Performance low pressure end blading

A method for optimizing thermodynamic performance of a steam turbine by matching a last stage blade flow area to condenser pressure by adjusting blade angular orientation to set gaging to an optimum value. The method is also used to correct incidence by setting blade angular orientation upstream of the last blade row.

BACKGROUND OF THE INVENTION 
This invention relates to steam turbines and, more particularly, to a 
method for optimizing for different exhaust pressures and different levels 
of mass flow without different size final stage turbine blades. 
The traditional approach to meeting the needs of the electric utilities 
over the years was to build larger units requiring increased exhaust 
annulus area with successive annulus area increases of about 25%. In this 
way, a new design with a single double flow exhaust configuration would be 
offered instead of an older design having the same total exhaust annulus 
area but with two double flow LP turbines. The newer design would have 
superior performance in comparison to the old design because of 
technological advances. 
In recent years, the market has emphasized replacement blading on operating 
units to extend life, to obtain the benefits of improved thermal 
performance (both output and heat rate), and to improve reliability and 
correction of equipment degradation. In addition, the present market 
requires upgraded versions of currently available designs with improved 
reliability, lower heat rate and increased flexibility. If the new designs 
were retrofittable on the older counterparts as well as being the optimum 
configurations for the diversity of applications, substantial economies 
could be achieved in both engineering and manufacturing resources. 
The latter stages of the steam turbine, because of their length, produce 
the largest proportion of the total turbine work and therefore have the 
greatest potential for improved heat rate. The last turbine stage operates 
at variable pressure ratio and consequently this stage design is extremely 
complex. Only the first turbine stage, if it is a partial-arc admission 
design, experiences a comparable variation in operating conditions. In 
addition to the last stage, the upstream low pressure (LP) turbine stages 
can also experience variations on operating conditions because of (1) 
differences in rated load end loading, (2) differences in site design 
exhaust pressure and deviations from the design values, (3) hood 
performance differences on various turbine frames, (4) LP inlet steam 
conditions resulting from cycle steam conditions and cycle variations, (5) 
location of extraction points, (6) operating load profile (base load 
versus cycling) and (7) zoned or multi-pressure condenser applications 
versus unzoned or single pressure condenser applications. 
While all but the lowest pressure feedwater heater extraction flow vary 
linearly with and in direct proportion to unit throttle flow, the lowest 
pressure heater extraction flow varies at a greater rate than the throttle 
flow and also varies in response to changes in condenser pressure. This 
produces changes in inlet angle to the downstream stage and to a lesser 
extent affects the performance of the stage that immediately preceded this 
extraction point. 
Since the last few stages in the turbine are tuned, tapered, twisted blades 
with more selective inlet angles, the seven factors identified above have 
greater influence on stage performance. 
FIG. 1 illustrates the effect of end loading in the inlet angle to the last 
stage stationary blade of an exemplary steam turbine. This graph plots 
"incidence" on the vertical axis against blade height on the horizontal 
axis for two different values of end loading, one at 6000 lb/hr/ft.sup.2 
(=29280 kg/hr/m.sup.2) and the other at 11500 lb/hr/ft.sup.2 (=56120 
kg/hr/m.sup.2). The dashed lines represent predicted values while the 
shaded areas represent ranges of measured values. Incidence is the 
difference between the blade and fluid angles at inlet. Note that while 
the incidence angle varies about the predicted design angle at full load, 
the incidence angle deviates from the predicted angle at partial load. 
Similar changes in inlet angle but of lesser magnitude were identified on 
the next upstream stator blade. 
There are many variations in extraction arrangements and standard blade 
gagings for steam turbines. Many of the differences between the L-2 stator 
blade gagings relate to non-reheat versus reheat applications. 
Furthermore, single flow elements of triple flow LP frames have different 
extraction arrangements but the same blading as the double flow element. 
In the triple flow systems, only one of the two flow paths (single flow or 
double flow) can be matched from the standpoint of incidence. 
If a double flow LP turbine were operating at optimum efficiency at a given 
exhaust pressure with a single pressure condenser and if the condenser 
were converted to a two zone multi-pressure condenser with the same 
surface area, the pressure at one end of the double flow element would 
increase while the pressure at the other end would decrease. Neither end 
would be operating at optimum efficiency although there would be an 
improvement in heat rate because the average condenser pressure would be 
lower with the zoned condenser. The end with the lower exhaust pressure 
needs more flow area while the end with the higher exhaust pressure needs 
less flow area. Prior studies have demonstrated that the total exhaust 
area for the optimum zoned condenser application is about the same or 
slightly smaller than the total flow area of the unzoned arrangement. The 
conventional approach to optimizing such a system would be to select 
different size last row blades in each half of the zoned double flow LP 
element. This would result in a greater proliferation of blade sizes to 
achieve optimum performance. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a method for improving 
steam turbine efficiency. 
It is another object of the present invention to provide a method of 
improving steam turbine efficiency without changing the sizing of last row 
blades in a low pressure turbine section. 
The above and other objects, features and advantages are attained in a 
plurality of steam turbines with a minimum number of last row blade sizes 
by setting blade gaging for an optimum flow area. 
Blade row flow (throat) area as well as blade annulus area determine 
blading performance. The ratio of flow area to annulus area is termed 
gaging and is a measure of the blade outlet area. The gaging, g, is the 
sine of the blade outlet angle and is also the ratio of the blade throat 
opening to the blade pitch on convergent (non-expanding) flow passages. 
Accordingly, the same flow area is obtained by either using a given blade 
with a large gaging or a somewhat larger blade with a smaller gaging. In 
fact, a large change in blade row area can be realized by varying the 
blade outlet angle. For example, a blade with a 30.degree. outlet angle, 
which has a gaging of 0.500, can, by rotation of .+-.2.degree., have a 
gaging range of 0.467 to 0.530, a 14% change. 
The next larger blade size could be 25% larger in annulus area but with a 
gaging variation such that its minimum gaging orientation would have a 
somewhat smaller blade flow (throat) area than the smaller blade at its 
maximum gaging orientation. Thus, a broad range of optimal flow areas can 
be attained by use of only a few blades through selection of the optimum 
gaging of the last row blades using blade orientation. 
In selecting the optimum last row gagings, the units with the better hoods 
have higher optimum gagings than the units with poorer hoods. Applying the 
teachings of this invention, the same last row blade, set at various 
gagings, would optimize the application for the various hoods rather than 
selecting a gaging that favors one end of the hood spectrum at the expense 
of the other or designing a blade that is some sort of compromise. 
The present invention thus comprises a method for optimizing thermodynamic 
performance of a steam turbine by matching a last stage blade flow area to 
condenser pressure by adjusting blade angular orientation to set gaging to 
an optimum value. Furthermore, the invention includes a method for 
correcting incidence by setting blade angular orientation upstream of the 
last blade row.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 2, there is shown a partial cross-sectional view of a low 
pressure (LP) section of a double flow steam turbine 8. Steam flow is 
indicated at S. After passing through a plurality of rotating blades 10 
and stationary nozzles 12, the steam S exits through hoods 14. The hoods 
14 convey the exhausted steam to a condenser 16 which cools the steam, 
converting it to water, which is then returned to a boiler (not shown) to 
be converted back to steam. 
The condenser 16 may be zoned or non-zoned. The zoned condenser is divided 
into sections 16A and 16B with steam in one section being isolated from 
steam in the other. Zoned condensers are used in turbines employing 
multiple exhaust ends. In such turbines, steam from a given LP flow path 
is directed to one zone of the condenser so that it can be cooled, while 
steam from another LP flow path is directed into another zone of the 
condenser. Such turbines are designed to develop additional power from 
downstream turbine stages. A more detailed description of a turbine with 
zoned condenser may be had by reference to U.S. Pat. No. 4,557,113 
assigned to Westinghouse Electric Corporation. 
The typical zoned condenser has a lower average condenser pressure than an 
unzoned condenser. The conventional single last row blade gaging of a 
steam turbine coupled to the zoned condenser would be nonoptimum for both 
zones of the zoned condenser. In accordance with conventional practice, 
two completely different last row blades would be needed to optimize the 
zoned condenser application and still another new blade would be needed 
for the unzoned application. With the teachings of this invention, the 
same last row blade would be used but with different gagings to meet the 
requirements of different exhaust pressures. The higher exhaust pressures 
would have the smaller gagings. The differences in orientation required to 
vary the gagings of a given blade would have negligible effect on the 
frequency of the tuned blades. 
FIG. 3 is an end view in cross-section, i.e., a radially directed 
cross-sectional view, of a pair of adjacent steam turbine blades 20 and 
22. The perpendicular distance 0 represents the throat or flow opening 
while the dimension P represents the pitch. For evenly spaced blades, 
pitch is the circumference divided by the number of blades. Gaging is 
defined as the ratio of net flow area to annular area which can be 
expressed as opening/pitch (O/P), where the opening is the width normal to 
the flow at the blade throat. It can be shown that the fluid angle exiting 
the blades can be represented by arcsin O/P so that fluid angle and gaging 
are clearly related. 
Variations in end loading affect the optimum gaging selection. Therefore, 
variations in blade orientation can be used to optimize the turbine heat 
rate for a myriad of applications. FIG. 1, however, illustrates that 
variations in end loading change the inlet angle to the stationary blade, 
producing incidence and an accompanying efficiency degradation. Table I 
illustrates the effect of gaging variations on the L-2C blade row. The 
lowest gagings occur in nonreheat applications (lower specific volume) 
while higher gagings occur in reheat units. 
The illustrated stationary blade gaging changes were made to reduce the 
incidence (deviation from design angle) on the mating rotating blades but 
the stationary blades were new designs. With gaging variations produced by 
changing the orientation of the rotating and stationary blades ahead of 
the last rotating row as well, a greater degree of performance 
optimization can be achieved without changing the blade profiles. It 
should be noted that the design of the stationary blades is much simpler 
than the design of the mating rotating blade and the cost of the 
stationary blade is considerably lower than the cost of the rotating 
blade. 
An example of losses attributable to different exhaust hood designs is 
shown in FIG. 4. Here, two substantially identical turbines are each 
coupled to substantially identical condensers using two different hood 
designs. The curve labeled A illustrates a larger pressure loss from 
blading to the condenser than is shown by curve B. Different hoods thus 
result in different exhaust pressures for the same mass flow and condenser 
pressure. As is well known, blade pressure determines the amount of work 
which can be extracted from a given turbine. The present invention 
provides a method for compensating for differences in hood designs by 
adjusting blade gaging to an optimum value for the exhaust pressure. 
Incidence also results from changes in steam extraction arrangements, 
particularly in regard to the location of the lowest pressure extractions 
in which the extracted mass flow varies with condenser pressure. 
Accordingly, gaging could be used to correct incidence at blade rows 
adjacent steam extraction positions although changes in stator blade 
orientation only may be sufficient. 
Moreover, the inlet flow angles to the end blades in a single flow element 
will be different than the inlet flow angle to the blades of a double flow 
element of a triple flow exhaust unit. The triple flow units may have a 
different extraction arrangement on the single flow element than on the 
double flow element of other units. To achieve the gaging changes, the 
same blade could be oriented differently on the root platform or the rotor 
steeple could be oriented differently or a combination of the two. 
The present invention achieves higher LP turbine efficiency by increasing 
the optimum performance range over which a blade of given profile is used. 
Many more different blade designs would be needed to achieve the same 
result with conventional practice. This concept is applicable to the blade 
rows of the last rotating row, both stationary and rotating blades, as 
well as the next two upstream stages although the effects are lesser in 
magnitude. 
While the principles of the invention have now been made clear in an 
illustrative embodiment, it will become apparent to those skilled in the 
art that many modifications of the structures, arrangements and components 
presented in the above illustrations may be made in the practice of the 
invention in order to develop alternative embodiments suitable to specific 
operating requirements without departing from the scope and principles of 
the invention as set forth in the claims which follow. 
TABLE I 
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Exit Exit 
Angle Gaging, g Angle Gaging, g 
Degrees Percent Degrees Percent 
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22 37.5 31 51.5 
23 39.1 32 53.0 
24 40.7 33 54.5 
25 42.3 34 55.9 
26 43.8 35 57.4 
27 45.4 36 58.8 
28 46.9 37 60.6 
29 48.5 38 61.6 
30 50.0 
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