Abstract:
Replacement low pressure end blading for a utility power steam turbine having an extended length compared to original equipment end blading providing higher efficiency. The blading incorporates extended flat areas on the blade trailing edge for improved flow characteristics and reduced losses. Mass distribution is used to tune the blade to avoid natural harmonic frequencies coincidental with turbine rotational frequencies or harmonics thereof. Blade root modifications are included to facilitate installation.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to steam turbines and, more particularly, to an end blade for optimizing performance of a final stage of turbine blading. 
     The traditional approach to meeting the needs of electric utilities over the years was to build larger units requiring increased exhaust annulus area with successive annulus area increases of about 25%. In this way, a new design with a single double flow exhaust configuration would be offered instead of an older design having the same total exhaust annulus area but with two double flow LP turbines. The newer design would have superior performance in comparison to the old design because of technological advances. 
     In recent years, the market has emphasized replacement blading on operating units to extend life, to obtain the benefits of improvied thermal performance (both output and heat rate), and to improve reliability and correction of equipment degradation. In addition, the present market requires upgraded versions of currently available turbine designs with improved reliability, lower heat rate and increased flexibility. 
     The latter stages of the steam turbine, because of their length, produced the largest proportion of the total turbine work and therefore have the greatest potential for improved heat rate. The last turbine stage operates at variable pressure ratio and consequently the stage design is extremely complex. All of the first turbine stage, if it is a partial-arc admission design, experiences a comparable variation in operating conditions. In addition to the last stage, the upstream low pressure (LP) turbine stages can also experience variations on operating conditions because of: (1) differences in rated load end loading; (2) differences in site design exhaust pressure and deviations from the design values; (3) hood performance differences on various turbine frames; (4) LP inlet steam conditions resulting from cycle steam conditions and cycle variations; (5) location of extraction points; (6) operating load profile (base load versus cycle); and (7) zoned or multi-pressure condenser applications versus unzoned or single pressure condenser applications. Since the last few stages in the turbine are tuned, tapered, twisted blades with more selected inlet angles, the seven factors identified above have greater influence in stage performance. Consequently, it is desirable to design last row blades for low pressure steam turbines in a manner to meet the requirements of the above listed seven factors. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an end blade for a low pressure steam turbine which optimizes efficiency of the end blading. 
     The present invention, in one form, comprises end blading for a low pressure steam turbine which has been extended in length as compared to prior blades used in the same design steam turbine. In addition, the end blading incorporates an extended flat area along a trailing edge to provide improved flow and reduced losses across the end blading. The end blading is tuned in three different modes, i.e., for vibration in a tangential direction, for vibration in an axial direction and for vibration in a torsional (twist) direction. The blade is tuned so that its natural frequency is distinct from harmonics of turbine running speed. The blade is tuned by shifting mass distribution within the blade to change its natural resonant frequency. In addition, the blade root is modified to give larger clearances under the platform to allow easier installation during retrofit application of the turbine blade. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a better understanding of the present invention, reference may be had to the following detailed description taken in conjunction with the accompanying drawings in which: 
     FIG. 1 is a view of the blade taken transverse to the normal plane of rotation and indicating a plurality of section lines used for establishing a blade profile; 
     FIG. 2 is a view of the blade of FIG. 1 rotated 90°; 
     FIG. 3 is a sectional view of the blade taken through the section lines B--B; 
     FIG. 4 is a sectional view of the blade of FIG. 1 taken through the section lines F--F; and 
     FIG. 5 is a computer generated graphical representation of a pair of turbine blades in accordance with the present invention indicating the extent of the flat trailing edge of the inventive blade. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring now to FIG. 1, there is shown a view of the blade taken transverse to the normal plane of rotation of the blade. In this plane, the blade 10 is essentially a tapered blade having a pair of connecting points located at section F--F and section B--B for attaching the blade to adjacent blades. Preferably, the blades are grouped in groups of four and tuned in such groups to avoid resonance in the tangential, axial and torsional modes with multiple harmonics. The tuning is achieved by mass distribution within the blade to avoid resonance with multiple harmonics. The tuning also is designed to avoid excitation of frequencies at multiples of the turbine speed. The connecting points 12, 14 at B--B and F--F are referred to an inner and outer latching wires and are located at eleven inches and twenty inches above the blade base section. The blade includes a zero taper angle at the base to simplify the manufacturing process. The axial width of the blade base section is 4.25 inches while the axial width of the blade tip section is 1.22 inches. To improve aerodynamic performance during transonic operation, the blades are designed with straight back suction surface from the point of throat to the blade trailing edge. This section can be seen in the computer generated drawing of FIG. 5. The straight back section surface is shown from point A to point B on the blade. From point B to point C at the leading edge of the blade, the blade is essentially a continuous spline. 
     Referring to FIG. 2, it can be seen that the blade root includes a plurality of lugs 20 for supporting the blade in a groove formed in a rotor of a turbine. The radii of the lugs has been modified to provide additional clearance under the platform for ease of installation of the blade into the platform groove. 
     In the cross-sectional views shown in FIGS. 3 and 4, the two latching wire lugs are shown at 22 and 24. The latching wires are welded to adjacent latching wires of adjacent blades to join the blades into groups of four. Lugs 22 are located at section B--B and luges 24 are located at section F--F. 
     The blades are designed and tuned in groups to avoid natural frequencies which coincide with the rotational frequency of the rotor to which the blade is attached. In addition, the strength of the blade in various modes of vibration is verified mathematically and then the blade is mechanically excited at resonant condition and all untuned modes of vibration up to the twentieth harmonic of the turbine running speed. 
     A better understanding of the blade can be had by reference to Table I which shows the dimensions of the blade taken at the cross-section lines indicated in FIG. 1. Note that the Table also specifies the inlets and exit openings between adjacent blades. These blades are arranged, as described above, in groups of four with 120 blades forming a blade row in one embodiment. The pitch and inlet/exit angles precisely define the arrangement of blades. 
     While the present invention has been described in what is considered to be a preferred embodiment, it is intended that it not be limited by the disclosed implementation but be interpreted within the full spirit and scope of the appended claims. 
     
                                           TABLE I__________________________________________________________________________BB70 L-OR FINAL;SECTION      K-K  J-J  H-H  G-G  F-F E-E                                 D-D  C-C  B-B  A-ARADIUS (IN)  21.0000             23.0010                  26.0000                       29.0000                            32.0000                                 .06632                                      36.0000                                           38.0000                                                41.0000                                                     44.5000__________________________________________________________________________1. WIDTH (IN)        4.25000             3.98599                  3.59000                       3.19487                            2.80004                                 2.53499                                      2.27502                                           2.02001                                                1.63994                                                     1.220002. CHORD (IN)        4.27696             4.06846                  3.80152                       3.57532                            3.38230                                 3.27467                                      3.18522                                           3.11362                                                3.02030                                                     2.986163. PITCH/WIDTH        .25872             .30214                  .37921                       .47526                            .59839                                 .70227                                      .82855                                           .98498                                                1.30905                                                     1.909854. PITCH/CHORD        .25709             .29602                  .35811                       .42470                            .49538                                 .54364                                      .59178                                           .63902                                                .71078                                                     .780275. STAGGER ANGLE        5.99407             11.14957                  18.87216                       26.44029                            34.00799                                 39.25621                                      44.50158                                           49.74360                                                57.49909                                                     66.50863(DEG)6. MAXIMUM   .49309             .49336                  .47970                       .44171                            .36554                                 .30734                                      .27120                                           34.75539                                                .23791                                                     .19786THICKNESS(I7. MAXIMUM   .11528             .12127                  .12619                       .12354                            .10807                                 .09385                                      .08514                                           .08157                                                .07877                                                     .06626THICKNESS/CH8. TURNING   99.00775             95.26683                  91.87936                       88.86644                            83.76492                                 77.73416                                      63.48453                                           45.30250                                                22.42356                                                     3.15092ANGLE(DEG)9. EXIT OPENING        .59287             .65578                  .74573                       .82308                            .88852                                 .91394                                      .92833                                           .92596                                                .87312                                                     .75481(IN)10. EXIT OPENING        37.00990             37.01522                  36.77622                       36.01430                            34.88362                                 33.54951                                      31.98439                                           30.03656                                                26.06724                                                     20.73475ANGLE11. INLET METAL        44.17650             47.84891                  51.44978                       55.15249                            61.38140                                 68.72656                                      84.54536                                           101.6240                                                131.52230                                                     156.12210ANGLE(D12. INLET INCL.        11.40081             16.53943                  22.84699                       25.47453                            25.91233                                 24.68350                                      22.48244                                           21.19228                                                17.00538                                                     12.38879ANGLE(D13. EXIT METAL        36.81575             36.88426                  36.67086                       35.98107                            34.85368                                 33.53928                                      31.97012                                           30.03510                                                26.05414                                                     20.72697ANGLE(DE14. EXIT INCL.        -.36321             -.26176                  -.21057                       -.06632 -.05841                            -.0.02031                                 -.01361                                      -.00290                                           -.00751                                                -.01513ANGLE(DE15. SUCTION SURFACE        .01252             .00007                  .00007                       .00006                            .00072                                 .00007                                      .00746                                           .00002                                                .00920                                                     .00020TURN16. AREA(IN**2)        1.59755             1.46661                  1.24542                       1.02627                            .75902                                 .64368                                      .54398                                           .49238                                                .44678                                                     .3869517. ALPHA (DEG)        2.32645             7.98010                  17.19555                       27.24394                            36.35089                                 41.96792                                      47.07823                                           51.99890                                                58.93754                                                     67.1677918. FX (IN**(-4))        .58790             .85758                  1.89608                       5.06472                            14.65036                                 33.54171                                      73.28596                                           156.72040                                                410.31290                                                     1125.0840019. FY (IN**(-4))        6.73463             7.85927                  10.37945                       15.39305                            25.44271                                 40.92631                                      63.75584                                           96.90266                                                152.39400                                                     202.7864020. FXY (IN**(-4))        .25013             1.00122                  2.90337                       7.23665                            17.32703                                 34.75539 65.56981                                      119.97750                                           245.89130                                                471.9702021. I TOR (IN**(-4))        .08412             .07587                  .05812                       .03850                            .01983                                 .01159                                      .00672                                           .00606                                                .00460                                                     .0028822. I MIN (IN**(-4))        .14826             .12501                  .08867                       .05230                            .02618                                 .01385                                      .00745                                           .00399                                                .00179                                                     .0007623. I MAX (IN**(-4))        1.73090             1.39427                  1.00242                       .74707                            .52668                                 .43801                                      .35995                                           .31623                                                .27049                                                     .2453424. X BAR    -.00058             -.00652                  .01980                       .00451                            .01969                                 -.01022                                      -.02008                                           - .01986                                                .01471                                                     .0186525. Y BAR    .00026             -.00594                  .01890                       .00473                            .01977                                 -.02021                                      -.02215                                           -.02510                                                -.02048                                                     .0191526. ZMINLE (IN**3)        -.18206             -.16007                  -.12497                       -.08167                            -.04801                                 -.03031                                      -.02025                                           -.01422                                                -.01034                                                     -.0094027. ZMAXLE (IN**3)        .81489             .73306                  .67205                       .56553                            .44324                                 .36516                                      .30290                                           .26391                                                .22716                                                     .2027128. ZMINTE (IN**3)        -.14026             -.12898                  -.10948                       -.08934                            -.06412                                 -.04616                                      -.03321                                           -.02463                                                -0.1722                                                     -.0142329. ZMAXTE (IN**3)        -.77418             -.62188                  -.44142                       -.33700                            -.24438                                 -.21485                                      -.18402                                           -.16882                                                -.15179                                                     -.1416530. CMINLE (IN**3)        -.81435             -.78097                  -.70950                       -.64040                            -.54539                                 -.47505                                      -.36699                                           -.28084                                                -.17292                                                     -.0803931. CAMXLE (IN**3)        2.12406             1.90199                  1.49159                       1.32100                            1.8827                                 1.19950                                      1.18834                                           1.19822                                                1.19072                                                     1.2103132. CMINTE (IN**3)        -1.05706             -.96921                  -.80994                       -.58547                            -.40831                                 -.30012                                      -.22427                                           -.16208                                                -.10386                                                     -.0530933. CMAXTE (IN**3)        -2.23578             -2.24203                  -2.27090                       -2.21684                            -2.15518                                 -2.03868                                      -1.95604                                           -1.87313                                                -1.78200                                                     -1.73196__________________________________________________________________________