CROSS-REFERENCE TO RELATED APPLICATIONS
None.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not Applicable.
BACKGROUND OF THE INVENTION
This invention relates to the cooling of an airfoil comprising a portion of a stator vane or nozzle of the first stage of a gas turbine engine; and more particularly, to the hole pattern formation in the airfoil for thin film cooling of a trailing edge of the airfoil.
In the construction of gas turbine engines, an annular array of turbine segments is provided to form a turbine stage. Generally, the turbine stage is defined by outer and inner annular bands spaced apart from each other with a plurality of vanes or airfoils extending between the bands and circumferentially spaced from one other. This construction, in turn, defines a path for a working fluid flowing through the turbine. In a gas turbine engine, this is a hot gas. As will be appreciated by those skilled in the art, the most extreme adverse operating conditions are generally encountered at the first stage of the turbine. That is because this stage is immediately downstream of the engine's combustion chamber and components comprising this stage must therefore withstand high thermal loads. As is known in the art, cooling systems for this engine stage utilize thin film cooling techniques to insure so adequate cooling is provided. Thin film cooling is accomplished by discharging air through orifices formed in portions of the nozzle. The discharged air then forms a protective thin film boundary layer between the hot stream of gases flowing through the first stage of the turbine and the surface of the nozzle.
Various problems with thin film cooling systems have been encountered and solutions to these problems have been addressed in U.S. Pat. Nos. 6,583,526, 6,561,757, 6,553,665, 6,527,274, 6,517,312, 6,506,013, 6,435,814, 6,402,466, 6,398,486, and 5,591,002, all of which are assigned to the same assignee as the present application.
The present invention is directed to an advanced film-cooling configuration for cooling the trailing edge of a nozzle used in the first stage of an advanced design gas turbine engine. The nozzle is a steam cooled component which operates at firing temperatures which require cooling of the airfoil to extend the low cycle fatigue (LCF), oxidation, and creep life of the component. While steam adequately cools the majority of the nozzle, it is not feasible for use in cooling the trailing edge of the nozzle. Rather, this requires a novel and advanced thin film cooling configuration in order for the trailing edge to not rapidly deteriorate once the turbine is in service which would require costly servicing or replacement of the nozzle and unacceptable down-time when the turbine is out of service.
BRIEF SUMMARY OF THE INVENTION
Briefly stated, the present invention is directed to thin film cooling of the trailing edge of a nozzle for the first stage of a gas turbine engine. Cooling is affected by use of a plurality of rows of film cooling holes located adjacent the trailing edge of the nozzle, on both the concave side and convex side of the nozzle. In particular, three rows of film cooling holes are formed in the sidewalls of the nozzle on the respective concave and convex sides thereof. A first and forward row of holes extends generally longitudinally of the nozzle and comprises holes of varying sizes and angles formed at predetermined locations on the nozzle. Second and third rows of holes also extend generally longitudinally of the nozzle and also comprise holes of varying sizes and angles formed at predetermined locations on the nozzle. The second row of holes comprises a middle row of holes and the third row an aft row. Holes comprising the second row are spaced a substantial distance from those comprising the first row. However, the second and third row of holes are formed relatively close together with the holes comprising the second row being staggered in location with respect to those comprising the third row. By placing the middle and aft rows of holes closer together, and staggering the hole arrangement in these two rows, an effective film flow is achieved which cools the trailing edge of the nozzle thereby to minimize cooling flow, optimize performance of the turbine engine, reduce NOx produced by the engine, prolong the service life of the nozzle and reduce service and repair costs.
Two embodiments of the invention are shown with the thin film cooling arrangement of the first embodiment including substantially more holes in each row than occurs in the second embodiment.
The foregoing and other objects, features, and advantages of the invention will be in part apparent and in part pointed out hereinafter.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
In the accompanying drawings which form part of the specification:
FIG. 1A is an orthographic view of the concave side of a first embodiment of a first stage nozzle for a gas turbine, and FIG. 1B is an orthographic view of the nozzle from the convex side;
FIG. 2 is a sectional view of an airfoil portion of the nozzle illustrating steam and air flow paths through the air foil;
FIG. 3 is a sectional view of the airfoil;
FIG. 4 is a detail view of the airfoil illustrating a film hole pattern formed in the concave side of the airfoil;
FIG. 5 is a view of the flow path side of the outer band at the trailing edge further illustrating the film hole pattern on the concave side of the airfoil;
FIGS. 6 and 7 are views similar to those of FIGS. 4 and 5, respectively, for the convex side of the airfoil;
FIGS. 8A is an orthographic view of the concave side of a second embodiment of a first stage nozzle for a gas turbine, and FIG. 8B is an orthographic view of the nozzle from the convex side;
FIG. 9 is a detail view of the airfoil illustrating a film hole pattern formed in the concave side of the airfoil;
FIG. 10 is a view of the flow path side of the outer band at the trailing edge further illustrating the film hole pattern in the concave side of the airfoil; and,
FIGS. 11 and 12 are views similar to those of FIGS. 9 and 10, respectively, for the convex side of the airfoil.
Corresponding reference numerals indicate corresponding parts throughout the several figures of the drawings.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The following detailed description illustrates the invention by way of example and not by way of limitation. The description clearly enables one skilled in the art to make and use the invention, describes several embodiments, adaptations, variations, alternatives, and uses of the invention, including what is presently believed to be the best mode of carrying out the invention.
Referring to the drawings, the present invention is directed to thin film cooling for a first stage nozzle assembly, indicated generally 10 in FIGS. 1A and 1B, of a gas turbine engine. While not shown in the drawings, those skilled in the art will appreciate that nozzle assembly 10 is comprised of a plurality of circumferentially arranged vanes or airfoils indicated generally 12, the respective segments being connected to one another to form an annular array which defines a path for hot gasses passing through the first stage.
With respect to FIGS. 1A and 1B, a nozzle assembly includes an outer band 14 and an inner band 16 between which airfoil 12 is mounted. Each assembly is supported within a shell (not shown) of the turbine in which turbine components are installed. Referring to FIG. 3, airfoil 12 is shown to a have a curved airfoil shape with a rounded leading edge 18 and a trailing edge 20. A steam inlet manifold 22 and a steam outlet manifold 24 are mounted on outer band 14 to circulate steam through the airfoil. Referring to FIG. 2, airfoil 12 is constructed as is generally known in the art with a series of internal flow passages indicated generally P for steam to circulate through the airfoil from inlet manifold 22 to outlet manifold 24. These flow paths will not be described in detail. In addition to circulating steam through airfoil 12, the present invention includes an air inlet 26 in outer band 14 and a plurality of air outlet holes or slots 28 for thin film cooling of the trailing edge of the airfoil. As described hereinafter, these openings are arranged in a predetermined pattern to maximize the thin film cooling of airfoil 12. The openings are formed in the sidewalls of the airfoil on both the concave side and convex side of the airfoil. The size of each opening and its location are determined in accordance with the present invention. As shown in FIGS. 5 and 7, at the outer end of the airfoil adjacent band 14, the sidewalls of the airfoil curve or flare outwardly. In addition, the airfoil has a circumferentially extending rail 30. The holes or openings are formed in this portion of the nozzle assembly as well to provide sufficient thin film cooling at the trailing edge of the airfoil.
The hole pattern or arrangement of the present invention comprises three rows of openings which extend longitudinally of the airfoil, on both the concave and convex sides of the nozzle assembly, and spaced inwardly of the trailing edge. As particularly shown in FIG. 4, on the concave side of the airfoil are three rows indicated generally RA, RB, and RC, and on the convex side of the airfoil, as shown in FIG. 6, are three rows indicated RJ, RK, and RL. To further provide adequate thin film cooling of trailing edge 20, additional holes or slots are also formed in the curved portions of the airfoil adjacent outer band 14, and on the portion of rail 30 adjacent the trailing edge of the airfoil. On the concave side of the nozzle assembly, and as shown in FIGS. 4 and. 5, these additional openings are indicated 1D-6D, 1E, 1F-4F, 1G-5G, and 1H-6H. On the convex side of the assembly, and as shown in FIGS. 6 and 7, these additional openings are indicated 1M-6M, 1N-7N, 1P-4P, and 1R.
Referring again to FIGS. 4 and 6, the rows of holes or openings formed in the respective sidewalls of the airfoil include a forward row (the row furthest away from the trailing edge), an aft row (the row closest to the trailing edge), and an intermediate row. On the concave side of the assembly, row RC is the forward row and includes 31 openings. Row RB is the intermediate row and comprises 49 openings. The aft row is row RA which includes 43 openings. In accordance with the invention, the spacing between intermediate row RB and aft row RA is substantially closer than the spacing between forward row RC and intermediate row RB. Further, the holes comprising intermediate row RB and those comprising aft row RC are arranged in a staggered pattern as shown in FIG. 4. Similarly in accordance with the invention, on the convex side of the assembly, the spacing between intermediate row RK (which has 51 openings) and aft row RL (which has 44 openings) is substantially closer than the spacing between forward row RJ (which has 29 openings) and intermediate row RK. Again, the holes comprising intermediate row RK and those comprising aft row RL are arranged in a staggered pattern as shown in FIG. 6.
Table 1 is a listing of all the holes comprising rows RA-RC, RJ-RL, and the other holes formed in the bands 14 and 16 and rail 30. The table includes each hole designation, the angle of the opening with respect to the outer surface of airfoil 12, and the X, Y, Z coordinates determining the location of the hole. The distances are measured with respect to the reference point Q (0,0,0) shown in FIG. 1B.
TABLE 1
|
|
ANGLE TO
DIAMETERSURFACE
HOLE #(in.)(°)X (in.)Y (in.)Z (in.)
|
|
1A0.03230−7.792−2.253.179
2A0.03230−7.777−2.137.223
3A0.03230−7.766−2.021.269
4A0.03230−7.757−7.905.314
5A0.03230−7.748−1.788.357
6A0.03230−7.741−1.670.398
7A0.03230−7.736−1.559.435
8A0.03230−7.732−1.453.469
9A0.03230−7.729−1.347.502
10A0.03230−7.727−1.241.535
11A0.03230−7.726−1.135.566
12A0.03230−7.726−1.028.596
13A0.03230−7.726−.921.625
14A0.03230−7.728−.814.653
15A0.03230−7.730−.706.680
16A0.03230−7.732−.598.707
17A0.03230−7.736−.490.732
18A0.03230−7.740−.382.756
19A0.03230−7.745−.274.780
20A0.03230−7.750−.165.802
21A0.03230−7.756−.056.822
22A0.03230−7.762.053.840
23A0.03230−7.770.162.860
24A0.03230−7.780.270.882
25A0.03230−7.790.378.906
26A0.03230−7.802.486.929
27A0.03230−7.812.594.950
28A0.03230−7.822.703.968
29A0.03230−7.832.813.983
30A0.03230−7.843.922.997
31A0.03230−7.8551.0431.012
32A0.03230−7.8701.1741.028
33A0.03230−7.8841.3051.043
34A0.03230−7.8981.4371.057
35A0.03230−7.9121.5681.070
36A0.03230−7.9311.7441.085
37A0.03230−7.9561.9641.102
38A0.03230−7.9802.1641.114
39A0.03230−8.0022.3451.122
40A0.03230−8.0312.5531.130
41A0.03230−8.0602.7621.128
42A0.03230−8.0912.9691.136
43A0.03230−8.0663.1621.244
1B0.03237−7.894−3.250.074
2B0.03237−7.906−3.049−.202
3B0.03230−7.845−2.827−.157
4B0.03230−7.790−2.630−.100
5B0.03230−7.779−2.544−.060
6B0.03230−7.744−2.427−.055
7B0.03230−7.730−2.311−.010
8B0.03230−7.715−2.195.033
9B0.03230−7.702−2.079.077
10B0.03230−7.691−1.963.122
11B0.03230−7.682−1.846.167
12B0.03230−7.675−1.729.210
13B0.03230−7.668−1.611.251
14B0.03230−7.664−1.506.286
15B0.03230−7.660−1.400.320
16B0.03230−7.658−1.294.352
17B0.03230−7.657−1.188.384
18B0.03230−7.657−1.081.415
19B0.03230−7.658−.974.445
20B0.03230−7.659−.867.474
21B0.03230−7.661−.760.502
22B0.03230−7.664−.652.529
23B0.03230−7.667−.544.555
24B0.03230−7.671−.436.580
25B0.03230−7.676−.328.604
26B0.03230−7.682−.220.627
27B0.03230−7.687−.111.648
28B0.03230−7.694−.002.668
29B0.03230−7.702.107.687
30B0.03230−7.711.216.707
31B0.03230−7.721.324.729
32B0.03230−7.733.432.752
33B0.03230−7.745.540.775
34B0.03230−7.756.649.795
35B0.03230−7.766.755.812
36B0.03230−7.777.868.827
37B0.03230−7.788.977.841
38B0.03230−7.8021.108.858
39B0.03230−7.8171.240.873
40B0.03230−7.8321.371.887
41B0.03230−7.8481.502.900
42B0.03230−7.8631.634.912
43B0.03230−7.8861.854.931
44B0.03230−7.9102.074.946
45B0.03230−7.9312.255.956
46B0.03230−7.9542.435.963
47B0.03230−7.9852.657.970
48B0.03230−8.0142.866.966
49B0.03230−8.0423.0721.028
1C0.032105−7.803−3.190−.429
2C0.032150−7.811−3.013−.421
3C0.032150−7.726−2.763−.348
4C0.032150−7.674−2.550−.304
5C0.032150−7.629−2.335−.267
6C0.032150−7.584−2.121−.230
7C0.032150−7.544−1.908−.190
8C0.032150−7.514−1.692−.146
9C0.032150−7.494−1.476−.098
10C0.032150−7.482−1.260−.048
11C0.032150−7.476−1.043−.001
12C0.032150−7.470−.824.035
13C0.032150−7.464−.604.062
14C0.032150−7.465−.383.090
15C0.032150−7.470−.163.120
16C0.03230−7.481.068.148
17C0.03230−7.494.288.169
18C0.03230−7.508.508.186
19C0.03230−7.523.729.198
20C0.03230−7.539.950.209
21C0.03230−7.5581.170.220
22C0.03230−7.5291.391.230
23C0.03230−7.5981.612.234
24C0.03230−7.6151.833.234
25C0.03230−7.6322.054.232
26C0.03230−7.65 12.276.228
27C0.03230−7.6672.496.206
28C0.03230−7.6732.712.152
29C0.03230−7.6782.919.094
30C0.03230−7.7053.073.102
31C0.03285−7.6553.210.102
1D0.03030−8.5373.4332.152
2D0.03030−8.8103.4591.880
3D0.03030−7.8253.5031.610
4D0.03030−7.4713.5651.340
5D0.030108−7.0173.668.993
6D0.030108−6.7143.751.760
1E0.03230−7.9803.2151.252
1F0.03230−7.9663.164.929
2F0.03230−7.8333.252.954
3F0.03230−7.6823.2711.036
4F0.03230−7.5303.2931.117
1G0.03230−7.8403.168.558
2G0.03230−7.7113.274.580
3G0.03230−7.5443.297.664
4G0.03230−7.3963.323.747
5G0.03230−7.2393.353.830
1H0.03230−7.5583.290.161
2H0.03230−7.4333.322.247
3H0.03230−7.2933.348.343
4H0.03230−7.1533.376.439
5H0.03230−7.0133.407.534
6H0.03230−6.8743.440.630
1J0.032108−8.349−3.250−.676
2J0.032150−8.144−2.937−.568
3J0.032150−8.091−2.727−.519
4J0.032150−8.048−2.515−.480
5J0.032150−8.014−2.298−.450
6J0.032150−7.988−2.080−.424
7J0.032150−7.970−1.861−.397
8J0.032150−7.959−1.643−.365
9J0.032150−7.956−1.425−.322
10J0.032150−7.959−1.208−.276
11J0.032150−7.961−.990−.240
12J0.032150−7.693−.770−.216
13J0.032150−7.966−.549−.193
14J0.032150−7.971−.329−.166
15J0.032150−7.979−.110−.137
16J0.03230−7.986.080−.114
17J0.03230−7.996.300−.090
18J0.03230−7.005.521−.070
19J0.03230−8.013.742−.054
20J0.03230−8.021.964−.037
21J0.03230−8.0311.185−.018
22J0.03230−8.0421.406−.003
23J0.03230−8.0521.627.004
24J0.03230−8.0611.849.008
25J0.03230−8.0732.070.016
26J0.03230−8.0842.292.018
27J0.03230−8.0912.512−.008
28J0.03230−8.0932.728−.061
29J0.03230−8.0932.939−.123
1K0.03230−8.349−3.250−.676
2K0.03230−8.144−2.937−.568
3K0.03230−8.091−2.727−.519
4K0.03230−8.048−2.515−.480
5K0.03230−8.014−2.298−.450
6K0.03230−7.988−2.080−.424
7K0.03230−7.970−1.861−.397
8K0.03230−7.959−1.643−.365
9K0.03230−8.108−2.206−.088
10K0.03230−8.102−2.092−.047
11K0.03230−8.097−1.972−.004
12K0.03230−8.093−1.865.038
13K0.03230−8.090−1.761.075
14K0.03230−8.089−1.656.111
15K0.03230−8.088−1.550.145
16K0.03230−8.088−1.444.179
17K0.03230−8.089−1.338.211
18K0.03230−8.091−1.232.243
19K0.03230−8.094−1.125.273
20K0.03230−8.096−1.018.303
21K0.03230−8.100−.911.332
22K0.03230−8.103−.804.359
23K0.03230−8.106−.696.386
24K0.03230−8.110−.588.412
25K0.03230−8.114−.480.437
26K0.03230−8.118−.372.462
27K0.03230−8.123−.264.486
28K0.03230−8.128−.155.508
29K0.03230−8.132−.046.528
30K0.03230−8.137.063.548
31K0.03230−8.142.172.568
32K0.03230−8.147.281.591
33K0.03230−8.153.389.615
34K0.03230−8.160.497.640
35K0.03230−8.167.605.663
36K0.03230−8.174.714.682
37K0.03230−8.181.834.700
38K0.03230−8.188.953.717
39K0.03230−8.1961.073.734
40K0.03230−8.2031.192.750
41K0.03230−8.2111.312.764
42K0.03230−8.2191.432.779
43K0.03230−8.2291.585.796
44K0.03230−8.2391.738.812
45K0.03230−8.2501.891.826
46K0.03230−8.2622.072.840
47K0.03230−8.2762.253.853
48K0.03230−8.2942.474.864
49K0.03230−8.3122.695.872
50K0.03230−8.3282.887.874
51K0.03230−8.3763.074.924
1L0.03530−8.164−2.262.065
2L0.03530−8.156−2.149.107
3L0.03530−8.149−2.035.150
4L0.03530−8.144−1.922.193
5L0.03530−8.140−1.813.232
6L0.03530−8.137−1.708.268
7L0.03530−8.135−1.603.302
8L0.03530−8.133−1.498.336
9L0.03530−8.133−1.392.369
10L0.03530−8.134−1.285.400
11L0.03530−8.136−1.179.431
12L0.03530−8.138−1.072.461
13L0.03530−8.140−.965.490
14L0.03730−8.143−.857.518
15L0.03730−8.146−.750.545
16L0.03730−8.149−.642.572
17L0.03730−8.153−.534.597
18L0.03730−8.157−.426.622
19L0.03730−8.161−.318.646
20L0.03730−8.165−.209.668
21L0.03730−8.170−.100.689
22L0.03730−8.174.008.709
23L0.03730−8.179.118.729
24L0.03730−8.184.226.751
25L0.03730−8.190.335.776
26L0.03730−8.197.443.801
27L0.03530−8.204.551.824
28L0.03530−8.211.660.844
29L0.03530−8.217.774.862
30L0.03530−8.224.893.879
31L0.03530−8.2311.013.895
32L0.03530−8.2381.133.912
33L0.03530−8.2461.252.928
34L0.03530−8.2531.372.942
35L0.03530−8.2621.509.958
36L0.03530−8.2721.661.974
37L0.03530−8.2831.814.988
38L0.03230−8.2941.9811.002
39L0.03230−8.3082.1621.015
40L0.03230−8.3242.3631.027
41L0.03230−8.3432.5841.040
42L0.03230−8.3602.7931.038
43L0.03230−8.3802.9831.053
44L0.03230−8.4763.1461.096
1M0.03030−8.9643.524−.771
2M0.03030−8.9643.529−.264
3M0.03030−8.9643.528.436
4M0.03030−8.9643.5201.003
5M0.030125−8.9643.5051.570
6M0.030125−8.9643.4842.136
1N0.03230−8.7243.208−.624
2N0.03230−8.6253.208−.558
3N0.03230−8.5263.210−.492
4N0.03230−8.4283.2 13−.426
5N0.03230−8.3293.218−.360
6N0.03230−8.2463.210−.304
7N0.03274−8.1543.166−.247
1P0.03230−8.6563.211.072
2P0.03230−8.5723.211.119
3P0.03230−8.4873.213.164
4P0.03230−8.4023.215.210
1R0.03230−8.6323.204.878
|
In FIGS. 8A-12, a second embodiment of a nozzle assembly of the present invention is indicated generally 110. This nozzle assembly includes an outer band 114 and an inner band 116 between which an airfoil 112 is mounted. Again, airfoil 112 has a curved airfoil shape with a rounded leading edge 118 and a trailing edge 120. Steam inlet manifold 122 and steam outlet manifold 124 are mounted on outer band 114 to circulate air through the airfoil, and an air inlet 126 admits air into the airfoil for discharge through holes or openings 128 for thin film cooling of the trailing edge of the airfoil. As with the previously described embodiment, the openings are formed in both the concave side and convex side of the airfoil in a predetermined pattern to maximize thin film cooling. The size of each opening and its location are again determined in accordance with the present invention. As shown in FIGS. 10 and 12, at the trailing edge of the airfoil, adjacent band 114, the sidewalls of the airfoil curve or flare outwardly to a circumferentially extending rail 130, and holes or openings are formed in this portion of the nozzle assembly.
The hole pattern for this embodiment again comprises three rows of openings which extend longitudinally of the airfoil, on both the concave and convex sides of the nozzle assembly, and spaced inwardly of the trailing edge. As particularly shown in FIG. 9, on the concave side of the airfoil are three rows indicated generally RA′, RB′, and RC′, and on the convex side of the airfoil, as shown in FIG. 11, are three rows indicated RJ′, RK′, and RL′. To further provide adequate thin film cooling, additional holes or slots are formed in the curved portions of the airfoil adjacent outer band 114, and on the portion of rail 30 adjacent the trailing edge of the airfoil. On the concave side of the nozzle assembly, and as shown in FIGS. 9 and 10, these additional openings are indicated 1D′-6D′, 1E′, 1F′-4F′, 1G′-5G′, and 1H′-6H′. On the convex side of the assembly, and as shown in FIGS. 11 and 12, these additional openings are indicated 1M′-6M′, 1N′-7N′, 1P′-4P′, and 1R′.
As shown in FIGS. 9 and 11, the rows of holes in the respective sidewalls of the airfoil include a forward row, an intermediate row, and an aft row. On the concave side of the assembly, row RC′ is the forward row and includes 31 openings. Row RB′ is the intermediate row and comprises 9 openings. The aft row is row RA′ and includes 43 openings. As previously described, the spacing between intermediate row RB′ and aft row RA′ is substantially closer than the spacing between forward row RC′ and intermediate row RB′. Further, the holes comprising intermediate row RB′ and those comprising forward row RC′ are arranged in a staggered pattern as shown in FIG. 9. On the convex side of the assembly, the spacing between intermediate row RK′ which has 10 openings, and aft row RL′ which has 44 openings, is substantially closer than the spacing between forward row RJ′ which has 29 openings, and intermediate row RK′. Again, the holes comprising intermediate row RK′ and those comprising aft row RL′ are arranged in a staggered pattern as shown in FIG. 11.
Table 2 is a listing of all the holes comprising rows RA′-RC′, RJ′-RL′, and the other holes formed in the curved outer portion of the airfoil and rai 130. The table includes each hole designation, the angle of the opening with respect to the outer surface of airfoil 112, and the X,Y,Z coordinates of the hole locations. As with FIGS. 1A and 1B, the distances are measured with respect to the reference point Q (0,0,0) shown in FIG. 8B.
TABLE 2
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ANGLE
TO
HOLE #DIAMETERSURFACEX (AB)Y (AA)Z (AC)
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|
1A.02730−7.792−2.253.179
2A.02730−7.777−2.137.223
3A.02730−7.766−2.021.269
4A.02730−7.757−7.905.314
5A.02730−7.748−1.788.357
6A.02730−7.741−1.670.398
7A.02730−7.736−1.559.435
8A.02730−7.732−1.453.469
9A.02730−7.729−1.347.502
10A.02730−7.727−1.241.535
11A.02730−7.726−1.135.566
12A.02730−7.726−1.028.596
13A.02730−7.726−.921.625
14A.02730−7.728−.814.653
15A.02730−7.730−.706.680
16A.02730−7.732−.598.707
17A.02730−7.736−.490.732
18A.02730−7.740−.382.756
19A.02730−7.745−.274.780
20A.02730−7.750−.165.802
21A.02730−7.756−.056.822
22A.02730−7.762.053.840
23A.02730−7.770.162.860
24A.02730−7.780.270.882
25A.02730−7.790.378.906
26A.02730−7.802.486.929
27A.02730−7.812.594.950
28A.02730−7.822.703.968
29A.02730−7.832.813.983
30A.02730−7.843.922.997
31A.02730−7.8551.0431.012
32A.02730−7.8701.1741.028
33A.02730−7.8841.3051.043
34A.02730−7.8981.4371.057
35A.02730−7.9121.5681.070
36A.02730−7.9311.7441.085
37A.02730−7.9561.9641.102
38A.02730−7.9802.1641.114
39A.02730−8.0022.3451.122
40A.02730−8.0312.5531.130
41A.02730−8.0602.7621.128
42A.02730−8.0912.9691.136
43A.02730−8.0663.1621.244
1B.02737−7.894−3.250.074
2B.02737−7.906−3.049−.202
3B.02730−7.845−2.827−.157
4B.02730−7.790−2.630−.100
5B.02730−7.779−2.544−.060
6B.02730−7.744−2.427−.055
7B.02730−7.730−2.311−.010
48B.02730−8.0142.866.966
49B.02730−8.0423.0721.028
1C.029105−7.803−3.190−.429
2C.029150−7.811−3.013−.421
3C.029150−7.726−2.763−.348
4C.029150−7.674−2.550−.304
5C.029150−7.629−2.335−.267
6C.029150−7.584−2.121−.230
7C.029150−7.544−1.908−.190
8C.029150−7.514−1.692−.146
9C.029150−7.494−1.476−.098
10C.029150−7.482−1.260−.048
11C.029150−7.476−1.043−.001
12C.029150−7.470−.824.035
13C.029150−7.464−.604.062
14C.029150−7.465−.383.090
15C.029150−7.470−.163.120
16C.02930−7.481.068.148
17C.02930−7.494.288.169
18C.02930−7.508.508.186
19C.02930−7.523.729.198
20C.02930−7.539.950.209
21C.02930−7.5581.170.220
22C.02930−7.5291.391.230
23C.02930−7.5981.612.234
24C.02930−7.6151.833.234
25C.02930−7.6322.054.232
26C.02930−7.6512.276.228
27C.02930−7.6672.496.206
28C.02930−7.6732.712.152
29C.02930−7.6782.919.094
30C.02930−7.7053.073.102
31C.02985−7.6553.210.102
1D.03030−8.5373.4332.152
2D.03030−8.8103.4591.880
3D.03030−7.8253.5031.610
4D.03030−7.4713.5651.340
5D.030108−7.0173.668.993
6D.030108−6.7143.751.760
1E.03230−7.9663.2151.252
1F.03230−7.9663.164.929
2F.03230−7.8333.252.954
3F.03230−7.6823.2711.036
4F.03230−7.5303.2931.117
1G.03230−7.8403.168.558
2G.03230−7.7113.274.580
3G.03230−7.5443.297.664
4G.03230−7.3963.323.747
5G.03230−7.2393.353.830
1H.03230−7.5583.290.161
2H.03230−7.4333.322.247
3H.03230−7.2933.348.343
4H.03230−7.1533.376.439
5H.03230−7.0133.407.534
6H.03230−6.8743.440.630
1J.028108−8.349−3.250−.676
2J.028150−8.144−2.937−.568
3J.028150−8.091−2.727−.519
4J.028150−8.048−2.515−.480
5J.028150−8.014−2.298−.450
6J.028150−7.988−2.080−.424
7J.028150−7.970−1.861−.397
8J.028150−7.959−1.643−.365
9J.028150−7.956−1.425−.322
10J.028150−7.959−1.208−.276
11J.028150−7.961−.990−.240
12J.028150−7.693−.770−.216
13J.028150−7.966−.549−.193
14J.028150−7.971−.329−.166
15J.028150−7.979−.110−.137
16J.02830−7.986.080−.114
17J.02830−7.996.300−.090
18J.02830−7.005.521−.070
19J.02830−8.013.742−.054
20J.02830−8.021.964−.037
21J.02830−8.0311.185−.018
22J.02830−8.0421.406−.003
23J.02830−8.0521.627.004
24J.02830−8.0611.849.008
25J.02830−8.0732.070.016
26J.02830−8.0842.292.018
27J.02830−8.0912.512−.008
28J.02830−8.0932.728−.061
29J.02830−8.0932.939−.123
1K.02830−8.349−3.250−.676
2K.02830−8.144−2.937−.568
3K.02830−8.091−2.727−.519
4K.02830−8.048−2.515−.480
5K.02830−8.014−2.298−.450
6K.02830−7.988−2.080−.424
7K.02830−7.970−1.861−.397
8K.02830−7.959−1.643−.365
50K.02730−8.3282.887.874
51K.02730−8.3763.074.924
1L.02930−8.164−2.262.065
2L.02930−8.156−2.149.107
3L.02930−8.149−2.035.150
4L.02930−8.144−1.922.193
5L.02930−8.140−1.813.232
6L.02930−8.137−1.708.268
7L.02930−8.135−1.603.302
8L.02930−8.133−1.498.336
9L.02930−8.133−1.392.369
10L.02930−8.134−1.285.400
11L.02930−8.136−1.179.431
12L.02930−8.138−1.072.461
13L.02930−8.140−.965.490
14L.03030−8.143−.857.518
15L.03030−8.146−.750.545
16L.03030−8.149−.642.572
17L.03030−8.153−.534.597
18L.03030−8.157−.426.622
19L.03030−8.161−.318.646
20L.03030−8.165−.209.668
21L.03030−8.170−.100.689
22L.03030−8.174.008.709
23L.03030−8.179.118.729
24L.03030−8.184.226.751
25L.03030−8.190.335.776
26L.03030−8.197.443.801
27L.02930−8.204.551.824
28L.02930−8.211.660.844
29L.02930−8.217.774.862
30L.02930−8.224.893.879
31L.02930−8.2311.013.895
32L.02930−8.2381.133.912
33L.02930−8.2461.252.928
34L.02930−8.2531.372.942
35L.02930−8.2621.509.958
36L.02930−8.2721.661.974
37L.02930−8.2831.814.988
38L.02830−8.2941.9811.002
39L.02830−8.3082.1621.015
40L.02830−8.3242.3631.027
41L.02830−8.3432.5841.040
42L.02830−8.3602.7931.038
43L.02830−8.3802.9831.053
44L.02830−8.4763.1461.096
1M.03030−8.9643.524−.771
2M.03030−8.9643.529−.264
3M.03030−8.9643.528.436
4M.03030−8.9643.5201.003
5M.030125−8.9643.5051.570
6M.030125−8.9643.4842.136
1N.03230−8.7243.208−.624
2N.03230−8.6253.208−.558
3N.03230−8.5263.210−.492
4N.03230−8.4283.213−.426
5N.03230−8.3293.218−.360
6N.03230−8.2463.210−.304
7N.03274−8.1543.166−.247
1P.03230−8.6563.211.072
2P.03230−8.5723.211.119
3P.03230−8.4873.213.164
4P.03230−8.4023.215.210
1R.03230−8.6323.204.878
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In view of the above, it will be seen that the several objects of the invention are achieved and other advantageous results are obtained. As various changes could be made in the above constructions without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.