

Me get the entropy on constant pressure line as 1,680 . .Enthalpy at exit

from nozzle

With tills enthalpyand at

= 1510,94 - 14,40

= 1296.54BTU

a = 1.660 we. enter the Srd* Stage

following condition of steams

with

the

(45) P = 154 psi T

z

5 4 5 ''?

s

% 1.6S0

V

= 5 . 7 5 cu ft per lb

How draw the velocity diagram and we get z Assume

T=R

478 ft per seq ; =0.4

and

n 26.6

Y = 20.6

; and for

v -= 3.78 qy. ft per lb

K = 0.ÜÛ59 /.

kb= Û.97 -

Vzy % % Yt A

- 0.37 -

478 53 2

x 0.0059

= 0.9220 Vgy

= kb X VZY ~ 0.922 X 478

= 440 ft per sec

Vg = 2 0 2 ft per sec, 818'" - 478^ + 44C^ ^ 202"" Blade r> = ?6

V,*"

818^

0.885 z 0.351 X 0,835

Now

with 5600 RPM

and blade speed of 560 ft per see , w© get

Circumference

= (%

Mean diameter

%

How nozzle exit area

x

60)/ 5600

=. ( 560 x 80)/ 3600

6,0 x 12 /tr

% ( M x v x 144) / =

For

= 0.825

- 6,0 ft

=22.92 in* =(13.3 x 5.78 X 144)/ 818

15,15 sq. in*

full peripheral admission f take

m = 0.9 for #qnare Koszles

Nozzle Area

13,15

Circumference x 8ino(x m

6 x 12 x @$2588 x 0$

. Maximum Height =

- 0.785 in. 2

Nozzle cross + sectional area No

♦ (0*785)

- 0*616

sq* in

(46)

No. of NoEzles With

= 15.15 / O.GIC

= 21.4

22 Nozzles the pitch rises to 5*27 inches p tdiich we do not

want* So using 24 Nozzles Nozzle breadth

the pitcli can hereduced to 2.8 Inches,

=

p^x Sin

x m

= 2.8 % 0*2588 x 0*9

= 0 *0o'= in. Nozzle exit area

=

. . Height of nozzles We

can

15,15 / 24

- 0.548 sq. in*

= 0.548 / 0.054

= 0*34 in.

calculate the discfriction losses from the same formula having

full admission, Hp

= m . n . (Vb/ 100)^ . d /v . d/: ^5^0 3

= 1.0!% 0.5 % ( 560 /lOO) X 22.9/ 5*78 % 22*9 /256Ü ,=1.4nH? Work done by blading : Disc:friction loss Taking à leakage loss Bt&ge n

=

Vg/2g z n % W / 550

=

813/64.4 xO.685 x 19.8/550

= 1145 / 352

-0,4 5 6 %

- 1.5 %

= "n X Losses

= 0,825 ( 1 - 0.01936)

At this stage we cen assume a carryover of 60 $ .*•

(Ah)^ = (Ah)^ - carryover x leaving loss = 14.40 - 0.6 % 0.81 = 13.914

I

Stage y\ c

Useful work

BTU

0.800 x ( 14.4/15.114)

-

n (6A

=

= 552 HP

x (Ah)^ 3

= 0.835

- 0*035 x 15.914

11.64 BTU per lb.

= 0*808

(47)

(E)

LAYOUT

OF'ROTOR

PROFILE

It is desirable in the design of turbines to have a smooth rotor contour from stage (f) to stage (2). In laying out the outline , the st:ge centers lines are spaced with reference to the following dimensions.

Stage Number

2

25

4

Azcial Length

7.0

o.O

5.U

12

15

4.1

4.45

Stage

Number

11

Axial Length

5.6

5

G

7

8

5.0

5.0

2.1

14

15 5.5

4.85

J

10

5.2

5."5

5.55

16

17

18

10

:.u

6.4

7.1

8.0

Before laying out these distances it was planned to have 13 stages ( pressure-)'

(a)

in

the turbine between the two end bearings.

CALCUL-'TICN OF RFNEAT FACTOR : Referring to Table (A) , we find the average st-ge efficiency =0.826

’ We have the condition of steam entering the pressure stage as follows. P,

= 100.J usi

h

= 1321. S'j BTU

5

Z.1.67C5

T

= 598'' F

V

=5.04 cu ftper sec

With this pressure and entropy we move to l.u" Hg pressui'e line on Ellenwood chart and get the following existing conditions at the exiiaust end.

(48)

= 9Ü1.0 X V

BTU

: = 18.G"t = 530.eu ft per sec

(Ah) a

= ( 1321*50 - 901.0 )

Referring to Steam Turbine of

Rgg for

80$.

= 420.50 BTU

by Prof. Ciiiu’ch page

240 , we get values

st i.ge

From our given conditions Initial superheat

=■ 218.2 F

* • Rgg = l.USl Making corrections for 18 stages we can calculate actual values by appL!,^ing the following formula , R

=

1 t (R

- 1) (1 - 1/ nb. of stages) ( 1 - ^5 0-2

=

1 t ( 1.J51 - 1 )( 1 _ 1/18)( 1 - U.J20 ) 02.

= 1.U419

Cumulative Energy from st-’ge (2) to stage (Z) =

(Ah)

:

= l.v419 X 420.50 = 43.*40 BTU*

)

(43)

(b)

CALCULATIOHE

F0~: T^EU' (A):

The cumulative energy calculated on the previous page is,now' to be divided among

18 consecutive stages from stage (2) through

stage (Z) , Tlie enthalpies of stages (f) , (S) , (X), (Y) and (Z) are kept the same as they were calculated previously. However, the energy distribution for stages (X) and (Y) may be changed slightly in order to adjust the actual cumulative heat drop. Energy'. Energy values of stages (2.) , (o), and (Z)

should, not be changed.

In order to distribute the energy into 18 stages we have made use of the fact that the energj^ is proportional to the square of the mean diameter of the blade rin_^. Tliis gives quite a good

prox­

imation . ” Estimated Stage efficiency ” is filled in Column (5) increas­ ing progressively upto Icth. stage and decreasing afterwards. The rehe t is c ’lcul ted from this and finally th

ideal velocity of

steam . In the last column'diameters arc entered from calculations : of the blade velocity.

N

>

Oi

O ^ 5 PQ O O r

m

Û0

\p

Â} H O X) o

(51)

IJL

'J ’-o vo

o r—

oo

cr^

oo

o ^

l-O

oo -o oo

CO

oo

rO — lo uo r~rO rO

oo

o

^

Vf-

LO

—

'-O r~-

vx> ro (\j (-0 roo

CTO

oo

oo 00 oo

^

cTv

o

LÔ O-v "O' ^

o

o

o

WÔ LÔ vO — LT) vD

o

vD V) vD LT) _ o cJ rO vo 00 (T\ (T (T\ (Jv cTi


( -16° , and draw Vgy =

596

=

0.44

ft per sec

28.5°

bh = 0.07 -

Y -26,0

Vif X K jSfX

'

i&ere for

= 0.J7 ^jy V3

=

506 54^

Blade y. (

K

= 0.002266

V - 16,15

cu ft per lb

X 0.002266 and TfR

= 0.4

0,3452 X

-256

- 44G ftper sec

thevelocity diagram , From the diagram,

Reduce the exit angle and take

f.

X 1015

-

0,9452

ft per sec

x 596

- 1,21

BTU Leaving

V^- t V ^ - y /----- — -----Vi

—

== 564 ft per sec

—

Loss

1015^- 596'+ 564 - 256^ --- ------- ------------ 1015"

= 0 .3 0 Combined y\ -

n

x

Lb

. , Useful Work

0,351 x 0,90

- 0,337

'b

-

in

xZ\h

=

0,857 x 21.25

- 17.30 BTU

-nb

For blade velocity

- 446 ft p e ' sec Vb X 60

Diameter

-

TT X RfM

- 23.32 in

446 X 60 — ---------5.14 % 3600

2,37ft

(71)

DESIGN OF STAGE (13) :

Estimated

Carryover

- ( V^/ 203.7

) pc

- 1.31 X O.CG Total

.

\\

{/i hj

- 1087

fte per sec

- 1040

ft per sec

r' jO X Take

f 0,865 =

carryover

= 0.8G5

20.71 + Ü.8G/.

z 0,44 X 1040

BTU

= 25.575

BTU

- 4G1 ft per v-.ec

(X = 16* , and draw the velocity disgram. From the di gram , ^

620 ft per sec

T: 28°

Reduce the exit angle and take

0

VV.

0.07 -

Ï-26

X K . -

where K

= 0.002145

(3.Vfor, V = 0.J7 - ^ 620 54 z 0.9455 X . Yy

Blade

and

z 0.8455 X 620

264 ft per sec

-

%

z 20.8b cu ft per lb

X 0.00214;

z, 586

1.59

f --- — — ___________

BTU

T4R

= 0.4

ft per sec. Leaving Loss

' 1040^- 620^+ SBc"- 264 % -- ---------- ------ --1049 I

/ -0.898 Combined

x H -- 0.-51 x 0.898 z 0,356 L L = n % Ah = 0.336 x 22.7. z-lü.JG Lb For blade velocity z 461 ft per sec

Diameter

Vb X GO % ---- — — n X RFM -

'

^ . z Li, Useful Work

- 20,50 in

z

461 X GO --------5.14 X 3600

z

BTU

0.42 ft

(72)

DESIGü OF STAGE

(14) :

Estimated Carryover

- ( V / 225.7 ) x 4 carryover 3

1.59

z

Totaljb h) z ^¥ 2. z 1128,5

0.317

X 0.66

^

u

z 24.50 + 0.J17

0.J17

BTU

=22.417

BTU

ft per sec

z 1083 : ft per sec Vb Take

= jO

z 16,

X z.0.44 X

1089

= 479 ftper sec

and draw the velocity diagram , From the di- .gram ,

z 642 ft per sec J3

=

28

Reduce the exit angle and take

k!b z 0.J7 -

y

= 25.5

X K

where for

= Ü.97 —

g 42

Vgy = kb V3

1

z.

and TfR

= 0.4

U.J4G6 X

z C , ,466

= 274 ft per sec

Blade "o =

z 28.0 cy ft per lb

X

642

=

1.50 BTU

- Vzy f V," ~ -— — ~

z

608 ft per sec Leaving Loss

lOdJ - 642 + 608 - 274 — ------ -— — . IU 80 -

2.

V

X 0.v01j4o

53 f =

K = 0.001346

U , jO

Combined n ~ ^ x n - 0,951 x -0,30 ■=. 0.837 l'-K 1b >K 'k b Useful Uork = ^ x/\h = 0.837 x 24.s = Lb For blade velocity Y t> - 470 ft per sec

Diameter

=

Vb X 60 — ---= TT X RDM

-

30.45 in.

479 X 60 -------------- = 3,14 x 3600

20.50 BTU

2.54 ft

(73)

St a g e

(M) ScAL£ 2.00 ji,

-OAc

rl"

i 274

STAGE

(i5)

74-5

6&0 --------p

STAGE

(16)

jjr 2? y -- ag

686

(74) DZSIGN OF STAGE

Estimated

Total 6^ h; L Vj. V Vb

( 15) :

Carryover

( V^/ 2.,5,7 ) x f* carryover

=

1.5Ü X 0.06

=:Ah^t

= U.j3

= 27..U f O.oU

-1188

ft per sec

-1146 . =r X

ft per sec

Take o< - 16

-

Vz - 0.44 x 1146

-

ÜTU

- 2U.13

BTU

604ft per sec the diagram ,

, and draw thevelocitydiagram . From

- 600 ft per sec j9 = Take

=

6

27" g

=

27*

= 0.37 -

Vir X K

- C.J7 -

680 X

where for

K ^ V -

0.00174; 40.u cu ft per lb

U.V01745

54

and

TpR

-0.4

= 0.0480 Vjy

- kb X

Vj

- 310 ft per sec

Blade ri /

= ".0480 X 630 5?

-

1,62

Vi - Viff V ^ - v / — ----------— ---

BTU

646 ft per sec Leaving Loss

1146^^ 680^+ 645 - 510 ---- ----------------1146"

-

= 0.830 Combined

x

Lb Useful Work

=_ .331

x 0.890

0. 826

L -

x Ah Lb For a blade velocity

Diameter

n

= 0.828 x 27.2 -

22.50

BTU

504 ft. per sec

Vb X 60 - ------- --77 X R?M - 5/.10 in.

-

504 X GO — ~------5.14 X 5600

- 2,6/6 ft

(75)

DESIGN OF STAGE

(16)

Estimated Car y over

Total A h , tVg * •

( V/ 223,7 ) x fo carryover

z

1.32 X 0.68

= 1.308

1.308 = 50.80 + 1.508

BTU

- 52 .108

BTU

z 1266 ft per sec

v^,

/'

-

Vb

- 1221 ft per sec = jO X

Take o( - 1G°

- 0.44 X 1221

- 538

, and draw the velocitydiagram

ft per sec ,From the

diagram ,

z 720 ft per sec j3 = Take

y

-Q r

':8" H8 °

kL — 0, 1b For a blade velocity z 538 ft per s c

Diajneter

X 60 z — ------IT X RPM

— 34,22 in.

530

X

25.21

BTU

00

%

z 2.656 ft 3.14 X 360Ù

(76)

DESIGN OF STAGE ( 17) :

Estimated

REVISED

Carryover

z

STAGE

( V3 / 2:'3.7 )

x '/

= 2.175 % 0.7 Total fih;

Take

l V 2.

z 1358ft ,er sec

Vz

z 1310ft per sec

Vb

=

cK = 17

z 1.57

z 0.44 X 1310

z

BTU

5Ü.85 BTU

576 ft per sec From the

^i'graÿ ,

780 it per sec

0 z Y" =

.0 X y,

carryover

= 35.53 t 1.52 %

,and draw the velocitydiagram.

V z

Take

ziZih;+ 1.52

(X)

3

2 0 ,7 5

=

"

20.Ts"

z, U.07 -

z 0,07

-

Vav X

780 X -^7

K

where

K

for

V

and

T-fR

z o,uul27

= lOv.15 cu ft per IL

0.00127 - 0,4

z 0,0554 Vjy.= • V,

Blade

z

kb X Viy =

Ü.J534 X .780

576 ft je ■ sec . ^

n z

V,^ - V^y

=

2,87 BTU

V ^- V/"

743 ft per sec Leaving Loss

1310 - 780^f

743 - 376

1310^ 0,883

Combined ^ % in x 11 =. 0,951 x 0.835 z 0,821 Lb 'n L Useful Work n xAh z 0,883 x 55,55 Lb For a blade velocity z 576 ft per sec

V^x GO Diameter

=

-

576 X 60 z

n X R?M

36.70

in.

z 29,0 B

— z3.0 ft 5.14 X oGvO

(77)

>o

- 0,97 -

Vty X K

where

K

-=. 0.00068

for V

- 565

fir?

-0.77 -

1126 gj-

cu ft per lb

X 0.000G8 and TrR

= 0.45

- O.JGO Vgy ZL .

.

V3 -

febX y,y

- O.L-bO X 1126

720 ftper sec

Blade va = I —

- 1080 ft per sec

10.40

BTU.Leaving Loss

1 7 8 ^ - 112G" + 1080 - 720 ----------------- ----1782^

---------------- ----

.

0,0 O4

Combined r\ = n x n _ 0.051 x 0,804 - 0.748 l^h 'w ' Useful work - y-j x A a z_ 0.748 x 64.68 T. ■For aDbladevelocity

Diameter

=735 ft per

V^x 60 ------ -TT X RPM - 50,0 in.

46.4u

sec

785 X 60 — --- ---- 3.14 X 5600

=.4.16 ft

BTU

(81)

UJ

00

AJ

00

u_

(82)

POKER

Since

ISp'üIEi'D

OF

THJ:

Tumi INF.

the turbine electrical out put is to be

7,5o0 lOJ , vre

can find the internal power to be delivered by the turbine. Generator Efficiency

*

—

0,98

%

0,98

0.Ü55 7" .— — I ■ , Y K?/ rating / 1000

—

Rating ^

—— -— Efficient load

O.ObS

7,800

7,800 /lOOO

6,000

j

-0.948 Mechanical Efficiency

—

100

-

100

—

(

6 ~~ — —— — y/ïïw rating / 1000

y

7,500 /I000

- 0.J85 Internal power delivered by the turbine KW rating

V 2

' -

7,500 d088 X 0.14,

1

8060 KW Internal work of turbine

-

Initial enthalpy - Final enthalpy after table (B)

- ( 1381.80 - 171.5R6 ) Steen Rote based on internal work

Steam

Flow

-

3413

-

3413

-

8.314 lb per KW

- ( 8.314 x 8060 )/ 3600

•5'- Brown & Brewery

ASME,

=

Trans.

-

410 .474 BTU

/ ( internal work) /

410.474

18.65 lb per sec

1SS3

(83)

CALCULATION

Table (D)

OF

STAGE

LEAKAGE

shows the results for the steam leakage between consecut­

ive stages of the turbine* In order to determine this leakage we first have to find the leakage through the High Pressure gland. It is assum­ ed at this stage that the high pressure end of the turbine shaft is 10 inches in diameter and that

15

labyrinth packing rings.are used

to prevent leakage and the clearance between ring and shaft is 0,015 inches. From

Figure 19(' ( referenece

1 ) , values of leakage in

lbs per hour for various diameters of the duTmiy wheels with varying number of labyrinth rings , For

10 in. diameter and 15 labyrinth

rings , the lec.kage is 550 lb per hr for a pressui'e of 100 psia and a clearance of 0,01 in.. So that this lea.lage is corrected for th< steam pressure after expansion through the nozzles in stage (l) is 1j..',9 psia .

Actual Leukige

Percentage

-

500 x

Leakage

190,'J X 0,015 — ------ : luO.U X 0,010

- 1555 lb per hr

1555 / ( steam flow x 50u0)

:

cJ

1555 / ( 10,55 X 5600 )

'

- P.518 < :Throttle Flow including the high pressure gland lei'kage -

16,0

/ 0,9768

^Ir.lO lb per sec

- Go, 760 lb per hr. All this steam pesées through the two- row velocity wheel. A portion of this steam leakgg. out through the high pressure gland packings

(84)

and is of no use . The remainder passes through the nozzles and blad­ ing to do useful work. This steam is the effective steam flow for stage (2) Steam Flow through

two- vo\i wheel

=

G8,7G0

- ( ob, 760 z 0,002:16)

= 66, 6ol lb per hr. - 10,(Jo lb per sec.

Effective steam flow through stage (2) C

61

, 601 - 15o5

-

67, 046 lb per hr.

In table (D) column (2) is the existing pressure across the blades in every stage and is entered from table (B), Column (h) giv\. gives the flow coefficients through an orifice for any given values of pressure ratio across the orifice. Value can be found from Fig ( 8 ) reproduced from page

GO ( reference 1), Column (-5) is the : v

assumed number of labyrinth rings to be used to prevent interstage leoicsige. IColiMp. (’6)-''is thé.-nominal intdf stage‘-le...kage in lb per hr for 12 in, shaft diameter from Fig 196 ( reference l). Corrected interstage leakage can be calculated as before . Assumed clearance between rotor and gland as 0,025 inches.

0,025 X actual leakage Corrected Leakage - Nominal les-kuge x 0,010 X

100 psi

X Flow Coefficient,

CC

-j-to

1 cd .

; ; ' .

•

• 'I Ti

. '

: N

■

TABLE (D; -- -— ^ ----2

3

?RES5URE

PRESSURE

1

D

iaP h

RA

n Io

) -2

4

■R.AT10

PSI

3 - 4 4 -5 5 - 6

6 -7 7 - 9

1 9 9 .9

9 - 9

176

0.9 7 0

9

859

I3j'0

114 0

0

837

0

834

954 5

66-0

10-11 11-12

5'4 43

0

0

3-797 0-782

33-6 & 5 2

13-14

'9

14-15

13-50

15-16

9

95

ü

764

0 75 2 0 713 0

690

0

6'5

i?

I6-17

5 65

17-19

3

19 -

RINGS

No

m i n a l

22

LEAKAGE ■Iki ïyr

P pevScc BTU

6 D isc friction

KW

7

8

N et STAGE WORK 1b

- ^.044 x Ic .26

-12. -8 BTU

(103)

STAGE

(lo) :

- ( V?/ 223.7) x % carryover

Estimated Cany over

= Total A h

•'

1.U5 X C.o8

1