CA2113062A1 - Steam turbine vane airfoil - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
A vane for a steam turbine having an improved airfoil that has been stiffened to increase the resistance of the vane to stall flutter without impairing the thermodynamic performance of the vane. The airfoil is tapered from its tip portion to its hub portion and has a novel shape that includes a higher degree of curvature in its hub region than in the mid-height and tip regions. This curvature is reflected in the camber angle defined by the leading and trailing edge positions of the airfoil. In the approximately 40% of the airfoil height adjacent the hub the camber angle is greater than 90° and in the approximately 20% of the airfoil height adjacent the hub, the camber angle is greater than 95°. In the remainder of the airfoil, the camber exceeds 80°.

Description

t 1 57,356 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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2~3~2 2 57,356 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 2~ ~-3~2 3 57,356 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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3 ~ ~ 2 4 57,356 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 k 1 ~L 3 ~) 6 2 5 57,356 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 -:.. . ~: . , . , , . . ~ , .. . . .

~113~2 6 57,356 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, 3~2 7 57,356 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 3~2 8 57,356 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 3 ~ ~ 2 57,356 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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?J~ ~ 3 ~62 57,356 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) ~ ~ 3~2 11 57~356 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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12 57,356 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 s~ 2 , .

13 57,356 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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Claims (9)

1. A steam turbine comprising:
a) a stationary cylinder for containing a steam flow, and a rotor enclosed by said cylinder;
b) a row of blades attached to the periphery of said rotor; and c) a row of vanes supported on said cylinder and disposed adjacent said row of blades, each of said vanes having an airfoil portion having:
(i) a radially inboard hub portion and a radially outboard tip portion, said hub and tip portions defining an airfoil radial height therebetween;
(ii) an upstream leading edge and a downstream trailing edge, said leading and trailing edges defining a camber angle therebetween, said camber angle being greater than 90° over a portion of said airfoil comprising approximately 40% of said airfoil radial height adjacent said hub portion.

2. The steam turbine according to claim 1, wherein said camber angle is greater than 80° over substantially the entirety of said airfoil radial height.

3. The steam turbine according to claim 1, wherein said camber angle is greater than 95° over a portion of said airfoil comprising approximately 20% of said airfoil radial height adjacent said hub portion.

4. The steam turbine according to claim 1, wherein each of said vanes airfoils further comprises:
a) a mid-height portion disposed approximately mid-way between said hub and tip portions; and b) a thickness defined by convex and concave surfaces extending between said leading an trailing edges, said convex and concave surface having a shape defined at said hub, mid-height an tip portions by X-Y coordinates, as follows:
Convex Surface Coordinates Point Hub Mid-Height Tip 1 (-1.94, -.80) (-2.39, -1.59) (-2-84, -2.38) 2 (-1.74, -.26) (-2.14, -.92) (-2.52, -1.58) 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) (-1.14, 1.34) (-1.38, 1.08) (-1.53, 0.81) 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 (1.11, 2.42) (1.47, 2.44) (1.86, 2.77) 11 (1.59, 2.02) (2.16, 2.05) (2.75, 2.37) Concave Surface Coordinates Point Hub Mid-Height Tip 1 (-1.94, --97) (-2-39, -1.75) (-2-84, -2.54) 2 (-1.70, -.383 (-2.69, -1.05) (-2-47, -1.72) 3 (-1.51, 0.05) (-1.84, -0.50) (-2.13, -1.05) 4 (-1.30, 0.47) (-1.56, 0.03) (-1.75, -0.40) (-1.06, 0.87) (-1.22, 0.54) (-1032, 0.22) 6 (-0.77, 1.24) (-0.82, 1.00) (-0.82, 0.78) 7 (-0.41, 1.56) (-0.34, 1-37) (0.25, 1.27 8 (0.01, 1.79) (0.21, 1.64) (0.39, 1.66) 9 (0.46, 1.91) (0.79, 1.80) (1.09, 1.93) (0.94, 1.92) (1.40, 1.85) (1.83, 2.10) 11 (1.59, 1.75) (2.16, 1.82) (2.72, 2.14)

5. In a steam turbine having a row of vanes supported on a cylinder and disposed adjacent a row of blades, each of said vanes comprising an airfoil, each of said airfoils having a radially inboard hub portion and a radially outboard tip portion, each of said airfoils having leading and trailing edges and a thickness defined by convex and concave surfaces extending between said leading and trailing edges, said convex and concave surfaces having a shape defined at said hub portion by X-Y coordinates, as follows:
Point Convex Surface Concave Surface 1 (-1.94, -.80) (-1-94, -0.97) 2 (-1.74, -.26) (-1.70, -0.38) 3 (-1.55, 0.27) (-1.51, 0.05) 4 (-1.35, 0.81) (-1-30, 0.47) (-1.14, 1.34) (-1.06, 0.87)

6 (-0.89, 1.85) (-0.77, 1.24)

7 (-0.53, 2.30) (-0.41, 1.56)

8 (-0.02, 2.57) (0.01, 1.79)

9 (0.56, 2.62) (0.46, 1.91) (1.11, 2.42) (0.94, 1.92) 11 (1.59, 2.02) (1.59, 1.75) 6. The vane according to claim 5, wherein said convex and concave surfaces having a shape further defined at said tip portion by X-Y coordinates, as follows:
Point Convex Surface Concave Surface 1 (-2.84, -2.38) (-2-84, -2.54) 2 (-2.52, -1.58) (-2.47, 1.72) 3 (-2.19, -0.78) (-2.13, 1.05) 4 (-1.87, 0.02) (-1.75, -0.40) (-1.53, 0.81) (-1.32, 0.22) 6 (-1.11, 1.56) (-0.82, 0.78) 7 (-0.56, 2.22) (-0.25, 1.27) 8 (0.16, 2.71) (0.39, 1.66) 9 (1.01, 2.90) (1.09, 1.93) (1.86, 2.77) (1.83, 2.10) 11 (2-75, 2.37) (2.72, 2.14) 7. The vane according to claim 5, wherein each of said vanes airfoils further comprises a mid-height portion disposed approximately mid-way between said hub and tip positions, and wherein said convex and concave surfaces have a shape further defined at said mid-height portion by X-Y
coordinates, as follows:
Point Convex Surface Concave Surface 1 (-2.39, -1.59) (-2.39, -1.75) 2 (-2.14, -.92) (-2.69, -1.05) 3 (-1.89, -.25) (-1.84, -0.50) 4 (-1.65, 0.42) (-1.56, 0.03) (-1.38, 1.08) (-1.22, 0.54) 6 (-1.05, 1.71) (-0.82, 1.00) 7 (-0.58, 2.25) (-0.34, 1.37) 8 (0.06, 2.59) (0.21, 1.64) 9 (0.77, 2.64) (0.79, 1.80) (1.47, 2.44) (1.40, 1.85) 11 (2.16, 2.05) (2.16, 1.82) 8. In a steam turbine, a row of stationary vanes comprising airfoils defined by the following parameters:
Parameter Hub Mid-Height Tip Pitch/Chord ratio .55 .56 .54 Pitch/Width ratio .71 .71 .71 Stagger angle 38.0 38.1 40.0 Max thickness/chord .166 .162 .144 Camber angle 101.7 87.6 83.4 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 turning angle 2.8 4.5 4.6 Maximum Thickness (cm) 1.9 2.4 2.7 Cross-section area (cm2) 13.5 21.1 29.2 Angle of principle coordinate axis 36.2 35.7 38.4 Imin (cm4) 11.6 25.2 38.8 Imax (cm4) 88.5 219 475