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 Table I wherein X, Y and Z values are in inches. Z represents a distance in inches from and perpendicular to a plane passing through the engine centerline. X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form the complete airfoil shape. The X and Y distances and optionally the Z distance may be scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil section for the bucket. The nominal airfoil given by the X, Y and Z distances lies within an envelop of ±0.016 inches.

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.

There are many considerations in the design and construction of turbine buckets, particularly their airfoils, including optimized aerodynamic efficiency and aerodynamic and mechanical bucket loading. Additionally, bucket airfoil design must also take into consideration the potential mismatch or engagement problems associated with bucket airfoils having tip shrouds. As will be appreciated, certain buckets in turbines are provided with bucket tip shrouds which circumferentially engage one another along leading and trailing edges in a circumferential direction. Typically, the shrouds mount a seal which cooperates with a fixed shroud to seal against hot gas bypass between high and lower pressure regions on opposite sides of the bucket airfoils. The shrouds are also provided on long and slender buckets to add stiffness to the bucket airfoils by the engagement of the shrouds with one another. However, with air-cooled buckets, differential thermal growth and twisting sometimes affords poor engagement of the shrouds with one another. That is, one edge of the shroud may be radially inwardly of the opposing edge of the adjacent shroud. Absent an ideal engagement between adjacent shrouds, adverse loading causes higher stress at points of contact. With loss or minimization of contact, the benefit of damping vibrations to avoid high cycle fatigue by using shrouds is minimized or lost. Less than optimum tip shroud engagement adversely impacts tip shroud creep life and reduces part life. It will also be appreciated that the failure of a single bucket including its airfoil causes the entire turbine to be taken offline. These are time-consuming and expensive repairs which include the cost of the outage to the user of the turbine.

BRIEF DESCRIPTION OF THE INVENTION

In accordance with a preferred embodiment of the present invention, there is provided a unique turbine bucket airfoil profile, preferably for air-cooled tip shrouded airfoils of the second stage of a gas turbine. The bucket airfoil profile yields substantially improved shroud-to-shroud engagement enabling significant increased part life and reduced repair costs. Additionally, the airfoil reduces local creep and affords improved HCF margin in the resulting airfoil. The bucket airfoil profile is defined by a unique loci of points to achieve the necessary efficiency, loading and tip shroud engagement requirements. These unique loci of points define the nominal airfoil profile ranging from 10-90% span of the airfoil height and are identified by the X, Y and Z Cartesian coordinates of Table I which follows. The points for the coordinate values shown in Table I are for a cold, i.e., room temperature profile at various cross-sections of the bucket airfoil within the 10-90% span of the airfoil height. The X, Y and Z coordinates are given in distance dimensions, e.g., units of inches. The X and Y coordinate values are joined smoothly with one another at each Z location to form smooth continuous arcuate airfoil profile sections. The Z coordinates are distances from and perpendicular to a plane passing through a turbine axis of rotation. Each defined airfoil profile section at each Z distance is joined smoothly with adjacent airfoil profile sections to form the complete airfoil shape.

It will be appreciated that as each bucket airfoil 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 and Z coordinates for manufacturing purposes. Because a manufactured bucket airfoil profile may be different from the nominal airfoil profile given by the following table, a distance of plus or minus 0.016 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 bucket airfoil. 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 similar turbine designs. Consequently, the X and Y coordinates in inches of the nominal airfoil profile given below are a function of the same constant or number. That is, the X and Y, and optionally the Z, coordinate values in inches 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 including a bucket airfoil having an airfoil shape, the airfoil having nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distance 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 including a bucket airfoil having an airfoil shape, the airfoil having an uncoated nominal airfoil profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant 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 including a bucket airfoil having an airfoil shape, the airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine axis and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections 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 including a bucket airfoil having an airfoil shape, the airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant to provide a scaled-up or scaled-down bucket airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a generalized schematic illustration of a turbine having a second stage turbine wheel employing the buckets and bucket airfoils hereof;

FIG. 2 is an end view of the shrouds formed on the bucket airfoils as viewed looking radially inwardly;

FIG. 3 is a side elevational view of a preferred embodiment of the bucket hereof;

FIGS. 4A-4K are representative cross-sectional views taken generally about on the lines variously indicated in FIG. 3 ;

FIG. 5 is an elevational view of the bucket hereof similarly as indicated in FIG. 3 and taken from the opposite side thereof;

FIG. 6 is an axial view of the bucket as it would appear in the turbine wheel and viewed from the leading edge;

FIG. 7 is a perspective view of the bucket hereof;

FIG. 8 is a perspective view of the engagement between adjacent shrouds in a misaligned condition; and

FIG. 9 is a schematic representation of misengaged shrouds, i.e., shingled shrouds.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to FIG. 1 , there is illustrated a portion of a turbine generally designated 10 in which a second stage turbine bucket 22 having an airfoil profile 23 as defined herein may be utilized. Turbine 10 includes a rotor 12 having first, second and third stage rotor wheels 14 , 16 and 18 having buckets 20 , 22 and 24 in conjunction with the respective stator vanes 26 , 28 and 30 of the various stages of the rotor. It will be appreciated that a three stage turbine is illustrated.

The second stage comprises the rotor wheel 16 on which buckets 22 are mounted in axial opposition to the upstream stator vanes 28 . It will be appreciated that a plurality of the buckets 22 are spaced circumferentially one from the other about the second stage wheel 16 and in this instance there are ninety-two buckets mounted on the second stage wheel 16 .

Referring now to FIGS. 5 and 6 , there are illustrated buckets 22 of the second stage. Each bucket 22 includes a bucket airfoil 30 mounted on a platform 32 , the bucket further including a shank 34 and a dovetail 36 . Adjacent the tip of the airfoil 30 is a shroud 38 mounting a seal 40 and a cutter tooth 42 . The shroud 38 lies in radial opposition to a fixed shroud forming part of the stationary casing of the turbine. The seals 40 are provided to seal between high and lower pressure regions on opposite sides of the airfoils which lie in the hot gas path of the turbine. The cutter tooth 42 on each shroud typically forms a wider groove in the fixed shroud to permit slight leakage flows past the seal 40 .

Referring to FIGS. 2 , 8 and 9 , the shrouds 38 have leading and trailing edges in a circumferential direction which engage the trailing and leading edges, respectively, of adjacent shrouds. The shrouds are not mechanically connected one to the other but are shaped to maintain engagement. It has been discovered that the leading and trailing edges of adjacent shrouds may have engagements which mismatch, which among other things, adversely impact the part life. For example, the shrouds may have a tendency to shingle relative to one another. That is, the trailing edge of one shroud may overlie or underlie the leading edge of an adjacent shroud, as illustrated in FIGS. 8 and 9 , with adverse consequences. The bucket airfoil has particular effect on the shroud engagement and the present airfoil profile reduces local creep and increases high cycle fatigue margin in the airfoil, ultimately leading to higher part life.

A Cartesian coordinate system of X, Y and Z values given in Table I defines the profile of airfoil 30 . The coordinate values for the X, Y and Z coordinates are set forth in inches in Table I although other units of dimensions may be used. The Cartesian coordinate system has orthogonally-related X, Y and Z axes. The Z axis extends perpendicular to a plane passing through the axis of rotation of the turbine rotor and normal to a plane containing the X and Y values, The coordinate values for Z in Table I represent distances in inches from and perpendicular to a plane passing through the axis of rotation of the turbine. The X axis extends in a direction parallel to the turbine rotor centerline and the Y axis extends in a tangential direction.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile of airfoil 40 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 of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil shape. These values represent the airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil.

The Table I values are generated and shown to three decimal places for determining the profile of the airfoil. 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., values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of ±0.016 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular bucket airfoil design and turbine.

The coordinate values given in Table I below provide the preferred nominal profile envelope ranging from 10-90% span of the airfoil height.

TABLE I
X(10%)	Y(10%)	Z(10%)	X(20%)	Y(20%)	Z(20%)
−0.4223	0.1413	40.213	−1.456	0.6117	41.4
−0.1007	0.8256	40.213	−1.5812	0.2658	41.4
−1.6189	0.0838	40.213	−0.7133	0.3439	41.4
−0.2487	0.5905	40.213	−1.4023	0.2375	41.4
−1.0913	0.1732	40.213	−1.1368	0.8641	41.4
−1.4158	0.081	40.213	−0.4471	0.975	41.4
−1.6613	0.1579	40.213	−0.3129	0.2331	41.4
−1.4392	0.5352	40.213	−0.2371	0.1983	41.4
−0.9176	0.8859	40.213	−0.5478	0.9912	41.4
−0.5872	0.1774	40.213	−0.0903	0.1193	41.4
−1.1964	0.7378	40.213	−1.5727	0.4498	41.4
−0.1837	0.0569	40.213	−0.6497	0.9968	41.4
−1.6585	0.2049	40.213	−1.2234	0.8101	41.4
−0.7135	0.9382	40.213	−0.3483	0.9493	41.4
−1.2812	0.6749	40.213	−1.5211	0.533	41.4
−1.6247	0.2939	40.213	−1.2083	0.3012	41.4
−1.0078	0.1859	40.213	−0.6309	0.3313	41.4
−0.7554	0.1953	40.213	−0.1592	0.8728	41.4
−0.9238	0.1939	40.213	−1.3056	0.7495	41.4
−1.6484	0.1129	40.213	0.0171	0.7701	41.4
−1.4562	0.0703	40.213	−1.2872	0.2744	41.4
−0.2619	0.0888	40.213	−1.0457	0.3381	41.4
−1.4974	0.0637	40.213	−1.6038	0.3085	41.4
−1.2556	0.1344	40.213	−0.0193	0.0756	41.4
−1.3821	0.6072	40.213	−1.5488	0.4925	41.4
−0.6708	0.1888	40.213	−0.8797	0.3525	41.4
−0.8169	0.9174	40.213	−1.6039	0.3573	41.4
−1.5392	0.0624	40.213	−0.7964	0.351	41.4
0.0809	0.7183	40.213	−0.4692	0.291	41.4
−0.5042	0.1616	40.213	−0.963	0.3483	41.4
−1.5762	0.3751	40.213	−0.8524	0.9748	41.4
−0.0317	−0.0166	40.213	−0.7517	0.9914	41.4
−0.8394	0.197	40.213	−1.592	0.4048	41.4
−1.0146	0.8445	40.213	0.1004	0.711	41.4
−1.1076	0.7948	40.213	−1.3659	0.2469	41.4
−0.3988	0.9296	40.213	−1.4396	0.2316	41.4
−1.336	0.1086	40.213	−0.5494	0.3136	41.4
−0.1967	0.8691	40.213	0.0501	0.0294	41.4
−1.6018	0.3353	40.213	0.258	0.5812	41.4
−0.6085	0.9472	40.213	−0.1629	0.1603	41.4
−1.174	0.1559	40.213	0.3326	0.5115	41.4
−0.0081	0.7749	40.213	−1.0457	0.9103	41.4
−0.5031	0.9442	40.213	0.1807	0.6479	41.4
−0.3415	0.117	40.213	−0.3902	0.2641	41.4
0.1684	0.6585	40.213	−1.1276	0.3224	41.4
−1.6437	0.2505	40.213	−0.2522	0.9148	41.4
−1.5806	0.0676	40.213	−0.0694	0.8242	41.4
0.328	0.5208	40.213	−1.5147	0.2329	41.4
−0.2962	0.9042	40.213	−1.4772	0.2296	41.4
−1.5117	0.4585	40.213	−1.3832	0.6832	41.4
−0.1069	0.0218	40.213	−1.5506	0.2441	41.4
0.6185	0.215	40.213	−0.9507	0.9475	41.4
1.8176	−1.7672	40.213	1.4833	−1.5812	41.4
0.2543	0.1957	40.213	0.9639	−0.2882	41.4
1.3994	−1.4268	40.213	0.2496	−0.1214	41.4
0.4043	0.448	40.213	1.5292	−1.6508	41.4
0.4538	0.3517	40.213	1.2462	−1.2383	41.4
0.9321	0.8278	40.213	0.8906	−0.7756	41.4
0.9872	−0.8917	40.213	1.4369	−1.5119	41.4
0.8755	−0.1196	40.213	1.4189	−1.0863	41.4
1.4957	−1.5654	40.213	0.4047	0.4391	41.4
1.4703	−1.1153	40.213	0.5418	0.2879	41.4
1.2686	−0.7446	40.213	0.7827	−0.6484	41.4
1.8161	−1.8444	40.213	1.7327	−1.7285	41.4
1.5429	−1.6354	40.213	1.5566	−1.3599	41.4
1.6191	−1.3946	40.213	1.3717	−0.9957	41.4
0.9356	−0.2063	40.213	1.2752	−0.8157	41.4
1.8269	−1.806	40.213	0.6707	0.1295	41.4
0.7505	0.0505	40.213	0.851	−0.1181	41.4
1.7879	−1.8727	40.213	1.1242	−0.5493	41.4
0.5494	0.2949	40.213	0.118	−0.019	41.4
0.7609	−0.6411	40.213	1.6436	−1.8123	41.4
1.0949	−1.0218	40.213	1.1478	−1.1037	41.4
0.0421	−0.0576	40.213	1.6014	−1.4517	41.4
1.2504	−1.2218	40.213	1.5112	−1.2684	41.4
1.1075	−0.472	40.213	1.7287	−1.7901	41.4
0.8138	−0.0339	40.213	0.6142	−0.4835	41.4
1.4207	−1.0221	40.213	1.0469	−0.9709	41.4
1.6812	−1.8477	40.213	1.6892	−1.636	41.4
0.4781	−0.3726	40.213	0.9081	−0.2027	41.4
0.3222	−0.2459	40.213	0.3133	−0.1752	41.4
1.5695	−1.3016	40.213	0.9434	−0.8401	41.4
1.6353	−1.7767	40.213	1.7386	−1.7598	41.4
0.819	−0.7024	40.213	0.7924	−0.0345	41.4
1.5894	−1.7059	40.213	0.4973	−0.3447	41.4
1.0514	−0.3827	40.213	1.6455	−1.5438	41.4
0.1143	−0.1013	40.213	1.7054	−1.8119	41.4
0.1851	−0.1474	40.213	1.6202	−1.7906	41.4
0.6416	−0.5216	40.213	1.0718	−0.4616	41.4
0.9942	−0.2941	40.213	0.3758	−0.2305	41.4
1.7107	−1.8746	40.213	0.7274	−0.586	41.4
1.3708	−0.9291	40.213	0.5563	−0.4036	41.4
1.3202	−0.8366	40.213	1.3899	−1.443	41.4
0.876	−0.7646	40.213	0.7323	0.0481	41.4
1.0415	−0.9564	40.213	0.6072	0.2095	41.4
1.4478	−1.4958	40.213	1.1973	−1.1708	41.4
1.7495	−1.8837	40.213	1.3239	−0.9055	41.4
1.3006	−1.2896	40.213	1.0184	−0.3745	41.4
1.7183	−1.5809	40.213	1.6745	−1.82	41.4
1.1475	−1.0879	40.213	1.2947	−1.3061	41.4
0.3887	−0.298	40.213	0.837	−0.7117	41.4
0.5802	−0.4636	40.213	0.4371	−0.2869	41.4
0.7018	−0.5808	40.213	0.1845	−0.0694	41.4
1.2159	−0.6531	40.213	0.9955	−0.9052	41.4
1.1622	−0.5622	40.213	1.5747	−1.7207	41.4
1.5198	−1.2084	40.213	0.6713	−0.5244	41.4
0.5177	−0.407	40.213	1.3426	−1.3744	41.4
1.1993	−1.1546	40.213	0.4743	0.3645	41.4
1.3504	−1.3578	40.213	1.1754	−0.6376	41.4
0.6855	0.1335	40.213	1.0977	−1.037	41.4
1.768	−1.6741	40.213	1.2258	−0.7264	41.4
1.6687	−1.4876	40.213	1.4654	−1.1772	41.4
X(30%)	Y(30%)	Z(30%)	X(40%)	Y(40%)	Z(40%)
1.0013	0.4872	42.597	−1.0081	1.107	43.784
−0.6898	1.071	42.597	−1.2735	0.5551	43.784
−0.7887	1.0678	42.597	−0.6281	1.1421	43.784
−1.0826	0.4754	42.597	−1.4061	0.8458	43.784
−1.3992	0.7693	42.597	−1.4354	0.5865	43.784
−0.8867	1.0537	42.597	−1.3061	0.5503	43.784
−1.3254	0.8353	42.597	−1.0378	0.6098	43.784
−1.2467	0.8953	42.597	−1.4905	0.6248	43.784
−0.9824	1.0286	42.597	−0.9152	1.1323	43.784
−1.4653	0.6958	42.597	−1.484	0.7212	43.784
−1.0748	0.9931	42.597	−1.4045	0.5555	43.784
−1.1631	0.9483	42.597	−1.4629	0.5846	43.784
−0.3056	0.9849	42.597	−1.1951	0.5743	43.784
0.4936	1.046	42.597	−1.4369	0.8074	43.784
0.0356	0.7857	42.597	−1.372	0.5502	43.784
−0.2186	0.2908	42.597	−1.339	0.5486	43.784
−0.9194	0.4926	42.597	−1.4635	0.766	43.784
−0.2904	0.3305	42.597	−1.0974	1.0715	43.784
−0.4392	0.3996	42.597	−0.8766	0.6173	43.784
−0.7557	0.4842	42.597	−1.495	0.6734	43.784
−0.8374	0.4915	42.597	−1.338	0.9138	43.784
−0.0799	0.2029	42.597	−0.8201	1.1465	43.784
0.3987	0.4503	42.597	−1.1824	1.0265	43.784
−0.364	0.3669	42.597	−0.724	1.1497	43.784
−0.1289	0.8956	42.597	−0.9574	0.617	43.784
0.1885	0.86	42.597	−1.1173	0.5958	43.784
0.0524	0.1057	42.597	−1.2627	0.9736	43.784
−0.6747	0.4709	42.597	−0.3511	1.064	43.784
−0.5162	0.4282	42.597	−0.264	1.023	43.784
−0.0452	0.8431	42.597	0.3943	0.4085	43.784
0.1164	0.0543	42.597	−0.638	0.5788	43.784
0.1134	0.7246	42.597	0.2652	0.6112	43.784
−0.2157	0.9434	42.597	−0.561	0.5544	43.784
−0.3984	1.0195	42.597	−0.1365	0.324	43.784
−0.1484	0.2482	42.597	−0.4122	0.4916	43.784
−0.5912	1.0635	42.597	−0.7165	0.5977	43.784
0.3309	0.5226	42.597	0.1135	0.1197	43.784
−0.5947	0.4521	42.597	−0.5335	1.1246	43.784
−0.013	0.1553	42.597	0.4559	0.3945	43.784
0.2609	0.5926	42.597	0.2306	0.0085	43.784
0.5851	−0.4048	42.597	−0.4857	0.5251	43.784
1.0307	−0.4344	42.597	−0.0718	0.2757	43.784
0.7972	−0.6556	42.597	−0.3406	0.4543	43.784
0.4642	0.3762	42.597	−0.2028	0.3701	43.784
0.5279	0.3003	42.597	0.1974	0.6795	43.784
0.9278	−0.2652	42.597	−0.0208	0.8683	43.784
0.8484	−0.7197	42.597	−0.441	1.0982	43.784
0.3594	−0.1664	42.597	−0.099	0.9244	43.784
0.4742	−0.2838	42.597	0.1727	0.0647	43.784
0.6392	−0.4666	42.597	−0.0086	0.2254	43.784
0.3004	−0.1093	42.597	−0.1801	0.9762	43.784
0.5897	0.2229	42.597	0.0531	0.1733	43.784
0.179	0.0012	42.597	0.0546	0.8084	43.784
0.5301	0.3439	42.597	−0.7961	0.6107	43.784
0.765	−0.0168	42.597	0.3308	0.5408	43.784
0.9798	−0.3496	42.597	−0.2708	0.4136	43.784
0.8747	−0.1816	42.597	0.1273	0.7454	43.784
0.7081	0.0642	42.597	0.943	−0.3205	43.784
0.8208	0.0987	42.597	0.5576	−0.349	43.784
0.7452	−0.5919	42.597	0.8089	−0.6851	43.784
0.6927	−0.5289	42.597	0.2875	−0.049	43.784
0.2403	−0.0534	42.597	0.9054	−0.7947	43.784
0.4172	−0.2247	42.597	0.5053	−0.2874	43.784
0.6497	0.1442	42.597	0.8574	−0.7297	43.784
1.3833	−1.0423	42.597	0.6304	0.1647	43.784
1.0808	−0.52	42.597	0.5157	0.3192	43.784
1.2252	−0.7794	42.597	0.5739	0.2425	43.784
0.949	−0.6495	42.597	0.7103	−0.5371	43.784
1.1777	−0.6925	42.597	0.9915	−0.4036	43.784
1.4082	−1.1308	42.597	0.4522	−0.2266	43.784
0.9984	−0.915	42.597	0.8937	−0.2379	43.784
1.2719	−0.8667	42.597	0.66	−0.4739	43.784
0.899	−0.7843	42.597	0.8434	−0.1559	43.784
1.1296	−0.606	42.597	0.7599	−0.6009	43.784
1.3179	−0.9543	42.597	0.3982	−1.665	43.784
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−1.1627	0.4575	42.597	1.1319	−0.6559	43.784
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1.3763	−1.4521	42.597	1.1774	−0.7407	43.784
1.5401	−1.3967	42.597	1.1839	−1.1912	43.784
1.0957	−1.0473	42.597	1.0859	−0.5714	43.784
1.1909	−1.1811	42.597	1.2221	−0.8259	43.784
1.5114	−1.658	42.597	1.579	−1.688	43.784
1.6414	−1.7484	42.597	1.3962	−1.1691	43.784
1.4526	−1.2191	42.597	1.2738	−1.3254	43.784
1.4217	−1.5205	42.597	0.9529	−0.86	43.784
1.6685	−1.6646	42.597	1.31	−0.997	43.784
1.4966	−1.3078	42.597	1.517	−1.6861	43.784
1.2844	−1.3161	42.597	1.2664	−0.9113	43.784
1.6647	−1.7285	42.597	1.548	−1.694	43.784
1.1435	−1.1141	42.597	1.4064	−1.5282	43.784
1.2378	−1.2484	42.597	1.45	−1.5962	43.784
1.5832	−1.4859	42.597	1.6061	−1.602	43.784
1.3306	−1.3839	42.597	1.4809	−1.3419	43.784
1.4667	−1.5892	42.597	1.6122	−1.6335	43.784
1.6258	−1.5753	42.597	1.4388	−1.2554	43.784
1.556	−1.7269	42.597	1.5645	−1.5153	43.784
1.6105	−1.7565	42.597	1.5229	−1.4285	43.784
1.5795	−1.7487	42.597	1.4936	−1.6642	43.784
1.6745	−1.696	42.597	1.3183	−1.3928	43.784
1.0472	−0.981	42.597	1.1384	−1.1244	43.784
X(50%)	Y(50%)	Z(50%)	X(60%)	Y(60%)	Z(60%)
−1.3858	0.7184	44.971	−0.9511	0.8607	46.169
−0.6795	0.7035	44.971	−1.336	0.8755	46.169
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−0.9148	0.7384	44.971	−1.3642	1.0304	46.169
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−0.9942	0.7357	44.971	−1.3586	0.8979	46.169
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−1.2732	1.0513	44.971	−0.4192	1.2364	46.169
−0.6585	1.2239	44.971	−0.6441	0.8056	46.169
−0.7518	1.2304	44.971	−1.2165	0.8362	46.169
−1.2933	0.6928	44.971	−0.9529	1.2977	46.169
−0.9376	1.2109	44.971	−0.8728	0.8577	46.169
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0.2207	0.0716	44.971	−1.0403	1.2719	46.169
0.2707	0.6357	44.971	−0.1778	0.5215	46.169
0.2228	1.0629	44.971	0.1054	0.2507	46.169
0.3319	0.5649	44.971	−0.1823	1.1009	46.169
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0.3913	0.4926	44.971	−0.039	0.9884	46.169
0.1657	0.1291	44.971	−0.3014	0.6179	46.169
0.0042	0.8981	44.971	0.0938	0.8635	46.169
−0.6038	0.6794	44.971	−0.1093	1.0464	46.169
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−0.389	1.1489	44.971	−0.3859	0.6624	46.169
−0.2537	0.4934	44.971	0.3889	0.5168	46.169
−0.3044	1.1088	44.971	0.5484	0.2934	46.169
0.0743	0.8362	44.971	−0.0605	0.4174	46.169
−0.1893	0.4469	44.971	0.1584	0.193	46.169
0.3274	0.0481	44.971	0.0512	0.3074	46.169
0.1098	0.1858	44.971	0.1567	0.7978	46.169
−0.3199	0.5375	44.971	0.2764	0.6602	46.169
0.505	0.344	44.971	0.0286	0.9273	46.169
0.0687	0.9589	44.971	−0.2582	1.1513	46.169
0.2075	0.7047	44.971	0.4952	0.3688	46.169
0.2745	0.0134	44.971	0.2615	0.0749	46.169
0.1421	0.7718	44.971	−0.4324	0.704	46.169
−0.3879	0.5788	44.971	−0.004	0.363	46.169
0.0527	0.2499	44.971	−0.1184	0.4704	46.169
−0.0654	0.3473	44.971	0.2175	0.7298	46.169
0.6287	−0.4159	44.971	0.3119	0.0147	46.169
0.8136	0.1251	44.971	−0.2387	0.5708	46.169
1.0437	−0.5324	44.971	0.997	−0.9405	46.169
0.9992	−0.4501	44.971	0.5526	−0.2946	46.169
0.954	0.3581	44.971	0.9619	−0.4134	46.169
0.8612	−0.2055	44.971	0.5057	−0.2318	46.169
0.531	−0.2904	44.971	0.911	−0.8094	46.169
1.0877	0.615	44.971	1.0396	−1.0062	46.169
0.5596	0.2679	44.971	0.9541	−0.8748	46.169
0.3795	−0.1062	44.971	0.8237	−0.679	46.169
0.8173	−0.6718	44.971	0.7857	−0.0943	46.169
0.4812	−0.2284	44.971	0.8752	−0.2531	46.169
0.6766	−0.4793	44.971	1.0463	−0.575	46.169
0.9089	−0.8018	44.971	0.7398	−0.0156	46.169
0.724	−0.5431	44.971	1.0878	−0.6561	46.169
0.765	−0.045	44.971	0.599	−0.3579	46.169
0.7153	0.0343	44.971	0.8675	−0.7441	46.169
0.6127	0.1909	44.971	0.6451	0.1402	46.169
0.4307	0.1671	44.971	0.8308	−0.1735	46.169
0.9541	−0.8672	44.971	0.6448	−0.4215	46.169
0.5802	−0.3529	44.971	1.1288	−0.7375	46.169
0.7709	−0.6073	44.971	1.0044	−0.494	46.169
0.908	−0.2866	44.971	0.7795	−0.6142	46.169
0.8833	−0.7366	44.971	0.9189	−0.333	46.169
0.6647	0.1129	44.971	0.5964	0.2171	46.169
1.1311	−0.698	44.971	0.735	−0.5497	46.169
1.2163	−0.8645	44.971	0.693	0.0626	46.169
1.3898	−1.532	44.971	0.4582	−0.1694	46.169
1.2185	−1.2641	44.971	0.6901	−0.4855	46.169
1.3	−1.032	44.971	0.4101	−0.1075	46.169
1.3412	−1.116	44.971	1.1695	−0.819	46.169
1.1315	−1.131	44.971	1.3686	−1.2289	46.169
1.0434	−0.9987	44.971	1.2496	−1.3372	46.169
1.4232	−1.2843	44.971	1.3738	−1.537	46.169
1.5177	−1.6215	44.971	1.428	−1.5676	46.169
1.2617	−1.3309	44.971	1.082	−1.0722	46.169
1.5412	−1.5995	44.971	1.3291	−1.1468	46.169
1.4887	−1.6295	44.971	1.2498	−0.9827	46.169
1.5043	−1.453	44.971	1.1662	−1.2045	46.169
1.2583	−0.9482	44.971	1.2895	−1.0647	46.169
1.1752	1.1975	44.971	1.1242	−1.1383	46.169
X(50%)	Y(50%)	Z(50%)	1.4865	−1.4756	46.169
0.9989	0.9328	44.971	1.4472	−1.3934	46.169
1.3823	−1.2001	44.971	1.208	−1.2708	46.169
1.5448	−1.5374	44.971	1.2098	−0.9008	46.169
1.3473	−1.4649	44.971	1.4828	−1.5378	46.169
1.5509	−1.569	44.971	1.4926	−1.5072	46.169
1.4638	−1.3688	44.971	1.408	−1.3111	46.169
1.4323	−1.5993	44.971	1.4593	−1.5598	46.169
1.0876	−1.0648	44.971	1.397	−1.5593	46.169
1.3046	−1.3978	44.971	1.2911	−1.4038	46.169
1.4556	−1.6214	44.971	1.3325	−1.4704	46.169
X(70%)	Y(70%)	Z(70%)	X(80%)	Y(80%)	Z(80%)	X(90%)	Y(90%)	Z(90%)
−1.0477	1.372	47.357	−1.1832	1.1642	48.544	−0.952	1.6067	49.742
−0.7661	1.4144	47.357	−1.1652	1.4146	48.544	−0.7837	1.6154	49.742
1.3185	1.0956	47.357	−0.7164	1.0663	48.544	−1.1727	1.4036	49.742
0.4749	0.834	47.357	−0.5352	1.4585	48.544	−0.4872	1.0457	49.742
1.2762	1.2281	47.357	−1.2311	1.3393	48.544	−0.6185	1.5814	49.742
0.6831	0.9369	47.357	−0.3267	0.8249	48.544	−0.3118	0.8998	49.742
0.5258	1.3628	47.357	−0.8643	1.1068	48.544	−0.8238	1.2185	49.742
0.2887	1.2419	47.357	−0.4562	1.4208	48.544	−0.1924	1.3136	49.742
0.9625	1.3969	47.357	−1.0433	1.4764	48.544	−1.078	1.5637	49.742
0.6115	0.9073	47.357	−0.3863	0.8734	48.544	−0.0725	1.1944	49.742
0.6105	1.3892	47.357	−1.0173	1.1166	48.544	−0.6146	1.1287	49.742
1.2435	1.2629	47.357	−1.2194	1.197	48.544	−1.0336	1.5848	49.742
0.5421	0.8728	47.357	−0.1713	1.225	48.544	−1.1691	1.4524	49.742
1.3189	1.1429	47.357	−1.2024	1.3805	48.544	−1.1499	1.4976	49.742
1.296	1.0529	47.357	−0.7894	1.09	48.544	−0.2569	0.8472	49.742
0.7569	0.9608	47.357	−1.2024	1.1793	48.544	−0.7517	1.1943	49.742
1.1704	0.9564	47.357	−0.7876	1.5135	48.544	−1.1572	1.3571	49.742
1.1417	0.9825	47.357	−0.6458	1.0364	48.544	−1.1097	1.3022	49.742
0.4437	1.3287	47.357	−0.6171	1.4847	48.544	−0.2559	1.3693	49.742
1.276	1.0319	47.357	−0.3078	1.3317	48.544	−0.4268	0.9994	49.742
1.2281	1.0025	47.357	−0.9599	1.4994	48.544	−1.0898	1.2881	49.742
1.1987	0.9931	47.357	−1.1622	1.1515	48.544	−0.5397	1.551	49.742
0.9094	0.9874	47.357	−1.117	1.1325	48.544	−0.3683	0.9507	49.742
1.1296	1.3375	47.357	−0.5114	0.9621	48.544	−1.0687	1.2759	49.742
1.3023	1.1882	47.357	−0.7015	1.5041	48.544	−0.1313	1.2552	49.742
1.2522	1.0153	47.357	−0.9405	1.1157	48.544	−0.5497	1.089	49.742
0.6976	1.4068	47.357	−0.8742	1.5121	48.544	−0.8979	1.2357	49.742
0.8325	0.9779	47.357	−0.4478	0.9192	48.544	−0.3915	1.4899	49.742
1.0642	0.9821	47.357	−1.1228	1.4419	48.544	−1.1439	1.3367	49.742
1.2062	1.2927	47.357	−0.5774	1.0013	48.544	−0.7001	1.6033	49.742
0.9869	0.9889	47.357	−1.2462	1.2913	48.544	−0.6819	1.164	49.742
0.8748	1.4112	47.357	−1.0934	1.1262	48.544	−1.0485	1.2658	49.742
0.3647	1.288	47.357	−1.243	1.2413	48.544	−1.1279	1.3183	49.742
0.0784	1.0784	47.357	−0.2381	1.2802	48.544	−0.8681	1.6166	49.742
0.1458	1.1364	47.357	−1.14	1.141	48.544	−1.1178	1.5348	49.742
0.2238	0.7534	47.357	−0.3805	1.3789	48.544	−0.9733	1.2457	49.742
0.6243	0.1666	47.357	0.373	0.0127	48.544	−0.464	1.5135	49.742
0.3469	0.7464	47.357	0.4168	−0.0503	48.544	−0.3223	1.4216	49.742
0.1128	0.5432	47.357	−0.1582	0.668	48.544	−0.2034	0.7931	49.742
0.5782	0.2427	47.357	0.6513	0.1169	48.544	0.0452	0.5053	49.742
0.2158	1.1912	47.357	0.5032	−0.1772	48.544	0.5946	0.2206	49.742
0.2954	0.0767	47.357	−0.1049	0.6128	48.544	0.2716	0.1997	49.742
0.3318	0.6123	47.357	0.3824	0.5618	48.544	0.7145	0.0028	49.742
0.434	0.4669	47.357	−0.0529	0.5563	48.544	0.4254	0.5132	49.742
0.1989	0.1981	47.357	0.6088	0.1923	48.544	0.3999	0.0109	49.742
0.2766	0.6834	47.357	0.1813	0.8439	48.544	0.2421	0.7973	49.742
0.4099	0.7917	47.357	0.334	0.6337	48.544	0.5115	0.3678	49.742
0.2267	0.6488	47.357	0.1274	0.9118	48.544	0.6351	0.1464	49.742
0.0045	0.4322	47.357	0.4757	0.4157	48.544	0.3358	0.6566	49.742
0.1495	0.2529	47.357	0.1915	0.2604	48.544	0.0023	0.5847	49.742
0.0992	0.3169	47.357	−0.2128	0.722	48.544	0.4688	0.4407	49.742
0.4832	0.3929	47.357	−0.0453	1.106	48.544	0.1832	0.3235	49.742
0.0137	1.0176	47.357	−0.0021	0.4987	48.544	0.092	1.0016	49.742
0.3425	0.0151	47.357	−0.2689	0.7744	48.544	0.4832	0.1165	49.742
0.1674	0.822	47.357	0.2378	0.1992	48.544	0.2895	0.7273	49.742
0.389	−0.047	47.357	0.2835	0.1374	48.544	0.0389	1.0673	49.742
0.3836	0.54	47.357	−0.107	1.1668	48.544	0.4417	−0.0527	49.742
0.4349	−0.1095	47.357	0.0478	0.4403	48.544	0.3149	0.1371	49.742
0.2476	0.1377	47.357	0.4296	0.489	48.544	0.1934	0.8663	49.742
0.0488	0.9545	47.357	0.4602	−0.1137	48.544	0.092	0.4453	49.742
0.1091	0.8891	47.357	0.0965	0.3809	48.544	−0.0509	0.6233	49.742
0.5312	0.3181	47.357	0.5651	0.2673	48.544	−0.1514	0.7376	49.742
0.169	0.5967	47.357	0.0717	0.9783	48.544	0.2276	0.2617	49.742
0.0478	0.375	47.357	0.5209	0.3416	48.544	−0.1006	0.6809	49.742
0.2859	0.6988	47.357	0.0142	1.0431	48.544	0.5648	−0.2448	49.742
0.0581	0.4884	47.357	0.2336	0.7749	48.544	0.1434	0.9345	49.742
0.9251	−0.3778	47.357	0.3285	0.0753	48.544	0.6751	0.0719	49.742
0.7426	−0.5566	47.357	0.2845	0.7048	48.544	0.5534	0.2943	49.742
0.8002	−0.1422	47.357	0.1444	0.321	48.544	0.138	0.3847	49.742
0.864	−0.299	47.357	0.9334	−0.4201	48.544	0.3811	0.5852	49.742
0.6695	0.0901	47.357	0.5878	−0.3054	48.544	−0.0158	1.1317	49.742
0.7137	0.0131	47.357	1.0331	−1.0228	48.544	0.5242	−0.1806	49.742
0.6132	−0.3632	47.357	0.6711	−0.4344	48.544	0.3577	0.0742	49.742
0.8272	−0.6866	47.357	1.112	−1.1547	48.544	0.7639	0−.569	49.742
0.9932	−0.9487	47.357	0.6933	0.0411	48.544	1.301	−1.2208	49.742
0.9107	−0.8174	47.357	1.0725	−1.0887	48.544	1.1491	−1.2251	49.742
0.6998	−0.492	47.357	0.9936	−0.9571	48.544	0.9784	−0.5322	49.742
0.8424	−0.2205	47.357	0.834	−0.6947	48.544	0.9417	−0.4562	49.742
1.0456	−0.6158	47.357	0.753	−0.5842	48.544	1.1589	−0.9144	49.742
0.4803	−0.1724	47.357	0.7121	−0.4992	48.544	1.1873	−1.2909	49.742
0.9657	−0.4568	47.357	1.0853	−0.7316	48.544	1.0727	−1.0935	49.742
1.0342	−1.0145	47.357	1.1226	−0.8098	48.544	1.2303	−1.0676	49.742
0.5251	−0.2357	47.357	1.0477	−0.6536	48.544	0.9962	−0.962	49.742
1.0849	−0.6953	47.357	0.8741	−0.7602	48.544	0.803	−0.6342	49.742
1.124	−0.7751	47.357	0.9718	−0.4977	48.544	1.266	−1.442	49.742
0.7573	−0.0644	47.357	1.01	−0.5756	48.544	1.0345	−1.0277	49.742
0.869	−0.752	47.357	0.5457	−0.2412	48.544	1.0149	−0.6085	49.742
0.6567	−0.4275	47.357	0.7936	−0.6294	48.544	1.0871	−0.7613	49.742
0.952	−0.883	47.357	0.7346	−0.0351	48.544	0.8419	−0.6997	49.742
1.1628	−0.855	47.357	0.8158	−0.1883	48.544	0.6452	−0.374	49.742
1.0058	−0.5361	47.357	0.8553	−0.2654	48.544	0.9193	−0.8307	49.742
0.785	−0.6215	47.357	0.6295	−0.3698	48.544	1.1946	−0.991	49.742
1.0751	−1.0805	47.357	0.8945	−0.3427	48.544	0.6052	−0.3093	49.742
X(70%)	Y(70%)	Z(70%)	X(80%)	Y(80%)	Z(80%)	X(90%)	Y(90%)	Z(90%)
0.5694	−0.2993	47.357	0.9141	−0.8258	48.544	1.2255	−1.3567	49.742
1.3177	−1.4775	47.357	1.1598	−0.8882	48.544	0.7533	−0.0778	49.742
1.2774	−1.4712	47.357	1.1988	−0.9665	48.544	0.7246	−0.5039	49.742
1.3922	−1.3364	47.357	0.9539	−0.8913	48.544	0.8298	−0.2288	49.742
1.4365	−1.4483	47.357	0.7754	−0.1116	48.544	1.1231	−0.8378	49.742
1.3542	−1.2661	47.357	1.3075	−1.2017	48.544	0.9578	−0.8963	49.742
1.1967	−1.2787	47.357	1.3443	−1.2802	48.544	0.8806	−0.7652	49.742
1.3407	−1.5	47.357	1.2915	−1.4414	48.544	0.9047	−0.3802	49.742
1.2779	−1.0955	47.357	1.2688	−1.4186	48.544	1.1111	−1.1592	49.742
1.403	−1.5009	47.357	1.3875	−1.3901	48.544	0.7918	−0.1532	49.742
1.1157	−1.1465	47.357	1.3225	−1.4501	48.544	0.6851	−0.4389	49.742
1.2013	−0.9351	47.357	1.3775	−1.4208	48.544	1.0511	−0.6849	49.742
1.2397	−1.0153	47.357	1.3539	−1.4426	48.544	0.8675	0.3043	49.742
1.4303	−1.4167	47.357	1.1905	−1.2866	48.544	1.3339	−1.3596	49.742
1.3161	−1.1758	47.357	1.2706	−1.1233	48.544	1.248	−1.3798	49.742
1.2372	−1.1345	47.357	1.2337	−1.0449	48.544	1.3102	−1.3814	49.742
1.3718	−1.5086	47.357	1.1512	−1.2206	48.544	1.2789	−1.3887	49.742
1.1563	−1.2125	47.357	1.3811	−1.3588	48.544	1.3439	−1.3289	49.742
1.4266	−1.479	47.357	1.2296	−1.3526	48.544	1.3375	−1.2974	49.742

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, optionally, Z coordinate values multiplied or divided by the same constant or number.

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 including a bucket airfoil having an airfoil shape, said airfoil having nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distance 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 according to claim 1 wherein said airfoil shape lies in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

4. A turbine bucket according to claim 1 wherein the airfoil has a shroud adjacent a tip of the airfoil.

5. A turbine bucket including a bucket airfoil having an airfoil shape, said airfoil having an uncoated nominal airfoil profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant to provide a scaled-up or scaled-down bucket airfoil.

6. A turbine bucket according to claim 5 forming part of a second stage of a turbine.

7. A turbine bucket according to claim 5 wherein said airfoil shape lies in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

8. A turbine bucket according to claim 5 wherein the airfoil has a shroud adjacent a tip of the airfoil.

9. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets including a bucket airfoil having an airfoil shape, said airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine axis and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape.

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

11. A turbine according to claim 9 wherein the turbine wheel has 92 buckets and X represents a distance parallel to the turbine axis of rotation.

12. A turbine according to claim 9 wherein each said airfoil shape lies in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

13. A turbine according to claim 9 wherein the turbine wheel comprises a second stage of the turbine, each said airfoil shape lying in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

14. A turbine according to claim 9 wherein the turbine wheel comprises a second stage of the turbine, the turbine wheel having 92 buckets and X represents a distance parallel to the turbine axis of rotation.

15. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets including a bucket airfoil having an airfoil shape, said airfoil having a nominal profile ranging from 10-90% span of the airfoil height substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a distance in inches from and perpendicular to a plane passing through an axis of rotation of the turbine and wherein X and Y are distances in inches which, when connected by smooth continuous arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form the complete airfoil shape, the X and Y distances being scalable as a function of the same constant to provide a scaled-up or scaled-down bucket airfoil.

16. A turbine according to claim 15 wherein the turbine wheel comprises a second stage of the turbine.

17. A turbine according to claim 15 wherein the turbine wheel has 92 buckets and X represents a distance parallel to the turbine axis of rotation.

18. A turbine according to claim 15 wherein each said airfoil shape lies in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

19. A turbine according to claim 15 wherein the turbine wheel comprises a second stage of the turbine, each said airfoil shape lying in an envelope within ±0.016 inches in a direction normal to any airfoil surface location.

20. A turbine according to claim 15 wherein the turbine wheel comprises a second stage of the turbine, the turbine wheel having 92 buckets and X represents a distance parallel to the turbine axis of rotation.