# Patent

## Title
Transition duct for gas turbine engine

## Abstract

A transition duct having an inlet opening and an outlet opening and a body portion extending between the inlet and outlet openings at respective inlet and outlet ends. The inlet opening defines a generally circular cross-section for the body portion and has a geometric center, and the outlet opening defines a generally rectangular arc-like cross-section. The body portion has an internal profile substantially in accordance with coordinate values X, Y and Z at an angle θ, as set forth in Table 1, where each of the X, Y and Z coordinate values are taken at a sweep angle θ passing through the section origin and measured from a first plane defined by the inlet end and increasing toward a second plane defined by the outlet end.

## Background
FIELD OF THE INVENTION
The present invention relates to a transition duct for a gas turbine engine and, more particularly, to a transition duct design having a longer structural life and an improved aero performance.
BACKGROUND OF THE INVENTION
Generally, combustion turbines have three main assemblies, including a compressor assembly, a combustor assembly, and a turbine assembly. In operation, the compressor assembly compresses ambient air. The compressed air is channeled into the combustor assembly where it is mixed with a fuel. The fuel and compressed air mixture is ignited creating a heated working gas. The heated working gas is typically at a temperature of between 2300 to 2900° F. (1200 to 1593° C.), and is expanded through the turbine assembly. The turbine assembly generally includes a rotating assembly comprising a centrally located rotating shaft and a plurality of rows of rotating blades attached thereto. A plurality of stationary vane assemblies, each including a plurality of stationary vanes, are connected to a casing of the turbine and are located interposed between the rows of rotating blades. The expansion of the working gas through the rows of rotating blades and stationary vanes or airfoils in the turbine assembly results in a transfer of energy from the working gas to the rotating assembly, causing rotation of the shaft.
The combustor assembly typically includes a plurality of combustors arranged in an annular array about the engine. The hot working gas from each combustor is transferred to the turbine by a respective transition duct. The outlet of the combustor is generally cylindrical, and the inlet to the turbine at the exit to each transition duct generally corresponds to an arcuate sector. Accordingly, the cross-sectional shape of the transition duct must change from a generally cylindrical shape at the combustor exit to a generally rectangular arc-like shape at the turbine inlet. In addition, since the combustors are typically mounted at a radial outward location relative to the turbine inlet, the transition ducts must define a gas path extending radially inwardly in the direction of the gas flow to the turbine.
The combination of complex geometry changes as well as extreme mechanical and thermal loading seen by the transition duct create a harsh operating environment that can lead to premature deterioration, requiring repair and replacement of the transition duct. In particular, as higher firing temperatures are utilized, increased transition duct failures may occur due to low cycle fatigue (LCF) cracks that may be observed at an upper panel of the transition. Accordingly, extreme care must be taken with respect to the design of these geometric transitions to avoid sharp geometric changes that may create regions of high stress, i.e., stress concentration points.
SUMMARY OF THE INVENTION
The present invention provides a transition duct having a geometric profile that is preferably optimized to reduce high stress concentrations from LCF. The present transition duct also has an improved structural dynamic response that effectively increases the separation of the transition frequency response from the combustion resonant frequencies, while also maintaining a desired aero efficiency in transferring hot working gas from the combustor to the turbine inlet.
In accordance with one aspect of the invention, a transition duct is provided having an inlet opening and an outlet opening and a body portion extending between the inlet and outlet openings at respective inlet and outlet ends. The inlet opening defines a generally circular cross-section for the body portion and has a geometric center. The body portion has an internal profile substantially in accordance with coordinate values X, Y and Z at sections defined by a respective angle θ, as set forth in Table 1, where each of the X, Y and Z coordinates are taken at a sweep angle θ passing through the section origin and measured from a first plane defined by the inlet end and increasing toward a second plane defined by the outlet end. The first plane and the section planes intersect at an angle origin line about which the angle θ is measured. The X and Y coordinate values are determined relative to a section origin at a substantially central geometric location within each respective section. The Z coordinate values are measured along a Z-axis extending perpendicular to the first plane, and having an origin at the center of the generally circular inlet opening and increasing toward the outlet end.
In accordance with another aspect of the invention, a transition duct is provided having an inlet opening and an outlet opening and a body portion extending between the inlet and outlet openings at respective inlet and outlet ends. The inlet opening defines a generally circular cross-section for the body portion and has a geometric center. The body portion has an internal profile including first, second, third and fourth profile sections located approximately at angles θ of 1.0°, 10.0°, 21.0° and 30.0°, respectively, taken at a sweep angle θ passing through the section origin and measured from a first plane defined by the inlet end and increasing toward a second plane defined by the outlet end. The first plane and the section planes intersect at an angle origin line about which the angle θ is measured, where each section defines a Cartesian X Y coordinate origin with corresponding quadrants determined relative to the section origin at a substantially central geometric location within each respective section, wherein the first section comprises a generally circular cross-section; the second section comprises a first side extending from the third quadrant to the second quadrant, a second side extending from the fourth quadrant to the first quadrant, an outer side extending between the first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between the third and fourth quadrants and curved concave inwardly toward the coordinate origin, the first and second sides extending in diverging relation from the inner side toward the outer side; the third section comprises a first substantially linear side extending from the third quadrant to the second quadrant, a second substantially linear side extending from the fourth quadrant to the first quadrant, an outer side extending between the first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between the third and fourth quadrants and curved concave inwardly toward the coordinate origin, the first and second sides extending in diverging relation from the inner side toward the outer side; and the fourth section comprises a first substantially linear side extending from the third quadrant to the second quadrant, a second substantially linear side extending from the fourth quadrant to the first quadrant, an outer side extending between the first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between the third and fourth quadrants and curved concave outwardly away from the coordinate origin, the first and second sides extending in diverging relation from the inner side toward the outer side.
In accordance with a further aspect of the invention, a transition duct is provided having an inlet opening and an outlet opening and a body portion extending between the inlet and outlet openings at respective inlet and outlet ends. The inlet opening defines a generally circular cross-section for the body portion and has a geometric center. The body portion has an internal profile including first, second, third and fourth profile sections substantially in accordance with coordinate values X, Y and Z located at angles θ of 1.0°, 10.0°, 21.0° and 30.0°, as set forth in Table 1, where each of the X, Y and Z coordinates are taken at a sweep angle θ passing through the section origin and measured from a first plane defined by the inlet end and increasing toward a second plane defined by the outlet end. The first plane and the section planes intersect at an angle origin line about which the angle θ is measured. The X and Y coordinate values are determined relative to a section origin at a substantially central geometric location within each respective section. The Z coordinate values are measured along a Z-axis extending perpendicular to the first plane, and having an origin at the center of the generally circular inlet opening and increasing toward the outlet end.



BRIEF DESCRIPTION OF THE DRAWINGS
While the specification concludes with claims particularly pointing out and distinctly claiming the present invention, it is believed that the present invention will be better understood from the following description in conjunction with the accompanying Drawing Figures, in which like reference numerals identify like elements, and wherein:
FIG. 1 is side elevation view of a portion of a gas turbine engine including a transition duct extending from a combustor to the entrance to a turbine section;
FIG. 2 is a cross-section view illustrating the coordinate system used to define the profile of the transition duct;
FIG. 3 is section view taken through the transition duct along section lines A-A in FIG. 2;
FIG. 4 is section view taken through the transition duct along section lines B-B in FIG. 2;
FIG. 5 is section view taken through the transition duct along section lines C-C in FIG. 2;
FIG. 6 is section view taken through the transition duct along section lines D-D in FIG. 2; and
FIG. 7 is a perspective view illustrating each of the section planes used to define the transition profile of the present invention.



DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, the present invention comprises a profile defining the interior surface of a transition duct 10. The transition duct 10 provides a conduit for conveying hot combustion gases from a combustor 12 for a gas turbine engine to the entrance 14 of a turbine assembly where the gases are directed toward a first row of vanes 16. An inlet ring 18 of generally circular cross-section may be provided at an inlet end 20 of the transition duct 10, supported by an inlet support 22. An outlet end 24 of the transition duct 10 may include an aft frame 26 having a generally rectangular arc-like shape. As is described further below, the transition duct 10 has a geometric profile that transitions from a generally circular cross-section, substantially corresponding to the shape of the outlet from the combustor 12, to a generally rectangular arc-like cross-section at the turbine entrance 14 (see also FIG. 7), while also defining a radially inwardly extending path for the gas flow.
The transition duct 10 may be formed by any known manufacturing process, and may comprise a body formed of an upper panel 28 and a lower panel 30 joined along longitudinally extending seams 32 (one illustrated) at longitudinal welds to form a panel assembly, as is known in the art. The upper and lower panels 28, 30 may also be provided with cooling holes in a manner known in the art. In addition, the upper and lower panels 28, 30 may be formed of a high temperature material such as a high temperature metal alloy including, without limitation, IN617 (Inconel 617) or H230 (Haynes 230). It should be noted that the transition duct 10 is not limited to any particular construction, and the invention encompasses any transition duct 10 that utilizes the profile described further below.
The interior surface of the body formed by the panels 28, 30 may preferably be provided with a coating to protect the interior of the transition duct 10 from deterioration, such as may be caused by prolonged exposure to the hot combustion gases traveling from the combustor 12. The coating may comprise a known coating material, such as is described in U.S. Pat. No. 6,644,032, incorporated herein by reference, or any other coating having similar protective properties. In addition, the coating is preferably a thin coating layer that will not substantially affect the beneficial profile characteristics provided by the present invention.
The profile of the transition duct 10 is described herein with reference to the uncoated surface profile of the interior surface of the body defined by the upper and lower panels 28, 30. Referring to FIG. 2, the profile of the transition duct 10 is described with reference to an angle θ to identify a location of a discrete section 34 (FIG. 7), i.e., a transverse cross-section, of the transition duct 10. In particular, each section 34 defines an origin located substantially at a geometric center of the section 34, as is illustrated for example by section origins O′, OA, OB, OC and OD in FIGS. 2-6. The angle θ identifying a particular discrete section 34 is a sweep angle measured between a first plane 36 defined by a section 34 at the inlet end 20 and a plane passing through the origin of the particular discrete section 34. The first plane 36 and the planes defined by the sections 34 intersect at an angle origin line 38 about which the angle θ is measured, where the line 38 is a distance D approximately 1223 mm from the section origin O′ at the inlet end 20. The value of the sweep angle θ increases from the first plane 36 toward a second plane 40 defined by the outlet end 24, where the total sweep angle of the illustrated transition duct 10 is approximately 31.07°.
Coordinate values X, Y and Z are provided to identify points on the transition duct 10 for each discrete section 34 at specified angles θ substantially in accordance with the X, Y and Z coordinate values as set forth in Table 1 below. The values given in Table 1 are in millimeters. However, it should be understood that the present invention is not limited to particular dimensions, in that the X, Y and Z values given in Table 1 could be scaled up or down, i.e., may represent unitless scaled values, depending on the diameter of the particular combustion liner with which the transition duct 10 of the present invention is intended to be used.
Further, it should be noted that the coordinate values given in Table 1 correspond to coordinates on the transition duct 10 when at room temperature, and that the given coordinate values will not necessarily correspond to the location of particular points on the transition duct 10 when the transition duct 10 is at an elevated temperature during transfer of hot combustion gases.
The X and Y coordinate values are determined with reference to respective X and Y axes having a zero point or origin of a Cartesian coordinate system at the origin of the particular section 34 located substantially at the geometric center within each respective section 34 (see FIGS. 3-6). The Z coordinate values are measured along a Z-axis extending perpendicular to the first plane 36, and having an origin at the center of the section 34 defined at the generally circular inlet opening of the inlet end 20, and the Z values increase in the direction extending toward the outlet end 40. The data in Table 1 corresponds to 1 degree increments of the angle θ, provided to define an optimized internal profile for the transition duct 10,
It should be apparent that although the X, Y and Z coordinate values given in Table 1 provide discrete sections 34 comprising wireframe sections for defining the transition profile, the entire profile is defined by a best-fit curve to the given sections to define a smoothly continuous internal flow path formed by the interior surface of the transition duct 10. Further it may be noted that the data provided in Table 1 is computer generated and that limited deviations from this data may occur, within manufacturing tolerances, during production of the transition duct 10.
Referring to FIGS. 3-6 first, second, third and fourth sections 34A, 34B, 34C and 34D depict the transition of the internal profile from the generally circular first cross-section 34A of FIG. 3, taken at θ=1°, to the generally rectangular arc-like fourth cross-section 34D of FIG. 6, taken at θ=30°. Each section may define a Cartesian X Y coordinate origin, as depicted by the section origins OA, OB, OC and OD, with corresponding quadrants I, II, III and IV determined relative each respective section origin. The quadrants are numbered sequentially in accordance with a conventional Cartesian coordinate system, starting in the upper right-hand quadrant and proceeding counterclockwise.
The second section 34B of FIG. 4 is taken at θ=10° and comprises a first side 42B extending from the third quadrant to the second quadrant, and a second side 44B extending from the fourth quadrant to the first quadrant. An outer side 46B extends between the first and second quadrants and curves concave inwardly toward the coordinate origin OB, and an inner side 48B extends between the third and fourth quadrants and curves concave inwardly toward the coordinate origin OB. The first and second sides 42B, 44B extend in diverging relation from the inner side 48B toward the outer side 46B.
The third section 34C of FIG. 5 is taken at θ=21′ and defines a generally expanded rectangular cross-section comprising a first substantially linear side 42C extending from the third quadrant to the second quadrant, and a second substantially linear side 44C extending from the fourth quadrant to the first quadrant. An outer side 46C extends between the first and second quadrants and curves concave inwardly toward the coordinate origin OC, and an inner side 48C extends between the third and fourth quadrants and curves concave inwardly toward the coordinate origin OC, where the outer and inner sides 46C, 48C have substantially less curvature than the outer and inner sides 46B, 48B of the second section 34B. The first and second sides 42C, 44C extend in diverging relation from the inner side 48C toward the outer side 46C.
The fourth section 34D of FIG. 6 comprises a first substantially linear side 42D extending from the third quadrant to the second quadrant, and a second substantially linear side 44D extending from the fourth quadrant to the first quadrant. An outer side 46D extends between the first and second quadrants and curves concave inwardly toward the coordinate origin OD, and an inner side 48D extends between the third and fourth quadrants and curves concave outwardly away from the coordinate origin OD, where the outer and inner sides 46D, 48D have substantially less curvature than the outer and inner sides 46D, 48D of the third section 34C. The first and second sides 42D, 44D extend in diverging relation from the inner side 48D toward the outer side 46D.
As an alternative embodiment to the invention the internal profile may be provided within an envelope of the profile given by the coordinate values of Table 1. By way of example and without limitation, the internal profile described herein may be provided within an envelope of ±6.350 mm normal to any surface with the X, Y and Z coordinate values and the angles θ noted in Table 1.
The transition duct 10 described herein provides a preferred transition duct internal profile for transitioning from a generally circular inlet to a generally rectangular arc-like outlet while minimizing stress concentrations and providing frequency separation between the natural frequency of the transition duct 10 and the combustion resonant frequencies, resulting in a reduced likelihood of low cycle fatigue cracks.
The X, Y and Z coordinate values, determined by the above-described Cartesian coordinated system, identified at corresponding sweep angles θ are summarized in the following Table 1.












TABLE 1







θ
X
Y
Z





















1.0
0.000
174.094
18.310



1.0
27.361
171.930
18.348



1.0
54.047
165.510
18.460



1.0
79.411
155.021
18.643



1.0
102.856
140.749
18.892



1.0
123.849
123.068
19.200



1.0
141.929
102.418
19.561



1.0
156.693
79.282
19.965



1.0
167.221
53.951
20.407



1.0
172.981
27.122
20.875



1.0
174.705
−0.271
21.353



1.0
172.481
−27.629
21.831



1.0
166.351
−54.383
22.298



1.0
156.392
−79.957
22.744



1.0
142.206
−103.440
23.154



1.0
124.128
−124.084
23.515



1.0
103.029
−141.638
23.821



1.0
79.494
−155.761
24.067



1.0
54.074
−166.115
24.248



1.0
27.365
−172.441
24.359



1.0
0.000
−174.571
24.396



1.0
−27.365
−172.441
24.359



1.0
−54.074
−166.115
24.248



1.0
−79.494
−155.761
24.067



1.0
−103.029
−141.638
23.821



1.0
−124.128
−124.084
23.515



1.0
−142.206
−103.440
23.154



1.0
−156.392
−79.957
22.744



1.0
−166.351
−54.383
22.298



1.0
−172.481
−27.629
21.831



1.0
−174.705
−0.271
21.353



1.0
−172.981
27.122
20.875



1.0
−167.221
53.951
20.407



1.0
−156.693
79.282
19.965



1.0
−141.929
102.418
19.561



1.0
−123.849
123.068
19.200



1.0
−102.856
140.749
18.892



1.0
−79.411
155.021
18.643



1.0
−54.047
165.510
18.460



1.0
−27.361
171.930
18.348



2.0
0.000
172.882
36.673



2.0
27.425
170.707
36.749



2.0
54.172
164.267
36.974



2.0
79.605
153.780
37.340



2.0
103.155
139.561
37.837



2.0
124.329
122.002
38.450



2.0
142.717
101.544
39.164



2.0
157.939
78.639
39.964



2.0
168.504
53.281
40.850



2.0
173.677
26.280
41.793



2.0
175.011
−1.190
42.752



2.0
172.708
−28.597
43.709



2.0
166.805
−55.460
44.647



2.0
157.321
−81.274
45.548



2.0
143.277
−104.895
46.373



2.0
124.908
−125.350
47.088



2.0
103.514
−142.641
47.691



2.0
79.778
−156.547
48.177



2.0
54.227
−166.748
48.533



2.0
27.432
−172.989
48.751



2.0
0.000
−175.094
48.825



2.0
−27.433
−172.989
48.751



2.0
−54.228
−166.748
48.533



2.0
−79.779
−156.547
48.177



2.0
−103.515
−142.640
47.691



2.0
−124.908
−125.349
47.088



2.0
−143.278
−104.894
46.373



2.0
−157.321
−81.274
45.548



2.0
−166.805
−55.459
44.647



2.0
−172.708
−28.597
43.709



2.0
−175.011
−1.190
42.752



2.0
−173.677
26.281
41.793



2.0
−168.504
53.281
40.850



2.0
−157.939
78.639
39.964



2.0
−142.717
101.545
39.164



2.0
−124.329
122.002
38.450



2.0
−103.154
139.561
37.837



2.0
−79.605
153.780
37.340



2.0
−54.172
164.267
36.974



2.0
−27.425
170.707
36.749



3.0
0.000
170.905
55.141



3.0
27.478
168.722
55.256



3.0
54.277
162.274
55.594



3.0
79.774
151.808
56.142



3.0
103.427
137.665
56.883



3.0
124.785
120.255
57.796



3.0
143.484
100.021
58.856



3.0
159.159
77.375
60.043



3.0
169.755
52.007
61.372



3.0
174.377
24.875
62.794



3.0
175.350
−2.646
64.237



3.0
172.969
−30.082
65.675



3.0
167.263
−57.025
67.087



3.0
158.221
−83.037
68.450



3.0
144.337
−106.783
69.694



3.0
125.685
−127.030
70.755



3.0
103.987
−144.013
71.645



3.0
80.044
−157.662
72.361



3.0
54.364
−167.676
72.886



3.0
27.488
−173.809
73.207



3.0
−0.001
−175.880
73.315



3.0
−27.491
−173.809
73.207



3.0
−54.366
−167.676
72.885



3.0
−80.046
−157.661
72.361



3.0
−103.988
−144.012
71.645



3.0
−125.687
−127.029
70.755



3.0
−144.338
−106.782
69.694



3.0
−158.222
−83.036
68.450



3.0
−167.263
−57.024
67.086



3.0
−172.969
−30.081
65.674



3.0
−175.350
−2.645
64.237



3.0
−174.377
24.876
62.794



3.0
−169.755
52.008
61.372



3.0
−159.158
77.376
60.043



3.0
−143.484
100.022
58.856



3.0
−124.785
120.255
57.796



3.0
−103.427
137.665
56.883



3.0
−79.774
151.808
56.142



3.0
−54.277
162.275
55.594



3.0
−27.478
168.722
55.256



4.0
0.000
168.192
73.764



4.0
27.518
166.005
73.917



4.0
54.359
159.563
74.367



4.0
79.914
149.138
75.096



4.0
103.668
135.097
76.078



4.0
125.210
117.866
77.283



4.0
144.222
97.888
78.680



4.0
160.345
75.533
80.243



4.0
170.973
50.178
82.016



4.0
175.077
22.952
83.920



4.0
175.712
−4.593
85.846



4.0
173.252
−32.037
87.765



4.0
167.719
−59.031
89.653



4.0
159.088
−85.199
91.483



4.0
145.377
−109.054
93.151



4.0
126.454
−129.070
94.550



4.0
104.440
−145.696
95.713



4.0
80.288
−159.044
96.646



4.0
54.480
−168.836
97.331



4.0
27.533
−174.836
97.751



4.0
−0.001
−176.864
97.892



4.0
−27.536
−174.836
97.751



4.0
−54.483
−168.835
97.331



4.0
−80.290
−159.043
96.646



4.0
−104.442
−145.695
95.713



4.0
−126.455
−129.068
94.550



4.0
−145.378
−109.052
93.150



4.0
−159.088
−85.198
91.482



4.0
−167.720
−59.029
89.653



4.0
−173.252
−32.035
87.765



4.0
−175.712
−4.592
85.846



4.0
−175.077
22.953
83.920



4.0
−170.972
50.179
82.016



4.0
−160.345
75.534
80.243



4.0
−144.222
97.888
78.680



4.0
−125.209
117.866
77.283



4.0
−103.667
135.098
76.078



4.0
−79.913
149.138
75.096



4.0
−54.359
159.563
74.367



4.0
−27.518
166.005
73.917



5.0
0.000
164.766
92.589



5.0
27.545
162.582
92.780



5.0
54.416
156.161
93.342



5.0
80.020
145.800
94.248



5.0
103.871
131.890
95.465



5.0
125.598
114.869
96.954



5.0
144.925
95.182
98.677



5.0
161.493
73.152
100.604



5.0
172.156
47.836
102.819



5.0
175.772
20.554
105.206



5.0
176.088
−6.987
107.615



5.0
173.547
−34.413
110.015



5.0
168.167
−61.430
112.378



5.0
159.916
−87.715
114.678



5.0
146.389
−111.656
116.773



5.0
127.203
−131.416
118.501



5.0
104.866
−147.631
119.920



5.0
80.503
−160.632
121.058



5.0
54.573
−170.163
121.891



5.0
27.564
−176.005
122.402



5.0
−0.001
−177.981
122.575



5.0
−27.567
−176.004
122.402



5.0
−54.575
−170.162
121.891



5.0
−80.505
−160.631
121.057



5.0
−104.868
−147.630
119.920



5.0
−127.205
−131.414
118.501



5.0
−146.390
−111.654
116.773



5.0
−159.917
−87.713
114.678



5.0
−168.168
−61.428
112.378



5.0
−173.547
−34.412
110.015



5.0
−176.088
−6.986
107.615



5.0
−175.772
20.556
105.206



5.0
−172.156
47.837
102.819



5.0
−161.492
73.152
100.604



5.0
−144.925
95.183
98.677



5.0
−125.598
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531.489



24.0
−49.684
32.112
530.245



24.0
−24.873
33.833
529.479



25.0
0.000
31.869
555.462



25.0
24.723
31.378
555.692



25.0
49.401
29.927
556.368



25.0
73.992
27.561
557.472



25.0
98.463
24.330
558.978



25.0
122.788
20.289
560.862



25.0
146.945
15.494
563.098



25.0
170.717
9.463
565.910



25.0
185.258
−7.751
573.938



25.0
182.974
−29.915
584.273



25.0
178.609
−51.977
594.560



25.0
174.081
−74.012
604.835



25.0
169.370
−96.015
615.096



25.0
164.015
−117.876
625.290



25.0
147.790
−134.125
632.867



25.0
123.618
−136.921
634.170



25.0
98.904
−136.087
633.782



25.0
74.182
−135.480
633.498



25.0
49.455
−135.073
633.309



25.0
24.725
−134.846
633.203



25.0
−0.006
−134.775
633.170



25.0
−24.736
−134.846
633.203



25.0
−49.465
−135.073
633.309



25.0
−74.191
−135.480
633.499



25.0
−98.913
−136.088
633.782



25.0
−123.626
−136.921
634.170



25.0
−147.797
−134.122
632.865



25.0
−164.018
−117.870
625.287



25.0
−169.372
−96.009
615.093



25.0
−174.082
−74.006
604.833



25.0
−178.610
−51.972
594.558



25.0
−182.975
−29.910
584.271



25.0
−185.257
−7.747
573.936



25.0
−170.714
9.465
565.910



25.0
−146.942
15.495
563.098



25.0
−122.785
20.290
560.862



25.0
−98.461
24.330
558.978



25.0
−73.990
27.561
557.471



25.0
−49.399
29.927
556.368



25.0
−24.723
31.378
555.692



26.0
0.000
30.974
581.420



26.0
24.601
30.561
581.621



26.0
49.169
29.340
582.217



26.0
73.674
27.339
583.193



26.0
98.088
24.590
584.534



26.0
122.391
21.128
586.223



26.0
146.562
16.989
588.241



26.0
170.428
11.744
590.799



26.0
185.392
−4.833
598.884



26.0
183.102
−26.680
609.540



26.0
178.611
−48.425
620.146



26.0
174.006
−70.150
630.742



26.0
169.273
−91.854
641.327



26.0
163.837
−113.395
651.834



26.0
147.117
−128.900
659.396



26.0
122.932
−130.717
660.282



26.0
98.375
−129.314
659.598



26.0
73.797
−128.255
659.082



26.0
49.203
−127.521
658.724



26.0
24.601
−127.094
658.515



26.0
−0.005
−126.955
658.447



26.0
−24.610
−127.094
658.515



26.0
−49.212
−127.522
658.724



26.0
−73.804
−128.256
659.082



26.0
−98.382
−129.314
659.598



26.0
−122.939
−130.718
660.283



26.0
−147.123
−128.898
659.395



26.0
−163.839
−113.390
651.831



26.0
−169.274
−91.849
641.325



26.0
−174.007
−70.146
630.740



26.0
−178.612
−48.421
620.144



26.0
−183.103
−26.676
609.538



26.0
−185.392
−4.830
598.883



26.0
−170.425
11.745
590.799



26.0
−146.559
16.990
588.241



26.0
−122.389
21.128
586.222



26.0
−98.087
24.590
584.534



26.0
−73.672
27.339
583.193



26.0
−49.168
29.340
582.217



26.0
−24.601
30.561
581.621



27.0
0.000
32.123
606.814



27.0
24.511
31.774
606.992



27.0
48.997
30.737
607.520



27.0
73.436
29.028
608.391



27.0
97.807
26.666
609.594



27.0
122.090
23.672
611.120



27.0
146.267
20.066
612.957



27.0
170.199
15.459
615.304



27.0
185.508
−0.566
623.470



27.0
183.223
−22.125
634.454



27.0
178.628
−43.580
645.387



27.0
173.960
−65.024
656.313



27.0
169.208
−86.453
667.231



27.0
163.697
−107.700
678.057



27.0
146.563
−122.551
685.624



27.0
122.391
−123.558
686.137



27.0
97.967
−121.678
685.180



27.0
73.506
−120.240
684.447



27.0
49.017
−119.228
683.931



27.0
24.512
−118.630
683.626



27.0
−0.002
−118.433
683.526



27.0
−24.516
−118.630
683.626



27.0
−49.021
−119.228
683.931



27.0
−73.509
−120.240
684.447



27.0
−97.970
−121.679
685.180



27.0
−122.394
−123.558
686.137



27.0
−146.566
−122.550
685.624



27.0
−163.698
−107.698
678.056



27.0
−169.209
−86.451
667.230



27.0
−173.960
−65.022
656.312



27.0
−178.628
−43.579
645.386



27.0
−183.224
−22.123
634.454



27.0
−185.508
−0.565
623.469



27.0
−170.197
15.460
615.304



27.0
−146.266
20.066
612.957



27.0
−122.089
23.672
611.120



27.0
−97.806
26.666
609.594



27.0
−73.436
29.028
608.391



27.0
−48.997
30.737
607.520



27.0
−24.511
31.774
606.992



28.0
0.000
35.676
631.344



28.0
24.452
35.375
631.505



28.0
48.886
34.474
631.983



28.0
73.282
32.984
632.776



28.0
97.624
30.913
633.877



28.0
121.895
28.270
635.282



28.0
146.080
25.067
636.985



28.0
170.056
20.942
639.179



28.0
185.611
5.354
647.467



28.0
183.327
−15.943
658.791



28.0
178.652
−37.138
670.060



28.0
173.935
−58.325
681.326



28.0
169.171
−79.505
692.587



28.0
163.597
−100.486
703.743



28.0
146.142
−114.796
711.352



28.0
121.990
−115.172
711.552



28.0
97.668
−112.919
710.354



28.0
73.293
−111.180
709.429



28.0
48.878
−109.947
708.773



28.0
24.437
−109.212
708.383



28.0
−0.016
−108.968
708.253



28.0
−24.468
−109.212
708.383



28.0
−48.907
−109.948
708.774



28.0
−73.321
−111.182
709.430



28.0
−97.695
−112.921
710.355



28.0
−122.014
−115.175
711.553



28.0
−146.164
−114.789
711.348



28.0
−163.606
−100.469
703.734



28.0
−169.175
−79.488
692.578



28.0
−173.939
−58.310
681.317



28.0
−178.655
−37.124
670.053



28.0
−183.329
−15.930
658.784



28.0
−185.608
5.366
647.461



28.0
−170.045
20.945
639.177



28.0
−146.070
25.069
636.984



28.0
−121.887
28.271
635.282



28.0
−97.618
30.913
633.877



28.0
−73.277
32.984
632.776



28.0
−48.883
34.475
631.983



28.0
−24.451
35.375
631.505



29.0
0.000
41.945
654.704



29.0
24.421
41.675
654.854



29.0
48.827
40.866
655.302



29.0
73.202
39.521
656.047



29.0
97.531
37.644
657.088



29.0
121.799
35.239
658.421



29.0
145.991
32.309
660.045



29.0
169.999
28.508
662.152



29.0
185.699
13.242
670.614



29.0
183.407
−7.818
682.288



29.0
178.678
−28.776
693.905



29.0
173.930
−49.730
705.520



29.0
169.160
−70.680
717.133



29.0
163.554
−91.425
728.632



29.0
145.896
−105.340
736.345



29.0
121.762
−105.295
736.320



29.0
97.509
−102.781
734.927



29.0
73.187
−100.831
733.846



29.0
48.816
−99.440
733.075



29.0
24.411
−98.608
732.614



29.0
−0.010
−98.331
732.460



29.0
−24.430
−98.609
732.614



29.0
−48.834
−99.441
733.076



29.0
−73.204
−100.832
733.846



29.0
−97.525
−102.783
734.928



29.0
−121.777
−105.296
736.321



29.0
−145.909
−105.336
736.343



29.0
−163.560
−91.414
728.626



29.0
−169.162
−70.670
717.127



29.0
−173.932
−49.720
705.515



29.0
−178.680
−28.767
693.900



29.0
−183.408
−7.811
682.284



29.0
−185.697
13.249
670.610



29.0
−169.992
28.510
662.151



29.0
−145.985
32.310
660.045



29.0
−121.794
35.240
658.421



29.0
−97.527
37.645
657.088



29.0
−73.199
39.522
656.047



29.0
−48.825
40.866
655.302



29.0
−24.420
41.675
654.854



30.0
0.000
51.170
676.592



30.0
24.441
50.916
676.739



30.0
48.868
50.153
677.179



30.0
73.267
48.882
677.913



30.0
97.623
47.105
678.939



30.0
121.923
44.821
680.258



30.0
146.153
42.034
681.867



30.0
170.198
38.368
683.983



30.0
185.821
23.186
692.749



30.0
183.411
2.319
704.797



30.0
178.648
−18.444
716.784



30.0
173.880
−39.206
728.771



30.0
169.107
−59.967
740.757



30.0
163.421
−80.501
752.612



30.0
145.485
−94.016
760.415



30.0
121.318
−93.624
760.189



30.0
97.066
−90.982
758.664



30.0
72.739
−88.929
757.479



30.0
48.355
−87.466
756.634



30.0
23.933
−86.592
756.129



30.0
−0.506
−86.309
755.966



30.0
−24.895
−86.616
756.143



30.0
−49.265
−87.510
756.659



30.0
−73.597
−88.992
757.515



30.0
−97.872
−91.061
758.709



30.0
−122.070
−93.716
760.242



30.0
−146.158
−93.822
760.303



30.0
−163.699
−79.984
752.314



30.0
−169.225
−59.451
740.459



30.0
−173.989
−38.733
728.498



30.0
−178.747
−18.014
716.536



30.0
−183.500
2.706
704.573



30.0
−185.722
23.526
692.552



30.0
−169.864
38.473
683.923



30.0
−145.852
42.071
681.845



30.0
−121.672
44.848
680.242



30.0
−97.421
47.122
678.930



30.0
−73.115
48.892
677.908



30.0
−48.767
50.157
677.177



30.0
−24.390
50.917
676.738



31.0
0.000
63.034
697.015



31.0
24.425
62.785
697.165



31.0
48.837
62.037
697.614



31.0
73.220
60.790
698.363



31.0
97.563
59.046
699.411



31.0
121.849
56.806
700.757



31.0
146.067
54.071
702.401



31.0
170.107
50.489
704.553



31.0
185.821
35.549
713.530



31.0
183.473
14.911
725.930



31.0
178.704
−5.624
738.269



31.0
173.938
−26.160
750.609



31.0
169.175
−46.697
762.948



31.0
163.588
−67.034
775.168



31.0
145.851
−80.583
783.309



31.0
121.716
−80.306
783.143



31.0
97.488
−77.647
781.545



31.0
73.181
−75.576
780.300



31.0
48.815
−74.095
779.411



31.0
24.410
−73.207
778.877



31.0
−0.014
−72.911
778.699



31.0
−24.437
−73.208
778.877



31.0
−48.840
−74.097
779.412



31.0
−73.205
−75.578
780.301



31.0
−97.510
−77.649
781.546



31.0
−121.738
−80.309
783.144



31.0
−145.870
−80.577
783.306



31.0
−163.596
−67.019
775.159



31.0
−169.178
−46.683
762.940



31.0
−173.941
−26.147
750.601



31.0
−178.706
−5.612
738.262



31.0
−183.475
14.922
725.924



31.0
−185.819
35.559
713.524



31.0
−170.098
50.492
704.551



31.0
−146.059
54.072
702.400



31.0
−121.842
56.807
700.757



31.0
−97.557
59.047
699.411



31.0
−73.216
60.790
698.363



31.0
−48.834
62.037
697.614



31.0
−24.424
62.785
697.165










While particular embodiments of the present invention have been illustrated and described, it would be obvious to those skilled in the art that various other changes and modifications can be made without departing from the spirit and scope of the invention. It is therefore intended to cover in the appended claims all such changes and modifications that are within the scope of this invention.

## Claims

1. A transition duct having an inlet opening and an outlet opening and a body portion extending between said inlet and outlet openings at respective inlet and outlet ends, said inlet opening defining a generally circular cross-section for said body portion and having a geometric center, said body portion having an internal profile substantially in accordance with coordinate values X, Y and Z at sections defined by a respective angle θ, as set forth in Table 1, where each of said X, Y and Z coordinates are taken at a sweep angle θ passing through said section origin and measured from a first plane defined by said inlet end and increasing toward a second plane defined by said outlet end, said first plane and said section planes intersecting at an angle origin line about which said angle θ is measured, said X and Y coordinate values are determined relative to a section origin at a substantially central geometric location within each respective section, and said Z coordinate values are measured along a Z-axis extending perpendicular to said first plane, and having an origin at the center of said generally circular inlet opening and increasing toward said outlet end.

2. The transition duct of claim 1, wherein said internal profile may be provided within an envelope of ±6.350 mm normal to any surface with said coordinate values X, Y and Z and said angles θ.

3. The transition duct of claim 1, wherein the distance between said angle origin line about which said angle θ is measured and said inlet origin at the center of said generally circular inlet opening is approximately 1223 mm.

4. The transition duct of claim 1, wherein said coordinates X, Y and Z represent unitless scaled values.

5. A transition duct having an inlet opening and an outlet opening and a body portion extending between said inlet and outlet openings at respective inlet and outlet ends, said inlet opening defining a generally circular cross-section for said body portion and having a geometric center, said body portion having an internal profile including first, second, third and fourth profile sections defining respective geometric centers comprising section origins, said first, second, third and fourth profile sections located approximately at angles Θ of 1.0°, 10.0°, 21.0° and 30.0°, respectively, taken at a sweep angle Θ passing through a respective one of said section origins and measured from a first plane defined by said inlet end and increasing toward a second plane defined by said outlet end, said first plane and said section planes intersecting at an angle origin line about which said angle Θ is measured, each said section defining a Cartesian X Y coordinate origin located at said geometric center within each said section with corresponding quadrants determined relative to a respective section origin within each respective section, each said section defining quadrants extending from said Cartesian X Y coordinate origin for each section, said quadrants for each section comprising:
a first quadrant corresponding to positive X and positive Y values relative to the Cartesian X Y coordinate origin;
a second quadrant corresponding to negative X and positive Y values relative to the Cartesian X Y coordinate origin;
a third quadrant corresponding to negative X and negative Y values relative to the Cartesian X Y coordinate origin; and
a fourth quadrant corresponding to positive X and negative Y values relative to the Cartesian X Y coordinate origin;
wherein said first section comprises a generally circular cross-section; said second section comprises a first side extending from the third quadrant to the second quadrant, a second side extending from the fourth quadrant to the first quadrant, an outer side extending between said first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between said third and fourth quadrants and curved concave inwardly toward the coordinate origin, said first and second sides extending in diverging relation from said inner side toward said outer side;
said third section comprises a first substantially linear side extending from the third quadrant to the second quadrant, a second substantially linear side extending from the fourth quadrant to the first quadrant, at least one of the first and second substantially linear sides having a linear portion, an outer side extending between said first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between said third and fourth quadrants and curved concave inwardly toward the coordinate origin, said first and second sides extending in diverging relation from said inner side toward said outer side; and
said fourth section comprises a first substantially linear side extending from the third quadrant to the second quadrant, a second substantially linear side extending from the fourth quadrant to the first quadrant, an outer side extending between said first and second quadrants and curved concave inwardly toward the coordinate origin, an inner side extending between said third and fourth quadrants and curved concave outwardly away from the coordinate origin, said first and second sides extending in diverging relation from said inner toward said outer side.

6. The transition duct of claim 5, wherein said second profile section is substantially in accordance with coordinate values X, Y and Z as follows:
















θ
X
Y
Z





















10.0
0.000
137.813
191.359



10.0
27.411
135.748
191.723



10.0
54.217
129.733
192.783



10.0
79.932
120.143
194.474



10.0
104.216
107.434
196.715



10.0
126.863
92.065
199.425



10.0
147.770
74.463
202.529



10.0
166.512
54.675
206.018



10.0
177.490
30.042
210.362



10.0
178.983
3.031
215.124



10.0
177.868
−24.041
219.898



10.0
174.883
−50.974
224.647



10.0
170.025
−77.642
229.349



10.0
163.264
−103.904
233.980



10.0
150.655
−127.815
238.196



10.0
130.213
−145.740
241.357



10.0
106.213
−158.965
243.689



10.0
80.849
−169.438
245.535



10.0
54.457
−177.055
246.878



10.0
27.363
−181.705
247.698



10.0
−0.092
−183.273
247.975



10.0
−27.537
−181.685
247.695



10.0
−54.619
−177.018
246.872



10.0
−80.997
−169.386
245.526



10.0
−106.346
−158.902
243.677



10.0
−130.330
−145.666
241.344



10.0
−150.734
−127.715
238.178



10.0
−163.298
−103.791
233.960



10.0
−170.049
−77.535
229.330



10.0
−174.898
−50.875
224.630



10.0
−177.875
−23.950
219.882



10.0
−178.983
3.113
215.110



10.0
−177.475
30.114
210.349



10.0
−166.474
54.727
206.009



10.0
−147.729
74.500
202.522



10.0
−126.826
92.093
199.420



10.0
−104.184
107.453
196.712



10.0
−79.906
120.154
194.472



10.0
−54.199
129.738
192.783



10.0
−27.401
135.750
191.723









where said X and Y coordinate values are determined relative to said Cartesian X Y origin, and said Z coordinate values are measured along a Z-axis extending perpendicular to said first plane, and having an origin at the center of said generally circular inlet opening and increasing toward said outlet end.

7. The transition duct of claim 6, wherein said internal profile may be provided within an envelope of ±6.350 mm normal to any surface with said coordinate values X, Y and Z.

8. The transition duct of claim 6, wherein said coordinates X, Y and Z represent unitless scaled values.

9. The transition duct of claim 5, wherein said third profile section is substantially in accordance with coordinate values X, Y and Z as follows:
















θ
X
Y
Z





















21.0
0.000
49.344
450.548



21.0
25.439
48.416
450.904



21.0
50.731
45.704
451.946



21.0
75.759
41.344
453.619



21.0
100.439
35.502
455.861



21.0
124.720
28.351
458.606



21.0
148.584
20.062
461.788



21.0
171.580
10.011
465.647



21.0
184.387
−9.886
473.285



21.0
182.474
−33.498
482.348



21.0
178.774
−57.018
491.377



21.0
174.619
−80.473
500.380



21.0
169.984
−103.848
509.353



21.0
164.741
−127.108
518.282



21.0
150.617
−146.420
525.695



21.0
126.933
−154.035
528.618



21.0
101.586
−156.315
529.493



21.0
76.196
−158.126
530.188



21.0
50.772
−159.453
530.698



21.0
25.323
−160.273
531.013



21.0
−0.139
−160.554
531.120



21.0
−25.587
−160.267
531.010



21.0
−51.022
−159.442
530.694



21.0
−76.432
−158.111
530.183



21.0
−101.808
−156.297
529.487



21.0
−127.140
−154.015
528.610



21.0
−150.771
−146.309
525.652



21.0
−164.791
−126.946
518.220



21.0
−170.016
−103.695
509.294



21.0
−174.646
−80.332
500.326



21.0
−178.796
−56.890
491.328



21.0
−182.491
−33.382
482.304



21.0
−184.369
−9.784
473.245



21.0
−171.502
10.066
465.626



21.0
−148.507
20.091
461.777



21.0
−124.655
28.373
458.598



21.0
−100.385
35.517
455.856



21.0
−75.718
41.353
453.616



21.0
−50.704
45.707
451.944



21.0
−25.425
48.417
450.904









where said X and Y coordinate values are determined relative to said Cartesian X Y origin, and said Z coordinate values are measured along a Z-axis extending perpendicular to said first plane, and having an origin at the center of said generally circular inlet opening and increasing toward said outlet end.

10. The transition duct of claim 9, wherein said internal profile may be provided within an envelope of ±6.350 mm normal to any surface with said coordinate values X, Y and Z.

11. The transition duct of claim 9, wherein said coordinates X, Y and Z represent unitless scaled values.

12. A transition duct having an inlet opening and an outlet opening and a body portion extending between said inlet and outlet openings at respective inlet and outlet ends, said inlet opening defining a generally circular cross-section for said body portion and having a geometric center, said body portion having an internal profile including first, second, third and fourth profile sections substantially in accordance with coordinate values X, Y and Z located at angles θ of 1.0°, 10.0°, 21.0° and 30.0°, respectively, as follows:
















θ
X
Y
Z





















1.0
0.000
174.094
18.310



1.0
27.361
171.930
18.348



1.0
54.047
165.510
18.460



1.0
79.411
155.021
18.643



1.0
102.856
140.749
18.892



1.0
123.849
123.068
19.200



1.0
141.929
102.418
19.561



1.0
156.693
79.282
19.965



1.0
167.221
53.951
20.407



1.0
172.981
27.122
20.875



1.0
174.705
−0.271
21.353



1.0
172.481
−27.629
21.831



1.0
166.351
−54.383
22.298



1.0
156.392
−79.957
22.744



1.0
142.206
−103.440
23.154



1.0
124.128
−124.084
23.515



1.0
103.029
−141.638
23.821



1.0
79.494
−155.761
24.067



1.0
54.074
−166.115
24.248



1.0
27.365
−172.441
24.359



1.0
0.000
−174.571
24.396



1.0
−27.365
−172.441
24.359



1.0
−54.074
−166.115
24.248



1.0
−79.494
−155.761
24.067



1.0
−103.029
−141.638
23.821



1.0
−124.128
−124.084
23.515



1.0
−142.206
−103.440
23.154



1.0
−156.392
−79.957
22.744



1.0
−166.351
−54.383
22.298



1.0
−172.481
−27.629
21.831



1.0
−174.705
−0.271
21.353



1.0
−172.981
27.122
20.875



1.0
−167.221
53.951
20.407



1.0
−156.693
79.282
19.965



1.0
−141.929
102.418
19.561



1.0
−123.849
123.068
19.200



1.0
−102.856
140.749
18.892



1.0
−79.411
155.021
18.643



1.0
−54.047
165.510
18.460



1.0
−27.361
171.930
18.348



10.0
0.000
137.813
191.359



10.0
27.411
135.748
191.723



10.0
54.217
129.733
192.783



10.0
79.932
120.143
194.474



10.0
104.216
107.434
196.715



10.0
126.863
92.065
199.425



10.0
147.770
74.463
202.529



10.0
166.512
54.675
206.018



10.0
177.490
30.042
210.362



10.0
178.983
3.031
215.124



10.0
177.868
−24.041
219.898



10.0
174.883
−50.974
224.647



10.0
170.025
−77.642
229.349



10.0
163.264
−103.904
233.980



10.0
150.655
−127.815
238.196



10.0
130.213
−145.740
241.357



10.0
106.213
−158.965
243.689



10.0
80.849
−169.438
245.535



10.0
54.457
−177.055
246.878



10.0
27.363
−181.705
247.698



10.0
−0.092
−183.273
247.975



10.0
−27.537
−181.685
247.695



10.0
−54.619
−177.018
246.872



10.0
−80.997
−169.386
245.526



10.0
−106.346
−158.902
243.677



10.0
−130.330
−145.666
241.344



10.0
−150.734
−127.715
238.178



10.0
−163.298
−103.791
233.960



10.0
−170.049
−77.535
229.330



10.0
−174.898
−50.875
224.630



10.0
−177.875
−23.950
219.882



10.0
−178.983
3.113
215.110



10.0
−177.475
30.114
210.349



10.0
−166.474
54.727
206.009



10.0
−147.729
74.500
202.522



10.0
−126.826
92.093
199.420



10.0
−104.184
107.453
196.712



10.0
−79.906
120.154
194.472



10.0
−54.199
129.738
192.783



10.0
−27.401
135.750
191.723



21.0
0.000
49.344
450.548



21.0
25.439
48.416
450.904



21.0
50.731
45.704
451.946



21.0
75.759
41.344
453.619



21.0
100.439
35.502
455.861



21.0
124.720
28.351
458.606



21.0
148.584
20.062
461.788



21.0
171.580
10.011
465.647



21.0
184.387
−9.886
473.285



21.0
182.474
−33.498
482.348



21.0
178.774
−57.018
491.377



21.0
174.619
−80.473
500.380



21.0
169.984
−103.848
509.353



21.0
164.741
−127.108
518.282



21.0
150.617
−146.420
525.695



21.0
126.933
−154.035
528.618



21.0
101.586
−156.315
529.493



21.0
76.196
−158.126
530.188



21.0
50.772
−159.453
530.698



21.0
25.323
−160.273
531.013



21.0
−0.139
−160.554
531.120



21.0
−25.587
−160.267
531.010



21.0
−51.022
−159.442
530.694



21.0
−76.432
−158.111
530.183



21.0
−101.808
−156.297
529.487



21.0
−127.140
−154.015
528.610



21.0
−150.771
−146.309
525.652



21.0
−164.791
−126.946
518.220



21.0
−170.016
−103.695
509.294



21.0
−174.646
−80.332
500.326



21.0
−178.796
−56.890
491.328



21.0
−182.491
−33.382
482.304



21.0
−184.369
−9.784
473.245



21.0
−171.502
10.066
465.626



21.0
−148.507
20.091
461.777



21.0
−124.655
28.373
458.598



21.0
−100.385
35.517
455.856



21.0
−75.718
41.353
453.616



21.0
−50.704
45.707
451.944



21.0
−25.425
48.417
450.904



30.0
0.000
51.170
676.592



30.0
24.441
50.916
676.739



30.0
48.868
50.153
677.179



30.0
73.267
48.882
677.913



30.0
97.623
47.105
678.939



30.0
121.923
44.821
680.258



30.0
146.153
42.034
681.867



30.0
170.198
38.368
683.983



30.0
185.821
23.186
692.749



30.0
183.411
2.319
704.797



30.0
178.648
−18.444
716.784



30.0
173.880
−39.206
728.771



30.0
169.107
−59.967
740.757



30.0
163.421
−80.501
752.612



30.0
145.485
−94.016
760.415



30.0
121.318
−93.624
760.189



30.0
97.066
−90.982
758.664



30.0
72.739
−88.929
757.479



30.0
48.355
−87.466
756.634



30.0
23.933
−86.592
756.129



30.0
−0.506
−86.309
755.966



30.0
−24.895
−86.616
756.143



30.0
−49.265
−87.510
756.659



30.0
−73.597
−88.992
757.515



30.0
−97.872
−91.061
758.709



30.0
−122.070
−93.716
760.242



30.0
−146.158
−93.822
760.303



30.0
−163.699
−79.984
752.314



30.0
−169.225
−59.451
740.459



30.0
−173.989
−38.733
728.498



30.0
−178.747
−18.014
716.536



30.0
−183.500
2.706
704.573



30.0
−185.722
23.526
692.552



30.0
−169.864
38.473
683.923



30.0
−145.852
42.071
681.845



30.0
−121.672
44.848
680.242



30.0
−97.421
47.122
678.930



30.0
−73.115
48.892
677.908



30.0
−48.767
50.157
677.177



30.0
−24.390
50.917
676.738









where each of said X, Y and Z coordinates are taken at a sweep angle θ passing through said section origin and measured from a first plane defined by said inlet end and increasing toward a second plane defined by said outlet end, said first plane and said section planes intersecting at an angle origin line about which said angle θ is measured, said X and Y coordinate values are determined relative to the section origin at a substantially central geometric location within each respective section, and said Z coordinate values are measured along a Z-axis extending perpendicular to said first plane, and having an origin at the center of said generally circular inlet opening and increasing toward said outlet end.

13. The transition duct of claim 12, wherein said internal profile may be provided within an envelope of ±6.350 mm normal to any surface with said coordinate values X, Y and Z and said angles θ.

14. The transition duct of claim 12, wherein the distance between said angle origin line about which said angle θ is measured and said inlet origin at the center of said generally circular inlet opening is approximately 1223 mm.

15. The transition duct of claim 12, wherein said coordinates X, Y and Z represent unitless scaled values.

16. The transition duct of claim 5, wherein said outer side of said third section comprises less curvature along a length of said outer side between said first and second sides of said third section than a curvature of said outer side of said second section.

17. The transition duct of claim 16, wherein said inner side of said third section comprises less curvature along a length of said inner side between said first and second sides of said third section than a curvature of said inner side of said second section.

18. The transition duct of claim 5, wherein said inner and outer sides of said third section are joined to said first and second sides of said third section at respective corners, each of said corners defining a radius that is less than a radius of each of said sides of said third section to define said third section as an expanded rectangle.