TEAR-DROP SHAPED PART-SPAN SHROUD

Abstract

A rotatable blade for use in a turbomachine includes an airfoil portion having a leading edge, a trailing edge a radially-inner end and a radially-outer end; a root section affixed to the radially-inner end of the airfoil portion. A part-span shroud is located on the airfoil portion between the root section and the radially-outer end. The part-span shroud is substantially tear-drop shaped such that its cross-sectional shape has a maximum thickness located within 20 to 40% of a chord length extending between leading and trailing edges of the part-span shroud, as measured from the leading edge of the part-span shroud.

Description

BACKGROUND OF THE INVENTION

The invention relates generally to rotating blades for use in turbomachines. More particularly, the invention relates to a rotating blades provided with part-span shrouds between adjacent blades.

The fluid flow path of a turbomachine such as a steam or gas turbine is generally formed by a stationary casing and a rotor. In this configuration, a number of stationary vanes are attached to the casing in a circumferential array, extending radially inward into the flow path. Similarly, a number of rotating blades are attached to the rotor in a circumferential array and extending radially outward into the flow path. The stationary vanes and rotating blades are arranged in alternating rows so that a row of vanes and the immediate downstream row of blades form a “stage”. The vanes serve to direct the flow path so that it enters the downstream row of blades at the correct angle. Airfoils of the blades extract energy from the working fluid, thereby developing the power necessary to drive the rotor and the load attached thereto.

The blades of the turbomachine may be subject to vibration and axial torsion as they rotate at high speeds. To address these issues, blades typically include part-span shrouds disposed on the airfoil portions at an intermediate radial distance between the tip and the root section of each blade. The part-span shrouds are typically affixed to each of the pressure (concave) and suction (convex) sides of each airfoil, such that the part-span shrouds on adjacent blades matingly engage and frictionally slide along one another during rotation of the rotor.

BRIEF DESCRIPTION OF THE INVENTION

In one exemplary but nonlimiting embodiment, there is provided a rotatable blade for a turbomachine, comprising an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end; a root section affixed to the radially-inner end of the airfoil portion; and a substantially tear-drop shaped part-span shroud located on the airfoil portion between the root section and the radially outer end, wherein the part-span shroud is provided with cross-sectional shape having a maximum thickness located within 20 to 40% of a chord length extending from a leading edge of the part-span shroud to a trailing edge of the part-span shroud, as measured from the leading edge of the part-span shroud.

In another exemplary aspect, there is provided a turbomachine comprising a rotor rotatably mounted within a stator, the rotor including a shaft; at least one rotor wheel mounted on the shaft, each of the at least one rotor wheels including a plurality of radially outwardly extending blades mounted thereon; and wherein each blade includes an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end, a pressure side and a suction side; a root section at the radially-inner end of the airfoil portion; and a part-span shroud located on the airfoil portion between the root section and the radially outer end, on the pressure side and the suction side, wherein the part-span shroud is provided with a substantially tear-drop cross-sectional shape having a maximum thickness located within 20 to 40% of a chord length extending between a leading edge of the part-span shroud and a trailing edge of the part-span shroud, as measured from the leading edge of the part span shroud.

In still another exemplary aspect, a turbomachine comprising a rotor rotatably mounted within a stator, the rotor including a shaft; at least one rotor wheel mounted on the shaft, each of the at least one rotor wheels including a plurality of radially outwardly extending blades mounted thereon; and wherein each blade includes an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end, a pressure side and a suction side; a root section at the radially-inner end of the airfoil portion; and a part-span shroud located on the airfoil portion between the root section and the radially outer end, on the pressure side and the suction side, wherein the part-span shroud is provided with a tear-drop cross-sectional shape having a maximum thickness located at 31%-37% of a chord length extending between a leading edge of the part-span shroud and a trailing edge of the part span shroud, as measured from the leading edge of the part-span shroud; and wherein the part-span shroud is disposed on the airfoil portion between about 40% and 80% of a radial height of the airfoil portion as measured from the root section of the blade.

These and other aspects, advantages and salient features of the invention will become apparent from the following detailed description, in conjunction with the drawings identified below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a perspective partial cutaway illustration of a conventional steam turbine;

FIG. 2 shows a cross-sectional illustration of a conventional gas turbine;

FIG. 3 shows a perspective illustration of two adjacent rotating blades incorporating part-span shrouds;

FIG. 4 shows an enlarged perspective illustration of a portion of two adjacent rotating blades including part-span shrouds taken from FIG. 3;

FIG. 5 shows a top view of a portion of two adjacent rotating blades incorporating part-span shrouds engageable along straight contact surfaces of the adjacent part-span shroud sections;

FIG. 6 is a schematic cross section of a known part-span shroud configuration;

FIG. 7 is a schematic cross section of a part-span shroud configuration according to an exemplary but nonlimiting embodiment of the invention;

FIG. 8 is a schematic section view similar to FIG. 7 but showing another exemplary embodiment with X-Y Cartesian coordinates that define the shape or profile of the part-span shroud;

FIG. 9 is a schematic section view similar to FIG. 8 but showing another exemplary embodiment with with X-Y Cartesian coordinates that define the shape or profile of the part-span shroud; and

FIG. 10 is a schematic section view similar to FIGS. 8 and 9 but showing still another exemplary embodiment with with X-Y Cartesian coordinates that define the shape or profile of the part-span shroud.

It is noted that the drawings of the disclosure are not necessarily to scale. The drawings are intended to depict only typical aspects of the disclosure, and therefore should not be considered as limiting the scope of the disclosure.

DETAILED DESCRIPTION OF THE INVENTION

As described below, embodiments of the invention are applicable to both steam and gas turbine engines employed in the production of electricity. It is understood, however, that the teachings are equally applicable to other electric machines including, but not limited to, gas turbine engine compressors, fans and gas turbines used in aviation. It should also be apparent to those skilled in the art that the present invention is applicable to differently scaled versions of the machines mentioned above.

FIG. 1 shows a perspective partial cut-away illustration of a steam turbine 10. The steam turbine 10 includes a rotor assembly 12 that includes a shaft or rotor 14 and a plurality of axially spaced rotor wheels 18. A plurality of rotatable blades or buckets 20 are mechanically coupled to each rotor wheel 18. More specifically, blades 20 are arranged in rows that extend circumferentially around each rotor wheel 18. A plurality of stationary vanes 22 extends circumferentially around the shaft 14 and are axially positioned between adjacent rows of blades 20. The stationary vanes 22 are secured to a surrounding stator and cooperate with the rotatable blades 20 to form one of a plurality of turbine stages and define a portion of a steam flow path through turbine 10.

In operation, steam 24 enters an inlet 26 of turbine 10 and is channeled through stationary vanes 22. Vanes 22 direct the steam 24 downstream against the blades 20. The steam 24 passes through the remaining stages, imparting a force on blades 20 causing shaft or rotor 14 to rotate. At least one end of turbine 10 may extend axially away from rotor 12 via shaft 14 and may be attached to a load or other machinery (not shown) such as, but not limited to, a generator, and/or another turbine. Accordingly, a large steam turbine unit may actually include several turbines that are co-axially coupled to the same shaft 14. Such a unit may, for example, include a high pressure turbine coupled to an intermediate-pressure turbine, which is in turn coupled to a low pressure turbine.

The steam turbine 10 shown in FIG. 1, comprises five stages. The five stages are referred to as L0, L1, L2, L3 and L4. Stage L4 is the first stage and is the smallest (in a radial direction) of the five stages. Stage L3 is the second stage and is the next stage in an axial direction. Stage L2 is the third stage and is shown in the middle of the five stages. Stage L1 is the fourth and next-to-last stage. Stage L0 is the last stage and is the largest (in a radial direction). It is to be understood that more or fewer than five stages may be present.

With reference to FIG. 2, a cross sectional illustration of a gas turbine 110 is shown. The gas turbine 110 includes a rotor assembly 112 that includes a shaft 114 and a plurality of axially spaced rotor wheels 118. In some embodiments, each rotor wheel 118. A plurality of rotating blades or buckets 120 are mechanically coupled to each rotor wheel 118. More specifically, blades 120 are arranged in rows that extend circumferentially around each rotor wheel 118. A plurality of stationary vanes 122 are secured to a surrounding stator and extend circumferentially around shaft 114, axially positioned between adjacent rows of blades 120.

During operation, air at atmospheric pressure is compressed by a compressor and delivered to a combustion stage. In the combustion stage (represented by combustors 124), the air leaving the compressor is heated by adding fuel to the air and burning the resulting air/fuel mixture. The gas flow resulting from combustion of fuel in the combustion stage then expands through the turbine 110, delivering some of its energy to drive the turbine 110 and produce mechanical power. To produce driving torque, turbine 110 consists of one or more stages. Each stage includes a row of vanes 122 and a row of rotating blades 120 mounted on a rotor wheel 118. Vanes 122 direct incoming gas from the combustion stage onto blades 120. This drives rotation of the rotor wheel 118, and as a result, shaft 114, producing mechanical power.

The following description specifically references blade 20, but is equally applicable to the blade 120. Turning to FIGS. 3 and 4, a pair of blades 20 is shown in greater detail. Each blade or bucket 20 includes an airfoil portion 32. A root section 34 is affixed to (or integral with) a radially-inward end of the airfoil portion 32. A blade attachment member 36 projects from the root section 34. In some embodiments, blade attachment member 36 may be a dovetail, but other blade attachment member shapes and configurations are well known in the art and are also contemplated herein. At a second, opposite end of airfoil portion 32 is a radially-outer tip 38. The airfoil configuration is formed to include a leading edge 40, a trailing edge 42, a suction side 44 and a pressure side 46.

A part-span shroud 48 is attached at an intermediate section of the airfoil portion 32 between the root section 34 and the tip 38. In the exemplary embodiment, part-span shroud sections 50, 52 are located, respectively, on the suction side 44 and pressure side 46 of the airfoil portion 32. In the exemplary embodiment illustrated in FIG. 3, the part-span shroud sections 50, 52 of adjacent blades 20 are designed to at least partially engage along mated Z-shaped edges 54, 56 (see FIG. 4) as in known part-span configurations, during operation of the turbine. The part-span shroud sections are joined to the airfoil portion at fillets 58 (shown for part-span shroud sections 52 but also employed with part-span shroud sections 50).

The blade stiffness and damping characteristics are improved as the part-span shrouds contact each other during untwisting of the blade. The plurality of blades 20 thus behave as a single, continuously coupled structure that exhibits improved stiffness and dampening characteristics when compared to a discrete and uncoupled design. Blades 20 also exhibit reduced vibratory stresses.

FIG. 5 illustrates another known configuration where part-span shroud sections 60, 62 on adjacent, respective blades 64, 66 are designed to engage along straight, substantially-parallel edges 68, 70.

FIG. 6 illustrates a known cross-sectional shape for a part-span shroud (on both the pressure and suction side of the airfoil), as shown and described, for example, in U.S. Pat. No. 5,695,323, and typically used with shroud configurations as shown in FIGS. 3-5. Note that the maximum thickness of the part-span cross-section is located approximately midway along the length of a chord 72 extending between the leading and trailing edges 74, 76 of the part-span shroud 78.

FIG. 7 illustrates a tear-drop cross-sectional shape for a part-span shroud 80 in accordance with an exemplary but nonlimiting embodiment of the invention. Here, the maximum thickness of the cross-sectional shape has been moved forward, nearer to the leading edge 82 of the part-span shroud. More specifically, the point of maximum thickness is located in a range of 20 to 40%, and preferably about 30% of the length of a chord 84 extending between the leading and trailing edges 82, 86 respectively, of the part-span shroud 80, as measured from the leading edge 82. Thus, the thickness of the part-span shroud varies in opposite directions from the location of maximum thickness.

The tear-drop shaped part-span shroud described above is located substantially midway along the radial length of the airfoil but could be located anywhere between about 40% or 80% of the radial height of the airfoil portion as measured from the root section of the blade.

In a more specific exemplary embodiment, the maximum thickness of the part-span shroud is located at 31% of the length of the chord 84 as measured from the leading edge 82, as shown in FIG. 8. The section shape or profile is defined by X-Y Cartesian coordinates where the zero reference point in the X direction is at the center of the chord along its length dimension, and the zero reference point in the Y direction is on the chord 84. The coordinates of the various points indicated on the section view are found in Table I below. Reference point 1 is at the Y=0 coordinate position at the leading edge of the airfoil and the point numbers progress sequentially in a counterclockwise direction.

TABLE I
SI No.	X	Y
1	−1.414	0
2	−1.411	−0.033
3	−1.401	−0.065
4	−1.384	−0.094
5	−1.362	−0.119
6	−1.362	−0.119
7	−1.26	−0.174
8	−1.153	−0.22
9	−1.044	−0.261
10	−0.934	−0.298
11	−0.822	−0.329
12	−0.708	−0.354
13	−0.594	−0.373
14	−0.478	−0.384
15	−0.362	−0.388
16	−0.246	−0.386
17	−0.129	−0.38
18	−0.014	−0.37
19	0.102	−0.357
20	0.217	−0.343
21	0.333	−0.327
22	0.447	−0.309
23	0.562	−0.289
24	0.676	−0.267
25	0.79	−0.243
26	0.903	−0.217
27	1.016	−0.189
28	1.129	−0.16
29	1.241	−0.129
30	1.352	−0.096
31	1.352	−0.096
32	1.377	−0.079
33	1.396	−0.057
34	1.409	−0.03
35	1.414	0
36	1.409	0.03
37	1.396	0.057
38	1.377	0.08
39	1.352	0.097
40	1.352	0.097
41	1.241	0.13
42	1.129	0.16
43	1.016	0.189
44	0.903	0.217
45	0.79	0.243
46	0.676	0.267
47	0.562	0.289
48	0.447	0.309
49	0.333	0.327
50	0.217	0.344
51	0.102	0.358
52	−0.014	0.37
53	−0.129	0.38
54	−0.246	0.387
55	−0.362	0.389
56	−0.478	0.384
57	−0.594	0.373
58	−0.708	0.354
59	−0.822	0.329
60	−0.934	0.298
61	−1.044	0.262
62	−1.153	0.221
63	−1.26	0.174
64	−1.362	0.119
65	−1.362	0.119
66	−1.384	0.094
67	−1.401	0.065
68	−1.411	0.034

In another exemplary embodiment, the maximum thickness is located at 36% of the length of the chord 84 as measured from the leading edge 82, as shown in FIG. 9. The section shape or profile is defined by the with X-Y Cartesian coordinates set out in a scheme similar to FIG. 8 and the coordinates of the various points indicated on the section view are found in Table II below.

TABLE II
SI No.	X	Y
1	−1.414	0
2	−1.412	−0.021
3	−1.408	−0.042
4	−1.401	−0.062
5	−1.391	−0.081
6	−1.38	−0.098
7	−1.38	−0.098
8	−1.292	−0.182
9	−1.197	−0.257
10	−1.095	−0.323
11	−0.988	−0.379
12	−0.875	−0.426
13	−0.76	−0.462
14	−0.641	−0.487
15	−0.521	−0.503
16	−0.399	−0.508
17	−0.278	−0.5
18	−0.158	−0.483
19	−0.039	−0.461
20	0.08	−0.436
21	0.198	−0.409
22	0.316	−0.381
23	0.434	−0.35
24	0.551	−0.319
25	0.668	−0.287
26	0.785	−0.255
27	0.902	−0.223
28	1.019	−0.19
29	1.136	−0.158
30	1.253	−0.126
31	1.369	−0.092
32	1.369	−0.092
33	1.39	−0.074
34	1.404	−0.051
35	1.411	−0.024
36	1.414	0
37	1.411	0.026
38	1.404	0.052
39	1.39	0.076
40	1.369	0.093
41	1.369	0.093
42	1.253	0.127
43	1.136	0.16
44	1.019	0.192
45	0.902	0.224
46	0.785	0.257
47	0.668	0.289
48	0.551	0.321
49	0.434	0.352
50	0.316	0.382
51	0.198	0.411
52	0.08	0.438
53	−0.039	0.462
54	−0.158	0.485
55	−0.278	0.502
56	−0.399	0.51
57	−0.521	0.505
58	−0.641	0.489
59	−0.76	0.463
60	−0.875	0.427
61	−0.988	0.381
62	−1.095	0.325
63	−1.197	0.259
64	−1.292	0.184
65	−1.38	0.1
66	−1.38	0.1
67	−1.391	0.082
68	−1.401	0.063
69	−1.408	0.043
70	−1.412	0.022

In still another exemplary embodiment, the maximum thickness is located at 37% of the length of the chord 84 as measured from the leading edge 82, as shown in FIG. 10. The section shape or profile is defined by the X-Y Cartesian coordinates set out in a scheme similar to FIGS. 8 and 9 and the coordinates of the various points indicated on the section view are found in Table III below.

TABLE III
SI No.	X	Y
1	−1.414	0
2	−1.411	−0.033
3	−1.401	−0.065
4	−1.384	−0.094
5	−1.362	−0.119
6	−1.362	−0.119
7	−1.26	−0.174
8	−1.153	−0.22
9	−1.044	−0.261
10	−0.934	−0.298
11	−0.822	−0.329
12	−0.708	−0.354
13	−0.594	−0.373
14	−0.478	−0.384
15	−0.362	−0.388
16	−0.246	−0.386
17	−0.129	−0.38
18	−0.014	−0.37
19	0.102	−0.357
20	0.217	−0.343
21	0.333	−0.327
22	0.447	−0.309
23	0.562	−0.289
24	0.676	−0.267
25	0.79	−0.243
26	0.903	−0.217
27	1.016	−0.189
28	1.129	−0.16
29	1.241	−0.129
30	1.352	−0.096
31	1.352	−0.096
32	1.377	−0.079
33	1.396	−0.057
34	1.409	−0.03
35	1.414	0
36	1.409	0.03
37	1.396	0.057
38	1.377	0.08
39	1.352	0.097
40	1.352	0.097
41	1.241	0.13
42	1.129	0.16
43	1.016	0.189
44	0.903	0.217
45	0.79	0.243
46	0.676	0.267
47	0.562	0.289
48	0.447	0.309
49	0.333	0.327
50	0.217	0.344
51	0.102	0.358
52	−0.014	0.37
53	0.129	0.38
54	−0.246	0.387
55	−0.362	0.389
56	−0.478	0.384
57	−0.594	0.373
58	−0.708	0.354
59	−0.822	0.329
60	−0.934	0.298
61	−1.044	0.262
62	−1.153	0.221
63	−1.26	0.174
64	−1.362	0.119
65	−1.362	0.119
66	−1.384	0.094
67	−1.401	0.065
68	−1.411	0.034
69	−0.822	0.329

It will be appreciated that the invention also contemplates geometric scaling of the part-span shroud profiles defined in the above Tables.

It will also be appreciated that for extended length airfoils, the part-span shrouds described herein may be used in combination with conventional airfoil tip shrouds located at the radially-outer tips 38 (FIGS. 3, 4) of the airfoils.

The blade 20 and part-span shroud 80 described above may be used in a variety of turbomachine environments. For example, blades having part-span shrouds 80 as described in connection with FIG. 7 may operate in any one or more of: a front stage of a compressor, a latter stage in a gas turbine or a low pressure section blade in a steam turbine. The cross-sectional shape shout at 80 is applicable to the part-span shroud configurations shown in FIGS. 3-5 but is not limited to those configurations.

While various embodiments are described herein, it will be appreciated from the specification that various combinations of elements, variations or improvements therein may be made by those skilled in the art, and are within the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. A rotatable blade for a turbomachine comprising:

an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end;

a root section affixed to the radially-inner end of the airfoil portion; and

a substantially tear-drop shaped part-span shroud located on the airfoil portion between the root section and the radially outer end, wherein said part-span shroud is provided with a cross-sectional shape having a maximum thickness located within 20 to 40% of a chord length extending from a leading edge of said part-span shroud to a trailing edge of said part-span shroud, as measured from said leading edge of said part-span shroud.

2. The rotatable blade of claim 1, wherein said maximum thickness is located at about 30% of said chord length.

3. The rotatable blade of claim 1, wherein said said maximum thickness is located between 31% and 37% of said chord length.

4. The rotatable blade of claim 1, wherein said maximum thickness is located at 31% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table I.

5. The rotatable blade of claim 1, wherein said maximum thickness is located at 36% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table II.

6. The rotatable blade of claim 1, wherein said maximum thickness is located at 37% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table III.

7. The rotatable blade of claim 1 wherein the part-span shroud is located substantially midway along a radial length of the airfoil portion.

8. The rotatable blade of claim 1 wherein the rotating blade operates as one of:

a front stage blade in a compressor,

a latter stage blade in a gas turbine, or

a low pressure section blade in a steam turbine.

9. The rotatable blade of claim 1 wherein part-span shrouds on respective pressure and suction sides of adjacent ones of said blades at least partially engage along adjacent, substantially Z-shaped contact surfaces.

10. The rotatable blade of claim 1 wherein part-span shrouds on respective pressure and suction sides of adjacent ones of said blades have substantially-straight contact surfaces.

11. A turbomachine comprising:

a rotor rotatably mounted within a stator, the rotor including:

a shaft;

at least one rotor wheel mounted on the shaft, each of the at least one rotor wheels including a plurality of radially outwardly extending blades mounted thereon; and

wherein each blade includes an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end, a pressure side and a suction side; a root section at the radially-inner end of said airfoil portion; and a part-span shroud located on said airfoil portion between said root section and said radially outer end, on said pressure side and said suction side, wherein said part-span shroud is provided with a substantially tear-drop cross-sectional shape having a maximum thickness located within 20 to 40% of a chord length extending between a leading edge of said part-span shroud and a trailing edge of said part-span shroud, as measured from said leading edge of said part-span shroud.

12. The turbomachine of claim 11 wherein said maximum thickness is located at 31% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table I.

13. The turbomachine of claim 11, wherein said maximum thickness is located at 36% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table II.

14. The turbomachine of claim 11, wherein said maximum thickness is located at 37% of said chord length and wherein said part-span shroud has a profile defined by the X-Y coordinates set forth in Table III.

15. The turbomachine of claim 11, wherein said blade operates as one of:

a front stage blade in a compressor,

a latter stage blade in a gas turbine, or

a low pressure section blade in a steam turbine.

16. The turbomachine of claim 11 wherein said part-span shroud is located substantially midway along a radial length of said airfoil portion.

17. A turbomachine comprising:

a rotor rotatably mounted within a stator, the rotor including:

a shaft;

at least one rotor wheel mounted on the shaft, each of the at least one rotor wheels including a plurality of radially outwardly extending blades mounted thereon; and

wherein each blade includes an airfoil portion having a leading edge and a trailing edge, a radially-inner end and a radially-outer end, a pressure side and a suction side; a root section at the radially-inner end of said airfoil portion; and a part-span shroud located on said airfoil portion between said root section and said radially outer end, on said pressure side and said suction side, wherein said part-span shroud is provided with a substantially tear-drop cross-sectional shape having a maximum thickness located at 31%, 36% or 37% of a chord length extending between a leading edge of said part-span shroud and a trailing edge of said part-span shroud, as measured from said leading edge of said part-span shroud; and wherein said part-span shroud is disposed on the airfoil portion between about 40% to 80% of a radial height of said airfoil portion as measured from the root section of the blade.

18. The turbomachine of claim 17 wherein said part-span shroud has a profile defined by the X-Y coordinates as set forth in any one of Tables respectively, or by geometric scaling of said coordinates.

19. The turbomachine of claim 17 wherein part-span shrouds on respective pressure and suction sides of adjacent ones of said blades at least partially engage along adjacent, substantially straight or Z-shaped contact surfaces.

20. The turbomachine of claim 17 wherein said part-span shroud is located substantially midway along said radial height of said airfoil portion.