Rotor blade for a second stage of a compressor

Information

  • Patent Grant
  • 7785074
  • Patent Number
    7,785,074
  • Date Filed
    Friday, February 16, 2007
    18 years ago
  • Date Issued
    Tuesday, August 31, 2010
    14 years ago
Abstract
A blade of a rotor of a second stage of a compressor can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X, Y, Z), where the axis (Z) is a radial axis intersecting the central axis of the compressor. The blade has a profile which can be identified by a series of closed intersection curves between the profile itself and planes (X, Y) lying at distances (Z) from the central axis. The blade also has a non-linearly variable trend of decreasing maximum thickness defined by the closed curves, substantially parallel to a base portion of the blade itself, fixable to the rotor. The variable trend of maximum thickness is substantially situated midway up the blade and is suitable for shifting the natural resonance frequencies of the blade itself outside a functioning velocity range of the rotor.
Description
BACKGROUND

1. Field of the Invention


The field of the present invention relates to a blade of a rotor of a second stage of a compressor.


More specifically, the invention relates to a blade of a rotor having a high aerodynamic efficiency of a second stage of a compressor.


2. Related Art


Compressors normally pressurize in their interior air removed from the outside.


The fluid penetrates the compressor through a series of inlet ducts.


In these channels, the gas has low pressure and low temperature characteristics, whereas as it passes through the compressor, the gas is compressed and its temperature increases.


In order to increase the efficiency, the compressor is normally divided into various stages, each of which has a rotor and a stator respectively equipped with a series of blades.


In recent years, technologically advanced compressors have been further improved, obtaining an increased improvement in efficiency, operating in particular on the aerodynamic conditions.


The geometric configuration of the blades in fact significantly influences the aerodynamic efficiency.


This depends on the fact that the geometric characteristics of the blade cause a distribution of the relative velocities in the fluid, consequently influencing the distribution of the limit layers along the walls and ultimately, losses due to friction.


In particular, in the case of rotor blades of a second stage of a compressor an extremely high efficiency is required, at the same time maintaining an appropriate aerodynamic and mechanical load.


What is needed is:


A blade of a rotor of a second stage of a compressor which avoids, or in any case reduces, resonance problems due to the stimulation of natural frequencies and at the same time allows a high aerodynamic efficiency;


A blade of a rotor of a second stage of a compressor which avoids or in any case reduces resonance problems due to the stimulation of natural frequencies and which allows a useful life of the blade itself; and


A rotor of a second phase of a compressor which allows a high aerodynamic efficiency, and at the same time allows a high reliability of the compressor to be obtained with a consequent increase in the power of the turbine itself, with the same compressor dimensions.


SUMMARY

Embodiments of the present invention meet the needs referenced above and exhibit additional characteristics by providing a rotor blade of a second stage of a compressor.


Further characteristics of the invention are indicated in the subsequent claims.





BRIEF DESCRIPTION OF THE DRAWINGS

The characteristics and advantages of a rotor blade of a second stage of a compressor according to the present invention will appear more evident from the following illustrative and non-limiting description, referring to the enclosed schematic drawings in which:



FIG. 1 is a raised view of a rotor blade of a compressor produced with an aerodynamic profile according to the present invention;



FIG. 2 is a raised view of the opposite side of the blade of FIG. 1; and



FIG. 3 is a diagram of the maximum thickness trend of a blade according to the present invention, with respect to its height.





DETAILED DESCRIPTION

With reference to the figures, a blade 10 is provided of a rotor of a second stage of a compressor.


Said blade 10 is defined by means of coordinates of a discreet combination of points, in a Cartesian reference system (X,Y,Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, not shown.


The profile of the blade 10 is identified by means of a series of closed intersection curves between the profile itself and planes (X,Y) lying at distances (Z) from the central axis.


The profile of said blade 10 comprises a first substantially concave surface 3, which is pressurized, and a second substantially convex surface 5 which is in depression and opposite the first.


The two surfaces 3, 5 are continuous and joined to each other, and together form the profile of said blade 10.


At a base portion 12, commonly called “foot” of the blade 10, according to the known art there is a connecting joint with the aerodynamic profile of the blade 10 itself, said base portion 12 being suitable for being fixed to said rotor of said compressor.


Said blade 10 comprises a thickening 30, i.e. a prolonged portion having a greater thickness with respect to the adjacent portions, which is substantially parallel to said base portion 12 so as to shift the resonance frequencies of said blade 10 outside the functioning frequency range of the rotor itself, thus reducing or in any case avoiding problems of instability and vibrations of the blade 10 and rotor.


This advantageously leads to an increase in both the useful life and reliability of the rotor and compressor itself.


Said thickening 30 relates to at least one section or closed curve, and is also substantially situated midway up the blade 10.


In other words, said thickening 30 confers a dynamic behaviour to said blade 10 which is such as to have flexural frequencies which fall outside a functioning velocity range of the rotor of said compressor and consequently such that there is no intensification of the maximum flexural deformation of the blade during the functioning of the compressor.


This consequently leads to a higher performance of the compressor, of the rotor and a longer useful life of its components, as problems of resonance such as those described above are avoided.


The clearances and tolerances of the blade and stator can consequently be dimensioned so as to further increase the performances of the compressor itself.


This is possible as the blade, upon deforming, is prevented from causing a contact and relative friction against the relative stator.


In particular, each closed curve has a maximum thickness determined by the maximum distance between said first surface 3 and said second surface 5.


Said maximum surface of each closed curve, along the height of the blade 10, moving towards a free end 14 of the blade 10, has a decreasing trend whose slope varies three times, defining four regions. For example, the variation in the trend of the maximum thickness is shown in FIG. 3, in which it is compared with the maximum thickness trend of a blade according to the known art. In particular, in FIG. 3, the abscissa indicates the height of the blade 10, wherein the ordinate represents the maximum thickness of the blade 10, adimensionalized by putting the thickness in correspondence with the foot of the blade equal to 1. In the diagram shown in FIG. 3, the upper line represents the maximum thickness trend of a blade according to the known art, whereas the lower line shows the trend of the maximum thickness of the blade according to the present invention.


Along the height of the blade 10 in the direction of a free end 14 of the blade 10, said maximum thickness preferably has a trend according to a polynomial function of the sixth degree and in particular said polynomial function is

Tmax=−21.119*h6+70.467*h5−85.603*h4+44.523*h3−7.8323*h2−1.1541*h+0.997

wherein h represents the percentage of the height of the blade 10, and wherein Tmax is the maximum adimensionalized thickness relating to the closed curve corresponding to that percentage of the height of the blade 10.


The profile of each blade 10 was also suitably shaped to be able to maintain the same efficiency at high levels.


The aerodynamic profile of each blade 10 is preferably defined by means of a series of closed curves whose coordinates are defined with respect to a Cartesian reference system X, Y, Z, wherein the axis Z is a radial axis intersecting the central axis of the turbine, and said closed curves lying at distances Z from the central axis are defined according to Table 1, whose values, expressed in millimeters, refer to an aerodynamic profile at room temperature, in particular 25° C.











TABLE I





X
Y
Z

















−32.517
32.876
230.276


−32.501
32.886
230.276


−32.466
32.898
230.276


−32.392
32.903
230.276


−32.249
32.868
230.276


−32.039
32.773
230.276


−31.685
32.561
230.276


−31.241
32.234
230.276


−30.677
31.764
230.276


−29.982
31.164
230.276


−29.084
30.379
230.276


−28.056
29.463
230.276


−26.970
28.476
230.276


−25.756
27.357
230.276


−24.412
26.106
230.276


−22.940
24.725
230.276


−21.407
23.274
230.276


−19.816
21.752
230.276


−18.164
20.161
230.276


−16.447
18.505
230.276


−14.664
16.784
230.276


−12.813
15.003
230.276


−10.890
13.163
230.276


−8.894
11.268
230.276


−6.886
9.385
230.276


−4.864
7.518
230.276


−2.823
5.670
230.276


−0.759
3.847
230.276


1.327
2.052
230.276


3.436
0.19861
230.276


5.572
−1.445
230.276


7.741
−3.134
230.276


9.952
−4.768
230.276


12.212
−6.339
230.276


14.528
−7.836
230.276


16.816
−9.204
230.276


19.065
−10.452
230.276


21.267
−11.595
230.276


23.415
−12.647
230.276


25.500
−13.615
230.276


27.518
−14.510
230.276


29.464
−15.340
230.276


31.249
−16.077
230.276


32.869
−16.731
230.276


34.322
−17.310
230.276


35.604
−17.818
230.276


36.717
−18.256
230.276


37.658
−18.626
230.276


38.462
−18.946
230.276


39.135
−19.219
230.276


39.688
−19.446
230.276


40.130
−19.629
230.276


40.469
−19.771
230.276


40.723
−19.878
230.276


40.900
−20.024
230.276


40.972
−20.196
230.276


40.974
−20.337
230.276


40.927
−20.475
230.276


40.798
−20.620
230.276


40.567
−20.693
230.276


40.271
−20.713
230.276


39.877
−20.737
230.276


39.363
−20.764
230.276


38.722
−20.793
230.276


37.941
−20.822
230.276


37.012
−20.849
230.276


35.926
−20.871
230.276


34.642
−20.885
230.276


33.160
−20.882
230.276


31.482
−20.846
230.276


29.607
−20.760
230.276


27.538
−20.601
230.276


25.290
−20.348
230.276


22.967
−19.991
230.276


20.570
−19.516
230.276


18.104
−18.909
230.276


15.573
−18.154
230.276


12.979
−17.233
230.276


10.333
−16.134
230.276


7.676
−14.853
230.276


5.106
−13.432
230.276


2.621
−11.879
230.276


0.14583
−10.207
230.276


−2.134
−8.429
230.276


−4.417
−6.555
230.276


−6.626
−4.601
230.276


−8.756
−2.579
230.276


−10.809
−0.493
230.276


−12.787
1.657
230.276


−14.694
3.867
230.276


−16.534
6.134
230.276


−18.254
8.374
230.276


−19.866
10.579
230.276


−21.378
12.741
230.276


−22.797
14.854
230.276


−24.130
16.912
230.276


−25.380
18.908
230.276


−26.547
20.840
230.276


−27.636
22.706
230.276


−28.605
24.412
230.276


−29.461
25.958
230.276


−30.203
27.342
230.276


−30.879
28.650
230.276


−31.447
29.793
230.276


−31.874
30.677
230.276


−32.205
31.389
230.276


−32.423
31.936
230.276


−32.547
32.360
230.276


−32.587
32.602
230.276


−32.583
32.758
230.276


−32.557
32.832
230.276


−32.532
32.863
230.276


−32.587
31.887
235.273


−32.571
31.897
235.273


−32.536
31.910
235.273


−32.462
31.913
235.273


−32.320
31.877
235.273


−32.113
31.778
235.273


−31.763
31.560
235.273


−31.324
31.231
235.273


−30.763
30.762
235.273


−30.071
30.163
235.273


−29.179
29.378
235.273


−28.157
28.463
235.273


−27.073
27.480
235.273


−25.860
26.368
235.273


−24.517
25.127
235.273


−23.041
23.759
235.273


−21.502
22.327
235.273


−19.899
20.828
235.273


−18.230
19.265
235.273


−16.493
17.642
235.273


−14.686
15.959
235.273


−12.808
14.219
235.273


−10.857
12.423
235.273


−8.830
10.575
235.273


−6.793
8.737
235.273


−4.744
6.914
235.273


−2.680
5.107
235.273


−0.598
3.321
235.273


1.506
1.562
235.273


3.634
−0.166
235.273


5.789
−1.860
235.273


7.976
−3.512
235.273


10.202
−5.116
235.273


12.468
−6.663
235.273


14.774
−8.140
235.273


17.044
−9.496
235.273


19.272
−10.741
235.273


21.453
−11.886
235.273


23.579
−12.941
235.273


25.646
−13.916
235.273


27.646
−14.820
235.273


29.575
−15.659
235.273


31.344
−16.407
235.273


32.950
−17.070
235.273


34.389
−17.658
235.273


35.661
−18.173
235.273


36.764
−18.616
235.273


37.698
−18.991
235.273


38.494
−19.314
235.273


39.163
−19.588
235.273


39.712
−19.816
235.273


40.150
−20.000
235.273


40.487
−20.143
235.273


40.739
−20.251
235.273


40.914
−20.398
235.273


40.983
−20.569
235.273


40.983
−20.709
235.273


40.935
−20.846
235.273


40.805
−20.988
235.273


40.577
−21.058
235.273


40.284
−21.072
235.273


39.893
−21.088
235.273


39.384
−21.105
235.273


38.749
−21.121
235.273


37.976
−21.135
235.273


37.057
−21.142
235.273


35.981
−21.140
235.273


34.711
−21.125
235.273


33.246
−21.088
235.273


31.586
−21.014
235.273


29.733
−20.885
235.273


27.690
−20.680
235.273


25.473
−20.377
235.273


23.183
−19.970
235.273


20.824
−19.443
235.273


18.399
−18.782
235.273


15.913
−17.971
235.273


13.369
−16.996
235.273


10.776
−15.850
235.273


8.172
−14.538
235.273


5.647
−13.107
235.273


3.196
−11.567
235.273


0.56458
−9.922
235.273


−1.507
−8.186
235.273


−3.767
−6.360
235.273


−5.971
−4.449
235.273


−8.113
−2.464
235.273


−10.185
−0.421
235.273


−12.189
1.674
235.273


−14.128
3.820
235.273


−16.008
6.013
235.273


−17.770
8.175
235.273


−19.424
10.300
235.273


−20.976
12.383
235.273


−22.434
14.418
235.273


−23.802
16.400
235.273


−25.085
18.327
235.273


−26.287
20.196
235.273


−27.412
22.002
235.273


−28.418
23.658
235.273


−29.308
25.160
235.273


−30.083
26.506
235.273


−30.795
27.775
235.273


−31.399
28.884
235.273


−31.854
29.741
235.273


−32.206
30.433
235.273


−32.444
30.964
235.273


−32.588
31.376
235.273


−32.642
31.613
235.273


−32.646
31.768
235.273


−32.624
31.842
235.273


−32.601
31.874
235.273


−32.636
30.926
241.239


−32.621
30.936
241.239


−32.586
30.948
241.239


−32.512
30.950
241.239


−32.371
30.908
241.239


−32.170
30.803
241.239


−31.829
30.575
241.239


−31.396
30.241
241.239


−30.840
29.772
241.239


−30.154
29.172
241.239


−29.271
28.384
241.239


−28.257
27.469
241.239


−27.177
26.491
241.239


−25.965
25.387
241.239


−24.621
24.159
241.239


−23.141
22.808
241.239


−21.593
21.397
241.239


−19.978
19.925
241.239


−18.294
18.392
241.239


−16.541
16.801
241.239


−14.716
15.154
241.239


−12.818
13.451
241.239


−10.846
11.694
241.239


−8.799
9.887
241.239


−6.742
8.090
241.239


−4.675
6.306
241.239


−2.594
4.538
241.239


−0.498
2.789
241.239


1.619
1.065
241.239


3.762
−0.629
241.239


5.933
−2.287
241.239


8.137
−3.906
241.239


10.373
−5.480
241.239


12.641
−7.005
241.239


14.943
−8.475
241.239


17.205
−9.839
241.239


19.424
−11.102
241.239


21.594
−12.267
241.239


23.709
−13.339
241.239


25.764
−14.328
241.239


27.753
−15.243
241.239


29.669
−16.096
241.239


31.427
−16.857
241.239


33.023
−17.535
241.239


34.453
−18.134
241.239


35.717
−18.659
241.239


36.814
−19.111
241.239


37.742
−19.492
241.239


38.535
−19.819
241.239


39.200
−20.096
241.239


39.747
−20.326
241.239


40.183
−20.512
241.239


40.518
−20.656
241.239


40.769
−20.766
241.239


40.937
−20.915
241.239


40.999
−21.084
241.239


40.996
−21.220
241.239


40.946
−21.354
241.239


40.816
−21.492
241.239


40.591
−21.560
241.239


40.302
−21.566
241.239


39.916
−21.573
241.239


39.415
−21.577
241.239


38.788
−21.578
241.239


38.027
−21.571
241.239


37.121
−21.553
241.239


36.061
−21.520
241.239


34.810
−21.467
241.239


33.368
−21.386
241.239


31.736
−21.260
241.239


29.915
−21.071
241.239


27.910
−20.798
241.239


25.738
−20.417
241.239


23.500
−19.924
241.239


21.197
−19.311
241.239


18.834
−18.569
241.239


16.412
−17.690
241.239


13.932
−16.667
241.239


11.403
−15.494
241.239


8.852
−14.175
241.239


6.369
−12.758
241.239


3.951
−11.247
241.239


1.595
−9.647
241.239


−0.701
−7.961
241.239


−2.939
−6.192
241.239


−5.123
−4.345
241.239


−7.257
−2.425
241.239


−9.341
−0.441
241.239


−11.372
1.594
241.239


−13.352
3.678
241.239


−15.283
5.808
241.239


−17.104
7.909
241.239


−18.820
9.975
241.239


−20.435
11.999
241.239


−21.954
13.976
241.239


−23.382
15.903
241.239


−24.722
17.776
241.239


−25.978
19.589
241.239


−27.155
21.341
241.239


−28.206
22.946
241.239


−29.135
24.402
241.239


−29.947
25.705
241.239


−30.695
26.934
241.239


−31.333
28.006
241.239


−31.812
28.837
241.239


−32.183
29.509
241.239


−32.440
30.024
241.239


−32.605
30.423
241.239


−32.673
30.653
241.239


−32.687
30.805
241.239


−32.670
30.880
241.239


−32.650
30.912
241.239


−32.605
30.688
244.222


−32.590
30.698
244.222


−32.555
30.710
244.222


−32.482
30.710
244.222


−32.342
30.665
244.222


−32.143
30.555
244.222


−31.807
30.318
244.222


−31.381
29.977
244.222


−30.830
29.500
244.222


−30.150
28.892
244.222


−29.274
28.094
244.222


−28.268
27.169
244.222


−27.194
26.183
244.222


−25.986
25.072
244.222


−24.644
23.839
244.222


−23.164
22.486
244.222


−21.614
21.074
244.222


−19.994
19.605
244.222


−18.303
18.077
244.222


−16.541
16.492
244.222


−14.706
14.852
244.222


−12.799
13.156
244.222


−10.818
11.407
244.222


−8.762
9.605
244.222


−6.697
7.813
244.222


−4.621
6.034
244.222


−2.532
4.271
244.222


−0.425
2.528
244.222


1.703
0.5625
244.222


3.856
−0.875
244.222


6.034
−2.522
244.222


8.240
−4.128
244.222


10.476
−5.691
244.222


12.743
−7.208
244.222


15.042
−8.677
244.222


17.298
−10.048
244.222


19.508
−11.324
244.222


21.669
−12.509
244.222


23.772
−13.608
244.222


25.814
−14.626
244.222


27.791
−15.570
244.222


29.697
−16.448
244.222


31.448
−17.229
244.222


33.038
−17.921
244.222


34.465
−18.531
244.222


35.726
−19.064
244.222


36.821
−19.520
244.222


37.749
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330.733


21.939
−30.739
330.733


20.571
−29.075
330.733


19.083
−27.245
330.733


17.542
−25.326
330.733


15.953
−23.315
330.733


14.319
−21.207
330.733


12.646
−19.001
330.733


10.938
−16.692
330.733


9.198
−14.277
330.733


7.434
−11.755
330.733


5.707
−9.209
330.733


4.017
−6.639
330.733


2.362
−4.047
330.733


0.51111
−1.436
330.733


−0.866
1.190
330.733


−2.449
3.829
330.733


−4.017
6.476
330.733


−5.574
9.131
330.733


−7.122
11.791
330.733


−8.660
14.456
330.733


−10.189
17.127
330.733


−11.654
19.716
330.733


−13.055
22.223
330.733


−14.391
24.649
330.733


−15.663
26.993
330.733


−16.868
29.256
330.733


−18.007
31.439
330.733


−19.079
33.541
330.733


−20.081
35.563
330.733


−20.968
37.413
330.733


−21.743
39.089
330.733


−22.409
40.590
330.733


−23.011
42.006
330.733


−23.513
43.242
330.733


−23.882
44.199
330.733


−24.157
44.973
330.733


−24.342
45.560
330.733


−24.469
46.004
330.733


−24.522
46.255
330.733


−24.528
46.418
330.733


−24.509
46.498
330.733


−24.486
46.532
330.733









At the same time, each blade 10 therefore has an aerodynamic profile which allows a high conversion efficiency and a high useful life to be maintained.


Furthermore, the aerodynamic profile of the blade 10 according to the invention is obtained with the values of Table 1 by piling up the series of closed curves and grouping them so as to obtain a continuous aerodynamic profile.


In order to take into account the dimensional variability of each blade 10, the profile of each blade 10 can have a tolerance of +/−2 mm in a normal direction with respect to the profile of the blade 10 itself.


The profile of each blade 10 can also comprise a coating, applied subsequently and which varies the profile itself.


Said antiwear coating preferably has a thickness defined in a normal direction at each surface of the blade 10 and ranging from 0 to 0.5 mm.


It is evident, moreover, that the values of the coordinates of Table 1 can be multiplied or divided by a corrective constant to obtain a profile in a greater or smaller scale, maintaining the same form.


According to another aspect of the present invention, a rotor of a second stage of a compressor is provided, which comprises a series of blades 10 of the type described above, each of which having a shaped aerodynamic profile, which are fixed to an outer surface of said rotor so as to be uniformly distanced thereon, and also oriented so as to confer a high efficiency to the compressor in which said rotor is preferably inserted.


According to another aspect of the present invention, a compressor is provided, comprising a rotor of the type described above.


It can thus be seen that a blade of a rotor of a second stage of a compressor according to the present invention achieves the objectives specified above.


The rotor blade of a second stage of a compressor of the present invention thus conceived, can undergo numerous modifications and variants, all included in the same inventive concept.


Furthermore, in practice, the materials used, as also the dimensions and components, can vary according to technical requirements.

Claims
  • 1. A blade of a rotor of a second stage of a compressor, which can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X, Y, Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, said blade having an aerodynamic profile which can be identified by a series of closed intersection curves between the profile itself and planes (X, Y) lying at distances (Z) from the central axis, said blade comprising: a base portion fixable to the rotor,the aerodynamic profile identified by a first substantially concave surface, which is pressurized, and a second substantially convex surface which is in depression and which is opposite to the first concave surface, said two surfaces being continuous and joined to each other to form the aerodynamic profile of said blade extending from a foot at said base portion to a free end of said blade distal from said base portion,wherein each closed curve substantially parallel to said base portion has a maximum thickness determined by a maximum distance between said first surface and said second surface, said maximum thickness of each closed curve, along the height of the blade in the direction of the free end of the blade, having a non-linearly variable trend decreasing at a higher rate from said base portion to a first predetermined height, then at a lower rate from the first predetermined height to a second predetermined height,said variable trend of maximum thickness halfway up the blade being suitable for shifting one or more natural resonance frequencies of the blade itself outside a functioning velocity range of said rotor.
  • 2. The blade according to claim 1, wherein along the height of the blade in the direction of its free end, said maximum thickness has a trend according to a polynomial function of the sixth degree.
  • 3. The blade according to claim 2, wherein said polynomial function of the sixth degree is: Tmax=−21.119*h6+70.467*h5−85.603*h4+44.523*h3−7.8323*h2−1.1541*h+0.997
  • 4. The blade according to claim 1, wherein the profile of said blade comprises an antiwear coating.
  • 5. The blade according to claim 4, wherein said coating has a thickness ranging from 0 mm to 0.5 mm.
  • 6. A rotor of a second stage of a compressor, wherein the rotor comprises: a series of blades according to claim 1.
  • 7. The rotor according to claim 6, wherein said series of blades constrained to an outer surface of said rotor and said series of blades is also uniformly distributed thereon in order to maximize the efficiency of the rotor itself.
  • 8. A compressor comprising a rotor according to claim 6.
  • 9. The blade according to claim 1, wherein said first predetermined height is about 25% of the height of the blade.
  • 10. The blade according to claim 9, wherein said second predetermined height is above about 50% of the height of the blade.
  • 11. The blade according to claim 10, further comprising said maximum thickness of each closed curve variable trend decreasing at a higher rate from said second predetermined height to a third predetermined height than the rate from the first predetermined height to the second predetermined height.
  • 12. The blade according to claim 11, further comprising said maximum thickness of each closed curve variable trend decreasing at a lower rate from said third predetermined height to the free end than the rate from the second predetermined height to the third predetermined height.
  • 13. The blade according to claim 1, wherein said second predetermined height is above about 50% of the height of the blade.
  • 14. A blade of a rotor of a compressor, which can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X, Y, Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, said blade having an aerodynamic profile which can be identified by a series of closed intersection curves between the profile itself and planes (X, Y) lying at distances (Z) from the central axis, said blade comprising: a base portion fixable to the rotor,the aerodynamic profile identified by a first substantially concave surface, which is pressurized, and a second substantially convex surface which is in depression and which is opposite to the first, said two surfaces being continuous and joined to each other to form the aerodynamic profile of said blade extending from a foot at said base portion to a free end of said blade distal from said base portion,said closed curves defined according to Table I, whose values, expressed in millimeters, refer to a profile at room temperature.
  • 15. The blade according to claim 14, wherein the aerodynamic profile of said blade has a tolerance of +/−2 mm in a normal direction with respect to the profile of the blade itself.
  • 16. A blade of a rotor of a compressor, which can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X, Y, Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, said blade having a profile which can be identified by means of a series of closed intersection curves between the profile itself and planes (X, Y) lying at distances (Z) from the central axis, said blade comprising said closed curves defined according to Table I, whose values, expressed in millimeters, refer to a profile at room temperature.
  • 17. The blade according to claim 16, wherein the profile of said blade has a tolerance of +/−2 mm in a normal direction with respect to the profile of the blade itself.
  • 18. The blade according to claim 16 wherein the values of the coordinates of Table I are multiplied by a corrective constant to obtain a scaled profile maintaining the same form.
  • 19. A rotor of a second stage of a compressor, the rotor comprising a series of blades according to claim 16.
  • 20. A blade of a rotor of a compressor, said blade having a profile which can be identified by a series of closed intersection curves between the profile itself and planes substantially perpendicular to a central axis of the blade, said blade comprising: a base portion fixable to the rotor; anda blade portion connected with a first end to the base portion and having a second end free standing, whereinthe aerodynamic profile is identified by a first substantially concave surface, and a second substantially convex surface which is opposite to the first concave surface, said two surfaces being continuous and joined to each other to form the aerodynamic profile of said blade extending from a foot at said base portion to the second end of said blade distal from said base portion,wherein each closed curve is substantially parallel to said base portion and has a maximum thickness determined by a maximum distance between said first surface and said second surface, said maximum thickness of each closed curve, along the height of the blade in the axial direction of the blade, having a non-linearly variable trend decreasing at a higher rate from said base portion to a first predetermined height, then at a lower rate from the first predetermined height to a second predetermined height, andthe second predetermined height being substantially half of the height of the blade.
Priority Claims (1)
Number Date Country Kind
MI2006A0340 Feb 2006 IT national
US Referenced Citations (24)
Number Name Date Kind
3012709 Schnell Dec 1961 A
3193185 Erwin et al. Jul 1965 A
3653110 King et al. Apr 1972 A
3692425 Erwin Sep 1972 A
3706512 Strelshik Dec 1972 A
4108573 Wagner Aug 1978 A
4116584 Bammert et al. Sep 1978 A
4128363 Fujikake et al. Dec 1978 A
4911612 Rodde et al. Mar 1990 A
4927331 Vuillet May 1990 A
5181678 Widnall et al. Jan 1993 A
5312696 Beers et al. May 1994 A
6129528 Bradbury et al. Oct 2000 A
6450770 Wang et al. Sep 2002 B1
6503053 Huebner Jan 2003 B2
6558122 Xu et al. May 2003 B1
6565324 Phillipsen et al. May 2003 B1
6685434 Humanchuk et al. Feb 2004 B1
6779977 Lagrange et al. Aug 2004 B2
6808368 Tomberg et al. Oct 2004 B1
6832897 Urban Dec 2004 B2
6881038 Beddard et al. Apr 2005 B1
7112043 Jarra Sep 2006 B2
20050047915 Jarrah Mar 2005 A1
Foreign Referenced Citations (1)
Number Date Country
0 732 505 Sep 1996 EP
Related Publications (1)
Number Date Country
20080044288 A1 Feb 2008 US