Note: Descriptions are shown in the official language in which they were submitted.
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STEAM TURBINE V~NE AIRFOIL
BACKGROUND_OF THE INVENTION
The present invention relates to vanes for a steam
turbine. More specifically, the present invention relates to
an improved vane for use in the latter stages o~ a steam
turbine in which the vane airfoil has been stiffened, thereby
preventing stall flutter, without decreasing vane performance.
The steam flow path of a steam turbine is formed by
a st~tionary cylinder and a rotor. A large number of
stationary vanes are attached to the cylinder in a
circumferential array and extend inward into the steam flow
path. Similarly, a large number of rotating blades are
attached to the rotor in a circumferential array and extend
outward into the steam flow path. The stationary vanes and
rotating blades are arranged in alternating rows so that a row
of vanes and the immediately downstream row of blades ~orms
a stage. The vanes serve to direct the flow of steam so that
it enters the downstrea~ row of hlades at the correct angle.
The blade airfoils extract energy from the steam, thereby
developiny the power necessary to drive the rotor and the load
attached to it.
Th amount of energy extracted by each stage depends
on the size and shape of the vane and blade airfoils, as well
as the quantity of vanes and blades in the stage. Thus, the ~- -
shapes of the airfoils are an extremely important factor in
the thermodynamic performance o~ the turbine and determining
the geometry of the airfoils is a vital portion of the turbine
design.
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... . . . . . ... . . . . . . .
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As the steam flows through the turbine its pressure
drops through each succeeding stage until the desired
discharge pressure is achieved. Thus, the steam properties
-- that is, temperature, pressure, velocity and moisture
content -- vary from stage to stage as the steam expands
through the flow path. Consequently, each stage employs vanes
and blades having an airfoil shape that is optimized for the
steam conditions associated with that stage. However, within
a given row the vane airfoils are identical.
Generally, the major thermodynamic losses in the
vane row occur due to friction losses as the steam flows over
the airfoil surface and separation of the boundary layer.
Friction losses are minimized by shaping the airfoil so as to
maintain the steam local velocity on the airfoil surface at
relatively low values. Separation of the boundary ~ayer is
prevented by causing the steam to constantly accelerate as it
flows toward the trailing edge of the airfoil. This constant
acceleration requires that the passage between adjacent
airfoils constantly converges from the vane inlet to the
gauging point.
The difficulty associated with designing a steam
turbine vane is exacerbated by the fact that the airfoil shape
determines, in large part, the mechanical characteristics of
the vane -- such as its stiffness and xesonant frequencies
as well as the thermodynamic performance of the vane. These
considerations impose constraints on the choice of vane
airfoil shape. Thus, of necessity, the optimum vane airfoil
shape for a given row is a matter of compromise between its
mechanical and aerodynamic properties.
One of the important characteris~ics of a vane is
its resistance to stall ~lutter. Briefly, stall flutter is
an aero-elastic instability wherein, under certain flow
conditions, vibratory deflections in the airfoil cause changes
in the aerodynamic loading on it that tend to increase, rather
than dampen, the deflections. Consequently, stall flutter can
increase the vibratory stress on the vane and cause high cycle
fatigue cracking. The resistance of a vane to stall flutter
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can be increased by increasing its stiffness. Unfortunately,
the changes in geometry associated with increasing the
stiffness of the airfoil tend to impair its thermodynamic
performance.
It is therefore desirable to provide a row of
improved steam turbine vanes having an airfoil shape that
provides sufficient stiffness to prevent stall flutt~r but
which does so without impairing the thermodynamic performance
of the vane.
SUMMARY OF THE INVENTION
Accordingly, it is the general object of the current
invention to provide a row of improved steam turbine vanes
having an airfoil shape that provides sufficient stiffness to
prevent stall flutter but which does so without impairing the
thermodynamic performance of the vane.
Briefly, this object, as well as other objects of
the curre~t invention, is accomplished in a steam turbine
comprising (i~ a stationary cylinder for containing a steam
flow and a rotor enclosed by the cylinder, (ii) a row of
blades attached to the periphery of the rotor, and (iii) a row
of vanes supported on the cylinder and disposed adjacent the
row of blades. Each of the vanes has an airfoil portion
having (i) a radially inboard hub portion and a radially
outboard tip portion, the hub and tip portions defining an
airfoil radial height therebetween, and tii) an upstream
leading edge and a downstream trailing edge, the leading and
trailing edges defining a camber angle therebetween. The
camber angle is greater than 90 over a portion of the airfoil
compri~inq approximately 4G~ of the airfoil radial height
adjacent the hub portion~
In the preferred embodiment of the invention, the
camber angle is greater than 80 over substantially the
entirety of the airfoil radial height. Moreover, in this
embodiment, the camber angle is greater than 95 over a
portion of the airfoil comprising approximately 20% of the
airfoil radial height adjacent the hub portion of the vane
airfoil.
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BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a portion of a longitudinal cross-
section through a steam turbine in the vicinity of one of the
later stages in the turbine containing a row of vanes
according to the current invention.
Figures 2-4 are cross-sections of the airfoil shown
in Figure 1 in the hub, mid-height, and tip regions,
respectively.
Figure 5 is a series of transverse cross-sections
through the airfoil at variou~ radial locations, as shown in
Figures 2-4, superimposed on one another as they would be if
projected onto a plane perpendicular to the radial direction.
Figure 6 is a diagram of two adjacent vane airfoils
according to the current invention illustrating various
performance related parameters.
Figure 7 is a graph showing the variation in the
camber angle of the airfoil along it radial height from the
hub to the tip region.
Figures 8-10 are graphs showing the calculated axial
distribution of the steam velocity ratio -- that is, the local
surface velocity to the vane row exit velocity -- along the
width of the airfoil, from the trailing edge to the leading - edge, over the airfoil suction surface, upper curve, and the
airfoil pressure surface, lower curve, at the hub, mid-height,
and tip regions, respectively.
DESCRIPTIQN OF THE PREFERRED EMBODIMENT
Referring to the drawings, there is shown in Figure
1 a portion of a cross-section through the low pressure
section of a steam turbine 1. As shown, the steam flow path
of the steam turbine 1 is formed by a stationary cylinder 2
and a rotor 3, the axis o rotation of the rotor defining the
axial direction. A row of blades 5 is attac~ed to the
periphery of the rotor 3 and extends radially outward into the
flow path in a circumferential array. A row of vanes 4 are
attached to the cylinde.r 2 and extends radially inward in a
circumferential array. The vanes 4 receive the steam flow 6
from an upstream row of blades (not shown) and direct it to
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the downstream row of blades 5 so that the steam enters the
blade row at the correct ang~e. The vanes 4 are manufactured
by a forging process and are installed int;o the turbine 1 as
segmental assemblies.
As shown in Figure l, each blade 5 is comprised of
an airfoil portion that extracts energy from the steam and a
root portion that serves to fix the blacle to the rotor 3.
Each vane 4 has an outer shroud 10 (by which it is affixed to
the sylinder 2), an inner shroud 11, and an airfoil portion
7 extending in the radial direction between the inner and
outer shrouds. Each airfoil 4 has tip portion 8 that is
attached to the outer shroud lO and a hub portion 9 that is
attached to the inner shroud ll, the radial height H of the
airfoil being defined between the tip 8 and hub 9 portions.
In addition, each airfoil 7 has a leading edge 13 and a
trailing edge 14~ In the preferred embodiment, the outer
, . .
shroud lO has a moisture removal slot 12 formed in its
upstream face. In the preferred embodiment, the inner and
outer shrouds, as well as the airfoil, are manufactured from
stainless steel.
According to the current invention, the vanes 4,
which are suitable for retrofit into an existing steam
turbine, are of improved design compared to traditional vanes.
Specifically, the current invention concerns airfoils 7 that
have been improved by increasing their stiffness, thereby
preventing stall flutter, without impairing their performance.
In ~act, it has been estimated that the novel shape of the
vane airfoils 7 according to the current invention will not
only provide sufficient stiffness to prevent stall flutter,
but will actually result in a reduction in steam flow energy
losses and, therefore, higher performance in the retro-fitted
steam turbine. Accordingly, the novel geometry of the airfoil
7 for the vane 4 of the currPnt invention is shown in Figures
2-5 and specified in Tables I-III.
Figures 2-4 show the re-designed vane airfoil 7
cross-section at three radial locations along the vane --
specifically, the airfoil cross-section 7' in the huh region
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g proximate the inner shroud 11 is shown in Figure 2, the
airfoil cross-section 7" at mid-height is shown in Figure 3,
and the airfoil cross-section 7"' in the tip region 8
proximate the outer shroud 10 is shown in Figure 4. As can
be seen, the airfoil at each cross-sec:tion has a convex
suction surface 15 and a concave pressure surface 16 formed
between the leading and trailing e~dges 13 and 14,
respectively. The suction and pressure surfaces 15 and 16,
respectively, define the thickness of the airfoil 7. Figure
5 is a so-called "stacked plot" of the airfoil shape -- that
is, the shape of the airfoil cross-sections at three radial
heights superimposed on one another as thay would be if
projected onto a plane perpendicular to the radial direction.
The novel geometry of the airfoil 7 for the vane 4
of the current invention is specified in Tables I-III. In
each table, the vane airfoil is specified at three radial
stations along the airfoil -- specifically, at the hub portion
9 of the airfoil, at mid height, and at the tip portion 8 of
the airfoil. In the preferred embodiment, the hub, mid-height
and tip portions correspond to radii of 109.6 cm (43.15 in),
141.1 cm (55.54 in), and 172.5 cm (67.93 in), respectively.
As those skilled in the art of vane design will appreciate,
th~ values of the parameters shown in Table I-III for the
radial station at the tip of the airfoil is based on a
projection of the airfoil cross-section out to the radial
station at the trailing edge 14 of the tip portion. Such
projection is necessary because the actual tip of the vane
does not lie in a radial plane, tapering as it does toward the
leading edge 13, as shown in Figure 1.
In Tables I and II, the airfoil is specified by
reference to coordinates of the X and Y axes shown in Figure
5. The X-Y coordinates of twenty two points along the suction
and pressure surfaces of the airfoil that de~ine t~e shape of
the airfoil cross-section at each of the three aforementioned
radial locations -- the hub 9, mid-height, and tip 8 regions -
- are specified. Although the location coordinates shown in
Tables I and II define an airfoil of a particular size,
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depending on the units chosen (in the preferred embodiment,
the units are in inches), the coordinates should be viewed as
being essentially non-dimensional, since the invention could
be practiced utilizing a larger or smaller airfoil, having the
same shape, by appropriately scaling the coordinates so as to
obtain multiples or fractions thereof -- i e., by multiplying :
each coordinate by a common factor.
TABLE I rconvex Suction Surface X-Y Coordinates)
Point Hub Mid-Heiaht Tip
10 1(-1.94, .80) (_~.39, -1.59) (-2.84, -2.38)
2~-1.7~, -.26) (-2-14, -.92) (-2-52, -1.5~
3(-1.55, 0.27) (-1-89, -.25) (-2.19, -0.78)
4(-1.35, 0.81) (-1-65, 0.42) (-1.87, 0.02) ~ ~
5(-1.1~, 1.34) (-1.38, 1.08) (-1.53, 0.81) : ~:
15 6(-0.89, 1.85) (-1.05, 1.71) (-1.11, 1.56) ~ :
7(-0.53, 2.30) (-0.58, 2.25) (-0.56, 2.22) ~:;
8(-0.02, 2.57) (0.06, 2.59) (0.16, 2.71) :
9(0.56, 2.62) (0.77, 2.64) (1.01, 2.90)
10(1.11, 2.42) (1-47, 2.44) (1-86, 2.77)
2011(1.59, 2.02) (2.1~, 2.05) (2.75, 2.37) :~
TABLE II ~Concave Pressure Surface Coordinatesl ~ :
Point Hub Mid-Heiq~ Ti~
1(-1.94, -0.37) (-2.3g, -1.75) (-2.~4, -2.54) : :
2(-1.70, -0.38) (-2.69, -1.~5) (-2-47, -~.72)
25 3(-1.51, 0.05) (-1.84, -0.50) (-2.13, -1.05)
4t-1.30, 0.47) (-1-56, 0.03) (-1-75, -0.
5(-1.06, 0.87) (-1.22, 0.54) (-1.32, 0.22) .
6(-0.77, 1.24) (-0.82, 1.00~ (-0.82, 0.78)
7(-0.41l 1.56) (_0.34, 1.37) (-0.25, 1.27)
30 8(0.01, 1.79) (0.21, 1.64) (0.39, 1.66)
9(0.46, 1.91) (0.79, 1.80) (1.0~, 1.93)
lO(0.94, 1.92) ~1.4G, 1.8S) (1-83, 2.10)
11(1.59l 1.75) (2.16, 1.~2) ~2.72, 2.143
The novel geometry of the airfoil 7 for the vane 4 of
the current invention is further specified in Table III by
reference to ~arious param~ters, each of which is discussed
below and illustrated in Figure 6, that affect the performance
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and mechanical integrity of the vane (all angles in Table III
are expressed in degrees).
TABLE III
Parameter Hub Mid-Height Tip
Pitch/Chord ratio .55 .56 .54
Pitch/Width ratio .71 ,.71 .71
Stagger angle 38.0 :38.1 ~0.0
Max thickness/chord .166 .162 .144
Camber angle 101.7 87.6 83.4
10 Inlet metal angle 57.7 71.2 74.2
Inlet included angle 28.9 30.2 30.9
- Exit metal angle 20.6 21.2 22.4
Exit opening (cm) 2.1 2.8 3.69
Suction surface
15 turning angle 2.8 4.5 4.6
Leading edge radius (mm) 3.7 3.6 3.8
Tailing edge radius (mm) .76 .76 .76
Maximum Thickness (cm) 1.9 2.4 2.7
Cross-section area (cm2) 13.5 21.1 29.2
20 Angle of principle
coordinate axis 36.2 35.7 38.4
Imin (cm ) 11.6 25.2 38.8
Imjn (cm4) 88.5 219 475
The chord of the blade is the distance from the
leading edge 13 to the trailing edge 14 and is indicated as
C in Figure 6. The pitch is the distance in the tangential
direction between the trailing edges of adjacent blades and
is indicated in Figure 6 as P. The width of the blade refers
to the distance from the leading to the trailing edge in the
axial direction - that is, the axial component of the chord -
- and is indicat~d by W in Figure 6. The pitch to chord ratio
and the pitch to width ratio are important parameters in
determining the performance of a row of vanes since there is
an optimum value of each of these parameters that will yield
the minimum vane loss -- if the values are too large, meaning
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there are few vanes, then each blade will carry too much load
and flow separation may occur, if the values are too high,
meaning there are too many vanes, the surface friction will
become excessive. Consequently, these parameters are included
in Table III.
The stagger angle is the angle the line 21 drawn
from the leading to the trailing edge makes with the axial
direction and is indicated in Figure 6 as S.
The maximum thickness to chord ratio is the ratio
of the maximum thickness of the airfoil transverse cross-
section, indicated by T in Figure 6, at the radial station,
to the chord length at that station.
The camber angle is indicated as CA in Figure 6 and
is defined by the angle between the leading and trailing edge
portions of the airfoil. Thus, the camber angle may be
expressed as by the equation CA = 180 - (IMA + EMA), where
IMA and EMA are the inlet and exit metal angles, respectively,
as defined below.
The inlet metal angle is the angle formed between
the circumferential direction and the line 25 that bisects the
lines 19 and 20, lines 19 and 20 being the lines that are
tangent with the suction surface 15 and the pressure surface
16, respectively, at the leading edge 13. The inlet metal
angle is indicated in Figure 6 as IMA. The inlet included
angle is the angle between the tangent lines 19 and 20 and is
indicated in Figure 6 as IIA.
The exit metal angle is the angle formed between the
circumferential direction and the line 27 that bisects the
lines 23 and 24, lines 23 and 24 being the lines that are
tangent with the suction surface 15 and the pressure surface
16, respectively, at the trailing edge 14. The exit metal
angle is indicated in Figure 6 as EMA.
The exit opening, or throat, is the shortPst
distance from the trailing edge 14 o~ one blade to the suction
surface 15 of the adjacent blade and is indicated in Figure
6 by 0. The gauging of the vane row is defined as the ratio
of the throat to the pitch and indicates the percentage of th~
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annular area available for steam flow. The exit opening angle
is the arc sin of the gauging.
The suction surface turning angle is the amount of
the suction surface turning from the throat: O to the trailing
edge 14 and is indicated in Figure 6 as STA. As can be seen,
the suction surface turning angle has been maintained below
5 to ensure that boundary layer separation does not occur in
the trailing edge 26 regionO
As previously discussed, too large a thickness of
the air~oil 7 in the trailiny edge 14 region will increase the
steam f 1QW losses due to separation of the boundary layer at
the trailing edge 14. Accordingly, in the preferred
embodiment of the invention, the airfoils 7 are forged so as
to have a trailing edge radius of less than 1.O mm, as shcwn
in Table III.
The principal coordinate axes of the airfoil are
indicated in Figure 6 as MIN and MAX. The minimum and maximum
second moments of inertia about these axes are shown in Table
III as Imjn and I~x, respectively. The radial distribution of
20 Imjn and the cross-sectional area have a strong influence on
the natural frequency of the vane, which, as discussed below,
affects the tendency of the vane to experience stall ~lutter.
The angle the principal coordinate axis MIN makes with the
axial direction is indicated in Figure 6 as PCA.
The vanes according to the current invention have
been improved so as to increase their stiffness, thereby
increasing their resistance to harmful stall flutter. The
propensity of an airfoil to experience stall flutter can be
characterized by two parameters, referred to the stall flutter
index C1 and the stall/unstall flutter index C2. C1 ! is a
measure of the ability of the airfoil to resist stall flutter
when standing alone, whereas C2 takes into account cascade
effects due to the fact that the airfoil is installed in a row
of vanes. The higher the values of C1 and C2, the less likely
it is that stall flutter will occur. Cl and C2 can be
expressed as the product of certain ratios, as follows:
Cl = (Pb/Ps) x [ (Cm ~ fn) /Ve~ x ~Am/Cm ) (1)
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C2 = (Pb/Ps) x [ (Cm x fn) /V~!] x (Am/Cm ) x ~ m x Pm) /Cm) ] (2 3
where:
Pb and Ps are the densities of the blade and
the steam exiting the vane row, respectively;
Cm is the airfoil chord length at mid-height;
~n is the airfoil natural ~Erequency;
Ve is the exit steam velocity;
Am is the airfoil cross-sectional area at mid-
height;
~m is the gauging at mid-height; and
Pm is the pitch at mid heigh~.
In the vanes 4 according the curxent invention, the
stall flutter index C1 has been increased from less than 4000,
as achieved in vanes having airfoils of traditional shape, to
15 almost 5000. Similarly, the stall/unstall flutter index C2
has been increased from less than 1000 to over 1200. These
higher values of C1 and C2 indicate a greatly increased
resistance of the vane airfoils to stall flutter.
According to the current invention, the vanes's
resistance to stall flutter has been increased by stiffening
the airfoil 7, so as to raise its natural frequency, and by
increasing its cross-sectional area. As inspection of
equations (1) and (2) above indicates, raising the air~oil's
natural frequency fn and increasing its cross-sectional area
Am result in higher values of C1 and C2.
Stiffening the airfoil along its entire radial
height is made difficult by the fact that, as shown in Figure
1, the vane airfoil 4 is tapered as it extends radially inward
from its tip 8 to its hub 9. This tapering is necesæary
because the blades 5 are tapered in the opposite direction for
reasons of strength (unlike the vanes 4, the blades are
subjected to high stress at the base of their airfoil due to
centrifugal force). As a result, the airfoil 7 in the hub
region 9 must have a relatively small width, W, ~aking it
difficult to sufficiently increase the stiffness and cross-
sectional area of the airfoil in that region.
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In the current invention, this problem was solved
by increasing the curvature of the airfoil. However, too
great an increase in the curvature of the airfoil in the wider
sections at the in tip portion 10 of airfoil can have a
deleterious effect on the convergence of the passages between
adjacent airfoils. Therefore, accordillg to the current
invention the curvature at the hub region 9 was increased
beyond that in the mid-height and tip regions, as can be seen
by comparing Figure 2 to Figures 3 and 4. This radial
curvature distribution is also reflected in the values of the
camber angle CA, shown in Figure 7. Figure 7 shows the novel
radial variation in camber angle from the hub region 9 (0%
bladè height) to the tip region 8 ~100% blade height) for the
vane according to the current invention. As can be seen, in
the approximately 40% of the airfoil height adjacent the hub
9, the camber angle is unusually high -- greater than 90.
In fact, in the approximately 20% of the airfoil height
adjacent the hub 9, the camber angle is greater than 95. In
the remainder of the airfoil, the ~amber is still relatively
high, exceeding 80.
According to the current invention, stiffening was
also accomplished by increasing the value of the second moment
of inertia Imjn about the MIN principle axis by reducing the
stagger angle S. Unfortunately, other things being constant,
reducing the stagger angle has the undesirable effect of
reducing the throat 0. Reducing the throat increases the
steam velocity and, therefore, the friction losses as the
steam flows over the airfoil surfaces. Accordingly, the
airfoil shap2 was given a shape that offset the effect of
increasing the stagger angle on the throat. These novèl
airfoil shapes are reflected in Figures 2-4 and further
specified in Tables I and II, as previously discussed.
The success of the aforementioned approach in
stiffening the airfoil without impairing thermodynamic
performancs is indicated by Figures 8-10, which show the
velocity ratio -- that is, the variation in the ratio of the
steam velocity at the surface of the airfoil at a given radial
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station to the velocity of the steam exiting the blade row at
that radial station -- along the width of the airfoil from the
trailing edge 14 (0% of the airfoil width W) to the leading
edge 13 (100% of the airfoil width). The upper curve shows
the velocity profile on the convex suction surface 15 and the
lower curve shows the velocity profile on the concave pressure
surface 16. As can be seen, the velocity ratio along the
entire width of the airfoil at each radial location is less
than 1.2, thereby resulting in low friction losses as the
steam flows over the airfoil. Such advantageous velocity
profiles are made possible by the airfoil surface contours,
shown in Figures 2-4.
Figures 8-10 also show that in the vane airfoil 7
according to the current invention, separation of the boundary
layer is prevented by configuring the airfoil geometry to
ensure that the steam does not decelerate too rapidly as it
expands toward the trailing edge 14. As can be seen, the
velocity ratio on the suction surface decreases by no more
than about 10% from its peak value, at approximately 30% of
the airfoil width, to its value at the trailing edge. Such
gentle deceleration ensures that boundary layer separation,
and the associated loss in steam energy, does not occur.
Although the present invention has been illustrated
with respect to a particular row of vanes in a steam turbine,
the invention may be utilized in other vane rows of a steam
turbine as well. Accordingly, the present invention may be
embodied in other specific forms without departing from the
spirit or essential attributes thereof and, accordingly,
reference should be made to the appended claims, rather than
to the foregoing specification, as indicating the scope o~ the
invention.
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