Second-stage turbine bucket airfoil

Abstract

The second-stage buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z. The X, Y and Z values may be scaled as a function of the same constant or number to provide a scaled-up or scaled-down airfoil section for the bucket.

Description

BACKGROUND OF THE INVENTION

The present invention relates to a turbine bucket for a gas turbine stage and particularly relates to a second-stage turbine bucket airfoil profile.

In recent years, advanced gas turbines have trended toward increasing firing temperatures and efforts to improve cooling of the various turbine components. In a particular gas turbine design of the assignee, a high output turbine that uses a combination of steam and air cooling to meet a 60% combined cycle efficiency is undergoing development. It will be appreciated that the design and construction of the turbine buckets and particularly the buckets of the second turbine stage of that turbine require optimized aerodynamic efficiency, as well as aerodynamic and mechanical bucket loading.

BRIEF SUMMARY OF THE INVENTION

In accordance with an embodiment of the present invention, there is provided a unique turbine bucket airfoil profile for a turbine stage, preferably the second stage, which may be defined by a unique loci of points to achieve the necessary efficiency in loading requirements whereby improved turbine performance is obtained. It will be appreciated that the nominal profile given by the X, Y, Z coordinates of Table I, which follows, define this unique loci of points. The coordinates given in inches in Table I are for a cold, i.e., room-temperature profile for each cross-section of the bucket. Each defined cross-section is joined smoothly with adjacent cross-sections to form the complete airfoil shape. It will also be appreciated that as the bucket heats up in use, the profile will change as a result of stress and temperature. Thus, the cold or room-temperature profile is given by the X, Y, Z coordinates for manufacturing purposes. Because a manufactured bucket airfoil profile may be different than the nominal airfoil profile given in the following table, a distance of ±0.160 inches from the nominal profile in a direction normal to any surface location along the nominal profile and which includes any coating process, defines the profile envelope for this design. The design is robust to this variation without impairment of the mechanical and aerodynamic functions.

It will also be appreciated that the airfoil can be scaled-up or scaled-down geometrically for introduction into other similar turbine designs. Consequently, the X, Y and Z coordinates of the nominal airfoil profile given below are a function of the same constant or number. That is, the X, Y and Z coordinate values given in the Table may be multiplied or divided by the same constant or number to provide a scaled-up or scaled-down version of the bucket airfoil profile, while retaining the airfoil section shape.

In a preferred embodiment according to the present invention, there is provided a turbine bucket having a bucket airfoil shape in an envelope within ±0.160 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

In a further preferred embodiment according to the present invention, there is provided a turbine bucket having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil bucket profile, the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine wheel having a plurality of buckets, each of the buckets having an airfoil shape in an envelope within ±0.160 inches in a direction normal to any bucket airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

In a further preferred embodiment according to the present invention, there is provided a turbine comprising a turbine wheel having a plurality of buckets, each of the buckets having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side elevational view of a turbine bucket including an airfoil, shank and dovetail constructed in accordance with a preferred embodiment of the present invention;

FIG. 2 is a view similar to FIG. 1 taken from the opposite side of the bucket;

FIG. 3 is a top, side and leading edge perspective view of the bucket hereof;

FIG. 4 is a top, side and trailing edge perspective view of the bucket hereof;

FIG. 5 is an axial view of the bucket hereof viewed from its leading edge;

FIG. 6 is an enlarged end view of the bucket as viewed radially inwardly;

FIG. 7 is a schematic illustration of a turbine having a second-stage turbine wheel employing the buckets hereof.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawing figures, particularly to FIGS. 1 and 2 , there is illustrated a turbine blade constructed in accordance with the present invention and including an airfoil 10 mounted on a platform 12 carried by a shank 14 . The radially inner end of the shank 14 carries a dovetail 16 for coupling the blade to a turbine wheel, not shown. The airfoil 10 , platform 12 and dovetail 16 are collectively referred to as a bucket, generally designated 17 . The airfoil 10 has a compound curvature with suction and pressure sides 18 and 20 , respectively. As conventional, it will be appreciated that the dovetail 16 mates in dovetail openings in a turbine wheel. A plurality of the present second-stage buckets, preferably fifty buckets, are circumferentially spaced one from the other about the wheel and turbine rotor axis. Additionally, there are wheelspace seals 22 , i.e., angel wings, formed on the axially forward and aft sides of shank 14 . Preferably, the bucket is integrally cast with cooling, preferably steam-cooling, passages, not shown, internal to the bucket including airfoil 10 .

Referring now to the drawing figures, there is shown a Cartesian coordinate system for X, Y and Z values. The coordinate values are set forth in inches in Table I which follows. The Cartesian coordinate system has orthogonally-related X, Y and Z axes with the Z axis extending perpendicular to a plane normal to a radius from the centerline of the turbine rotor, i.e., normal to a plane containing the X and Y values. The Z distance commences at zero in the X, Y plane at the radially innermost aerodynamic section. The X axis lies parallel to the turbine rotor centerline, i.e., the rotary axis. By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile of airfoil 10 can be ascertained. By connecting the X and Y values with smooth, continuing arcs, each profile section at each distance Z is fixed. The surface profiles at the various surface locations between the distances Z are connected smoothly to one another to form the airfoil. The tabular values given in Table I below are in inches and represent airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil. The sign convention assigns a positive value to the value Z and positive and negative values for the X and Y coordinate values, as typically used in a Cartesian coordinate system.

The Table I values are generated and shown to three decimal places for determining the profiles of the airfoil. Further, there are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Accordingly, the values for the profile given in Table I are for a nominal airfoil. It will therefore be appreciated that typical manufacturing tolerances, i.e., plus or minus values and coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of ±0.160 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular bucket design and turbine.

The coordinate values given in Table I below in inches provide the preferred nominal profile envelope.

TABLE I
X	Y	Z
20.086	0.709	0.000
20.474	1.437	0.000
20.121	0.594	0.000
21.223	1.830	0.000
20.348	0.514	0.000
20.591	0.491	0.000
20.879	1.707	0.000
20.713	0.481	0.000
20.835	0.471	0.000
20.667	1.586	0.000
21.106	1.797	0.000
20.956	0.458	0.000
21.198	0.421	0.000
20.385	1.352	0.000
20.771	1.650	0.000
20.229	0.538	0.000
20.087	0.830	0.000
20.229	1.164	0.000
20.568	1.514	0.000
20.470	0.501	0.000
20.303	1.262	0.000
20.990	1.756	0.000
20.166	1.060	0.000
21.077	0.441	0.000
20.116	0.949	0.000
21.709	1.868	0.000
22.184	1.763	0.000
21.586	1.872	0.000
21.669	0.294	0.000
21.830	1.854	0.000
21.950	1.832	0.000
22.325	−0.029	0.000
21.343	1.853	0.000
21.464	1.867	0.000
22.068	1.801	0.000
21.317	0.396	0.000
21.436	0.366	0.000
21.553	0.332	0.000
21.783	0.251	0.000
22.297	1.717	0.000
22.006	0.151	0.000
21.896	0.203	0.000
22.115	0.095	0.000
22.221	0.035	0.000
22.407	1.664	0.000
22.427	−0.096	0.000
22.527	−0.166	0.000
23.520	0.557	0.000
22.625	−0.240	0.000
22.720	−0.316	0.000
23.313	0.859	0.000
23.584	0.453	0.000
22.904	−0.477	0.000
22.617	1.539	0.000
22.993	−0.561	0.000
23.454	0.660	0.000
23.079	−0.647	0.000
23.078	1.140	0.000
23.238	0.955	0.000
23.247	−0.825	0.000
23.328	−0.917	0.000
23.159	1.049	0.000
22.813	−0.396	0.000
23.407	−1.010	0.000
22.812	1.392	0.000
22.993	1.228	0.000
23.560	−1.200	0.000
23.635	−1.296	0.000
23.385	0.760	0.000
22.904	1.312	0.000
23.164	−0.735	0.000
22.716	1.463	0.000
22.514	1.604	0.000
23.484	−1.104	0.000
24.725	−2.374	0.000
24.056	−1.896	0.000
24.198	−0.876	0.000
23.762	0.133	0.000
24.123	−1.998	0.000
24.684	−2.259	0.000
24.255	−2.204	0.000
24.483	−1.682	0.000
24.386	−2.410	0.000
24.321	−2.307	0.000
24.602	−2.029	0.000
24.451	−2.513	0.000
24.850	−2.718	0.000
23.971	−0.309	0.000
23.850	−1.593	0.000
24.516	−2.617	0.000
24.522	−1.798	0.000
24.562	−1.913	0.000
24.648	−2.823	0.000
24.282	−1.105	0.000
24.719	−2.921	0.000
24.443	−1.566	0.000
24.885	−2.835	0.000
24.832	−2.937	0.000
23.705	0.241	0.000
24.190	−2.101	0.000
24.323	−1.220	0.000
24.363	−1.336	0.000
24.066	−0.534	0.000
24.241	−0.990	0.000
24.808	−2.603	0.000
23.921	−0.197	0.000
24.582	−2.720	0.000
24.767	−2.489	0.000
24.111	−0.648	0.000
24.155	−0.762	0.000
23.708	−1.394	0.000
23.817	0.024	0.000
24.403	−1.451	0.000
24.019	−0.421	0.000
23.780	−1.493	0.000
23.920	−1.693	0.000
24.643	−2.144	0.000
23.646	0.347	0.000
23.870	−0.087	0.000
23.989	−1.794	0.000
21.149	0.561	0.500
20.134	0.824	0.500
20.915	1.814	0.500
20.424	0.662	0.500
20.700	1.699	0.500
20.667	0.637	0.500
20.504	1.554	0.500
21.030	0.586	0.500
20.332	1.381	0.500
20.196	1.179	0.500
20.189	0.722	0.500
20.128	0.946	0.500
20.599	1.630	0.500
20.304	0.681	0.500
20.414	1.471	0.500
20.805	1.761	0.500
20.788	0.623	0.500
20.546	0.649	0.500
20.258	1.284	0.500
20.909	0.607	0.500
20.150	1.066	0.500
21.029	1.859	0.500
21.146	1.894	0.500
21.268	0.531	0.500
21.385	0.496	0.500
21.727	0.365	0.500
21.614	0.414	0.500
21.837	0.313	0.500
22.154	0.130	0.500
22.050	0.194	0.500
22.326	1.729	0.500
22.354	−0.010	0.500
21.500	0.457	0.500
22.104	1.831	0.500
22.217	1.783	0.500
21.751	1.925	0.500
21.871	1.903	0.500
21.989	1.871	0.500
21.945	0.255	0.500
21.508	1.943	0.500
21.630	1.939	0.500
22.255	0.062	0.500
21.265	1.920	0.500
21.386	1.936	0.500
23.223	0.914	0.500
23.295	0.815	0.500
23.364	0.715	0.500
23.231	−0.856	0.500
23.071	1.105	0.500
23.148	1.011	0.500
23.533	−1.239	0.500
23.385	−1.045	0.500
22.729	−0.323	0.500
22.818	1.370	0.500
22.906	1.285	0.500
22.990	1.196	0.500
23.696	−1.338	0.500
22.904	−0.493	0.500
22.632	1.528	0.500
22.727	1.451	0.500
23.071	−0.671	0.500
22.432	1.668	0.500
22.534	1.601	0.500
23.309	−0.950	0.500
23.460	−1.142	0.500
22.638	−0.241	0.500
22.546	−0.161	0.500
23.555	0.402	0.500
23.614	0.295	0.500
22.817	−0.407	0.500
23.430	0.612	0.500
23.493	0.508	0.500
23.152	−0.763	0.500
22.988	−0.582	0.500
22.451	−0.084	0.500
24.660	−2.981	0.500
24.589	−2.882	0.500
24.150	−0.935	0.500
24.192	−1.050	0.500
24.233	−1.165	0.500
24.773	−2.998	0.500
24.209	−2.256	0.500
24.065	−0.706	0.500
24.108	−0.820	0.500
24.399	−2.569	0.500
24.525	−2.778	0.500
23.975	−0.479	0.500
24.021	−0.592	0.500
23.815	−1.638	0.500
23.746	−1.537	0.500
24.752	−2.665	0.500
24.793	−2.780	0.500
24.827	−2.897	0.500
23.928	−0.366	0.500
23.883	−1.740	0.500
24.670	−2.435	0.500
24.711	−2.550	0.500
23.779	−0.032	0.500
23.830	−0.143	0.500
24.080	−2.048	0.500
24.015	−1.945	0.500
24.549	−2.089	0.500
24.589	−2.204	0.500
24.629	−2.320	0.500
23.671	0.187	0.500
23.726	0.078	0.500
24.145	−2.152	0.500
23.677	−1.437	0.500
24.470	−1.858	0.500
24.509	−1.974	0.500
23.880	−0.254	0.500
24.336	−2.465	0.500
24.273	−2.360	0.500
24.352	−1.511	0.500
24.392	−1.627	0.500
24.431	−1.742	0.500
24.462	−2.674	0.500
23.949	−1.842	0.500
24.273	−1.280	0.500
24.313	−1.395	0.500
20.986	0.725	1.000
20.866	0.749	1.000
20.631	1.737	1.000
21.222	0.665	1.000
21.105	0.698	1.000
21.186	1.981	1.000
20.953	1.911	1.000
20.734	1.804	1.000
20.625	0.786	1.000
20.841	1.862	1.000
20.360	1.493	1.000
20.443	1.583	1.000
20.534	1.664	1.000
20.504	0.803	1.000
20.225	1.291	1.000
20.745	0.768	1.000
20.180	0.934	1.000
20.168	1.055	1.000
20.286	1.396	1.000
21.068	1.951	1.000
20.266	0.854	1.000
20.383	0.822	1.000
20.184	1.176	1.000
21.428	2.011	1.000
21.550	2.010	1.000
22.246	1.801	1.000
22.350	1.738	1.000
21.338	0.627	1.000
21.890	0.368	1.000
22.137	1.857	1 000
21.784	0.429	1.000
21.676	0.486	1.000
21.565	0.537	1.000
21.307	2.002	1.000
21.672	1.998	1.000
22.094	0.235	1.000
21.993	0.304	1.000
21.453	0.585	1.000
21.910	1.945	1.000
22.383	0.010	1.000
22.289	0.088	1.000
22.193	0.163	1.000
22.025	1.905	1.000
21.792	1.977	1.000
22.821	−0.414	1.000
22.737	−0.325	1.000
22.642	1.518	1.000
22.732	1.435	1.000
23.505	−1.273	1.000
23.062	−0.690	1.000
22.983	−0.597	1.000
22.903	−0.505	1.000
22.452	1.670	1.000
22.549	1.596	1.000
23.215	−0.880	1.000
23.139	−0.785	1.000
22.819	1.349	1.000
23.434	−1.174	1.000
23.362	−1.075	1.000
23.521	0.355	1.000
23.578	0.248	1.000
23.633	0.139	1.000
23.643	−1.475	1.000
23.401	0.568	1.000
23.462	0.462	1.000
23.203	0.876	1.000
23.272	0.775	1.000
23.337	0.672	1.000
22.652	−0.238	1.000
22.475	−0.070	1.000
23.059	1.073	1.000
23.132	0.976	1.000
23.574	−1.374	1.000
22.564	−0.153	1.000
22.902	1.260	1.000
22.982	1.168	1.000
23.289	−0.977	1.000
24.018	−0.758	1.000
24.060	−0.873	1.000
24.343	−2.620	1.000
24.282	−2.514	1.000
24.710	−3.053	1.000
24.693	−2.721	1.000
24.733	−2.836	1.000
24.766	−2.953	1.000
23.930	−0.531	1.000
23.974	−0.644	1.000
24.465	−2.831	1.000
24.404	−2.726	1.000
24.653	−2.605	1.000
24.159	−2.303	1.000
24.613	−2.490	1.000
23.788	−0.193	1.000
23.837	−0.305	1.000
23.884	−0.418	1.000
24.597	−3.036	1.000
24.527	−2.936	1.000
23.686	0.029	1.000
23.738	−0.082	1.000
24.534	−2.259	1.000
24.573	−2.374	1.000
24.097	−2.198	1.000
24.418	−1.912	1.000
24.456	−2.027	1.000
24.495	−2.143	1.000
24.035	−2.093	1.000
23.710	−1.576	1.000
23.907	−1.885	1.000
24.340	−1.680	1.000
24.379	−1.796	1.000
23.777	−1.679	1.000
24.263	−1.449	1.000
24.302	−1.564	1.000
23.971	−1.989	1.000
23.842	−1.782	1.000
24.183	−1.218	1.000
24.223	−1.333	1.000
24.221	−2.408	1.000
24.102	−0.988	1.000
24.143	−1.103	1.000
20.312	1.508	1.500
20.579	0.936	1.500
20.236	1.048	1.500
20.663	1.843	1.500
21.227	2.066	1.500
20.819	0.890	1.500
20.564	1.772	1.500
20.699	0.914	1.500
21.107	2.041	1.500
20.253	1.401	1.500
20.990	2.005	1.500
20.768	1.906	1.500
21.174	0.800	1.500
20.471	1.693	1.500
21.057	0.835	1.500
20.459	0.959	1.500
20.205	1.164	1.500
20.386	1.605	1.500
20.215	1.285	1.500
20.877	1.960	1.500
20.939	0.865	1.500
20.341	0.989	1.500
21.592	2.076	1.500
21.624	0.611	1.500
22.226	0.196	1.500
22.132	0.274	1.500
21.712	2.057	1.500
21.348	2.081	1.500
21.515	0.666	1.500
22.372	1.752	1.500
21.831	2.028	1.500
21.403	0.716	1.500
22.035	0.349	1.500
22.406	0.031	1.500
21.946	1.989	1.500
21.731	0.552	1.500
21.835	0.489	1.500
22.272	1.822	1.500
22.167	1.885	1.500
22.059	1.941	1.500
22.317	0.115	1.500
21.470	2.084	1.500
21.289	0.760	1.500
21.936	0.421	1.500
22.895	1.243	1.500
23.121	−0.801	1.500
22.741	−0.324	1.500
22.660	−0.232	1.500
23.471	−1.302	1.500
22.898	−0.511	1.500
23.538	−1.404	1.500
22.561	1.598	1.500
23.048	−0.703	1.500
23.604	−1.506	1.500
22.820	−0.417	1.500
23.193	−0.900	1.500
22.650	1.514	1.500
23.540	0.208	1.500
23.593	0.098	1.500
22.469	1.678	1.500
23.428	0.425	1.500
23.485	0.317	1.500
23.334	−1.099	1.500
22.974	−0.607	1.500
22.817	1.336	1.500
23.246	0.743	1.500
23.309	0.639	1.500
23.369	0.533	1.500
22.577	−0.143	1.500
23.264	−0.999	1.500
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23.226	−2.126	9.000
22.579	−0.488	9.000
22.970	−1.470	9.000
22.677	1.272	9.000
22.449	1.813	9.000
22.544	1.599	9.000
23.209	−0.406	9.000
22.876	0.720	9.000
23.183	−2.017	9.000
22.949	0.497	9.000
22.711	−0.815	9.000
22.927	−1.360	9.000
22.841	−1.142	9.000
22.490	−0.271	9.000
23.140	−1.908	9.000
22.838	0.831	9.000
22.634	1.382	9.000
22.798	−1.033	9.000
22.719	1.163	9.000
22.884	−1.251	9.000
22.623	−0.597	9.000
22.799	0.942	9.000
23.098	−1.798	9.000
23.148	−0.179	9.000
23.179	−0.292	9.000
22.497	1.706	9.000
22.913	0.609	9.000
22.760	1.053	9.000
23.052	0.160	9.000
23.084	0.047	9.000
22.754	−0.924	9.000
23.055	−1.689	9.000
22.667	−0.706	9.000
22.984	0.385	9.000
23.018	0.272	9.000
22.590	1.490	9.000
22.446	−0.162	9.000
23.606	−2.983	9.000
23.435	−1.318	9.000
23.462	−1.432	9.000
23.446	−2.670	9.000
23.489	−1.546	9.000
23.623	−2.118	9.000
23.408	−1.203	9.000
23.353	−0.975	9.000
23.381	−1.089	9.000
23.495	−2.777	9.000
23.325	−0.861	9.000
23.268	−0.633	9.000
23.297	−0.747	9.000
23.770	−2.807	9.000
23.785	−2.923	9.000
23.239	−0.519	9.000
23.701	−2.461	9.000
23.725	−2.576	9.000
23.400	−2.562	9.000
23.714	−3.009	9.000
23.649	−2.232	9.000
23.675	−2.347	9.000
23.546	−2.883	9.000
23.269	−2.236	9.000
23.570	−1.889	9.000
23.596	−2.003	9.000
23.312	−2.345	9.000
23.356	−2.454	9.000
23.749	−2.691	9.000
23.516	−1.660	9.000
23.543	−1.775	9.000
21.402	3.193	9.500
21.420	2.104	9.500
21.131	2.610	9.500
21.363	2.206	9.500
21.247	2.408	9.500
21.189	2.509	9.500
21.016	2.813	9.500
21.060	3.190	9.500
20.965	2.917	9.500
21.073	2.711	9.500
21.305	2.307	9.500
20.929	3.028	9.500
21.173	3.220	9.500
20.960	3.132	9.500
21.289	3.220	9.500
22.397	−0.009	9.500
22.353	0.099	9.500
21.585	1.796	9.500
22.117	2.453	9.500
21.792	1.379	9.500
21.694	3.006	9.500
21.925	2.744	9.500
21.842	1.274	9.500
21.940	1.062	9.500
21.988	0.956	9.500
21.531	1.899	9.500
22.219	0.422	9.500
21.476	2.002	9.500
21.777	2.924	9.500
21.993	2.650	9.500
22.339	2.043	9.500
22.082	0.743	9.500
22.056	2.552	9.500
21.638	1.692	9.500
22.035	0.850	9.500
22.309	0.207	9.500
21.508	3.145	9.500
22.232	2.250	9.500
22.390	1.938	9.500
21.854	2.836	9.500
22.174	0.529	9.500
22.286	2.147	9.500
21.690	1.588	9.500
22.128	0.636	9.500
22.264	0.314	9.500
22.176	2.352	9.500
21.741	1.484	9.500
21.891	1.168	9.500
21.605	3.081	9.500
22.746	1.078	9.500
22.440	−0.117	9.500
23.232	−2.183	9.500
22.931	0.526	9.500
22.484	−0.225	9.500
23.124	−0.146	9.500
22.578	1.512	9.500
22.785	0.968	9.500
22.612	−0.550	9.500
22.570	−0.442	9.500
22.860	0.748	9.500
23.027	−1.638	9.500
22.697	−0.767	9.500
22.655	−0.659	9.500
22.896	0.637	9.500
23.211	−0.484	9.500
22.966	0.415	9.500
22.822	−1.093	9.500
23.094	−0.033	9.500
23.154	−0.259	9.500
22.999	0.303	9.500
22.823	0.858	9.500
22.527	−0.333	9.500
22.863	−1.202	9.500
22.439	1.833	9.500
23.031	0.191	9.500
22.987	−1.529	9.500
22.946	−1.420	9.500
23.191	−2.075	9.500
22.487	1.727	9.500
22.622	1.405	9.500
22.739	−0.876	9.500
23.183	−0.371	9.500
22.533	1.620	9.500
22.665	1.296	9.500
23.109	−1.857	9.500
23.063	0.079	9.500
22.780	−0.985	9.500
23.068	−1.747	9.500
22.706	1.187	9.500
22.904	−1.311	9.500
23.150	−1.966	9.500
23.348	−1.050	9.500
23.556	−1.959	9.500
23.316	−2.401	9.500
23.607	−2.186	9.500
23.374	−1.164	9.500
23.679	−2.528	9.500
23.274	−2.292	9.500
23.531	−1.845	9.500
23.403	−2.617	9.500
23.359	−2.509	9.500
23.479	−1.618	9.500
23.656	−2.414	9.500
23.557	−2.929	9.500
23.499	−2.829	9.500
23.505	−1.731	9.500
23.721	−2.757	9.500
23.632	−2.300	9.500
23.453	−1.504	9.500
23.701	−2.642	9.500
23.294	−0.824	9.500
23.450	−2.723	9.500
23.321	−0.937	9.500
23.267	−0.710	9.500
23.427	−1.391	9.500
23.239	−0.597	9.500
23.582	−2.072	9.500
23.736	−2.872	9.500
23.400	−1.277	9.500
23.664	−2.956	9.500
21.400	2.246	10.000
21.216	3.269	10.000
21.078	2.859	10.000
21.331	3.268	10.000
21.105	3.238	10.000
21.030	2.964	10.000
21.442	3.237	10.000
21.346	2.348	10.000
21.238	2.552	10.000
21.292	2.450	10.000
21.130	2.756	10.000
21.005	3.181	10.000
20.991	3.073	10.000
21.184	2.654	10.000
21.951	1.101	10.000
22.133	0.677	10.000
21.937	2.764	10.000
21.997	0.995	10.000
22.230	2.267	10.000
21.636	3.113	10.000
21.453	2.143	10.000
22.177	0.570	10.000
22.333	2.061	10.000
22.088	0.783	10.000
22.043	0.889	10.000
22.282	2.164	10.000
21.797	2.948	10.000
22.000	2.668	10.000
21.558	1.937	10.000
22.351	0.142	10.000
21.610	1.834	10.000
21.710	1.626	10.000
21.720	3.034	10.000
21.856	1.312	10.000
21.506	2.040	10.000
22.175	2.369	10.000
21.660	1.730	10.000
22.393	0.035	10.000
21.760	1.522	10.000
22.265	0.356	10.000
21.543	3.183	10.000
22.061	2.570	10.000
21.904	1.207	10.000
22.383	1.956	10.000
22.308	0.249	10.000
22.119	2.470	10.000
22.221	0.463	10.000
21.808	1.417	10.000
21.869	2.858	10.000
23.073	−0.001	10.000
22.982	0.333	10.000
22.848	0.775	10.000
22.612	1.427	10.000
22.774	0.994	10.000
22.950	0.444	10.000
22.803	−1.045	10.000
23.130	−0.225	10.000
22.921	−1.371	10.000
23.238	−0.675	10.000
22.682	−0.721	10.000
22.655	1.319	10.000
23.101	−0.113	10.000
22.882	−1.262	10.000
22.917	0.555	10.000
23.211	−0.562	10.000
22.696	1.211	10.000
22.519	0.288	10.000
22.842	−1.154	10.000
22.479	1.746	10.000
22.961	−1.480	10.000
22.601	−0.504	10.000
22.723	−0.829	10.000
23.000	−1.588	10.000
23.039	−1.697	10.000
23.184	−0.450	10.000
23.078	−1.806	10.000
23.157	−0.338	10.000
23.117	−1.914	10.000
22.560	−0.396	10.000
23.236	−2.240	10.000
23.196	−2.131	10.000
22.525	1.640	10.000
22.763	−0.937	10.000
22.642	−0.612	10.000
23.043	0.110	10.000
23.013	0.222	10.000
22.735	1.103	10.000
22.811	0.885	10.000
22.569	1.534	10.000
22.883	0.665	10.000
23.157	−2.023	10.000
22.432	1.852	10.000
22.436	−0.073	10.000
22.477	−0.181	10.000
23.469	−1.688	10.000
23.452	−2.775	10.000
23.507	−2.876	10.000
23.342	−1.125	10.000
23.633	−2.479	10.000
23.673	−2.707	10.000
23.405	−2.670	10.000
23.318	−2.456	10.000
23.686	−2.821	10.000
23.290	−0.899	10.000
23.418	−1.462	10.000
23.361	−2.563	10.000
23.518	−1.914	10.000
23.613	−2.903	10.000
23.277	−2.348	10.000
23.264	−0.787	10.000
23.316	−1.012	10.000
23.654	−2.593	10.000
23.589	−2.253	10.000
23.542	−2.027	10.000
23.612	−2.366	10.000
23.393	−1.350	10.000
23.566	−2.140	10.000
23.367	−1.237	10.000
23.443	−1.575	10.000
23.493	−1.801	10.000
21.346	2.352	10.500
21.006	3.184	10.500
21.131	2.760	10.500
21.331	3.271	10.500
21.184	2.658	10.500
20.992	3.077	10.500
21.400	2.250	10.500
21.238	2.556	10.500
21.293	2.454	10.500
21.106	3.242	10.500
21.031	2.968	10.500
21.216	3.273	10.500
21.442	3.240	10.500
21.079	2.863	10.500
21.936	2.767	10.500
21.797	2.951	10.500
21.903	1.212	10.500
21.636	3.116	10.500
22.060	2.573	10.500
22.332	2.064	10.500
21.453	2.148	10.500
22.350	0.148	10.500
21.609	1.839	10.500
22.174	2.372	10.500
21.710	1.631	10.500
21.506	2.045	10.500
22.220	0.469	10.500
21.759	1.527	10.500
21.869	2.861	10.500
22.000	2.671	10.500
22.042	0.895	10.500
21.558	1.942	10.500
22.132	0.682	10.500
22.281	2.167	10.500
21.856	1.317	10.500
22.382	1.960	10.500
21.544	3.185	10.500
22.118	2.473	10.500
22.392	0.041	10.500
21.660	1.735	10.500
21.720	3.037	10.500
22.087	0.789	10.500
21.808	1.422	10.500
22.264	0.362	10.500
21.996	1.001	10.500
22.229	2.270	10.500
22.307	0.255	10.500
21.950	1.106	10.500
22.176	0.576	10.500
22.881	0.669	10.500
22.599	−0.498	10.500
23.099	−0.108	10.500
22.879	−1.256	10.500
22.680	−0.714	10.500
23.208	−0.557	10.500
23.232	−2.232	10.500
22.810	0.889	10.500
23.153	−2.015	10.500
22.846	0.779	10.500
23.035	−1.690	10.500
23.041	0.115	10.500
22.980	0.338	10.500
22.760	−0.930	10.500
22.523	1.644	10.500
22.918	−1.364	10.500
23.154	−0.332	10.500
22.720	−0.822	10.500
22.840	−1.147	10.500
22.568	1.537	10.500
22.476	−0.175	10.500
22.640	−0.606	10.500
23.127	−0.220	10.500
22.915	0.559	10.500
23.181	−0.445	10.500
23.011	0.227	10.500
22.800	−1.039	10.500
23.113	−1.907	10.500
22.611	1.430	10.500
22.517	−0.282	10.500
22.434	−0.067	10.500
23.234	−0.669	10.500
22.948	0.449	10.500
22.996	−1.581	10.500
23.074	−1.798	10.500
22.734	1.107	10.500
22.477	1.750	10.500
22.694	1.215	10.500
22.558	−0.390	10.500
23.192	−2.124	10.500
22.957	−1.473	10.500
23.070	0.004	10.500
22.430	1.855	10.500
22.653	1.323	10.500
22.772	0.998	10.500
23.355	−2.556	10.500
23.440	−1.569	10.500
23.680	−2.814	10.500
23.561	−2.133	10.500
23.464	−1.682	10.500
23.607	−2.359	10.500
23.414	−1.456	10.500
23.272	−2.340	10.500
23.489	−1.794	10.500
23.260	−0.782	10.500
23.446	−2.768	10.500
23.286	−0.894	10.500
23.607	−2.896	10.500
23.364	−1.231	10.500
23.538	−2.020	10.500
23.313	−2.448	10.500
23.513	−1.907	10.500
23.338	−1.119	10.500
23.584	−2.246	10.500
23.501	−2.868	10.500
23.312	−1.006	10.500
23.648	−2.586	10.500
23.668	−2.700	10.500
23.389	−1.344	10.500
23.400	−2.662	10.500
23.628	−2.473	10.500
21.7589	1.5287	10.874
21.9359	2.7692	10.874
21.5437	3.1875	10.874
21.0059	3.1865	10.874
21.2925	2.4564	10.874
21.1842	2.6602	10.874
21.4533	2.1499	10.874
21.7097	1.6331	10.874
21.9996	2.673	10.874
21.6357	3.118	10.874
21.1057	3.2439	10.874
21.1305	2.7623	10.874
21.4	2.2522	10.874
21.6598	1.7371	10.874
22.0602	2.5748	10.874
21.7197	3.0389	10.874
21.2164	3.275	10.874
21.0789	2.8655	10.874
21.3464	2.3544	10.874
21.6093	1.8409	10.874
22.1183	2.4751	10.874
21.797	2.9533	10.874
21.3314	3.2733	10.874
21.031	2.9705	10.874
21.558	1.9442	10.874
22.1743	2.3742	10.874
21.8686	2.8629	10.874
21.4421	3.2419	10.874
20.992	3.0789	10.874
21.2384	2.5583	10.874
21.506	2.0472	10.874
22.8812	0.6717	10.874
22.2203	0.4713	10.874
22.6941	1.2174	10.874
22.434	−0.0646	10.874
22.4772	1.7519	10.874
22.2285	2.2723	10.874
21.9962	1.0029	10.874
21.9498	1.1085	10.874
22.9153	0.5615	10.874
22.1764	0.578	10.874
22.7338′	1.109	10.874
22.3919	0.0429	10.874
22.523	1.646	10.874
22.5992	−0.4956	10.874
22.281	2.1696	10.874
21.903	1.214	10.874
22.9482	0.4509	10.874
22.1321	0.6845	10.874
22.7724	1.0003	10.874
22.3496	0.1502	10.874
22.5676	1.5396	10.874
22.5583	−0.3877	10.874
22.332	2.0661	10.874
21.8555	1.3192	10.874
22.0872	0.7908	10.874
22.8098	0.8911	10.874
22.3069	0.2574	10.874
22.611	1.4326	10.874
22.5171	−0.2799	10.874
22.3817	1.9619	10.874
21.8075	1.4241	10.874
22.0419	0.897	10.874
22.8461	0.7816	10.874
22.2638	0.3644	10.874
22.6531	1.3252	10.874
22.4757	−0.1722	10.874
22.4301	1.8572	10.874
23.1311	−0.4422	10.874
23.041	0.1174	10.874
22.6398	−0.6036	10.874
22.8395	−1.1448	10.874
23.0352	−1.6875	10.874
23.3379	−1.1165	10.874
23.2078	−0.5545	10.874
23.0702	0.0058	10.874
22.8	−1.0364	10.874
22.9962	−1.5789	10.874
23.1922	−2.1215	10.874
23.3635	−1.2291	10.874
23.2342	−0.6668	10.874
23.0987	−0.106	10.874
22.7603	−0.9281	10.874
22.9572	−1.4703	10.874
23.1527	−2.0131	10.874
23.389	−1.3416	10.874
23.2604	−0.7792	10.874
23.1267	−0.218	10.874
22.9801	0.34	10.874
22.7203	−0.8195	10.874
22.9181	−1.3618	10.874
23.1133	−1.9047	10.874
23.4143	−1.4542	10.874
23.2864	−0.8916	10.874
23.1541	−0.3301	10.874
23.011	−0.2288	10.874
22.6802	−0.7116	10.874
22.8789	−1.2532	10.874
23.0742	−1.7961	10.874
23.4395	−1.5668	10.874
23.3122	−1.0041	10.874
23.6795	−2.8119	10.874
23.232	−2.2298	10.874
23.5843	−2.2437	10.874
23.4459	−2.7655	10.874
23.313	−2.4459	10.874
23.6068	−2.3569	10.874
23.3996	−2.6598	10.874
23.4891	−1.7921	10.874
23.607	−2.8936	10.874
23.6282	−2.4703	10.874
23.3554	−2.5532	10.874
23.5134	−1.9049	10.874
23.6483	−2.5839	10.874
23.5375	−2.0178	10.874
23.4644	−1.6794	10.874
23.6679	−2.6976	10.874
23.2721	−2.338	10.874
23.5611	−2.1307	10.874
23.5014	−2.8661	10.874

It will also be appreciated that the airfoil disclosed in the above Table may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil section shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values multiplied or divided by the same constant or number.

Referring now to FIG. 7 , there is illustrated a turbine in which the turbine bucket having the airfoil defined herein may be utilized. In the illustrated turbine, the turbine rotor, designated 40 , has first, second, third and fourth-stage rotor wheels 42 , 44 , 46 and 48 , respectively, mounting buckets which, in conjunction with respective stator vanes 41 , 43 , 45 and 47 , form the various stages of the rotor. Particularly, the second stage comprises a second-stage rotor wheel 44 on which the airfoils 10 hereof are mounted in opposition to second-stage stator vanes 43 . It will be appreciated that a plurality of the airfoils 10 are spaced circumferentially one from the other about the second-stage wheel 44 and, in this instance, there are fifty buckets mounted on the second-stage wheel 44 .

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A turbine bucket having a bucket airfoil shape in an envelope within ±0.160 inches in a direction normal to any airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

2. A turbine bucket according to claim 1 forming part of a second stage of a turbine.

3. A turbine bucket having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil bucket profile;the X, Y and Z values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

4. A turbine bucket according to claim 3 forming part of a second stage of a turbine.

5. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets having an airfoil shape in an envelope within ±0.160 inches in a direction normal to any bucket airfoil surface location wherein the airfoil has an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at a radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape.

6. A turbine according to claim 5 wherein the turbine wheel comprises a second stage of the turbine.

7. A turbine according to claim 5 wherein the turbine wheel has fifty buckets and X represents a distance parallel to a rotary axis of the turbine wheel.

8. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form the complete airfoil shape;the X and Y values being scaled as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.

9. A turbine according to claim 8 wherein the turbine wheel comprises a second stage of the turbine.

10. A turbine according to claim 8 wherein the turbine wheel has fifty buckets and X represents a distance parallel to a rotary axis of the turbine wheel.