2 MODERN POWER STATION PRACTICE

'1

tSA'

wII::~

~WIL.

~...

t2

ENTROPY.

a. b - CONVERSla-I OF HEAT ENERGY TO KINETIC ENERGY

b.c -'REABSORPTla-I OF KINETIC ENERGY TO HEAT

ENERGY

WATER

SPEOFIC VOLUME V

e

x)0'IL.oJ<C

j:ZW

SUPERHEATEDST'EAM

.!7',,~'~J~;-~.'~~, I -

ENTROPY.b.c.d.e.. HEATINGAT CONST~T PRESSURE

e.f.g. . IDEALEXPANSIONAT CONST"NT ENTROPY,

g.o. . EXTRACTIONOF LATENT HEAT INCONDEH5Fk

o.b. . IDEALPRESSUREINCREASEATCOHsrAlftENTROPY INFEED PUMP

FIG. 1.1.1A.Basic routine cycle with superheating

:- PlfI

,\ SUPERHEATED>STEAM

i I' VAPOURW I

P,I-9

TURBINES' 3

proportionately smaller. Further, unlesshigh~density high condition steam is used ata high rate of flow, the high-pressure blades become very small and inefficient.

A lower exhaust pressure lowers the temperature at which heat is rejected, thus in-creasing the cycle efficiency. For condensing turbines the vacuum obtainable is determinedprimarily by the temperature of the cooling water at the site chosen. Any possible im.provement in vacuum is very effective in increasing the work done, since a narrow butlarge addition is made to the T/cJ>area (see Chapter 4).

e ge g

wcr:JI-«crwDo~WI-

SUPERHEATEDStEAM

ENTROPY ~ ENTROPY ~

AVERAGE TEMPERATURE OF

b.c.d.e. AND Lg. HAS INCREASED,DUE TO REHEATING

b.e.d.e. - HEATING AT CONSTANT PRESSURE

e.f. -IDEAL EXPANSION AT CONSTANT ENTROPYBEFORE REHEATING

f.g. - REHEATING AT CONSTANT PRESSURE

g.h.i. -IDEAL EXPANSION AT CONSTANT ENTROPYAfTER REHEATING

i.a. - EXTRACTION OF LATENT HEAT IN CONDENSER

a.b. -IDEAL PRESSURE INCREASE AT CONSTANT

ENTROPY IN FEED PUMP

FIG. 1.1.1B. Effect of reheating

On large turbines (i.e. 100 MW and over) it becomes economic to increase the cycleefficiency by using reheat, which is a way of partially overcoming temperature limitations.By returning partially expanded steam to a reheater, the average temperature at whichheat is added is increased and, by expanding this reheated steam through the remainingstages of the turbine, the exhaust wetness is considerably less than it would otherwisebe (Fig. 1.1.IB). Conversely, if the maximum tolerable wetness is allowed, the initialpressure of the steam can be appreciably increased.

Regenerative heating of the boiler feed-water is widely used in modern power plant.the effect being to increase the average temperature at which heat is added to the cycle,thus improving the cycle efficiency (see Chapter 3).

-4 MODERN POWER STATION PRACTICE

1.1.2. The Nozzle

When steam is-allowed to expand through a narrow orifice, it assumes kinetic energyat the expense of its enthalpy. When this kinetic energy is extracted by turbine blades,the result is an isentropic expansion, modified by the effect of frictional reheating (Fig.1.1.2A(a».

If, however, the steam expands into a chamber, the whole of the generated kineticenergy will be reabsorbed as frictional reheat and the final enthalpy wHl be the same asthe original (Fig. 1.1.2A(b». This process is known as throttling and is inherently wasteful

PoPo

o

>-CL..J~~i5

<1ENERGYDISSIPATED

BY INTERNAL

REHEAT

>-CL..J~Fzw

LOSSOFAVAILABILITY

LOSSOF

AVAILABILITY

ENTROPY ~

(0)

ENTROPY ~

(b)

USEFUL EXTRACTION OF KINETIC ENERGY

(TURBINE BLADING)

COMPLETE DISSIPATION OF KINETIC ENERGY

(1:HROTTLING)

a-b - CONVERSION OF HEAT ENERGY TO KINETIC ENERGYb-c - REABSORPTIONOF KINETICENERGY TO t fA

ENERGY

FIG. 1.1.2A. Extraction and dissipation of kinetic energy

since the kinetic energy is irretrievably thrown away; this is reflected by the large rise ine..ntropy.(Rise in entropy may be regarded as loss of availability of the energy.) Throttlingis used where it is necessary to dispose of energy in the form of enthalpy~ e.g. in governingvalves at partial loads, labyrinth glands and blade tip seals.

Figure 1.1.2B(a) illustrates the expansion process. Two chambers are connected by asmall orifice or nozzle of cross-sectional area a ft2; the left-hand chamber A is supplied

with steam at pressure Pa and temperature fa; the right chamber B is fitted with an exhaustpipe and valve, to enable its pressure Pb to be varied.

When the valve is closed

and the flow

Pb = Pa

G=O

As the valve is opened, Pb will fall and the pressure difference (Pa-Pb) will cause a flowthrough the nozzle, the steam assuming kinetic energy at the expense of its enthalpy.

).,I

1#

~<

TURBINES 5

(;

CONVERGENTNOZZLE

VALVE

(0) EXPANSIONPROCESS

CONVERGENT. DIVERGENTNOZZLE

CONVERGENT - DIVERGENTNOZZLESFOR TURBINE FIRST STAGE

FIG. 1.1.2B.Flow through nozzles

(b) NOZZLE PROFILES

6 MODERN POWER STATION PRACTICE

If there were no friction, the expansion through the nozzle would be isentropic, inwhich case the drop in enthalpy Ho could be measured on the Mollier chart from thevertical line between the point (Pata) and Ph'

The corresponding kinetic energy would be

C2-~2gJ

where Co is the ideal or isentropic exit velocity

Therefore Co = y'(2gJlJHo) = 223'7 y'lJHo ft/sec

where lJHois in Btu/lb,and J is the mechanical equivalent.

In fact there is friction, and the actual velocity

C1 = cpCo

where cpis the nozzle coefficient, experimentally determined.C2

2g~ = lJH1,the actual heat dropso that lJH1 = cp2lJHo

aG = C1X-

VThe flow

where v is the specific volume after expansion, in ft3/1b, obtained from the Mollier chart.As the pressure Ph falls, so the velocity C1 and the flow G increase. When Ph reaches a

certain value~the velocity C1 will reach the acoustic velocity (Ca) appropriate to the exitpressure and temperature. A fall in pressure beyond this will not be transmitted upstream(since pressure variations travel at acoustic velocity) and hence no additional velocityand flow will be induced.

At exit pressures lower than the above value, it is necessary to design the nozzle with adivergent portion beyond the throat, in order to avoid severe shock losses (Fig. 1.1.2B(b)).This permits a smooth pressure gradient between throat and exit, and the developmentof a supersonic exit velocity.

It can be shown that, for superheated steam, acoustic velocity is reached when the

pressure ratio Ph = 0'547 (termed the critical value). For saturated or wet steam, thePa

Pcritical pressure ratio -.!!...= O'580.

PaThe maximum flow G which can pass through a nozzle, the pressure ratio across which

is critical or less, is given by

VPa

G = 0'309A - lb/secVa

which is obviously independent of the pressure P beyond the nozzle.

Pa = pressure before the nozzle in Ib/in2 absolute,va = specific volume before the nozzle in ft3/1b,A = throat area of nozzle in in2.

TURBINES 7

From this it can be seen that for the steam conditions given by Pa and va' the maximumflow through the turbine, and hen~e the maximum power output, is limited by the throatarea of the first row of nozzles.

In a nozzle-governed turbine, the area A may be reduced in stops by "blanking off"groups of nozzles. Thus there are several loads where those nozzles in use are runningfull, known as "control points"; these are the more economical points at which to run,since in between them a certain amount of throttling takes place at one of the controlvalves.

In a throttle-governed turbine, the flow is controlled at all partial loads by varyingthe pressure in front of the nozzles. This method simplifies the control valve gear, but isless efficient at partial loads.

1.1.3. Moving Blades

In blading designed on the impulse principle, steam from the nozzles impinges onmoving blades, which bend the steam path through an angle as near 1800as is practicable.The change of momentum of the steam produces a force on the blades which drives therotor, and in this way the kinetic energy of the steam is absorbed. Figure 1.1.3A(a) showsthe velocity diagram for this type of blading. This is a vector djagram of steam velocitiesrelating the absolute steam velocity C1leaving the stationary blades to the velocity of thesteam relative to the moving blades W 1, U being the tangential velocity of the movingblades. Similarly for the steam leaving the moving blades, the diagram relates the velocityof the steam leaving the moving blades W2 with the absolute leaving velocity C2. The

efficiency depends on the ratio ~ termed the velocity ratio, as shown in Figure 1.1.3B.Typical design velocity ratios for impulse blading lie between 0.45 and 0.55.

(Note: It is common practice to use the theoretical velocity ratio ~. Since C1 = rpCo,Co

~ is smaller than the corresponding ratio Cu .)~ 1

The other principle used in turbine blading is that of reaction, whereby there is someheat drop in the moving blades, so that they act as nozzles. The jets of steam issuingfrom the moving blades exert a propulsive force on the blades, as in Hero's first turbine.A pure reaction turbine would use all its heat drop in this way; but such a machine hasbeen found to be impracticable. The 50 % impulse-reaction turbine (in which half theheat drop takes place in the fixed blades and half in the moving blades) is, however, verysuccessful and Figure 1.1.3A(b) shows the velocity diagram.

Figure 1.1.3B also shows the shape of the efficiency curve for this type of blading.Being comparatively flat, velocity ratios from 0.55 to 0.75 may be used without muchchange in efficiency, i.e. a high efficiency is maintained over a wide range of load.

Nowadays most impulse type turbines are designed for pure impulse at the blade rootsonly, and a varying degree of reaction up the blades, depending on their length (seesection 1.5).

8 MODERN POWER STATION PRACTICE

J.I.

)/

/" /" ,,"""",-

(0) IMPULSE(W2< Wl~

IJ. J.I.

(b) 50% REACTION (W2 > Wl)

KEY

Ct = ACTUAL STEAMVELOCITYLEAVING STATIONARY BLADES

ex= ANGLE BETWEEN THE PATHSOF THE MOVING BLADES ANDTHE STEAM LEAVING THESTATIONARY BLADES

I.l = VELOCITY OF MOVING BLADES

W t = RELATIVE STEAM VELOCITYENTERING MOVING BLADES

{J= ANGLE BETWEEN THE PATHOF THE MOVING BLADES ANDTHE RELATIVE PATH OF THESTEAM LEAVING THE MOVING

BLADES

C2 = ACTUAL STEAM VELOCITYLEAVING MOVING BLADES

FIG. 1.1.3A. Velocity diagrams for blading

TURBINES 9

100

80

~ 60z1&1Uii::; 40

20

o

o 0.2 004 0.6 0.8 1.0 1.2

.VELOCITYRATIO

FIG. 1.1.38. Efficiency curves for blading

1.1.4. Stage Efficiency

The efficiency of a turbine state (Le. a nozzle-blade combination) is the product of thefollowing:

(a) The expansion efficiency {,=

(b) The diagram efficiency {=

Kinetic energy produced/lb of steam

}Enthalpy supplied fib of steam

Work done on rotor fib of steam

}Kinetic energy produced fib of steam

(c) The fixed blading leakage factor(d) The moving blading leakage factor(e) The dryness fraction

(In the wet region it is found in practice that for each additional 1%moisture thereis about 1%loss of efficiency. Hence the dryness fraction is included in the product.)

The efficiency of a well-designed stage in a modern turbine is about 85%of the remain-ing 15% of the available energy; some is dissipated as heat due to friction and some isrejected in the form of kinetic energy. The latter may be partially or wholly reclaimedby the nozzles of a subsequent similar stage, if carefully designed, and this is known as"carry-over" .

The kinetic energy leaving the last stage in the turbine cannot be reclaimed and istermed the "leaving loss". To minimise this loss it is important that the velocity of thesteam leaving the last wheel should be small and for this reason the annular area (Le.nXthe blade heightXmean diameter) of the last row of blading is made as large aseconomically practicable.

.

10 MODERN POWER STATION PRACTICE

1.1.5. The Condition Line

The condition line for the turbine is the locus of the condition of the steam as it flowsthrough the blading, plotted on the Mollier or Hj(/>diagram (Fig. 1.1.5). An ideal stateline would be isentropic (vertical on this diagram) but frictional reheating in the stationaryand moving blades gives the condition line an increase of entropy at each stage.

STOP VALVECONDITION

. Po P1

:J:>-n.~:J:~ZW

~FIRST STAGE MAY BE

LESS EFFIOENT DUE

TO LOW VELOOTY RATIO

to

LESSEFFICIENTDUETOWETNESS

FINAL CONDITION

OF STEAM IF BROUGHT

TTST

.

I. ',I ',I , '',' ,

WASTED KINETIC

ENERGY (LEAVING

LOSS)\FINAL CONDITION

OF MOVING STEAM

(LEAVING LAST ROW)

ENTROPY .FIG. 1.1.5. Turbine condition line

For a typical stage, the work done or useful heat drop is represented by lJH1Btujlband the isentropic heat drop by lJHoBtujlb.

ffi. lJH1

The stage e clency =-{)Ho

For the whole turbine the useful heat drop is represented by LlH1 Btujlb and theisentropic heat drop by LlHo Btujlb.

h b.. I ffi . LlH1

T e tur me Interna e clency =-LlHo

The lines of constant pressure on the chart diverge as the entropy is increased andhence the sum of the stage isentropic heat drops is greater than the turbine isentropic

-TURBINES 11

heat drop, the ratio being known as the "reheat factor" R.

MHo = };{)Ho

Since LJH1 = };{)H1

Turbine internal efficiency = R X stage efficiency.

1.1.6. Output and Specific Heat Consumption

To calculate the output of any regenerative turbine, with or without reheat, it is necess-ary to divide the turbine into groups of stages between tapping points.

E = GGXLJHG kWG 3412

where GG = steam flow through group (lbjh),

LJHG= useful heat drop for group (Btujlb).

Gross group output

Net generator output

where em = mechanical efficiency,

ee = electrical efficiency.

= GA IbjkWh'E

where GA = steam flow at stop valve (lbjh).

Specific steam consumption

Specific heat consumption

For a turbine generator without reheat

GAH1-GJih,E

GA= E (HI -hi) BtujkWh

where HI = initial steam enthalpy at stop valve (Btujlb),

hi = final feed water enthalpy after feed train (Btu/lb).

pecific heat consumption

or a turbine generator with single reheat

GAH1+ GBH3-GBH2 -GAhlE

where H2 = steam enthalpy before reheater (Btujlb),

H3 = steam enthalpy after reheater (Btujlb).

fhe additional second term represents the specific heat input from the reheater.I For a dual pressure steam turbine without reheat