2
MODERN
POWER
STATION PRACTICE
'1
tSA'
w II:: ~ ~ W IL.
~ ...
t2
ENTROPY
.
a. b - CONVERSla-I OF HEAT ENERGY TO KINETIC ENERGY b.c - 'REABSORPTla-I OF KINETIC ENERGY TO HEAT
ENERGY
WATER
:-
i W
,\
Pl fI I' I
SUPERHEATED>
STEAM
VAPOUR
P,I-
9
SPEOFIC VOLUME V
e SUPERHEATED ST'EAM
x
)0' IL. oJ
.!7',,~'~J~;-~.'~~,
I
-
ENTROPY . b.c.d.e.. HEATING AT CONST~T PRESSURE e.f.g.
. IDEAL EXPANSIONAT CONST"NT ENTROPY,
g.o.
. EXTRACTION OF LATENT HEAT INCONDEH5Fk . IDEALPRESSURE INCREASE AT COHsrAlft ENTROPY INFEED PUMP
o.b.
FIG. 1.1.1A.Basic routine
cycle with superheating
3
TURBINES'
proportionately smaller. Further, unlesshigh~density high condition steam is used at a 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 increasing the cycle efficiency. For condensing turbines the vacuum obtainable is determined primarily 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 but large addition is made to the T/cJ>area (see Chapter 4). e
g
e g SUPERHEATED StEAM w cr :J I« cr w
Do ~ W I-
ENTROPY
~
ENTROPY
AVERAGE TEMPERATURE
~ OF
b.c.d.e. AND Lg. HAS INCREASED, DUE TO REHEATING
b.e.d.e. e.f. f.g. g.h.i. i.a. a.b.
- HEATING AT CONSTANT PRESSURE -IDEAL EXPANSION AT CONSTANT ENTROPY BEFORE REHEATING - REHEATING AT CONSTANT PRESSURE -IDEAL EXPANSION AT CONSTANT ENTROPY AfTER REHEATING - EXTRACTION OF LATENT HEAT IN CONDENSER -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 cycle efficiency by using reheat, which is a way of partially overcoming temperature limitations. By returning partially expanded steam to a reheater, the average temperature at which heat is added is increased and, by expanding this reheated steam through the remaining stages of the turbine, the exhaust wetness is considerably less than it would otherwise be (Fig. 1.1.IB). Conversely, if the maximum tolerable wetness is allowed, the initial pressure 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 energy at 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 kinetic energy will be reabsorbed as frictional reheat and the final enthalpy wHl be the same as the original (Fig. 1.1.2A(b». This process is known as throttling and is inherently wasteful Po
Po
o
<1 ENERGY
>CL
>CL ..J ~
..J ~
DISSIPATED
~ i5
F z w
BY INTERNAL
REHEAT
LOSSOF LOSSOF
AVAILABILITY
AVAILABILITY
ENTROPY
~
ENTROPY
~
(b)
(0)
COMPLETE DISSIPATION OF KINETIC ENERGY (1:HROTTLING)
USEFUL EXTRACTION OF KINETIC ENERGY (TURBINE BLADING)
a-b - CONVERSION OF HEAT ENERGY TO KINETIC ENERGY b-c - REABSORPTIONOF KINETIC ENERGY 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 in e..ntropy.(Rise in entropy may be regarded as loss of availability of the energy.) Throttling is used where it is necessary to dispose of energy in the form of enthalpy~ e.g. in governing valves at partial loads, labyrinth glands and blade tip seals. Figure 1.1.2B(a) illustrates the expansion process. Two chambers are connected by a small 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 exhaust pipe and valve, to enable its pressure Pb to be varied. When the valve is closed Pb
and the flow
= Pa
G=O
As the valve is opened, Pb will fall and the pressure difference (Pa-Pb) will cause a flow through the nozzle, the steam assuming kinetic energy at the expense of its enthalpy.
5
TURBINES
.,I )
1#
~ <
(;
VALVE
(0) EXPANSIONPROCESS
CONVERGENT NOZZLE
CONVERGENT. DIVERGENT NOZZLE
CONVERGENT - DIVERGENTNOZZLES FOR TURBINE FIRST STAGE
(b) NOZZLE PROFILES FIG. 1.1.2B.Flow through nozzles
6
MODERN
POWER
STATION
PRACTICE
If there were no friction, the expansion through the nozzle would be isentropic, in which case the drop in enthalpy Ho could be measured on the Mollier chart from the vertical 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 drop so that lJH1 = cp2lJHo The flow
G
a
= C1X- V
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 exit pressure and temperature. A fall in pressure beyond this will not be transmitted upstream (since pressure variations travel at acoustic velocity) and hence no additional velocity and flow will be induced. At exit pressures lower than the above value, it is necessary to design the nozzle with a divergent 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 development of 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, the Pa
P critical pressure ratio -.!!...= O'580.
Pa The maximum flow G which can pass through a nozzle, the pressure ratio across which is critical or less, is given by G
=
0'309A
Pa
-
V Va
lb/sec
which is obviously independent of the pressure P beyond the nozzle. Pa
= pressure before = specific volume
the nozzle in Ib/in2 absolute, before the nozzle in ft3/1b, A = throat area of nozzle in in2. va
7
TURBINES
From this it can be seen that for the steam conditions given by Pa and va' the maximum flow through the turbine, and hen~e the maximum power output, is limited by the throat area 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 running full, 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 control valves. In a throttle-governed turbine, the flow is controlled at all partial loads by varying the pressure in front of the nozzles. This method simplifies the control valve gear, but is less efficient at partial loads. 1.1.3. Moving Blades In blading designed on the impulse principle, steam from the nozzles impinges on moving 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 the rotor, and in this way the kinetic energy of the steam is absorbed. Figure 1.1.3A(a) shows the velocity diagram for this type of blading. This is a vector djagram of steam velocities relating the absolute steam velocity C1leaving the stationary blades to the velocity of the steam relative to the moving blades W 1, U being the tangential velocity of the moving blades. Similarly for the steam leaving the moving blades, the diagram relates the velocity of the steam leaving the moving blades W2 with the absolute leaving velocity C2. The
~
termed the velocity ratio, as shown in Figure 1.1.3B. efficiency depends on the ratio 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
~~
~. Co
Since C1
= rpCo,
is smaller than the corresponding ratio Cu . 1 The other principle used in turbine blading is that of reaction, whereby there is some heat drop in the moving blades, so that they act as nozzles. The jets of steam issuing from 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 has been found to be impracticable. The 50 % impulse-reaction turbine (in which half the heat drop takes place in the fixed blades and half in the moving blades) is, however, very successful 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 much change 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 roots only, and a varying degree of reaction up the blades, depending on their length (see section 1.5).
)
8
MODERN
POWER
STATION
PRACTICE
) J.I.
"
/
"
/
/
"",-,,""
(0) IMPULSE(W2< Wl~
IJ.
J.I.
(b) 50% REACTION KEY Ct = ACTUAL STEAM VELOCITY LEAVING STATIONARY BLADES ex= ANGLE BETWEEN THE PATHS OF THE MOVING BLADES AND THE STEAM LEAVING THE STATIONARY BLADES I.l = VELOCITY OF MOVING
BLADES
(W2 > Wl)
W t = RELATIVE STEAM VELOCITY ENTERING MOVING BLADES {J = ANGLE BETWEEN THE PATH OF THE MOVING BLADES AND THE RELATIVE PATH OF THE STEAM LEAVING THE MOVING BLADES C2 = ACTUAL STEAM VELOCITY LEAVING MOVING BLADES
FIG. 1.1.3A. Velocity diagrams for blading
9
TURBINES 100
80
~ z
60
1&1
U ii: :; 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 the following: (a) The expansion efficiency
{,=
Kinetic energy produced/lb of steam Enthalpy supplied fib of steam
}
Work done on rotor fib of steam (b) The diagram efficiency
{ = 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 there is 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 remaining 15% of the available energy; some is dissipated as heat due to friction and some is rejected in the form of kinetic energy. The latter may be partially or wholly reclaimed by 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 is termed the "leaving loss". To minimise this loss it is important that the velocity of the steam 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 as economically 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 flows through the blading, plotted on the Mollier or Hj(/>diagram (Fig. 1.1.5). An ideal state line would be isentropic (vertical on this diagram) but frictional reheating in the stationary and moving blades gives the condition line an increase of entropy at each stage. STOP VALVE CONDITION
.
Po
P1
to
~
FIRST STAGE MAY BE LESS EFFIOENT DUE TO LOW VELOOTY RATIO
:J: >n.
~ :J: ~ Z W
FINAL CONDITION OF STEAM IF BROUGHT
LESS EFFICIENT DUETO WETNESS
TTST WASTED KINETIC
. I
. I
I ','
,
,'
,'
,'
ENTROPY
\
ENERGY (LEAVING LOSS)
FINAL
OF
CONDITION
MOVING
(LEAVING
STEAM LAST
ROW)
.
FIG. 1.1.5. Turbine condition line
For a typical stage, the work done or useful heat drop is represented by lJH1 Btujlb and the isentropic heat drop by lJHoBtujlb. . lJH1 The stage e fficlency ={)Ho For the whole turbine the useful heat drop is represented by LlH1 Btujlb and the isentropic heat drop by LlHo Btujlb.
.. . LlH1 Th e tur b me InternaI efficlency =LlHo The lines of constant pressure on the chart diverge as the entropy is increased and hence 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 necessary to divide the turbine into groups of stages between tapping points. E
Gross group output where
GG
= steam
G
=
GGXLJHG kW 3412
flow through group (lbjh),
LJHG = useful heat drop for group (Btujlb). Net generator output where em = mechanical efficiency, ee
= electrical efficiency.
Specific steam consumption
= GA
IbjkWh
'E
where GA
= steam
flow at stop valve (lbjh).
For a turbine generator without reheat Specific heat consumption
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). or a turbine generator with single reheat pecific heat consumption
where H2
=
GAH1+ GBH3-GBH2 -GAhl E
steam enthalpy before reheater (Btujlb),
H3 = steam enthalpy after reheater (Btujlb). fhe additional second term represents the specific heat input from the reheater. For a dual pressure steam turbine without reheat I
