OPTIMIZED AERODYNAMIC PROFILE FOR A TURBINE VANE, IN PARTICULAR FOR A NOZZLE OF A TURBINE

Information

  • Patent Application
  • 20180328204
  • Publication Number
    20180328204
  • Date Filed
    May 10, 2018
    6 years ago
  • Date Published
    November 15, 2018
    6 years ago
Abstract
When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.
Description
INTRODUCTION

The present disclosure relates to an aerodynamic profile for a turbine vane.


In particular, the disclosure relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.


The disclosure relates in particular to a nozzle vane of a turbine having a plurality of stages, preferably five stages.


Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.


It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.


Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.


An object of the disclosure is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.


This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the vane and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.


This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.


Furthermore, the aerodynamic profile of the disclosure is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.


It is stated above that the profile of the disclosure is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.


The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.


It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.


In addition, the aerodynamic profile may be positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the radial axis of the vane, along which the coordinate Zadim is measured.


These variations take account in particular to at least one of manufacturing tolerances of the profile, the setting of the profile to adapt to the environment when in operation, and possible deformation occurring when mounting the vane and integrating the same in the nozzle.


With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the same stage of the turbine.





BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:



FIG. 1 is a fragmentary axial diagrammatic section view of a turbine including a vane of profile that corresponds to that of the present disclosure;



FIG. 2 shows a vane of the turbine.





DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises five stages referenced respectively S1 to S5. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.


In FIG. 1, the vanes of the nozzles of stages S1 to S5 are given references N1 to N5 (these vanes are shown in dashed lines, for ease of representation), whereas the blades of rotary wheels of stages S1 to S5 are given respective references W1 to W5.


In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks forming parts of the wheels W1 to W5 are constrained to rotate together.


The disclosure relates a vane of one of the nozzles of the turbine that, as mentioned above, preferably comprises five stages as shown, without this number being limiting.


As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane is fastened to the outer ring of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring and to the inner shroud.


In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.


The nominal profile from which the aerodynamic profile of the disclosure is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.











TABLE 1





X
Y
Zadim

















−15.4967
−4.24116
−0.150


−15.5137
−4.29028
−0.150


−15.5216
−4.36542
−0.150


−15.4956
−4.47905
−0.150


−15.4085
−4.6162
−0.150


−15.2503
−4.7576
−0.150


−15.0259
−4.89843
−0.150


−14.7365
−5.03423
−0.150


−14.3828
−5.16159
−0.150


−13.9657
−5.27668
−0.150


−13.4864
−5.37522
−0.150


−12.9467
−5.45286
−0.150


−12.3493
−5.50425
−0.150


−11.6972
−5.52132
−0.150


−10.9954
−5.49767
−0.150


−10.2493
−5.42897
−0.150


−9.46517
−5.31192
−0.150


−8.64941
−5.14515
−0.150


−7.80968
−4.92459
−0.150


−6.95863
−4.63397
−0.150


−6.11449
−4.25411
−0.150


−5.29827
−3.77373
−0.150


−4.53581
−3.18484
−0.150


−3.84128
−2.50138
−0.150


−3.21626
−1.74652
−0.150


−2.65809
−0.94073
−0.150


−2.15871
−0.10328
−0.150


−1.71083
0.750898
−0.150


−1.30849
1.61002
−0.150


−0.94582
2.46392
−0.150


−0.61577
3.303181
−0.150


−0.31308
4.120109
−0.150


−0.03439
4.908414
−0.150


0.222654
5.662702
−0.150


0.459527
6.378374
−0.150


0.677931
7.051249
−0.150


0.877652
7.678273
−0.150


1.060006
8.256431
−0.150


1.224417
8.78388
−0.150


1.370878
9.259205
−0.150


1.49972
9.681538
−0.150


1.611224
10.05073
−0.150


1.705819
10.36732
−0.150


1.784127
10.63259
−0.150


1.847942
10.84832
−0.150


1.894873
11.01834
−0.150


1.886217
11.14977
−0.150


1.83709
11.2275
−0.150


1.791752
11.26375
−0.150


1.75137
11.28259
−0.150


1.712049
11.29219
−0.150


1.659347
11.29325
−0.150


1.579716
11.26793
−0.150


1.49604
11.18251
−0.150


1.439238
11.03272
−0.150


1.366325
10.84184
−0.150


1.276772
10.60711
−0.150


1.168819
10.32708
−0.150


1.041875
10.0006
−0.150


0.89534
9.627275
−0.150


0.728923
9.207281
−0.150


0.542093
8.741544
−0.150


0.335637
8.231076
−0.150


0.108566
7.678177
−0.150


−0.13817
7.084882
−0.150


−0.40594
6.454694
−0.150


−0.6943
5.790812
−0.150


−1.00569
5.098149
−0.150


−1.34174
4.381748
−0.150


−1.70301
3.646599
−0.150


−2.09215
2.899194
−0.150


−2.51554
2.148719
−0.150


−2.97809
1.404758
−0.150


−3.48265
0.67694
−0.150


−4.03128
−0.02427
−0.150


−4.62849
−0.68434
−0.150


−5.27817
−1.28537
−0.150


−5.97815
−1.81048
−0.150


−6.71661
−2.25175
−0.150


−7.47904
−2.60616
−0.150


−8.24799
−2.88167
−0.150


−9.00631
−3.098
−0.150


−9.74181
−3.27403
−0.150


−10.446
−3.42457
−0.150


−11.1148
−3.55053
−0.150


−11.745
−3.64934
−0.150


−12.3333
−3.71831
−0.150


−12.8765
−3.75865
−0.150


−13.3714
−3.77765
−0.150


−13.8157
−3.78504
−0.150


−14.2087
−3.79217
−0.150


−14.5498
−3.80737
−0.150


−14.8382
−3.84123
−0.150


−15.0723
−3.89709
−0.150


−15.2492
−3.97363
−0.150


−15.3665
−4.06315
−0.150


−15.4372
−4.142
−0.150


−15.7148
−2.889
−0.075


−15.7396
−2.93593
−0.075


−15.7588
−3.01063
−0.075


−15.7493
−3.12929
−0.075


−15.6839
−3.28167
−0.075


−15.5504
−3.45221
−0.075


−15.3516
−3.63549
−0.075


−15.0871
−3.82668
−0.075


−14.7571
−4.0225
−0.075


−14.3613
−4.21848
−0.075


−13.8998
−4.40971
−0.075


−13.3735
−4.59058
−0.075


−12.7835
−4.75388
−0.075


−12.1317
−4.88981
−0.075


−11.4218
−4.98916
−0.075


−10.6588
−5.04237
−0.075


−9.84951
−5.03988
−0.075


−9.00227
−4.972
−0.075


−8.128
−4.82653
−0.075


−7.24176
−4.5869
−0.075


−6.36389
−4.23716
−0.075


−5.51712
−3.77054
−0.075


−4.72318
−3.19023
−0.075


−3.9944
−2.51334
−0.075


−3.33332
−1.76255
−0.075


−2.7364
−0.95952
−0.075


−2.19685
−0.12317
−0.075


−1.70773
0.731265
−0.075


−1.26299
1.591487
−0.075


−0.858
2.44753
−0.075


−0.48674
3.289924
−0.075


−0.14437
4.110697
−0.075


0.172351
4.903262
−0.075


0.465606
5.662015
−0.075


0.736852
6.382154
−0.075


0.987475
7.059415
−0.075


1.21762
7.690506
−0.075


1.428252
8.272398
−0.075


1.618923
8.803159
−0.075


1.789593
9.281335
−0.075


1.94047
9.706062
−0.075


2.071683
10.07723
−0.075


2.183692
10.39538
−0.075


2.27693
10.66189
−0.075


2.353104
10.87852
−0.075


2.410152
11.0493
−0.075


2.410381
11.18378
−0.075


2.364208
11.26552
−0.075


2.319495
11.30439
−0.075


2.278968
11.32505
−0.075


2.239605
11.33598
−0.075


2.186461
11.3386
−0.075


2.105501
11.31506
−0.075


2.018792
11.231
−0.075


1.953484
11.08307
−0.075


1.869691
10.89462
−0.075


1.76701
10.66277
−0.075


1.643816
10.38603
−0.075


1.499582
10.06322
−0.075


1.333842
9.693907
−0.075


1.146456
9.278207
−0.075


0.937103
8.817
−0.075


0.706402
8.311364
−0.075


0.4538
7.763498
−0.075


0.18003
7.17556
−0.075


−0.11581
6.550966
−0.075


−0.43354
5.893119
−0.075


−0.77505
5.206868
−0.075


−1.14136
4.497132
−0.075


−1.53375
3.769408
−0.075


−1.95471
3.03039
−0.075


−2.40884
2.288663
−0.075


−2.89966
1.553201
−0.075


−3.43003
0.833688
−0.075


−4.00228
0.14083
−0.075


−4.61999
−0.51155
−0.075


−5.28558
−1.10731
−0.075


−5.99722
−1.63039
−0.075


−6.74631
−2.06949
−0.075


−7.51979
−2.41876
−0.075


−8.3015
−2.68096
−0.075


−9.07541
−2.86707
−0.075


−9.82865
−2.99083
−0.075


−10.5517
−3.06505
−0.075


−11.2379
−3.09699
−0.075


−11.8816
−3.09199
−0.075


−12.4784
−3.05491
−0.075


−13.0246
−2.99192
−0.075


−13.5182
−2.91364
−0.075


−13.9591
−2.83086
−0.075


−14.3485
−2.75517
−0.075


−14.6878
−2.69495
−0.075


−14.9787
−2.65866
−0.075


−15.2215
−2.65366
−0.075


−15.414
−2.68154
−0.075


−15.5515
−2.73876
−0.075


−15.6387
−2.80061
−0.075


−15.7456
−2.30652
0.000


−15.7755
−2.35194
0.000


−15.8021
−2.4263
0.000


−15.804
−2.54819
0.000


−15.7542
−2.7106
0.000


−15.64
−2.90076
0.000


−15.4623
−3.11318
0.000


−15.2197
−3.34305
0.000


−14.9115
−3.58688
0.000


−14.5367
−3.84013
0.000


−14.0944
−4.09731
0.000


−13.5844
−4.35182
0.000


−13.0066
−4.59504
0.000


−12.3614
−4.81574
0.000


−11.6513
−5.00203
0.000


−10.8802
−5.1396
0.000


−10.0545
−5.21258
0.000


−9.18404
−5.20348
0.000


−8.28306
−5.09318
0.000


−7.37094
−4.86495
0.000


−6.47191
−4.50661
0.000


−5.61094
−4.01753
0.000


−4.80703
−3.41079
0.000


−4.07073
−2.70686
0.000


−3.4041
−1.92886
0.000


−2.80236
−1.09938
0.000


−2.25883
−0.23704
0.000


−1.76645
0.642871
0.000


−1.31877
1.527869
0.000


−0.91092
2.407841
0.000


−0.53755
3.27358
0.000


−0.19374
4.117003
0.000


0.123967
4.931347
0.000


0.417944
5.710864
0.000


0.689801
6.450615
0.000


0.940901
7.146275
0.000


1.17184
7.794335
0.000


1.383409
8.391774
0.000


1.575372
8.936535
0.000


1.747718
9.42713
0.000


1.900563
9.862713
0.000


2.03394
10.24321
0.000


2.148252
10.56919
0.000


2.243754
10.84212
0.000


2.321955
11.06393
0.000


2.381026
11.23862
0.000


2.384307
11.3763
0.000


2.337407
11.46024
0.000


2.291388
11.49978
0.000


2.249607
11.5204
0.000


2.209487
11.53077
0.000


2.155535
11.53227
0.000


2.074099
11.50615
0.000


1.988575
11.41844
0.000


1.921836
11.2686
0.000


1.836172
11.07774
0.000


1.731439
10.84281
0.000


1.606174
10.56223
0.000


1.459983
10.23474
0.000


1.292533
9.859815
0.000


1.103811
9.437532
0.000


0.893657
8.968701
0.000


0.6625
8.454506
0.000


0.410068
7.897032
0.000


0.136794
7.2986
0.000


−0.15795
6.662527
0.000


−0.4744
5.992435
0.000


−0.81422
5.293081
0.000


−1.17824
4.569292
0.000


−1.56833
3.826894
0.000


−1.98725
3.072698
0.000


−2.43864
2.314726
0.000


−2.92549
1.561451
0.000


−3.45089
0.822486
0.000


−4.01794
0.108792
0.000


−4.63013
−0.56629
0.000


−5.28932
−1.18798
0.000


−5.99425
−1.74089
0.000


−6.73909
−2.21098
0.000


−7.51258
−2.5889
0.000


−8.29961
−2.87185
0.000


−9.08417
−3.06262
0.000


−9.85105
−3.1696
0.000


−10.5876
−3.2033
0.000


−11.2838
−3.17558
0.000


−11.9323
−3.09885
0.000


−12.5281
−2.9852
0.000


−13.0682
−2.84646
0.000


−13.5525
−2.69638
0.000


−13.9825
−2.54744
0.000


−14.361
−2.41094
0.000


−14.691
−2.2956
0.000


−14.9752
−2.20819
0.000


−15.2163
−2.15783
0.000


−15.4134
−2.14805
0.000


−15.5614
−2.17862
0.000


−15.6588
−2.22629
0.000


−15.8328
−1.07008
0.100


−15.8701
−1.11224
0.100


−15.9084
−1.18458
0.100


−15.9292
−1.30915
0.100


−15.9065
−1.48364
0.100


−15.8259
−1.69888
0.100


−15.6865
−1.94961
0.100


−15.4856
−2.23165
0.100


−15.2201
−2.54036
0.100


−14.8892
−2.87212
0.100


−14.4899
−3.22067
0.100


−14.02
−3.57839
0.100


−13.4773
−3.93522
0.100


−12.8598
−4.27826
0.100


−12.1669
−4.59206
0.100


−11.3998
−4.85684
0.100


−10.5626
−5.04795
0.100


−9.66533
−5.13862
0.100


−8.72567
−5.10158
0.100


−7.76931
−4.91649
0.100


−6.8265
−4.57527
0.100


−5.92453
−4.08658
0.100


−5.08214
−3.47082
0.100


−4.30824
−2.75331
0.100


−3.60388
−1.95926
0.100


−2.96472
−1.11155
0.100


−2.38426
−0.22934
0.100


−1.85672
0.672288
0.100


−1.37653
1.580685
0.100


−0.93626
2.483912
0.100


−0.53199
3.373102
0.100


−0.15895
4.239839
0.100


0.186397
5.077009
0.100


0.506601
5.878525
0.100


0.803185
6.63926
0.100


1.077503
7.3547
0.100


1.330458
8.021056
0.100


1.562574
8.635279
0.100


1.773809
9.19515
0.100


1.964117
9.699129
0.100


2.133424
10.1464
0.100


2.28178
10.53688
0.100


2.409347
10.87126
0.100


2.516394
11.15106
0.100


2.604161
11.37836
0.100


2.671403
11.55718
0.100


2.683809
11.69933
0.100


2.639011
11.78829
0.100


2.592399
11.83047
0.100


2.549422
11.85244
0.100


2.508326
11.86331
0.100


2.452985
11.86479
0.100


2.369754
11.83708
0.100


2.283092
11.74608
0.100


2.20979
11.59463
0.100


2.115691
11.40177
0.100


2.0009
11.16422
0.100


1.864048
10.88029
0.100


1.704865
10.54864
0.100


1.523174
10.16865
0.100


1.319095
9.740345
0.100


1.092677
9.264458
0.100


0.8442
8.742281
0.100


0.573756
8.175809
0.100


0.281511
7.567561
0.100


−0.03274
6.920767
0.100


−0.36964
6.239365
0.100


−0.73048
5.5281
0.100


−1.11615
4.791981
0.100


−1.52829
4.036898
0.100


−1.96948
3.269773
0.100


−2.44282
2.498528
0.100


−2.95133
1.731837
0.100


−3.49771
0.979195
0.100


−4.08538
0.251953
0.100


−4.71745
−0.43676
0.100


−5.39477
−1.07323
0.100


−6.11611
−1.64258
0.100


−6.87711
−2.12952
0.100


−7.66914
−2.51998
0.100


−8.47897
−2.80308
0.100


−9.28935
−2.97394
0.100


−10.0812
−3.03528
0.100


−10.8366
−2.9975
0.100


−11.541
−2.87647
0.100


−12.185
−2.69232
0.100


−12.7645
−2.46602
0.100


−13.2798
−2.21756
0.100


−13.7339
−1.96416
0.100


−14.1321
−1.7206
0.100


−14.4804
−1.4992
0.100


−14.784
−1.30841
0.100


−15.0474
−1.15456
0.100


−15.2752
−1.04539
0.100


−15.4685
−0.98526
0.100


−15.6233
−0.97779
0.100


−15.7315
−1.00364
0.100


−15.8947
−0.21454
0.200


−15.9367
−0.25472
0.200


−15.9822
−0.32585
0.200


−16.0155
−0.45189
0.200


−16.0115
−0.63348
0.200


−15.9556
−0.86403
0.200


−15.8448
−1.13864
0.200


−15.6756
−1.45352
0.200


−15.4434
−1.80376
0.200


−15.1467
−2.18584
0.200


−14.7815
−2.59318
0.200


−14.3441
−3.01762
0.200


−13.8302
−3.4482
0.200


−13.2361
−3.87102
0.200


−12.559
−4.26836
0.200


−11.7972
−4.61675
0.200


−10.9527
−4.88611
0.200


−10.035
−5.04207
0.200


−9.06437
−5.05091
0.200


−8.07213
−4.8883
0.200


−7.09472
−4.54805
0.200


−6.1628
−4.0453
0.200


−5.29544
−3.40677
0.200


−4.50022
−2.66228
0.200


−3.77692
−1.83936
0.200


−3.12115
−0.96137
0.200


−2.52602
−0.04811
0.200


−1.9848
0.884486
0.200


−1.49115
1.823188
0.200


−1.03828
2.756273
0.200


−0.62242
3.674741
0.200


−0.23885
4.570027
0.200


0.116232
5.434729
0.200


0.445531
6.262541
0.200


0.750708
7.048148
0.200


1.033066
7.786931
0.200


1.293865
8.474861
0.200


1.533424
9.108875
0.200


1.751847
9.686631
0.200


1.949128
10.20652
0.200


2.125064
10.66775
0.200


2.279596
11.07027
0.200


2.412814
11.41482
0.200


2.524905
11.70302
0.200


2.616898
11.93709
0.200


2.687999
12.12103
0.200


2.706068
12.2672
0.200


2.66196
12.36007
0.200


2.614147
12.40394
0.200


2.569746
12.42653
0.200


2.527502
12.43729
0.200


2.470734
12.43798
0.200


2.38608
12.40754
0.200


2.299673
12.31193
0.200


2.223381
12.15717
0.200


2.125431
11.96011
0.200


2.00608
11.7173
0.200


1.864134
11.42691
0.200


1.699418
11.08752
0.200


1.511878
10.69843
0.200


1.301731
10.25962
0.200


1.069138
9.771791
0.200


0.814381
9.236278
0.200


0.537685
8.655058
0.200


0.239078
8.030785
0.200


−0.08149
7.366684
0.200


−0.42499
6.666931
0.200


−0.79246
5.936235
0.200


−1.18481
5.179714
0.200


−1.60394
4.403468
0.200


−2.0525
3.614577
0.200


−2.5333
2.82086
0.200


−3.04835
2.030403
0.200


−3.60141
1.253363
0.200


−4.196
0.501147
0.200


−4.83467
−0.21374
0.200


−5.51873
−0.87746
0.200


−6.24763
−1.47478
0.200


−7.01881
−1.98826
0.200


−7.82511
−2.40047
0.200


−8.65398
−2.69532
0.200


−9.48679
−2.86194
0.200


−10.3005
−2.89691
0.200


−11.0714
−2.81154
0.200


−11.7805
−2.62609
0.200


−12.4173
−2.3685
0.200


−12.9799
−2.0676
0.200


−13.4715
−1.74751
0.200


−13.8984
−1.42784
0.200


−14.2688
−1.12467
0.200


−14.5907
−0.84995
0.200


−14.8712
−0.61217
0.200


−15.1154
−0.41673
0.200


−15.3295
−0.27081
0.200


−15.5155
−0.1787
0.200


−15.6711
−0.14615
0.200


−15.7846
−0.15712
0.200


−15.988
−0.31339
0.300


−16.031
−0.35492
0.300


−16.0775
−0.42834
0.300


−16.112
−0.55794
0.300


−16.1108
−0.74478
0.300


−16.0617
−0.98382
0.300


−15.9582
−1.27032
0.300


−15.7927
−1.59864
0.300


−15.568
−1.96798
0.300


−15.2761
−2.37102
0.300


−14.9135
−2.80136
0.300


−14.4755
−3.25011
0.300


−13.9576
−3.70561
0.300


−13.3556
−4.15309
0.300


−12.666
−4.57333
0.300


−11.8865
−4.9407
0.300


−11.0187
−5.22053
0.300


−10.0735
−5.37415
0.300


−9.075
−5.36237
0.300


−8.06121
−5.15726
0.300


−7.07385
−4.759
0.300


−6.14596
−4.18844
0.300


−5.2962
−3.47746
0.300


−4.53075
−2.65904
0.300


−3.84582
−1.76397
0.300


−3.23353
−0.81744
0.300


−2.68583
0.161045
0.300


−2.19115
1.153839
0.300


−1.74262
2.148412
0.300


−1.33483
3.134359
0.300


−0.96404
4.102982
0.300


−0.62492
5.045797
0.300


−0.31316
5.955456
0.300


−0.02538
6.825577
0.300


0.240466
7.650803
0.300


0.485886
8.426507
0.300


0.712597
9.148576
0.300


0.920958
9.813931
0.300


1.111273
10.42015
0.300


1.283641
10.96559
0.300


1.437874
11.44942
0.300


1.573748
11.87163
0.300


1.691265
12.23301
0.300


1.790462
12.53525
0.300


1.872071
12.78077
0.300


1.935465
12.97346
0.300


1.950104
13.12427
0.300


1.901487
13.2182
0.300


1.850114
13.26081
0.300


1.803164
13.28137
0.300


1.759285
13.28955
0.300


1.701251
13.28618
0.300


1.61726
13.24835
0.300


1.536775
13.14377
0.300


1.467174
12.98139
0.300


1.37766
12.7746
0.300


1.268883
12.5198
0.300


1.139858
12.21502
0.300


0.990543
11.85875
0.300


0.821052
11.45025
0.300


0.631654
10.98946
0.300


0.422553
10.4771
0.300


0.194052
9.914498
0.300


−0.05367
9.303676
0.300


−0.32093
8.647416
0.300


−0.60769
7.948892
0.300


−0.91558
7.212473
0.300


−1.24563
6.442761
0.300


−1.59911
5.64493
0.300


−1.97846
4.825141
0.300


−2.38687
3.990457
0.300


−2.82712
3.14838
0.300


−3.30218
2.307208
0.300


−3.81499
1.47606
0.300


−4.36875
0.66532
0.300


−4.96723
−0.11273
0.300


−5.61357
−0.84399
0.300


−6.31012
−1.51181
0.300


−7.05644
−2.09747
0.300


−7.84881
−2.57907
0.300


−8.67679
−2.93397
0.300


−9.52051
−3.1448
0.300


−10.3523
−3.20492
0.300


−11.1425
−3.12524
0.300


−11.867
−2.92948
0.300


−12.5135
−2.65233
0.300


−13.0807
−2.32816
0.300


−13.5741
−1.98561
0.300


−14.0022
−1.64656
0.300


−14.3722
−1.32511
0.300


−14.6917
−1.03224
0.300


−14.9673
−0.77573
0.300


−15.2066
−0.56295
0.300


−15.4172
−0.40157
0.300


−15.6012
−0.29524
0.300


−15.7579
−0.25111
0.300


−15.8745
−0.25629
0.300


−16.0665
1.626574
0.400


−16.1143
1.588472
0.400


−16.169
1.518427
0.400


−16.2184
1.390498
0.400


−16.2398
1.200635
0.400


−16.2211
0.951797
0.400


−16.1534
0.647719
0.400


−16.0274
0.293446
0.400


−15.8471
−0.11018
0.400


−15.6023
−0.55629
0.400


−15.2882
−1.03851
0.400


−14.8989
−1.54803
0.400


−14.4282
−2.07328
0.400


−13.8701
−2.59945
0.400


−13.2184
−3.10673
0.400


−12.4675
−3.5679
0.400


−11.6149
−3.94536
0.400


−10.6673
−4.19249
0.400


−9.64886
−4.26601
0.400


−8.59943
−4.13387
0.400


−7.56585
−3.79178
0.400


−6.58413
−3.26548
0.400


−5.67493
−2.58941
0.400


−4.84376
−1.80055
0.400


−4.0899
−0.92875
0.400


−3.40534
−0.00122
0.400


−2.78199
0.961233
0.400


−2.21158
1.941666
0.400


−1.68769
2.926713
0.400


−1.20533
3.905365
0.400


−0.76043
4.868154
0.400


−0.34913
5.806573
0.400


0.032607
6.71279
0.400


0.387565
7.580163
0.400


0.717447
8.403096
0.400


1.023284
9.176839
0.400


1.306617
9.897041
0.400


1.567366
10.56063
0.400


1.805696
11.1651
0.400


2.021549
11.70877
0.400


2.214646
12.19083
0.400


2.38463
12.61133
0.400


2.531521
12.9711
0.400


2.655454
13.27186
0.400


2.757175
13.5161
0.400


2.836734
13.70768
0.400


2.866394
13.85975
0.400


2.825617
13.95992
0.400


2.776749
14.00758
0.400


2.730427
14.03209
0.400


2.686334
14.0435
0.400


2.627021
14.04386
0.400


2.539246
14.01024
0.400


2.451243
13.90835
0.400


2.368289
13.7483
0.400


2.261638
13.54462
0.400


2.131888
13.29348
0.400


1.977947
12.99292
0.400


1.799773
12.64134
0.400


1.597447
12.23798
0.400


1.371328
11.78272
0.400


1.12171
11.27626
0.400


0.849084
10.71989
0.400


0.553832
10.11562
0.400


0.235764
9.46635
0.400


−0.10469
8.775211
0.400


−0.46901
8.046827
0.400


−0.8577
7.285835
0.400


−1.27166
6.497551
0.400


−1.71289
5.688364
0.400


−2.18404
4.865582
0.400


−2.68711
4.036778
0.400


−3.22442
3.210412
0.400


−3.79842
2.395875
0.400


−4.41199
1.604001
0.400


−5.06772
0.846962
0.400


−5.76805
0.139027
0.400


−6.51397
−0.50362
0.400


−7.30571
−1.06049
0.400


−8.13885
−1.50878
0.400


−9.00259
−1.82309
0.400


−9.8755
−1.98246
0.400


−10.7264
−1.97636
0.400


−11.5216
−1.82052
0.400


−12.2363
−1.54564
0.400


−12.8604
−1.19129
0.400


−13.3956
−0.79394
0.400


−13.8513
−0.38411
0.400


−14.2388
0.016298
0.400


−14.5691
0.391788
0.400


−14.8519
0.731731
0.400


−15.0965
1.027983
0.400


−15.3113
1.274204
0.400


−15.5023
1.466012
0.400


−15.6739
1.598572
0.400


−15.8266
1.663875
0.400


−15.9454
1.672742
0.400


−16.3218
1.290539
0.500


−16.3676
1.248614
0.500


−16.4182
1.173902
0.500


−16.4603
1.041141
0.500


−16.4724
0.847458
0.500


−16.4418
0.59586
0.500


−16.3602
0.290183
0.500


−16.2203
−0.06516
0.500


−16.02
−0.46701
0.500


−15.7525
−0.9092
0.500


−15.4121
−1.38434
0.500


−14.9928
−1.88262
0.500


−14.4883
−2.39116
0.500


−13.8929
−2.89356
0.500


−13.2011
−3.36782
0.500


−12.4089
−3.78432
0.500


−11.5176
−4.10445
0.500


−10.539
−4.28145
0.500


−9.50195
−4.26871
0.500


−8.45293
−4.03726
0.500


−7.44061
−3.59241
0.500


−6.49784
−2.96706
0.500


−5.63947
−2.20066
0.500


−4.86544
−1.33152
0.500


−4.17341
−0.38743
0.500


−3.55371
0.605938
0.500


−2.99764
1.629231
0.500


−2.49613
2.666367
0.500


−2.04075
3.703979
0.500


−1.62616
4.731627
0.500


−1.24718
5.73996
0.500


−0.89908
6.720631
0.500


−0.57772
7.666226
0.500


−0.27998
8.570312
0.500


−0.00387
9.427386
0.500


0.251831
10.23277
0.500


0.488829
10.98223
0.500


0.707139
11.67266
0.500


0.906984
12.30159
0.500


1.08842
12.86731
0.500


1.251119
13.369
0.500


1.394689
13.80672
0.500


1.519028
14.1813
0.500


1.624169
14.49449
0.500


1.710604
14.74892
0.500


1.778422
14.9484
0.500


1.800774
15.10417
0.500


1.754023
15.20356
0.500


1.70168
15.24901
0.500


1.653209
15.27101
0.500


1.607833
15.27976
0.500


1.547747
15.27625
0.500


1.461202
15.23618
0.500


1.37977
15.12648
0.500


1.306995
14.95866
0.500


1.213133
14.74508
0.500


1.099206
14.48185
0.500


0.964295
14.16686
0.500


0.80849
13.79852
0.500


0.63198
13.376
0.500


0.435154
12.89923
0.500


0.218313
12.36891
0.500


−0.01806
11.78635
0.500


−0.27368
11.1536
0.500


−0.54892
10.47356
0.500


−0.84345
9.749385
0.500


−1.15901
8.985612
0.500


−1.4963
8.186822
0.500


−1.85652
7.35827
0.500


−2.24194
6.506157
0.500


−2.65559
5.637548
0.500


−3.09983
4.759763
0.500


−3.5772
3.880845
0.500


−4.09171
3.010413
0.500


−4.64704
2.15901
0.500


−5.24722
1.338884
0.500


−5.89482
0.563243
0.500


−6.59288
−0.1515
0.500


−7.34256
−0.78608
0.500


−8.14277
−1.31645
0.500


−8.98527
−1.71652
0.500


−9.85239
−1.95902
0.500


−10.7129
−2.03066
0.500


−11.5302
−1.94071
0.500


−12.2741
−1.71635
0.500


−12.9302
−1.40034
0.500


−13.4973
−1.03172
0.500


−13.9824
−0.64263
0.500


−14.3961
−0.25721
0.500


−14.7491
0.107334
0.500


−15.0515
0.438793
0.500


−15.3137
0.727264
0.500


−15.5426
0.967132
0.500


−15.7444
1.153499
0.500


−15.9237
1.281151
0.500


−16.0811
1.341166
0.500


−16.202
1.3446
0.500


−16.516
2.356814
0.600


−16.5616
2.313915
0.600


−16.6113
2.237769
0.600


−16.652
2.103373
0.600


−16.6635
1.90808
0.600


−16.6331
1.654394
0.600


−16.553
1.345665
0.600


−16.4185
0.984962
0.600


−16.2201
0.5781
0.600


−15.9535
0.130486
0.600


−15.6124
−0.34998
0.600


−15.1899
−0.85246
0.600


−14.6788
−1.3626
0.600


−14.0726
−1.86194
0.600


−13.3656
−2.32581
0.600


−12.555
−2.722
0.600


−11.645
−3.01063
0.600


−10.6515
−3.14545
0.600


−9.60744
−3.08993
0.600


−8.55757
−2.82427
0.600


−7.54658
−2.3547
0.600


−6.60835
−1.70629
0.600


−5.75498
−0.92048
0.600


−4.98747
−0.03306
0.600


−4.2986
0.925059
0.600


−3.67833
1.929244
0.600


−3.11903
2.961531
0.600


−2.6117
4.006224
0.600


−2.14847
5.050417
0.600


−1.72455
6.083971
0.600


−1.33494
7.097607
0.600


−0.97517
8.083044
0.600


−0.64149
9.032954
0.600


−0.33118
9.94096
0.600


−0.04246
10.80158
0.600


0.225719
11.61012
0.600


0.474588
12.36243
0.600


0.704044
13.05543
0.600


0.914172
13.68664
0.600


1.104859
14.25439
0.600


1.275723
14.75788
0.600


1.42634
15.19717
0.600


1.55663
15.57311
0.600


1.666661
15.88747
0.600


1.756954
16.14287
0.600


1.827963
16.34304
0.600


1.854484
16.49945
0.600


1.809854
16.60078
0.600


1.758212
16.64787
0.600


1.709891
16.6712
0.600


1.664344
16.68116
0.600


1.603654
16.6792
0.600


1.515295
16.64112
0.600


1.431232
16.53189
0.600


1.356348
16.36323
0.600


1.259573
16.14868
0.600


1.142059
15.88424
0.600


1.0028
15.56783
0.600


0.841864
15.19783
0.600


0.659413
14.77343
0.600


0.45587
14.29452
0.600


0.231566
13.76179
0.600


−0.01295
13.17656
0.600


−0.27727
12.54084
0.600


−0.56172
11.85755
0.600


−0.8658
11.12982
0.600


−1.19086
10.36208
0.600


−1.53756
9.558951
0.600


−1.9069
8.72566
0.600


−2.30078
7.868297
0.600


−2.72188
6.9938
0.600


−3.17241
6.109434
0.600


−3.65473
5.223118
0.600


−4.17257
4.344245
0.600


−4.72946
3.483112
0.600


−5.32929
2.651599
0.600


−5.97539
1.863095
0.600


−6.66997
1.132707
0.600


−7.41622
0.480788
0.600


−8.21363
−0.06891
0.600


−9.05575
−0.48866
0.600


−9.92419
−0.75503
0.600


−10.7896
−0.85475
0.600


−11.617
−0.79553
0.600


−12.3761
−0.60017
0.600


−13.0495
−0.30622
0.600


−13.6324
0.04849
0.600


−14.1313
0.428916
0.600


−14.5577
0.807859
0.600


−14.9223
1.167185
0.600


−15.2338
1.4957
0.600


−15.5014
1.783846
0.600


−15.7328
2.025403
0.600


−15.9358
2.214068
0.600


−16.1154
2.344553
0.600


−16.2735
2.407035
0.600


−16.3954
2.411661
0.600


−16.6987
3.811905
0.700


−16.7419
3.766853
0.700


−16.7884
3.688976
0.700


−16.8251
3.553839
0.700


−16.8321
3.358875
0.700


−16.7962
3.10662
0.700


−16.7082
2.800969
0.700


−16.5617
2.446087
0.700


−16.3494
2.047789
0.700


−16.065
1.612934
0.700


−15.7024
1.15059
0.700


−15.2547
0.672864
0.700


−14.7156
0.195478
0.700


−14.0796
−0.26161
0.700


−13.3434
−0.67274
0.700


−12.5074
−1.0053
0.700


−11.5799
−1.22024
0.700


−10.5818
−1.27939
0.700


−9.54706
−1.15154
0.700


−8.51736
−0.82589
0.700


−7.53111
−0.31303
0.700


−6.61553
0.361659
0.700


−5.78061
1.162409
0.700


−5.02579
2.056412
0.700


−4.3456
3.016693
0.700


−3.72816
4.018793
0.700


−3.16721
5.046476
0.700


−2.65415
6.084783
0.700


−2.18054
7.120828
0.700


−1.74319
8.145409
0.700


−1.33813
9.149727
0.700


−0.96163
10.12578
0.700


−0.61026
11.06631
0.700


−0.28187
11.96511
0.700


0.024945
12.81677
0.700


0.31093
13.61668
0.700


0.576682
14.36086
0.700


0.82197
15.04627
0.700


1.046558
15.67053
0.700


1.250158
16.23201
0.700


1.432292
16.72997
0.700


1.592556
17.16446
0.700


1.73092
17.53633
0.700


1.847545
17.84731
0.700


1.943034
18.10001
0.700


2.018112
18.29806
0.700


2.048767
18.45327
0.700


2.006771
18.55539
0.700


1.956957
18.60413
0.700


1.909761
18.62935
0.700


1.864695
18.64137
0.700


1.803954
18.64234
0.700


1.713742
18.60876
0.700


1.625306
18.50296
0.700


1.547389
18.33559
0.700


1.446554
18.12281
0.700


1.323977
17.86054
0.700


1.178511
17.54677
0.700


1.010157
17.17988
0.700


0.81905
16.75908
0.700


0.605544
16.28428
0.700


0.37009
15.75611
0.700


0.113235
15.17588
0.700


−0.16452
14.54558
0.700


−0.46325
13.86805
0.700


−0.78234
13.1464
0.700


−1.12262
12.38488
0.700


−1.48459
11.58809
0.700


−1.86904
10.76122
0.700


−2.27745
9.91022
0.700


−2.71194
9.041813
0.700


−3.17464
8.163262
0.700


−3.66779
7.282411
0.700


−4.19355
6.407729
0.700


−4.75474
5.548852
0.700


−5.3548
4.716947
0.700


−5.9983
3.925735
0.700


−6.68758
3.189741
0.700


−7.42488
2.527043
0.700


−8.20939
1.958367
0.700


−9.03627
1.50848
0.700


−9.89078
1.199139
0.700


−10.7487
1.045555
0.700


−11.5785
1.044201
0.700


−12.3515
1.176728
0.700


−13.0481
1.411194
0.700


−13.6603
1.713189
0.700


−14.19
2.049935
0.700


−14.6447
2.394817
0.700


−15.034
2.727624
0.700


−15.3669
3.034724
0.700


−15.6516
3.306283
0.700


−15.8972
3.533597
0.700


−16.1104
3.710781
0.700


−16.2976
3.830353
0.700


−16.46
3.880547
0.700


−16.582
3.874978
0.700


−16.952
4.777241
0.800


−16.9913
4.728793
0.800


−17.0311
4.647382
0.800


−17.0572
4.509943
0.800


−17.0506
4.31515
0.800


−16.9988
4.065922
0.800


−16.8921
3.766576
0.800


−16.7238
3.421924
0.800


−16.4878
3.037651
0.800


−16.1774
2.621568
0.800


−15.7865
2.183656
0.800


−15.3087
1.736973
0.800


−14.7383
1.298472
0.800


−14.0711
0.889672
0.800


−13.3057
0.537736
0.800


−12.4457
0.276346
0.800


−11.5039
0.142862
0.800


−10.5055
0.172405
0.800


−9.48647
0.388344
0.800


−8.48668
0.793992
0.800


−7.53799
1.371377
0.800


−6.65809
2.090305
0.800


−5.8526
2.919132
0.800


−5.11994
3.829964
0.800


−4.4549
4.799466
0.800


−3.85023
5.808024
0.800


−3.2976
6.838957
0.800


−2.78963
7.878552
0.800


−2.32046
8.915442
0.800


−1.88551
9.939905
0.800


−1.48034
10.94308
0.800


−1.10123
11.91707
0.800


−0.7456
12.85499
0.800


−0.41187
13.75085
0.800


−0.09893
14.59937
0.800


0.193671
15.39604
0.800


0.465816
16.13712
0.800


0.717262
16.81956
0.800


0.947449
17.4411
0.800


1.155871
18.00022
0.800


1.341979
18.49617
0.800


1.50546
18.929
0.800


1.646289
19.29954
0.800


1.76476
19.60949
0.800


1.861515
19.86144
0.800


1.937577
20.0589
0.800


1.9702
20.21355
0.800


1.930043
20.3163
0.800


1.881483
20.3662
0.800


1.835034
20.39267
0.800


1.790165
20.406
0.800


1.729261
20.40871
0.800


1.637777
20.37769
0.800


1.54633
20.27382
0.800


1.467827
20.106
0.800


1.36602
19.89276
0.800


1.242155
19.62995
0.800


1.094969
19.31563
0.800


0.924384
18.9482
0.800


0.730457
18.52688
0.800


0.513512
18.05161
0.800


0.274059
17.52298
0.800


0.012641
16.94232
0.800


−0.27028
16.31164
0.800


−0.5744
15.63363
0.800


−0.89919
14.91145
0.800


−1.24489
14.14913
0.800


−1.61191
13.35123
0.800


−2.00099
12.52295
0.800


−2.41315
11.67003
0.800


−2.84998
10.79895
0.800


−3.31343
9.916796
0.800


−3.80585
9.031441
0.800


−4.32959
8.151322
0.800


−4.88715
7.285751
0.800


−5.48218
6.445768
0.800


−6.1177
5.64351
0.800


−6.79605
4.892594
0.800


−7.51831
4.208413
0.800


−8.28417
3.609253
0.800


−9.08977
3.115851
0.800


−9.92481
2.749168
0.800


−10.7703
2.525418
0.800


−11.5996
2.449103
0.800


−12.3845
2.507932
0.800


−13.1027
2.675861
0.800


−13.743
2.919556
0.800


−14.3036
3.206789
0.800


−14.7891
3.510627
0.800


−15.2061
3.811043
0.800


−15.5626
4.0929
0.800


−15.8687
4.342356
0.800


−16.1311
4.551984
0.800


−16.3571
4.714226
0.800


−16.5523
4.82174
0.800


−16.7181
4.862185
0.800


−16.8399
4.848948
0.800


−16.8973
5.520457
0.856


−16.9354
5.471326
0.856


−16.9741
5.389621
0.856


−16.9992
5.252391
0.856


−16.9916
5.058164
0.856


−16.9381
4.810009
0.856


−16.8286
4.512629
0.856


−16.6559
4.171306
0.856


−16.4137
3.792347
0.856


−16.0954
3.384182
0.856


−15.6946
2.957435
0.856


−15.2055
2.525775
0.856


−14.6231
2.106767
0.856


−13.9441
1.722346
0.856


−13.1684
1.399602
0.856


−12.3015
1.171227
0.856


−11.3581
1.072176
0.856


−10.3638
1.133239
0.856


−9.3531
1.372993
0.856


−8.36165
1.791104
0.856


−7.41692
2.369159
0.856


−6.53359
3.078924
0.856


−5.71624
3.891599
0.856


−4.96425
4.782369
0.856


−4.27355
5.729795
0.856


−3.63811
6.715442
0.856


−3.05059
7.723199
0.856


−2.50565
8.740322
0.856


−1.99931
9.756104
0.856


−1.5256
10.75988
0.856


−1.08074
11.74285
0.856


−0.66155
12.69716
0.856


−0.26616
13.61604
0.856


0.106335
14.49367
0.856


0.456731
15.32474
0.856


0.784965
16.10489
0.856


1.090424
16.83053
0.856


1.372699
17.49865
0.856


1.630898
18.10713
0.856


1.864344
18.6545
0.856


2.072459
19.14005
0.856


2.25494
19.56384
0.856


2.411835
19.92669
0.856


2.543575
20.23026
0.856


2.650985
20.47705
0.856


2.735335
20.67048
0.856


2.775152
20.82299
0.856


2.740375
20.92737
0.856


2.694745
20.97971
0.856


2.649977
21.00866
0.856


2.605898
21.02456
0.856


2.545185
21.03075
0.856


2.451924
21.0052
0.856


2.35445
20.90677
0.856


2.268999
20.74216
0.856


2.158276
20.53313
0.856


2.023324
20.27551
0.856


1.862727
19.96742
0.856


1.676314
19.60728
0.856


1.464036
19.19437
0.856


1.226185
18.7286
0.856


0.963319
18.21055
0.856


0.676032
17.64151
0.856


0.364897
17.02346
0.856


0.030479
16.35902
0.856


−0.32653
15.6513
0.856


−0.70592
14.9042
0.856


−1.10778
14.12225
0.856


−1.53263
13.31067
0.856


−1.98094
12.47508
0.856


−2.45367
11.62179
0.856


−2.95243
10.75793
0.856


−3.47941
9.891474
0.856


−4.03604
9.03053
0.856


−4.62552
8.185076
0.856


−5.25021
7.365582
0.856


−5.91207
6.583522
0.856


−6.61278
5.851988
0.856


−7.35233
5.185007
0.856


−8.12991
4.599458
0.856


−8.94116
4.113508
0.856


−9.7767
3.745629
0.856


−10.6199
3.510076
0.856


−11.4479
3.412625
0.856


−12.2351
3.443491
0.856


−12.9605
3.58128
0.856


−13.6118
3.796232
0.856


−14.1854
4.057999
0.856


−14.6841
4.340819
0.856


−15.1137
4.624032
0.856


−15.4814
4.891945
0.856


−15.7969
5.129933
0.856


−16.0671
5.329981
0.856


−16.2991
5.484055
0.856


−16.4987
5.583816
0.856


−16.6665
5.615713
0.856


−16.7876
5.596142
0.856


−17.7231
3.883676
0.900


−17.7575
3.830571
0.900


−17.7944
3.746303
0.900


−17.8225
3.607207
0.900


−17.821
3.409512
0.900


−17.771
3.156134
0.900


−17.6553
2.855268
0.900


−17.4625
2.517102
0.900


−17.1884
2.15054
0.900


−16.8266
1.767782
0.900


−16.3724
1.382753
0.900


−15.8239
1.00891
0.900


−15.1811
0.662379
0.900


−14.4451
0.36457
0.900


−13.62
0.141527
0.900


−12.7159
0.021946
0.900


−11.751
0.034314
0.900


−10.7519
0.204277
0.900


−9.75338
0.550172
0.900


−8.79143
1.072541
0.900


−7.8873
1.744906
0.900


−7.05606
2.543602
0.900


−6.30211
3.441629
0.900


−5.6214
4.412736
0.900


−5.00914
5.43637
0.900


−4.45696
6.493919
0.900


−3.95524
7.569357
0.900


−3.49866
8.650805
0.900


−3.08695
9.72955
0.900


−2.70759
10.79307
0.900


−2.3541
11.83222
0.900


−2.02263
12.83945
0.900


−1.71001
13.8079
0.900


−1.41453
14.7317
0.900


−1.13628
15.60603
0.900


−0.87562
16.42666
0.900


−0.63312
17.19002
0.900


−0.40925
17.8931
0.900


−0.20474
18.53368
0.900


−0.02006
19.11019
0.900


0.144441
19.62182
0.900


0.288604
20.06853
0.900


0.412529
20.45113
0.900


0.5166
20.77128
0.900


0.601511
21.03159
0.900


0.668324
21.23561
0.900


0.699272
21.39293
0.900


0.660427
21.49804
0.900


0.609535
21.5469
0.900


0.562128
21.57325
0.900


0.516666
21.58621
0.900


0.45512
21.58817
0.900


0.36307
21.55601
0.900


0.271556
21.4503
0.900


0.196879
21.27873
0.900


0.104031
21.05888
0.900


−0.0073
20.78741
0.900


−0.13751
20.46196
0.900


−0.28795
20.0815
0.900


−0.46139
19.64639
0.900


−0.65639
19.1561
0.900


−0.87176
18.61102
0.900


−1.10695
18.01245
0.900


−1.36177
17.36252
0.900


−1.63591
16.66391
0.900


−1.92896
15.91982
0.900


−2.24065
15.13402
0.900


−2.57104
14.31086
0.900


−2.92112
13.45553
0.900


−3.29239
12.57382
0.900


−3.68681
11.67215
0.900


−4.10681
10.75762
0.900


−4.55513
9.837926
0.900


−5.03389
8.921073
0.900


−5.5461
8.016155
0.900


−6.09595
7.133881
0.900


−6.68701
6.285927
0.900


−7.32336
5.486202
0.900


−8.00722
4.750062
0.900


−8.73839
4.094531
0.900


−9.51556
3.541724
0.900


−10.3291
3.112185
0.900


−11.1595
2.815511
0.900


−11.9834
2.649783
0.900


−12.7776
2.604847
0.900


−13.5219
2.663074
0.900


−14.2012
2.803385
0.900


−14.8053
3.003289
0.900


−15.3295
3.23835
0.900


−15.7817
3.484469
0.900


−16.1776
3.715886
0.900


−16.5306
3.901629
0.900


−16.8482
4.020522
0.900


−17.1244
4.072647
0.900


−17.3495
4.071816
0.900


−17.5178
4.035174
0.900


−17.6286
3.980022
0.900


−17.7009
5.363159
0.922


−17.7414
5.312795
0.922


−17.7917
5.233434
0.922


−17.8503
5.100788
0.922


−17.8984
4.904544
0.922


−17.9128
4.641047
0.922


−17.867
4.314822
0.922


−17.7374
3.938875
0.922


−17.5092
3.53089
0.922


−17.1768
3.107748
0.922


−16.7481
2.675808
0.922


−16.2215
2.248556
0.922


−15.5948
1.84422
0.922


−14.8688
1.482353
0.922


−14.0466
1.187983
0.922


−13.1367
0.987096
0.922


−12.1539
0.906098
0.922


−11.1205
0.971314
0.922


−10.0667
1.206851
0.922


−9.02919
1.624897
0.922


−8.03563
2.206585
0.922


−7.10454
2.92809
0.922


−6.24625
3.764088
0.922


−5.45925
4.685551
0.922


−4.74038
5.669769
0.922


−4.08274
6.69623
0.922


−3.47681
7.746596
0.922


−2.91771
8.807818
0.922


−2.40047
9.868231
0.922


−1.91977
10.91711
0.922


−1.47046
11.94477
0.922


−1.04787
12.94246
0.922


−0.6481
13.90241
0.922


−0.26905
14.81813
0.922


0.088562
15.6848
0.922


0.423709
16.49829
0.922


0.735389
17.25504
0.922


1.022744
17.9521
0.922


1.284931
18.58722
0.922


1.521196
19.1589
0.922


1.731088
19.66636
0.922


1.914525
20.10953
0.922


2.071773
20.4892
0.922


2.203459
20.80699
0.922


2.310586
21.06544
0.922


2.394608
21.26808
0.922


2.442019
21.42492
0.922


2.416907
21.53649
0.922


2.371439
21.59255
0.922


2.326079
21.6244
0.922


2.281723
21.64189
0.922


2.220132
21.64981
0.922


2.12457
21.62636
0.922


2.022392
21.52925
0.922


1.928681
21.36544
0.922


1.815238
21.15315
0.922


1.679736
20.89005
0.922


1.521825
20.57374
0.922


1.339456
20.20358
0.922


1.127907
19.78115
0.922


0.889143
19.30555
0.922


0.624779
18.77682
0.922


0.335551
18.19623
0.922


0.021838
17.56588
0.922


−0.31577
16.88842
0.922


−0.67655
16.16701
0.922


−1.05974
15.40534
0.922


−1.46481
14.60769
0.922


−1.89245
13.77942
0.922


−2.3442
12.92678
0.922


−2.82188
12.05666
0.922


−3.32751
11.17653
0.922


−3.86297
10.29438
0.922


−4.42981
9.41859
0.922


−5.02978
8.558375
0.922


−5.667
7.725672
0.922


−6.34462
6.933394
0.922


−7.06336
6.194527
0.922


−7.82349
5.524336
0.922


−8.62543
4.942994
0.922


−9.46212
4.467676
0.922


−10.3232
4.118964
0.922


−11.1883
3.906364
0.922


−12.0331
3.828999
0.922


−12.8331
3.881039
0.922


−13.5672
4.040969
0.922


−14.2248
4.274457
0.922


−14.8022
4.554369
0.922


−15.3046
4.850835
0.922


−15.745
5.134001
0.922


−16.1375
5.379489
0.922


−16.5021
5.549351
0.922


−16.8331
5.635669
0.922


−17.1164
5.643215
0.922


−17.3384
5.595686
0.922


−17.4973
5.525203
0.922


−17.6013
5.456255
0.922


−18.4452
5.556824
0.955


−18.4889
5.504071
0.955


−18.548
5.423846
0.955


−18.6284
5.292815
0.955


−18.7193
5.098805
0.955


−18.8021
4.831585
0.955


−18.8517
4.485857
0.955


−18.8348
4.064628
0.955


−18.7124
3.58434
0.955


−18.4579
3.073741
0.955


−18.0655
2.561423
0.955


−17.5468
2.062984
0.955


−16.9112
1.592034
0.955


−16.1629
1.167862
0.955


−15.3073
0.813758
0.955


−14.3543
0.553503
0.955


−13.3187
0.410007
0.955


−12.2208
0.405107
0.955


−11.0869
0.563153
0.955


−9.95159
0.904845
0.955


−8.84982
1.429558
0.955


−7.80963
2.120504
0.955


−6.84742
2.949756
0.955


−5.96909
3.887387
0.955


−5.17175
4.904209
0.955


−4.44993
5.97631
0.955


−3.7927
7.081224
0.955


−3.19114
8.201653
0.955


−2.63949
9.324297
0.955


−2.13129
10.43698
0.955


−1.66019
11.52878
0.955


−1.22031
12.58995
0.955


−0.80667
13.61188
0.955


−0.41559
14.58712
0.955


−0.04683
15.51019
0.955


0.298721
16.37661
0.955


0.620152
17.18257
0.955


0.916766
17.92485
0.955


1.187856
18.601
0.955


1.431883
19.20973
0.955


1.647918
19.75037
0.955


1.835755
20.22292
0.955


1.995828
20.62813
0.955


2.12905
20.96763
0.955


2.236804
21.24399
0.955


2.320878
21.46083
0.955


2.373717
21.62631
0.955


2.356622
21.74635
0.955


2.312215
21.80867
0.955


2.265289
21.84403
0.955


2.220502
21.86212
0.955


2.158085
21.86994
0.955


2.061293
21.84613
0.955


1.956784
21.74883
0.955


1.858162
21.58506
0.955


1.73801
21.37289
0.955


1.594258
21.10981
0.955


1.426921
20.79318
0.955


1.23434
20.42219
0.955


1.012754
19.998
0.955


0.764111
19.51967
0.955


0.488613
18.988
0.955


0.185643
18.40494
0.955


−0.14333
17.77209
0.955


−0.49726
17.0919
0.955


−0.87534
16.36756
0.955


−1.27675
15.60279
0.955


−1.70114
14.80207
0.955


−2.14945
13.97102
0.955


−2.62325
13.11608
0.955


−3.12438
12.24433
0.955


−3.6548
11.36349
0.955


−4.21638
10.48179
0.955


−4.81055
9.607864
0.955


−5.4398
8.751859
0.955


−6.10877
7.926826
0.955


−6.82083
7.146909
0.955


−7.57686
6.426683
0.955


−8.3784
5.785269
0.955


−9.22282
5.243253
0.955


−10.1012
4.820715
0.955


−10.9982
4.536211
0.955


−11.8904
4.4014
0.955


−12.7494
4.414598
0.955


−13.5475
4.564138
0.955


−14.2645
4.818435
0.955


−14.8955
5.136675
0.955


−15.4501
5.475562
0.955


−15.955
5.782148
0.955


−16.4375
6.001549
0.955


−16.894
6.108481
0.955


−17.3011
6.11782
0.955


−17.6419
6.055404
0.955


−17.9107
5.954599
0.955


−18.1119
5.843228
0.955


−18.2546
5.740056
0.955


−18.3496
5.656666
0.955


−20.0645
4.454851
1.000


−20.1097
4.393092
1.000


−20.173
4.301512
1.000


−20.2646
4.156162
1.000


−20.3798
3.946389
1.000


−20.5084
3.661446
1.000


−20.633
3.291626
1.000


−20.7286
2.830279
1.000


−20.7578
2.277281
1.000


−20.674
1.645733
1.000


−20.4238
0.970476
1.000


−19.9841
0.299426
1.000


−19.3617
−0.32769
1.000


−18.5773
−0.88457
1.000


−17.6515
−1.34778
1.000


−16.603
−1.69382
1.000


−15.4535
−1.90164
1.000


−14.2278
−1.95394
1.000


−12.954
−1.83761
1.000


−11.6628
−1.53958
1.000


−10.3935
−1.04136
1.000


−9.18471
−0.34475
1.000


−8.06849
0.531881
1.000


−7.05974
1.553173
1.000


−6.16424
2.685651
1.000


−5.37822
3.897069
1.000


−4.69299
5.159524
1.000


−4.09128
6.446728
1.000


−3.55957
7.739236
1.000


−3.0884
9.022202
1.000


−2.66779
10.28247
1.000


−2.28817
11.50853
1.000


−1.941
12.6904
1.000


−1.61907
13.81939
1.000


−1.31752
14.88828
1.000


−1.03577
15.89168
1.000


−0.77398
16.82515
1.000


−0.53243
17.685
1.000


−0.31009
18.46797
1.000


−0.10955
19.17275
1.000


0.066205
19.79907
1.000


0.216212
20.34707
1.000


0.340984
20.8176
1.000


0.442056
21.21235
1.000


0.52159
21.53409
1.000


0.582089
21.78681
1.000


0.61841
21.97746
1.000


0.599788
22.11167
1.000


0.554588
22.18424
1.000


0.50173
22.22318
1.000


0.454618
22.23691
1.000


0.390725
22.23552
1.000


0.297514
22.19593
1.000


0.200934
22.08768
1.000


0.102081
21.9205
1.000


−0.01972
21.70479
1.000


−0.16421
21.43668
1.000


−0.33044
21.11302
1.000


−0.51834
20.73218
1.000


−0.72879
20.29387
1.000


−0.96221
19.79841
1.000


−1.22229
19.24844
1.000


−1.51202
18.64704
1.000


−1.82589
17.99391
1.000


−2.16289
17.29159
1.000


−2.5224
16.54336
1.000


−2.90393
15.75316
1.000


−3.30786
14.9258
1.000


−3.73558
14.0671
1.000


−4.18901
13.18362
1.000


−4.67039
12.28258
1.000


−5.18213
11.37189
1.000


−5.72658
10.46004
1.000


−6.30508
9.555574
1.000


−6.92232
8.670125
1.000


−7.58589
7.819135
1.000


−8.30172
7.019901
1.000


−9.07234
6.290738
1.000


−9.89681
5.651694
1.000


−10.7695
5.124381
1.000


−11.6839
4.744233
1.000


−12.6163
4.543129
1.000


−13.5278
4.539363
1.000


−14.374
4.721296
1.000


−15.1343
5.028242
1.000


−15.8317
5.359192
1.000


−16.497
5.623956
1.000


−17.1386
5.765943
1.000


−17.7371
5.778933
1.000


−18.2674
5.685344
1.000


−18.716
5.524628
1.000


−19.0835
5.334013
1.000


−19.3761
5.138054
1.000


−19.6026
4.954339
1.000


−19.7723
4.793721
1.000


−19.8944
4.663017
1.000


−19.9778
4.565302
1.000


−20.266
6.375169
1.022


−20.32
6.31403
1.022


−20.3964
6.223367
1.022


−20.5098
6.079714
1.022


−20.6593
5.873165
1.022


−20.8399
5.593376
1.022


−21.0402
5.229079
1.022


−21.2433
4.770158
1.022


−21.4247
4.208868
1.022


−21.5301
3.537667
1.022


−21.4861
2.772311
1.022


−21.2303
1.955788
1.022


−20.721
1.163174
1.022


−20.0169
0.41978
1.022


−19.1399
−0.24764
1.022


−18.1025
−0.80156
1.022


−16.9278
−1.21258
1.022


−15.645
−1.46501
1.022


−14.2847
−1.54611
1.022


−12.8773
−1.4483
1.022


−11.4538
−1.15833
1.022


−10.063
−0.63351
1.022


−8.74309
0.1044
1.022


−7.52123
1.024258
1.022


−6.41463
2.092689
1.022


−5.42607
3.271613
1.022


−4.55388
4.529108
1.022


−3.78065
5.830488
1.022


−3.08964
7.14935
1.022


−2.47142
8.467628
1.022


−1.91567
9.769352
1.022


−1.41203
11.04054
1.022


−0.95096
12.26914
1.022


−0.52441
13.44483
1.022


−0.12515
14.55857
1.022


0.247773
15.60436
1.022


0.594147
16.57735
1.022


0.913391
17.47366
1.022


1.207296
18.28942
1.022


1.472683
19.02354
1.022


1.705205
19.67636
1.022


1.903318
20.2483
1.022


2.067627
20.74017
1.022


2.200263
21.1535
1.022


2.30422
21.49092
1.022


2.383008
21.7563
1.022


2.432441
21.95707
1.022


2.429304
22.10135
1.022


2.393758
22.18521
1.022


2.342711
22.23302
1.022


2.295799
22.25
1.022


2.230798
22.25065
1.022


2.135209
22.21222
1.022


2.029993
22.10892
1.022


1.908931
21.95284
1.022


1.757669
21.75138
1.022


1.577492
21.49942
1.022


1.369438
21.19342
1.022


1.134434
20.83106
1.022


0.87319
20.41123
1.022


0.583529
19.93547
1.022


0.259803
19.40821
1.022


−0.1014
18.83336
1.022


−0.49218
18.20856
1.022


−0.91148
17.53638
1.022


−1.35833
16.82011
1.022


−1.83207
16.06383
1.022


−2.33294
15.2727
1.022


−2.86186
14.45287
1.022


−3.42016
13.61128
1.022


−4.00941
12.75561
1.022


−4.63139
11.89432
1.022


−5.28752
11.03635
1.022


−5.97814
10.19058
1.022


−6.70849
9.371037
1.022


−7.48611
8.596477
1.022


−8.31623
7.888081
1.022


−9.19971
7.268667
1.022


−10.1274
6.75414
1.022


−11.0909
6.370527
1.022


−12.0763
6.15543
1.022


−13.0451
6.141522
1.022


−13.9575
6.355678
1.022


−14.7385
6.773186
1.022


−15.3992
7.287862
1.022


−16.0088
7.786295
1.022


−16.6915
8.049633
1.022


−17.3616
8.05539
1.022


−17.9582
7.918026
1.022


−18.4654
7.712217
1.022


−18.8885
7.476016
1.022


−19.2398
7.244026
1.022


−19.5307
7.035225
1.022


−19.7642
6.852327
1.022


−19.9439
6.696841
1.022


−20.0763
6.572077
1.022


−20.1684
6.479504
1.022


−20.9155
6.234441
1.041


−20.9717
6.169319
1.041


−21.0515
6.073086
1.041


−21.1711
5.921603
1.041


−21.3318
5.706044
1.041


−21.532
5.41759
1.041


−21.764
5.0457
1.041


−22.0159
4.580415
1.041


−22.2686
4.012211
1.041


−22.4666
3.323794
1.041


−22.5311
2.516274
1.041


−22.3815
1.630112
1.041


−21.9352
0.739523
1.041


−21.2557
−0.09928
1.041


−20.3812
−0.86419
1.041


−19.3228
−1.51036
1.041


−18.1062
−2.00212
1.041


−16.766
−2.32358
1.041


−15.3352
−2.46488
1.041


−13.8491
−2.42471
1.041


−12.3343
−2.19775
1.041


−10.8416
−1.72063
1.041


−9.4171
−1.00379
1.041


−8.09426
−0.08138
1.041


−6.89799
1.013929
1.041


−5.83468
2.239226
1.041


−4.90667
3.559392
1.041


−4.09539
4.933975
1.041


−3.37876
6.330793
1.041


−2.74551
7.729364
1.041


−2.18388
9.112043
1.041


−1.6816
10.46342
1.041


−1.22719
11.77031
1.041


−0.81108
13.02164
1.041


−0.42309
14.20726
1.041


−0.06125
15.32062
1.041


0.274545
16.35653
1.041


0.583895
17.31085
1.041


0.86936
18.1794
1.041


1.127633
18.9609
1.041


1.353166
19.6559
1.041


1.543823
20.26496
1.041


1.700177
20.78892
1.041


1.824719
21.22935
1.041


1.920912
21.58899
1.041


1.992826
21.87187
1.041


2.036469
22.08547
1.041


2.034299
22.2376
1.041


2.000146
22.32735
1.041


1.946799
22.37826
1.041


1.898381
22.39389
1.041


1.83211
22.39037
1.041


1.737745
22.34415
1.041


1.633732
22.23549
1.041


1.507435
22.07842
1.041


1.348855
21.87609
1.041


1.160552
21.62224
1.041


0.943803
21.31307
1.041


0.700581
20.94557
1.041


0.432713
20.51799
1.041


0.136248
20.03307
1.041


−0.19643
19.49651
1.041


−0.56864
18.91224
1.041


−0.97072
18.27679
1.041


−1.40185
17.59295
1.041


−1.86109
16.86414
1.041


−2.34799
16.09463
1.041


−2.86323
15.29002
1.041


−3.40787
14.45668
1.041


−3.98339
13.60182
1.041


−4.59152
12.73346
1.041


−5.23435
11.86057
1.041


−5.91305
10.99222
1.041


−6.62848
10.13812
1.041


−7.38805
9.314915
1.041


−8.20053
8.544167
1.041


−9.07249
7.851699
1.041


−10.0014
7.261132
1.041


−10.9743
6.787773
1.041


−11.9839
6.467115
1.041


−13.0034
6.341475
1.041


−13.9853
6.452218
1.041


−14.8763
6.811475
1.041


−15.58
7.37604
1.041


−16.1895
7.973011
1.041


−16.8182
8.474527
1.041


−17.5538
8.577624
1.041


−18.2212
8.399015
1.041


−18.7793
8.121202
1.041


−19.2409
7.807669
1.041


−19.6174
7.48707
1.041


−19.9297
7.192183
1.041


−20.1977
6.943943
1.041


−20.4201
6.738624
1.041


−20.5952
6.570871
1.041


−20.7258
6.438985
1.041


−20.8177
6.342399
1.041


−20.876
6.27879
1.041









In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface where it is assembled with the inner shroud. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface where it is assembled with the outer ring.


By convention, the stacking axis AE of a vane of a nozzle, is an axis that extends in the radial direction Z and is an axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.


As mentioned at the beginning of the present description, the aerodynamic profile of the disclosure is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile. Also, the aerodynamic profile is positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the stacking axis of the vane. In other words, the stagger angle may vary by ±10°, particularly by ±5°, more particularly by ±3°.


The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.


By way of example, the total height H is preferably about 113 mm ±10%. By way of example, the plane P0 is situated at a distance of about 446 mm ±10% from the axis A.


In the above table, the profile is characterized by eighteen section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These eighteen section planes include eighteen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The eighteen section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.


It is advantageous for the nozzle that includes the vane of the disclosure to have 150 to 170 vanes, more particularly 160 vanes, that present aerodynamic profiles as defined above.

Claims
  • 1. An aerodynamic profile for a turbine vane, the profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
  • 2. The aerodynamic profile as claimed in claim 1, wherein said profile is defined within an envelope of ±1 mm in a direction normal to the surface of the nominal profile.
  • 3. The aerodynamic profile as claimed in claim 1, wherein the coordinates X,Y of said profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
  • 4. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±10° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
  • 5. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±5° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
  • 6. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±3° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
  • 7. The aerodynamic profile as claimed in claim 1, wherein the vane is a nozzle vane forming a part of a stator of a turbine.
  • 8. A turbine vane, presenting the aerodynamic profile as claimed in claim 1.
  • 9. A turbine, including turbine vanes presenting aerodynamic profiles as claimed in claim 1.
  • 10. A turbine as claimed in claim 9, including a nozzle that is stationary in rotation, having 150 to 170 vanes that present the aerodynamic profiles.
  • 11. A turbine as claimed in claim 9, including a nozzle that is stationary in rotation, having 160 vanes that present the aerodynamic profiles.
  • 12. A turbine nozzle forming a portion of a turbine stator, wherein all the vanes of the nozzle present the aerodynamic profile as claimed in claim 1.
  • 13. A turbine nozzle as claimed in claim 12, including 150 to 170 vanes that present the aerodynamic profiles.
  • 14. A turbine nozzle as claimed in claim 12, including 160 vanes that present the aerodynamic profiles.
CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to U.S. Patent Application No. 62/504,556, filed on May 11, 2017, the entirety of which is incorporated by reference herein.

Provisional Applications (1)
Number Date Country
62504556 May 2017 US