CN100379941C - 用于涡轮叶片的翼面形状 - Google Patents

用于涡轮叶片的翼面形状 Download PDF

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CN100379941C
CN100379941C CNB2004100457776A CN200410045777A CN100379941C CN 100379941 C CN100379941 C CN 100379941C CN B2004100457776 A CNB2004100457776 A CN B2004100457776A CN 200410045777 A CN200410045777 A CN 200410045777A CN 100379941 C CN100379941 C CN 100379941C
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turbine
airfoil
blade
aerofoil
distance
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CN1573021A (zh
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X·J·张
A·A·丘拉托
R·K·布拉克
D·S·佩塞特斯基
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
    • F01D5/12—Blades
    • F01D5/14—Form or construction
    • F01D5/18—Hollow blades, i.e. blades with cooling or heating channels or cavities; Heating, heat-insulating or cooling means on blades
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
    • F01D5/12—Blades
    • F01D5/14—Form or construction
    • F01D5/141—Shape, i.e. outer, aerodynamic form
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2220/00—Application
    • F05D2220/30—Application in turbines
    • F05D2220/32—Application in turbines in gas turbines
    • F05D2220/321—Application in turbines in gas turbines for a special turbine stage
    • F05D2220/3212—Application in turbines in gas turbines for a special turbine stage the first stage of a turbine
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2240/00—Components
    • F05D2240/20—Rotors
    • F05D2240/30—Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor
    • F05D2240/301—Cross-sectional characteristics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2250/00—Geometry
    • F05D2250/70—Shape
    • F05D2250/74—Shape given by a set or table of xyz-coordinates
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S416/00—Fluid reaction surfaces, i.e. impellers
    • Y10S416/02—Formulas of curves

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  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Fluid Mechanics (AREA)
  • Turbine Rotor Nozzle Sealing (AREA)

Abstract

第一级涡轮叶片(16)具有大致按照表I提出的X、Y和Z的笛卡儿坐标值的翼面轮廓(36)，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以单位为英寸的翼面高度而转换成单位为英寸的Z距离，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面(38)的单位为英寸的距离，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状。X、Y和Z距离可作为同一常数或数字的函数进行缩放以便提供放大或缩小的翼面截面。通过X、Y和Z给出的标定翼面在垂直于翼面表面的方向上位于±0.055寸的范围内。

Description

用于涡轮叶片的翼面形状
技术领域
本发明涉及一种燃气涡轮级叶片的翼面，并且更特别是本发明涉及一种第一级涡轮叶片翼面轮廓。
背景技术
对于燃气涡轮的热燃气路径段来说必须满足许多系统需要，以便满足包括改善总体效率以及翼面负载的设计要求。特别是，涡轮节的第一级的叶片必须满足特定阶段的热和操作需要。与空气冷却叶片翼面相关的特殊问题是第一级叶片的后边缘的根部冷却孔处的系统破裂。破裂问题使得叶片寿命减小。
发明内容
按照本发明的优选实施例，提供一种用于最好是第一级叶片的燃气涡轮叶片的特定翼面形状，从而提高燃气涡轮的性能并解决破裂问题。确信破裂的原因是由于根部冷却孔附近的机械和热负载引起的低循环疲劳所造成的。减小后边缘的根部冷却孔处的热和机械应力可以减小或消除破裂问题并造成部件寿命显著延长。其翼面形状还改善不同级涡轮之间的相互作用，并提供改善的空气动力效率。同时将减小第一级翼面的热和机械应力。
通过点的独特位置来限定叶片翼面轮廓以便实现所需效率和负载需要，由此获得改善的涡轮性能。点的独特位置限定标定翼面轮廓并通过以下的表I的X、Y和Z的笛卡儿坐标来限定。表I所示的1320个点的座标值是相对于涡轮中心线的并用于叶片翼面沿着其长度的不同截面处的冷(室温)叶片。正X、Y和Z方向分别是轴向朝着涡轮排出端、向后看时发动机转动方向的切向以及径向向外朝向叶片尖端。X和Y座标以距离尺寸(例如单位为英寸)给出，并在每个Z位置处平滑连接以便形成平滑连续的翼面截面。Z座标以从0～1的无量纲形式给出。通过将表I无量纲的Z值与翼面高度尺寸相乘，可以获得叶片翼面的翼面形状(即轮廓)。X、Y平面内的每个限定的翼面截面与Z方向上的相邻轮廓截面平滑连接以便形成完整的翼面轮廓。得到的翼面特别具有减小的机械和热应力，其减小或消除后边缘的根部冷却孔处的破裂问题。
将理解到当每个叶片翼面在使用时受到加热时，轮廓将由于机械负载和温度而变化。因此，通过X、Y和Z座标给出冷或室温曲线以便于制造。由于制造的叶片翼面轮廓可不同于以下表格给出的标定翼面轮廓，在垂直于沿着标定轮廓的任何表面位置的方向上离开标定轮廓的正或负0.055英寸的距离限定该叶片翼面的轮廓范围。该轮廓形状可经受这种变化而不降低叶片的机械和空气动力性能。
同样将理解到叶片可在几何上放大或缩小以便引入类似的涡轮设计。因此，下面给出的标定翼面轮廓的X和Y座标(英寸)和无量纲的Z座标(当转换成英寸时)可以是同一常数或数字的函数。即，X、Y和Z座标值(英寸)可乘以或除以同一常数或数字以便提供叶片翼面轮廓的放大或缩小形式，同时保持翼面截面的形状。
在本发明的优选实施例中，提供一种涡轮叶片，其包括具有翼面形状的叶片翼面，翼面具有大致按照表I提出的X、Y和Z的笛卡儿坐标值的标定翼面轮廓，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以翼面高度(英寸)而转换成Z距离(英寸)，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面的距离(英寸)，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状。
在本发明的另一优选实施例中，提供一种涡轮叶片，其包括叶片翼面，翼面具有大致按照表I提出的X、Y和Z的笛卡儿坐标值的未覆盖涂层标定翼面轮廓，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以翼面高度(英寸)而转换成Z距离(英寸)，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面的距离(英寸)，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状，X、Y和Z距离能够作为同一常数或数字的函数，以便提供放大或缩小的翼面。
按照本发明的又一优选实施例，提供一种涡轮，涡轮包括具有多个叶片的涡轮叶轮，每个叶片包括具有翼面形状的翼面，翼面具有大致按照表I提出的X、Y和Z的笛卡儿坐标值的标定轮廓，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以翼面高度(英寸)而转换成Z距离(英寸)，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面的距离(英寸)，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状。
按照本发明的又一优选实施例，提供一种涡轮，涡轮包括具有多个叶片的涡轮叶轮，每个叶片包括具有翼面，翼面具有大致按照表I提出的X、Y和Z的笛卡儿坐标值的未覆盖涂层标定翼面轮廓，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以翼面高度(英寸)而转换成Z距离(英寸)，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面的距离(英寸)，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状，X、Y和Z距离能够作为同一常数或数字的函数，以便提供放大或缩小的翼面。
附图说明
图1是通过涡轮的多个级的热燃气路径的示意图并表示本发明优选实施例的第一级叶片翼面；
图2是结合平台及其大致或几乎轴向的鸠尾件连接形式表示本发明优选实施例的叶片的透视图；
图3是大致周向看到的图2叶片以及相关的平台和鸠尾件连接形式的侧立视图；
图4是表示叶片翼面轮廓的叶片的顶部视图；以及
图5是从上游方向看到的叶片和相关的平台和鸠尾件连接形式的端视图。
部件列表
热燃气路径10、燃气涡轮12、喷嘴14、18、22、叶片16、20、24、转子17、热燃气路径26、转子轮19、平台30、柄部32、尖端33、鸠尾件34、叶片翼面36、轮廓截面38、根部31、转子轴线39、排出位置40、后边缘42。
具体实施方式
现在参考附图，特别是参考图1，其中表示包括多个涡轮级的燃气涡轮12的热燃气路径10。表示出有三个级。例如，第一级包括多个周向间隔开的喷嘴14和叶片16。喷嘴在周向上相互间隔开并围绕转子的轴线固定。当然，第一级叶片16安装在涡轮转子17上。还表示涡轮12的第二级，其包括多个周向间隔开的喷嘴18和多个安装在转子17上的周向间隔开的叶片20。还表示出第三级，其包括多个周向间隔开的喷嘴22和安装在转子17上的叶片。将理解到喷嘴和叶片位于涡轮的热燃气路径10上，热燃气流过热燃气路径10的方向由箭头26表示。
将理解到例如第一级的叶片16的叶片安装在形成转子17一部分的转子叶轮19上。每个叶片16设置平台30、柄部32和大致或几乎轴向的鸠尾件34(例如大约偏离轴线15度)，以便与转子叶轮19上的互补形状的配合鸠尾件(未示出)连接。但是可以设置具有本发明翼面轮廓的轴向的鸠尾件。还将理解到每个叶片16具有图2～5所示的叶片翼面36。因此，从平面30中心处的叶片根部31到叶片尖端33的任何截面处，每个叶片16具有翼面形状的叶片翼面轮廓(图4)。
为了限定每个第一级叶片翼面的翼面形状，在空间上提供独特的一组点的位置，该点满足级的要求，并可以制造。这些独特点的位置满足级效率和减小热和机械应力的需要。通过在空气动力和机械负载之间进行重复以便使得涡轮以有效、安全和平稳的方式运行来获得这些点的位置。限定叶片翼面轮廓的点的独特位置包括一组相对于涡轮转动轴线的1320个点。下面表I给出的X、Y和Z值的笛卡儿座标系限定叶片翼面沿着其长度的不同位置上的轮廓。表I中的X和Y座标的座标值以英寸给出，当这些值适当转换时也可以使用其他单位的尺寸。表I中的Z值以0～1的无量纲形式给出。表中给出的无量纲Z值乘以翼面高度(英寸)以便将Z值转换成Z座标值(例如英寸)。笛卡儿坐标系具有垂直的X、Y和Z轴，并且X轴平行于涡轮转子中心线(即转动轴线)并且正X座标值是轴向朝着后部(即涡轮的排出端)。正Y座标值在转子转动方向(向后看)的切向上延伸，并且正Z座标值径向向外朝着叶片尖端。
通过限定垂直于X、Y平面的Z方向上给定位置的X和Y座标值，可以确定沿着叶片长度的每个Z距离上的叶片翼面的轮廓截面(例如图2所示的轮廓截面38)。通过以平滑连续圆弧连接X和Y值，确定每个距离Z上的每个轮廓截面38。距离Z之间的不同表面位置的翼面轮廓通过平滑地相互连接相邻的轮廓截面38来确定以便形成翼面轮廓。这些值表示环境温度下的非操作或非热条件下的翼面轮廓，并且是未覆盖涂层翼面。
表I值产生并表示成具有三个小数位以便确定翼面轮廓。在翼面实际轮廓中还必须考虑到典型的制造误差和涂层。因此，表I中给出的轮廓值用于标定翼面。因此将理解到包括任何涂层厚度的±典型制造误差(即±值)加入下面表I给出的X和Y值中。因此，在垂直于沿着翼面轮廓的任何表面位置的方向上的±0.055的距离限定特定叶片结构和涡轮的翼面轮廓范围，即在标定的冷或室温下的实际翼面表面上的测量点和相同温度下下面表格给出的那些点的理想位置之间变化的范围。叶片翼面结构在该变化范围内经久耐用而不降低机械和空气动力性能。叶片翼面结构还在后边缘的根部冷却孔处造成减小的机械和热应力。低循环疲劳的减小增加了启动-关闭次数，由此显著增加部件寿命。
下面表I给出的座标值提供优选的标定轮廓范围。
表I
  X   Y   Z   X   Y   Z   X   Y   Z
  -1.2586   0.2667   0.0435   -0.3936   0.8693   0.0435   0.7563   0.0508   0.0435
  -1.4302   -0.0286   0.0435   -0.4577   -0.0148   0.0435   1.2571   -1.3560   0.0435
  -1.5168   -0.3555   0.0435   -0.1178   -0.0139   0.0435   1.2594   -1.0697   0.0435
  -1.2776   -0.4864   0.0435   -0.1891   0.8735   0.0435   1.1408   -0.7492   0.0435
  -1.0083   -0.2769   0.0435   -0.6543   -0.0723   0.0435   0.7580   -0.6303   0.0435
  -1.1343   0.4298   0.0435   -0.5270   0.8400   0.0435   1.0091   -0.4338   0.0435
  -1.3322   0.1515   0.0435   -0.3220   0.0006   0.0435   0.9584   -0.9071   0.0435
  -0.7774   0.7317   0.0435   0.0096   0.8250   0.0435   0.8584   -0.1271   0.0435
  -1.4834   -0.1544   0.0435   -0.3256   0.8764   0.0435   1.1365   -1.1988   0.0435
  -1.4687   -0.4803   0.0435   0.6454   0.2233   0.0435   1.3249   -1.2641   0.0435
  -1.1658   -0.4082   0.0435   0.1409   -0.0999   0.0435   1.2134   -0.9410   0.0435
  -0.8963   -0.1986   0.0435   0.4397   0.4960   0.0435   1.0900   -0.6222   0.0435
  -1.2191   0.3225   0.0435   0.4262   -0.2866   0.0435   0.8412   -0.7388   0.0435
  -1.3992   0.0324   0.0435   0.1895   0.7276   0.0435   0.9515   -0.3098   0.0435
  -1.5145   -0.2873   0.0435   0.5667   0.3351   0.0435   1.0320   -1.0223   0.0435
  -1.3416   -0.5100   0.0435   0.2605   -0.1661   0.0435   0.7913   -0.0079   0.0435
  -1.0621   -0.3192   0.0435   0.3465   0.5960   0.0435   1.2029   -1.3183   0.0435
  X   Y   Z   X   Y   Z   X   Y   Z
  -1.0888   0.4808   0.0435   0.5283   -0.3775   0.0435   1.2817   -1.1344   0.0435
  -1.2962   0.2097   0.0435   0.0720   0.7973   0.0435   1.1654   -0.8130   0.0435
  -0.7173   0.7642   0.0435   0.6833   0.1664   0.0435   0.7147   -0.5774   0.0435
  -1.4587   -0.0907   0.0435   0.0785   -0.0720   0.0435   1.0368   -0.4963   0.0435
  -1.5040   -0.4225   0.0435   0.4835   0.4436   0.0435   0.9203   -0.8503   0.0435
  -1.2194   -0.4506   0.0435   0.3727   -0.2440   0.0435   0.8904   -0.1875   0.0435
  -0.9531   -0.2367   0.0435   0.2444   0.6869   0.0435   1.1023   -1.1396   0.0435
  -1.1777   0.3769   0.0435   0.6243   -0.4749   0.0435   0.7203   0.1089   0.0435
  -1.3665   0.0924   0.0435   0.6065   0.2795   0.0435   1.3168   -1.3294   0.0435
  -1.5025   -0.2200   0.0435   0.2016   -0.1313   0.0435   1.2368   -1.0052   0.0435
  -1.4094   -0.5123   0.0435   0.3941   0.5469   0.0435   1.1157   -0.6856   0.0435
  -1.1142   -0.3634   0.0435   0.4781   -0.3312   0.0435   0.8001   -0.6842   0.0435
  -1.0411   0.5298   0.0435   0.1321   0.7646   0.0435   0.9807   -0.3716   0.0435
  -0.8381   -0.1628   0.0435   0.0144   -0.0482   0.0435   -0.8314   0.7341   0.1388
  -0.5244   -0.0297   0.0435   0.5258   0.3898   0.0435   -1.0994   0.5162   0.1388
  -0.6554   0.7933   0.0435   0.3175   -0.2038   0.0435   -1.3117   0.2432   0.1388
  -0.1854   -0.0040   0.0435   0.2967   0.6428   0.0435   -1.2733   -0.3673   0.1388
  -0.1215   0.8633   0.0435   0.5770   -0.4255   0.0435   -1.4673   -0.0652   0.1388
  -0.7171   -0.0992   0.0435   0.9956   -0.9644   0.0435   -0.9932   -0.1654   0.1388
  -0.4608   0.8570   0.0435   0.8254   -0.0672   0.0435   -1.4082   -0.3771   0.1388
  -0.3901   -0.0047   0.0435   1.1702   -1.2583   0.0435   -0.9453   0.6554   0.1388
  -0.0511   -0.0288   0.0435   1.3043   -1.1989   0.0435   -1.1906   0.4120   0.1388
  -0.2573   0.8779   0.0435   1.1896   -0.8769   0.0435   -1.3827   0.1242   0.1388
  X   Y   Z   X   Y   Z   X   Y   Z
  -0.5900   -0.0490   0.0435   0.6701   -0.5256   0.0435   -1.1559   -0.2946   0.1388
  -0.5920   0.8187   0.0435   1.0637   -0.5591   0.0435   -1.4922   -0.2012   0.1388
  -0.2536   0.0008   0.0435   0.8812   -0.7942   0.0435   -0.8772   -0.0897   0.1388
  -0.0551   0.8472   0.0435   0.9215   -0.2484   0.0435   -1.2733   -0.3673   0.1388
  -0.7783   -0.1295   0.0435   1.0675   -1.0807   0.0435   -0.7713   0.7686   0.1388
  -1.0504   0.5651   0.1388   0.6469   0.1822   0.1388   0.8579   -0.1758   0.1388
  -1.2733   0.3009   0.1388   -0.0140   0.0106   0.1388   1.0432   -1.0500   0.1388
  -1.4437   -0.0001   0.1388   0.4440   0.4628   0.1388   1.2452   -1.3105   0.1388
  -1.0486   -0.2069   0.1388   0.2890   -0.1550   0.1388   1.2134   -1.0026   0.1388
  -1.4610   -0.3337   0.1388   0.2019   0.7096   0.1388   1.0880   -0.6797   0.1388
  -0.8894   0.6963   0.1388   0.5482   -0.3842   0.1388   0.7299   -0.5933   0.1388
  -1.1461   0.4650   0.1388   0.5688   0.2966   0.1388   0.9499   -0.3621   0.1388
  -1.3482   0.1843   0.1388   0.1127   -0.0453   0.1388   0.9323   -0.8742   0.1388
  -1.2120   -0.3351   0.1388   0.3535   0.5677   0.1388   0.7916   -0.0541   0.1388
  -1.4840   -0.1324   0.1388   0.3975   -0.2411   0.1388   1.1134   -1.1694   0.1388
  -0.9360   -0.1262   0.1388   0.0879   0.7881   0.1388   1.2849   -1.1977   0.1388
  -1.3401   -0.3849   0.1388   0.6415   -0.4865   0.1388   1.1644   -0.8730   0.1388
  -0.7094   0.7996   0.1388   0.6845   0.1240   0.1388   1.0347   -0.5519   0.1388
  -0.9990   0.6116   0.1388   0.4869   0.4084   0.1388   0.8137   -0.7035   0.1388
  -1.2330   0.3572   0.1388   0.2321   -0.1155   0.1388   0.8895   -0.2374   0.1388
  -1.4149   0.0629   0.1388   0.2549   0.6650   0.1388   -1.1882   0.4426   0.2342
  -1.1023   -0.2507   0.1388   0.4994   -0.3349   0.1388   -1.3776   0.1643   0.2342
  -1.4872   -0.2701   0.1388   0.6083   0.2397   0.1388   -1.0852   -0.1597   0.2342
  X   Y   Z   X   Y   Z   X   Y   Z
  -0.8167   -0.0559   0.1388   0.0502   -0.0154   0.1388   -1.4594   -0.1571   0.2342
  -0.4910   0.0578   0.1388   0.3997   0.5160   0.1388   -0.8010   0.0202   0.2342
  -0.1469   0.0495   0.1388   0.3441   -0.1969   0.1388   -0.7768   0.7860   0.2342
  -0.3082   0.8960   0.1388   0.1463   0.7508   0.1388   -1.0498   0.5898   0.2342
  -0.6909   0.0020   0.1388   0.5955   -0.4347   0.1388   -1.2701   0.3355   0.2342
  -0.6457   0.8269   0.1388   1.0070   -0.9909   0.1388   -1.2569   -0.2647   0.2342
  -0.3532   0.0704   0.1388   0.7212   0.0652   0.1388   -1.4330   0.0415   0.2342
  -0.1028   0.8692   0.1388   1.1828   -1.2891   0.1388   -0.9765   -0.0800   0.2342
  -0.4460   0.8834   0.1388   1.2365   -1.0680   0.1388   -1.3885   -0.2655   0.2342
  -0.5589   0.0438   0.1388   1.1139   -0.7440   0.1388   -0.8921   0.7163   0.2342
  -0.2151   0.0616   0.1388   0.6863   -0.5394   0.1388   -1.1442   0.4936   0.2342
  -0.2390   0.8934   0.1388   0.9789   -0.4250   0.1388   -1.3441   0.2228   0.2342
  -0.7546   -0.0252   0.1388   0.8937   -0.8167   0.1388   -1.1389   -0.2005   0.2342
  -0.5805   0.8502   0.1388   0.8252   -0.1147   0.1388   -1.4617   -0.0899   0.2342
  -0.4224   0.0668   0.1388   1.0786   -1.1096   0.1388   -0.8611   -0.0103   0.2342
  -0.0798   0.0323   0.1388   1.2938   -1.2656   0.1388   -1.2569   -0.2647   0.2342
  -0.0369   0.8479   0.1388   1.1893   -0.9377   0.1388   -0.7164   0.8159   0.2342
  -0.3774   0.8925   0.1388   1.0616   -0.6157   0.1388   -1.3228   -0.2775   0.2342
  -0.6256   0.0251   0.1388   0.7723   -0.6480   0.1388   -0.9993   0.6346   0.2342
  -0.2840   0.0686   0.1388   0.9201   -0.2995   0.1388   -1.2302   0.3898   0.2342
  -0.1703   0.8844   0.1388   0.9701   -0.9323   0.1388   -1.4078   0.1040   0.2342
  -0.5138   0.8691   0.1388   0.7569   0.0059   0.1388   -1.0316   -0.1187   0.2342
  0.5284   0.3529   0.1388   1.1477   -1.2296   0.1388   -1.4374   -0.2204   0.2342
  X   Y   Z   X   Y   Z   X   Y   Z
  0.1733   -0.0788   0.1388   1.2601   -1.1331   0.1388   -0.8354   0.7528   0.2342
  0.3054   0.6175   0.1388   1.1393   -0.8084   0.1388   -1.0980   0.5428   0.2342
  0.4492   -0.2872   0.1388   1.0071   -0.4883   0.1388   -1.3081   0.2798   0.2342
  0.0268   0.8207   0.1388   0.8542   -0.7598   0.1388   -1.1955   -0.2371   0.2342
  -1.4515   -0.0233   0.2342   0.1158   0.7597   0.2342   -1.4309   -0.0474   0.3295
  -0.9196   -0.0437   0.2342   0.6127   -0.4517   0.2342   -1.4297   0.0181   0.3295
  -0.9468   0.6768   0.2342   0.6780   0.0944   0.2342   -1.4170   0.0824   0.3295
  -0.1256   0.8772   0.2342   0.4888   0.3732   0.2342   -1.4138   -0.1103   0.3295
  -0.4594   0.8952   0.2342   0.2182   -0.0859   0.2342   -1.3964   0.1446   0.3295
  -0.4790   0.1146   0.2342   0.2703   0.6296   0.2342   -1.3698   -0.1577   0.3295
  -0.1449   0.0880   0.2342   0.4752   -0.3034   0.2342   -1.3696   0.2044   0.3295
  -0.2578   0.9026   0.2342   0.6051   0.2078   0.2342   -1.3380   0.2619   0.3295
  -0.6761   0.0708   0.2342   1.2633   -1.1920   0.2342   -1.3073   -0.1755   0.3295
  -0.5906   0.8642   0.2342   1.1448   -0.8765   0.2342   -1.3029   0.3173   0.3295
  -0.3443   0.1191   0.2342   1.0165   -0.5648   0.2342   -1.2651   0.3709   0.3295
  -0.0618   0.8556   0.2342   0.7804   -0.6628   0.2342   -1.2424   -0.1682   0.3295
  -0.3925   0.9033   0.2342   0.8749   -0.2589   0.2342   -1.2424   -0.1682   0.3295
  -0.5456   0.1047   0.2342   0.9699   -0.9416   0.2342   -1.2254   0.4231   0.3295
  -0.2105   0.1032   0.2342   0.7131   0.0368   0.2342   -1.1839   0.4739   0.3295
  -0.1911   0.8931   0.2342   1.1410   -1.2320   0.2342   -1.1809   -0.1456   0.3295
  -0.7393   0.0474   0.2342   1.2162   -1.0657   0.2342   -1.1403   0.5229   0.3295
  -0.5256   0.8820   0.2342   1.0945   -0.7514   0.2342   -1.1238   -0.1135   0.3295
  -0.4117   0.1194   0.2342   0.6562   -0.5032   0.2342   -1.0948   0.5701   0.3295
  X   Y   Z   X   Y   Z   X   Y   Z
  -0.0804   0.0682   0.2342   0.9619   -0.4415   0.2342   -1.0698   -0.0762   0.3295
  -0.0001   0.8285   0.2342   0.8586   -0.7727   0.2342   -1.0473   0.6153   0.3295
  -0.3252   0.9059   0.2342   0.8129   -0.1391   0.2342   -1.0162   -0.0384   0.3295
  -0.6114   0.0900   0.2342   1.0404   -1.0565   0.2342   -0.9977   0.6583   0.3295
  -0.6542   0.8421   0.2342   1.2514   -1.2553   0.2342   -0.9613   -0.0026   0.3295
  -0.2771   0.1136   0.2342   1.1695   -0.9392   0.2342   -0.9462   0.6989   0.3295
  0.0441   0.0166   0.2342   1.0430   -0.6268   0.2342   -0.9048   0.0307   0.3295
  0.4058   0.4795   0.2342   0.7400   -0.6089   0.2342   -0.8927   0.7368   0.3295
  0.3257   -0.1673   0.2342   0.9047   -0.3194   0.2342   -0.8467   0.0612   0.3295
  0.1697   0.7193   0.2342   0.9336   -0.8848   0.2342   -0.8373   0.7719   0.3295
  0.5681   -0.4011   0.2342   0.7473   -0.0213   0.2342   -0.7870   0.0884   0.3295
  0.5285   0.3188   0.2342   1.1086   -1.1728   0.2342   -0.7800   0.8039   0.3295
  0.1619   -0.0488   0.2342   1.2411   -1.1284   0.2342   -0.7259   0.1121   0.3295
  0.3173   0.5812   0.2342   1.1198   -0.8139   0.2342   -0.7210   0.8325   0.3295
  0.4268   -0.2565   0.2342   0.9895   -0.5030   0.2342   -0.6633   0.1319   0.3295
  0.0592   0.7964   0.2342   0.8199   -0.7174   0.2342   -0.6604   0.8574   0.3295
  0.6420   0.1514   0.2342   0.8444   -0.1988   0.2342   -0.5996   0.1473   0.3295
  -0.0174   0.0443   0.2342   1.0055   -0.9988   0.2342   -0.5983   0.8785   0.3295
  0.4479   0.4269   0.2342   1.1901   -1.2751   0.2342   -0.5350   0.1582   0.3295
  0.2728   -0.1255   0.2342   1.1932   -1.0024   0.2342   -0.5349   0.8952   0.3295
  0.2212   0.6758   0.2342   1.0690   -0.6890   0.2342   -0.4704   0.9072   0.3295
  0.5223   -0.3517   0.2342   0.6986   -0.5556   0.2342   -0.4697   0.1644   0.3295
  0.5672   0.2636   0.2342   0.9336   -0.3802   0.2342   -0.4052   0.9141   0.3295
  X   Y   Z   X   Y   Z   X   Y   Z
  0.1038   -0.0146   0.2342   0.8965   -0.8284   0.2342   -0.4041   0.1657   0.3295
  0.3624   0.5311   0.2342   0.7806   -0.0800   0.2342   -0.3396   0.9155   0.3295
  0.3770   -0.2111   0.2342   1.0748   -1.1145   0.2342   -0.3386   0.1621   0.3295
  -0.2742   0.9113   0.3295   0.7854   -0.6735   0.3295   -1.1367   0.5566   0.4249
  -0.2736   0.1536   0.3295   0.8011   -0.1612   0.3295   -1.1091   -0.0266   0.4249
  -0.2094   0.9012   0.3295   0.8233   -0.7271   0.3295   -1.0916   0.6018   0.4249
  -0.2093   0.1405   0.3295   0.8315   -0.2194   0.3295   -1.0548   0.0068   0.4249
  -0.1461   0.1230   0.3295   0.8604   -0.7812   0.3295   -1.0446   0.6449   0.4249
  -0.1459   0.8850   0.3295   0.8610   -0.2779   0.3295   -1.0012   0.0415   0.4249
  -0.0842   0.1014   0.3295   0.8899   -0.3368   0.3295   -0.9957   0.6859   0.4249
  -0.0841   0.8631   0.3295   0.8967   -0.8358   0.3295   -0.9466   0.0745   0.4249
  -0.0244   0.8359   0.3295   0.9182   -0.3960   0.3295   -0.9448   0.7245   0.4249
  -0.0238   0.0760   0.3295   0.9324   -0.8908   0.3295   -0.8921   0.7604   0.4249
  0.0330   0.8042   0.3295   0.9458   -0.4555   0.3295   -0.8905   0.1050   0.4249
  0.0352   0.0472   0.3295   0.9674   -0.9463   0.3295   -0.8375   0.7935   0.4249
  0.0878   0.7682   0.3295   0.9728   -0.5153   0.3295   -0.8329   0.1324   0.4249
  0.0925   0.0153   0.3295   0.9993   -0.5753   0.3295   -0.7812   0.8234   0.4249
  0.1402   0.7288   0.3295   1.0018   -1.0021   0.3295   -0.7738   0.1564   0.4249
  0.1482   -0.0193   0.3295   1.0253   -0.6355   0.3295   -0.7232   0.8500   0.4249
  0.1902   0.6863   0.3295   1.0356   -1.0583   0.3295   -0.7133   0.1767   0.4249
  0.2023   -0.0564   0.3295   1.0509   -0.6959   0.3295   -0.6636   0.8730   0.4249
  0.2380   0.6414   0.3295   1.0689   -1.1148   0.3295   -0.6516   0.1930   0.4249
  0.2548   -0.0957   0.3295   1.0762   -0.7564   0.3295   -0.6027   0.8920   0.4249
  X   Y   Z   X   Y   Z   X   Y   Z
  0.2838   0.5945   0.3295   1.1012   -1.1719   0.3295   -0.5889   0.2050   0.4249
  0.3057   -0.1370   0.3295   1.1013   -0.8170   0.3295   -0.5407   0.9068   0.4249
  0.3279   0.5459   0.3295   1.1262   -0.8777   0.3295   -0.5256   0.2123   0.4249
  0.3552   -0.1801   0.3295   1.1382   -1.2256   0.3295   -0.4777   0.9170   0.4249
  0.3704   0.4960   0.3295   1.1506   -0.9386   0.3295   -0.4618   0.2150   0.4249
  0.4033   -0.2247   0.3295   1.1738   -0.9999   0.3295   -0.4141   0.9222   0.4249
  0.4116   0.4449   0.3295   1.1972   -1.0612   0.3295   -0.3980   0.2130   0.4249
  0.4501   -0.2707   0.3295   1.1997   -1.2352   0.3295   -0.3503   0.9221   0.4249
  0.4518   0.3931   0.3295   1.2227   -1.1216   0.3295   -0.3346   0.2063   0.4249
  0.4908   0.3404   0.3295   1.2369   -1.1852   0.3295   -0.2868   0.9165   0.4249
  0.4957   -0.3178   0.3295   -1.4013   0.0618   0.4249   -0.2718   0.1951   0.4249
  0.5289   0.2870   0.3295   -1.3967   0.1254   0.4249   -0.2239   0.9055   0.4249
  0.5401   -0.3660   0.3295   -1.3888   -0.0004   0.4249   -0.2099   0.1796   0.4249
  0.5660   0.2329   0.3295   -1.3815   0.1873   0.4249   -0.1623   0.8889   0.4249
  0.5834   -0.4153   0.3295   -1.3587   0.2469   0.4249   -0.1491   0.1601   0.4249
  0.6022   0.1782   0.3295   -1.3502   -0.0502   0.4249   -0.1024   0.8669   0.4249
  0.6257   -0.4654   0.3295   -1.3302   0.3040   0.4249   -0.0897   0.1368   0.4249
  0.6375   0.1229   0.3295   -1.2972   0.3585   0.4249   -0.0446   0.8399   0.4249
  0.6670   -0.5164   0.3295   -1.2914   -0.0734   0.4249   -0.0317   0.1102   0.4249
  0.6719   0.0671   0.3295   -1.2605   0.4108   0.4249   0.0110   0.8086   0.4249
  0.7054   0.0107   0.3295   -1.2279   -0.0716   0.4249   0.0247   0.0804   0.4249
  0.7073   -0.5681   0.3295   -1.2279   -0.0716   0.4249   0.0643   0.7735   0.4249
  0.7381   -0.0462   0.3295   -1.2212   0.4610   0.4249   0.0797   0.0480   0.4249
  X   Y   Z   X   Y   Z   X   Y   Z
  0.7468   -0.6205   0.3295   -1.1798   0.5096   0.4249   0.1152   0.7351   0.4249
  0.7700   -0.1035   0.3295   -1.1666   -0.0542   0.4249   0.1331   0.0131   0.4249
  0.1639   0.6938   0.3295   0.9951   -1.0007   0.3295   -0.7012   0.2419   0.4249
  0.1851   -0.0239   0.3295   1.0098   -0.6462   0.3295   -0.6671   0.8919   0.4249
  0.2105   0.6503   0.3295   1.0279   -1.0554   0.3295   -0.6404   0.2549   0.4249
  0.2355   -0.0630   0.3295   1.0350   -0.7048   0.3295   -0.6072   0.9085   0.4249
  0.2553   0.6048   0.3295   1.0600   -0.7635   0.3295   -0.5789   0.2635   0.4249
  0.2845   -0.1039   0.3295   1.0603   -1.1104   0.3295   -0.5463   0.9209   0.4249
  0.2984   0.5577   0.3295   1.0849   -0.8223   0.3295   -0.5168   0.2675   0.4249
  0.3322   -0.1463   0.3295   1.0915   -1.1661   0.3295   -0.4846   0.9288   0.4249
  0.3400   0.5093   0.3295   1.1096   -0.8811   0.3295   -0.4547   0.2669   0.4249
  0.3786   -0.1901   0.3295   1.1334   -0.9404   0.3295   -0.4226   0.9320   0.4249
  0.3803   0.4598   0.3295   1.1410   -1.2031   0.3295   -0.3927   0.2618   0.4249
  0.4195   0.4095   0.3295   1.1563   -0.9999   0.3295   -0.3604   0.9302   0.4249
  0.4238   -0.2352   0.3295   1.1808   -1.0588   0.3295   -0.3313   0.2522   0.4249
  0.4578   0.3584   0.3295   1.1970   -1.1790   0.3295   -0.2987   0.9231   0.4249
  0.4679   -0.2813   0.3295   1.2041   -1.1182   0.3295   -0.2706   0.2384   0.4249
  0.4950   0.3066   0.3295   -1.3715   0.1697   0.3295   -0.2377   0.9109   0.4249
  0.5110   -0.3284   0.3295   -1.3639   0.2313   0.3295   -0.2111   0.2207   0.4249
  0.5314   0.2542   0.3295   -1.3633   0.1083   0.3295   -0.1780   0.8936   0.4249
  0.5530   -0.3764   0.3295   -1.3461   0.2908   0.3295   -0.1527   0.1992   0.4249
  0.5668   0.2011   0.3295   -1.3303   0.0564   0.3295   -0.1199   0.8714   0.4249
  0.5941   -0.4253   0.3295   -1.3213   0.3478   0.3295   -0.0957   0.1744   0.4249
  X   Y   Z   X   Y   Z   X   Y   Z
  0.6013   0.1474   0.3295   -1.2911   0.4021   0.3295   -0.0638   0.8447   0.4249
  0.6342   -0.4748   0.3295   -1.2754   0.0287   0.3295   -0.0401   0.1466   0.4249
  0.6350   0.0932   0.3295   -1.2566   0.4538   0.3295   -0.0098   0.8138   0.4249
  0.6678   0.0385   0.3295   -1.2186   0.5031   0.3295   0.0140   0.1160   0.4249
  0.6735   -0.5251   0.3295   -1.2136   0.0253   0.3295   0.0419   0.7794   0.4249
  0.6999   -0.0167   0.3295   -1.2136   0.0253   0.3295   0.0667   0.0830   0.4249
  0.7120   -0.5760   0.3295   -1.1779   0.5501   0.3295   0.0916   0.7419   0.4249
  0.7311   -0.0723   0.3295   -1.1528   0.0376   0.3295   0.1180   0.0478   0.4249
  0.7497   -0.6275   0.3295   -1.1352   0.5953   0.3295   0.1391   0.7018   0.4249
  0.7617   -0.1284   0.3295   -1.0950   0.0606   0.4249   0.1679   0.0107   0.4249
  0.7867   -0.6795   0.3295   -1.0906   0.6385   0.4249   0.1847   0.6596   0.4249
  0.7916   -0.1848   0.3295   -1.0440   0.6797   0.4249   0.2164   -0.0282   0.4249
  0.8208   -0.2415   0.3295   -1.0403   0.0900   0.4249   0.2285   0.6154   0.4249
  0.8231   -0.7320   0.3295   -0.9954   0.7186   0.4249   0.2635   -0.0687   0.4249
  0.8494   -0.2985   0.3295   -0.9867   0.1216   0.4249   0.2707   0.5698   0.4249
  0.8587   -0.7849   0.3295   -0.9450   0.7549   0.4249   0.3095   -0.1107   0.4249
  0.8774   -0.3559   0.3295   -0.9325   0.1520   0.4249   0.3115   0.5228   0.4249
  0.8937   -0.8383   0.3295   -0.8928   0.7886   0.4249   0.3510   0.4748   0.4249
  0.9049   -0.4135   0.3295   -0.8768   0.1797   0.4249   0.3542   -0.1538   0.4249
  0.9281   -0.8921   0.3295   -0.8387   0.8194   0.4249   0.3894   0.4259   0.4249
  0.9318   -0.4713   0.3295   -0.8196   0.2041   0.4249   0.3978   -0.1981   0.4249
  0.9583   -0.5294   0.3295   -0.7830   0.8470   0.4249   0.4268   0.3762   0.4249
  0.9619   -0.9462   0.3295   -0.7610   0.2249   0.4249   0.4405   -0.2434   0.4249
  X   Y   Z   X   Y   Z   X   Y   Z
  0.9843   -0.5877   0.3295   -0.7258   0.8713   0.4249   0.4632   0.3259   0.4249
  0.4821   -0.2895   0.5202   -1.3430   0.2795   0.6156   -0.2112   0.2688   0.6156
  0.4987   0.2748   0.5202   -1.3379   0.2193   0.6156   -0.1983   0.9101   0.6156
  0.5229   -0.3365   0.5202   -1.3331   0.3393   0.6156   -0.1552   0.2454   0.6156
  0.5334   0.2232   0.5202   -1.3133   0.3966   0.6156   -0.1419   0.8876   0.6156
  0.5628   -0.3842   0.5202   -1.3091   0.1666   0.6156   -0.1006   0.2189   0.6156
  0.5671   0.1710   0.5202   -1.2869   0.4512   0.6156   -0.0874   0.8610   0.6156
  0.6001   0.1182   0.5202   -1.2573   0.1362   0.6156   -0.0474   0.1897   0.6156
  0.6018   -0.4326   0.5202   -1.2553   0.5030   0.6156   -0.0349   0.8306   0.6156
  0.6322   0.0650   0.5202   -1.2196   0.5520   0.6156   0.0044   0.1581   0.6156
  0.6400   -0.4817   0.5202   -1.1974   0.1288   0.6156   0.0155   0.7968   0.6156
  0.6636   0.0113   0.5202   -1.1974   0.1288   0.6156   0.0548   0.1243   0.6156
  0.6775   -0.5313   0.5202   -1.1805   0.5985   0.6156   0.0638   0.7601   0.6156
  0.6943   -0.0427   0.5202   -1.1388   0.6425   0.6156   0.1039   0.0887   0.6156
  0.7143   -0.5814   0.5202   -1.1373   0.1370   0.6156   0.1102   0.7210   0.6156
  0.7244   -0.0972   0.5202   -1.0948   0.6843   0.6156   0.1517   0.0512   0.6156
  0.7504   -0.6320   0.5202   -1.0797   0.1558   0.6156   0.1547   0.6797   0.6156
  0.7538   -0.1520   0.5202   -1.0488   0.7238   0.6156   0.1974   0.6367   0.6156
  0.7826   -0.2071   0.5202   -1.0248   0.1816   0.6156   0.1982   0.0123   0.6156
  0.7859   -0.6831   0.5202   -1.0007   0.7609   0.6156   0.2387   0.5922   0.6156
  0.8109   -0.2624   0.5202   -0.9712   0.2100   0.6156   0.2435   -0.0281   0.6156
  0.8208   -0.7345   0.5202   -0.9508   0.7954   0.6156   0.2787   0.5465   0.6156
  0.8386   -0.3181   0.5202   -0.9171   0.2376   0.6156   0.2876   -0.0698   0.6156
  X   Y   Z   X   Y   Z   X   Y   Z
  0.8551   -0.7864   0.5202   -0.8990   0.8270   0.6156   0.3175   0.4999   0.6156
  0.8659   -0.3740   0.5202   -0.8618   0.2626   0.6156   0.3307   -0.1125   0.6156
  0.8888   -0.8386   0.5202   -0.8455   0.8556   0.6156   0.3551   0.4523   0.6156
  0.8927   -0.4301   0.5202   -0.8050   0.2840   0.6156   0.3727   -0.1563   0.6156
  0.9190   -0.4864   0.5202   -0.7904   0.8809   0.6156   0.3918   0.4039   0.6156
  0.9220   -0.8912   0.5202   -0.7470   0.3015   0.6156   0.4138   -0.2010   0.6156
  0.9449   -0.5430   0.5202   -0.7338   0.9029   0.6156   0.4274   0.3548   0.6156
  0.9547   -0.9442   0.5202   -0.6878   0.3152   0.6156   0.4540   -0.2464   0.6156
  0.9704   -0.5997   0.5202   -0.6759   0.9212   0.6156   0.4621   0.3050   0.6156
  0.9869   -0.9974   0.5202   -0.6279   0.3247   0.6156   0.4934   -0.2926   0.6156
  0.9955   -0.6566   0.5202   -0.6170   0.9356   0.6156   0.4960   0.2546   0.6156
  1.0187   -1.0508   0.5202   -0.5675   0.3298   0.6156   0.5291   0.2038   0.6156
  1.0204   -0.7136   0.5202   -0.5572   0.9458   0.6156   0.5320   -0.3394   0.6156
  1.0451   -0.7706   0.5202   -0.5068   0.3303   0.6156   0.5614   0.1524   0.6156
  1.0497   -1.1047   0.5202   -0.4968   0.9516   0.6156   0.5698   -0.3869   0.6156
  1.0697   -0.8277   0.5202   -0.4463   0.3263   0.6156   0.5929   0.1006   0.6156
  1.0850   -1.1554   0.5202   -0.4361   0.9530   0.6156   0.6069   -0.4349   0.6156
  1.0940   -0.8850   0.5202   -0.3862   0.3180   0.6156   0.6238   0.0483   0.6156
  1.1171   -0.9427   0.5202   -0.3756   0.9496   0.6156   0.6433   -0.4834   0.6156
  1.1403   -1.0004   0.5202   -0.3268   0.3055   0.6156   0.6540   -0.0043   0.6156
  1.1433   -1.1641   0.5202   -0.3155   0.9413   0.6156   0.6791   -0.5325   0.6156
  1.1658   -1.0571   0.5202   -0.2684   0.2890   0.6156   0.6836   -0.0573   0.6156
  1.1795   -1.1172   0.5202   -0.2562   0.9281   0.6156   0.7127   -0.1106   0.6156
  X   Y   Z   X   Y   Z   X   Y   Z
  0.7143   -0.5819   0.6156   -1.0553   0.7753   0.7109   0.1651   0.6635   0.7109
  0.7412   -0.1642   0.6156   -1.0089   0.2768   0.7109   0.1809   0.0552   0.7109
  0.7489   -0.6318   0.6156   -1.0079   0.8111   0.7109   0.2052   0.6198   0.7109
  0.7692   -0.2180   0.6156   -0.9585   0.8440   0.7109   0.2243   0.0147   0.7109
  0.7829   -0.6820   0.6156   -0.9552   0.3021   0.7109   0.2441   0.5749   0.7109
  0.7967   -0.2721   0.6156   -0.9072   0.8739   0.7109   0.2666   -0.0269   0.7109
  0.8164   -0.7326   0.6156   -0.9013   0.3270   0.7109   0.2819   0.5292   0.7109
  0.8237   -0.3264   0.6156   -0.8542   0.9005   0.7109   0.3080   -0.0695   0.7109
  0.8494   -0.7836   0.6156   -0.8463   0.3492   0.7109   0.3187   0.4826   0.7109
  0.8504   -0.3810   0.6156   -0.7996   0.9238   0.7109   0.3484   -0.1130   0.7109
  0.8766   -0.4357   0.6156   -0.7899   0.3677   0.7109   0.3545   0.4352   0.7109
  0.8819   -0.8348   0.6156   -0.7436   0.9435   0.7109   0.3880   -0.1573   0.7109
  0.9024   -0.4906   0.6156   -0.7323   0.3821   0.7109   0.3894   0.3872   0.7109
  0.9139   -0.8863   0.6156   -0.6864   0.9596   0.7109   0.4234   0.3385   0.7109
  0.9279   -0.5457   0.6156   -0.6738   0.3924   0.7109   0.4267   -0.2022   0.7109
  0.9455   -0.9382   0.6156   -0.6283   0.9718   0.7109   0.4566   0.2893   0.7109
  0.9530   -0.6009   0.6156   -0.6148   0.3984   0.7109   0.4647   -0.2479   0.7109
  0.9767   -0.9902   0.6156   -0.5695   0.9799   0.7109   0.4891   0.2396   0.7109
  0.9778   -0.6563   0.6156   -0.5554   0.4000   0.7109   0.5020   -0.2941   0.7109
  1.0023   -0.7118   0.6156   -0.5103   0.9838   0.7109   0.5208   0.1894   0.7109
  1.0076   -1.0425   0.6156   -0.4961   0.3970   0.7109   0.5386   -0.3408   0.7109
  1.0267   -0.7674   0.6156   -0.4509   0.9832   0.7109   0.5519   0.1388   0.7109
  1.0379   -1.0951   0.6156   -0.4372   0.3895   0.7109   0.5745   -0.3881   0.7109
  X   Y   Z   X   Y   Z   X   Y   Z
  1.0511   -0.8230   0.6156   -0.3918   0.9782   0.7109   0.5824   0.0878   0.7109
  1.0748   -0.8788   0.6156   -0.3790   0.3779   0.7109   0.6098   -0.4358   0.7109
  1.0856   -1.1289   0.6156   -0.3332   0.9686   0.7109   0.6122   0.0365   0.7109
  1.0973   -0.9352   0.6156   -0.3217   0.3624   0.7109   0.6415   -0.0151   0.7109
  1.1215   -0.9908   0.6156   -0.2756   0.9544   0.7109   0.6446   -0.4840   0.7109
  1.1384   -1.1047   0.6156   -0.2655   0.3432   0.7109   0.6702   -0.0671   0.7109
  1.1452   -1.0466   0.6156   -0.2193   0.9356   0.7109   0.6788   -0.5325   0.7109
  -1.3151   0.3906   0.7109   -0.2106   0.3207   0.7109   0.6984   -0.1193   0.7109
  -1.3127   0.3315   0.7109   -0.1645   0.9126   0.7109   0.7124   -0.5814   0.7109
  -1.3030   0.4486   0.7109   -0.1570   0.2951   0.7109   0.7262   -0.1718   0.7109
  -1.2872   0.2786   0.7109   -0.1116   0.8857   0.7109   0.7456   -0.6307   0.7109
  -1.2814   0.5039   0.7109   -0.1048   0.2669   0.7109   0.7535   -0.2245   0.7109
  -1.2533   0.5562   0.7109   -0.0607   0.8553   0.7109   0.7783   -0.6803   0.7109
  -1.2385   0.2457   0.7109   -0.0540   0.2362   0.7109   0.7804   -0.2775   0.7109
  -1.2204   0.6056   0.7109   -0.0117   0.8217   0.7109   0.8069   -0.3306   0.7109
  -1.1836   0.6521   0.7109   -0.0045   0.2034   0.7109   0.8105   -0.7301   0.7109
  -1.1804   0.2350   0.7109   0.0352   0.7853   0.7109   0.8330   -0.3839   0.7109
  -1.1804   0.2350   0.7109   0.0437   0.1687   0.7109   0.8423   -0.7803   0.7109
  -1.1435   0.6958   0.7109   0.0802   0.7466   0.7109   0.8588   -0.4374   0.7109
  -1.1213   0.2395   0.7109   0.0906   0.1324   0.7109   0.8736   -0.8307   0.7109
  -1.1006   0.7369   0.7109   0.1235   0.7059   0.7109   0.8842   -0.4911   0.7109
  -1.0639   0.2545   0.7109   0.1363   0.0945   0.7109   0.9046   -0.8813   0.7109
  0.9093   -0.5449   0.7109   -0.6010   0.4722   0.8063   0.4374   -0.2038   0.8063
  X   Y   Z   X   Y   Z   X   Y   Z
  0.9342   -0.5988   0.7109   -0.5835   1.0243   0.8063   0.4476   0.2789   0.8063
  0.9352   -0.9322   0.7109   -0.5429   0.4701   0.8063   0.4734   -0.2495   0.8063
  0.9587   -0.6529   0.7109   -0.5253   1.0260   0.8063   0.4789   0.2298   0.8063
  0.9654   -0.9833   0.7109   -0.4850   0.4635   0.8063   0.5088   -0.2957   0.8063
  0.9828   -0.7071   0.7109   -0.4672   1.0234   0.8063   0.5096   0.1804   0.8063
  0.9947   -1.0350   0.7109   -0.4279   0.4526   0.8063   0.5397   0.1305   0.8063
  1.0069   -0.7614   0.7109   -0.4094   1.0162   0.8063   0.5436   -0.3424   0.8063
  1.0309   -1.0814   0.7109   -0.3716   0.4378   0.8063   0.5692   0.0804   0.8063
  1.0310   -0.8157   0.7109   -0.3524   1.0046   0.8063   0.5778   -0.3895   0.8063
  1.0541   -0.8704   0.7109   -0.3164   0.4193   0.8063   0.5982   0.0299   0.8063
  1.0763   -0.9254   0.7109   -0.2964   0.9887   0.8063   0.6115   -0.4369   0.8063
  1.0872   -1.0834   0.7109   -0.2625   0.3975   0.8063   0.6267   -0.0208   0.8063
  1.1021   -0.9789   0.7109   -0.2418   0.9686   0.8063   0.6448   -0.4847   0.8063
  1.1175   -1.0356   0.7109   -0.2098   0.3726   0.8063   0.6548   -0.0718   0.8063
  -1.2875   0.4444   0.8063   -0.1888   0.9446   0.8063   0.6775   -0.5329   0.8063
  -1.2874   0.5024   0.8063   -0.1586   0.3450   0.8063   0.6824   -0.1231   0.8063
  -1.2731   0.5587   0.8063   -0.1376   0.9169   0.8063   0.7096   -0.1745   0.8063
  -1.2652   0.3912   0.8063   -0.1087   0.3151   0.8063   0.7098   -0.5813   0.8063
  -1.2494   0.6118   0.8063   -0.0883   0.8860   0.8063   0.7364   -0.2262   0.8063
  -1.2196   0.6618   0.8063   -0.0601   0.2830   0.8063   0.7417   -0.6300   0.8063
  -1.2194   0.3563   0.8063   -0.0409   0.8522   0.8063   0.7628   -0.2781   0.8063
  -1.1852   0.7087   0.8063   -0.0128   0.2490   0.8063   0.7731   -0.6790   0.8063
  -1.1631   0.3425   0.8063   0.0046   0.8158   0.8063   0.7888   -0.3301   0.8063
  X   Y   Z   X   Y   Z   X   Y   Z
  -1.1631   0.3425   0.8063   0.0332   0.2134   0.8063   0.8042   -0.7282   0.8063
  -1.1471   0.7527   0.8063   0.0482   0.7774   0.8063   0.8145   -0.3824   0.8063
  -1.1059   0.7937   0.8063   0.0780   0.1763   0.8063   0.8349   -0.7776   0.8063
  -1.1050   0.3434   0.8063   0.0902   0.7371   0.8063   0.8399   -0.4348   0.8063
  -1.0619   0.8318   0.8063   0.1218   0.1379   0.8063   0.8649   -0.4873   0.8063
  -1.0480   0.3546   0.8063   0.1307   0.6952   0.8063   0.8652   -0.8273   0.8063
  -1.0155   0.8671   0.8063   0.1644   0.0983   0.8063   0.8896   -0.5400   0.8063
  -0.9928   0.3733   0.8063   0.1698   0.6521   0.8063   0.8952   -0.8772   0.8063
  -0.9671   0.8993   0.8063   0.2061   0.0576   0.8063   0.9141   -0.5928   0.8063
  -0.9390   0.3953   0.8063   0.2077   0.6079   0.8063   0.9250   -0.9272   0.8063
  -0.9166   0.9282   0.8063   0.2445   0.5628   0.8063   0.9382   -0.6458   0.8063
  -0.8851   0.4173   0.8063   0.2467   0.0159   0.8063   0.9545   -0.9774   0.8063
  -0.8643   0.9537   0.8063   0.2804   0.5170   0.8063   0.9623   -0.6988   0.8063
  -0.8302   0.4368   0.8063   0.2864   -0.0266   0.8063   0.9839   -1.0276   0.8063
  -0.8104   0.9756   0.8063   0.3154   0.4705   0.8063   0.9863   -0.7518   0.8063
  -0.7741   0.4521   0.8063   0.3253   -0.0699   0.8063   1.0100   -0.8050   0.8063
  -0.7551   0.9938   0.8063   0.3496   0.4234   0.8063   1.0325   -0.8587   0.8063
  -0.7170   0.4632   0.8063   0.3634   -0.1140   0.8063   1.0341   -1.0520   0.8063
  -0.6986   1.0080   0.8063   0.3830   0.3758   0.8063   1.0553   -0.9122   0.8063
  -0.6592   0.4699   0.8063   0.4007   -0.1586   0.8063   1.0802   -0.9648   0.8063
  -0.6414   1.0183   0.8063   0.4157   0.3276   0.8063   1.0805   -1.0214   0.8063
  -1.2628   0.5580   0.9016   -0.1661   0.9544   0.9016   0.6447   -0.4843   0.9016
  -1.2600   0.6149   0.9016   -0.1600   0.3954   0.9016   0.6652   -0.1203   0.9016
  X   Y   Z   X   Y   Z   X   Y   Z
  -1.2433   0.6695   0.9016   -0.1186   0.9226   0.9016   0.6762   -0.5320   0.9016
  -1.2429   0.5051   0.9016   -0.1123   0.3638   0.9016   0.6919   -0.1709   0.9016
  -1.2177   0.7206   0.9016   -0.0729   0.8883   0.9016   0.7073   -0.5799   0.9016
  -1.1995   0.4687   0.9016   -0.0659   0.3305   0.9016   0.7183   -0.2216   0.9016
  -1.1861   0.7682   0.9016   -0.0289   0.8518   0.9016   0.7380   -0.6281   0.9016
  -1.1502   0.8126   0.9016   -0.0207   0.2955   0.9016   0.7442   -0.2725   0.9016
  -1.1451   0.4519   0.9016   0.0134   0.8134   0.9016   0.7684   -0.6766   0.9016
  -1.1451   0.4519   0.9016   0.0233   0.2590   0.9016   0.7699   -0.3236   0.9016
  -1.1107   0.8539   0.9016   0.0543   0.7734   0.9016   0.7952   -0.3749   0.9016
  -1.0881   0.4493   0.9016   0.0662   0.2212   0.9016   0.7984   -0.7252   0.9016
  -1.0682   0.8921   0.9016   0.0938   0.7321   0.9016   0.8202   -0.4263   0.9016
  -1.0315   0.4570   0.9016   0.1081   0.1823   0.9016   0.8281   -0.7740   0.9016
  -1.0232   0.9273   0.9016   0.1321   0.6897   0.9016   0.8449   -0.4778   0.9016
  -0.9763   0.4719   0.9016   0.1489   0.1424   0.9016   0.8575   -0.8231   0.9016
  -0.9759   0.9594   0.9016   0.1693   0.6463   0.9016   0.8693   -0.5295   0.9016
  -0.9266   0.9884   0.9016   0.1889   0.1015   0.9016   0.8867   -0.8722   0.9016
  -0.9223   0.4904   0.9016   0.2055   0.6020   0.9016   0.8934   -0.5814   0.9016
  -0.8754   1.0138   0.9016   0.2279   0.0597   0.9016   0.9155   -0.9216   0.9016
  -0.8683   0.5091   0.9016   0.2407   0.5570   0.9016   0.9174   -0.6333   0.9016
  -0.8225   1.0354   0.9016   0.2661   0.0172   0.9016   0.9412   -0.6852   0.9016
  -0.8135   0.5254   0.9016   0.2752   0.5114   0.9016   0.9434   -0.9715   0.9016
  -0.7681   1.0529   0.9016   0.3035   -0.0260   0.9016   0.9651   -0.7371   0.9016
  -0.7576   0.5373   0.9016   0.3088   0.4652   0.9016   0.9838   -1.0102   0.9016
  X   Y   Z   X   Y   Z   X   Y   Z
  -0.7125   1.0661   0.9016   0.3402   -0.0699   0.9016   0.9884   -0.7893   0.9016
  -0.7009   0.5447   0.9016   0.3417   0.4184   0.9016   1.0107   -0.8419   0.9016
  -0.6560   1.0749   0.9016   0.3738   0.3712   0.9016   1.0343   -0.8940   0.9016
  -0.6438   0.5475   0.9016   0.3762   -0.1142   0.9016   1.0373   -0.9987   0.9016
  -0.5991   1.0790   0.9016   0.4054   0.3235   0.9016   1.0550   -0.9470   0.9016
  -0.5867   0.5460   0.9016   0.4117   -0.1591   0.9016   -1.2360   0.6722   0.9970
  -0.5419   1.0784   0.9016   0.4363   0.2754   0.9016   -1.2308   0.7279   0.9970
  -0.5299   0.5401   0.9016   0.4465   -0.2044   0.9016   -1.2202   0.6189   0.9970
  -0.4850   1.0732   0.9016   0.4666   0.2269   0.9016   -1.2115   0.7805   0.9970
  -0.4736   0.5298   0.9016   0.4807   -0.2502   0.9016   -1.1835   0.8292   0.9970
  -0.4287   1.0635   0.9016   0.4964   0.1781   0.9016   -1.1800   0.5805   0.9970
  -0.4183   0.5156   0.9016   0.5145   -0.2963   0.9016   -1.1497   0.8740   0.9970
  -0.3733   1.0494   0.9016   0.5257   0.1291   0.9016   -1.1278   0.5601   0.9970
  -0.3641   0.4976   0.9016   0.5477   -0.3429   0.9016   -1.1278   0.5601   0.9970
  -0.3192   1.0311   0.9016   0.5545   0.0797   0.9016   -1.1118   0.9154   0.9970
  -0.3110   0.4762   0.9016   0.5805   -0.3897   0.9016   -1.0722   0.5535   0.9970
  -0.2665   1.0090   0.9016   0.5828   0.0300   0.9016   -1.0706   0.9536   0.9970
  -0.2593   0.4519   0.9016   0.6107   -0.0199   0.9016   -1.0267   0.9886   0.9970
  -0.2154   0.9833   0.9016   0.6128   -0.4369   0.9016   -1.0162   0.5570   0.9970
  -0.2090   0.4248   0.9016   0.6382   -0.0700   0.9016   -0.9805   1.0204   0.9970
  -0.9610   0.5675   0.9970   0.1373   0.6785   0.9970   0.8277   -0.4754   0.9970
  -0.9322   1.0491   0.9970   0.1699   0.1439   0.9970   0.8472   -0.8191   0.9970
  -0.9068   0.5820   0.9970   0.1730   0.6351   0.9970   0.8518   -0.5261   0.9970
Figure C20041004577700251
Figure C20041004577700261
在第一级涡轮叶片的优选实施例中，有92个叶片翼面。在涡轮的优选实施例中在平台中心的叶片翼面根部31位于离开涡轮中心线(即转子轴线39)28英寸的半径R1上。这与Z等于0.000处表1的无量纲的Z值相对应。在优选实施例中从平台36中心的根部31到尖端33的翼面36的实际高度(即叶片实际Z高度)是4.3英寸。因此，在优选实施例中叶片16的尖端33位于离开涡轮中心线32.3英寸的半径R2上。尽管没有形成本发明的一部分，每个第一级叶片翼面36包括多个内部空气冷却通道(未示出)，该通道将冷却空气排出到靠近后边缘42的排出位置40的热燃气路径内。
同样将理解到以上表中披露的叶片可以在几何尺寸上放大或缩小以便用于其他类似的涡轮结构中。因此，表I中提出的座标值可向上或向下缩放，使得翼面轮廓形状保持不变。表I中座标的缩放类型将由表I的X、Y和Z座标值表示，其中无量纲的Z座标值通过乘以和除以恒定值转换成英寸。
虽然本发明已经结合当前认为是最实用和优选的实施例进行描述，将理解到本发明不局限于所披露的实施例，相反，本发明旨在覆盖包括在所附权利要求的精神和范围内的变型和等同配置。

Claims (10)

1.一种涡轮叶片(16)，其包括具有翼面形状的叶片翼面(36)，所述翼面具有按照表I提出的X、Y和Z的笛卡儿坐标值的标定轮廓，其中Z值是从0～1的无量纲值，该值可通过将Z值乘以单位为英寸的翼面高度而转换成单位为英寸的Z距离，并且其中在由平滑连续圆弧连接时X和Y是沿着叶片在每个距离Z上限定翼面轮廓截面(38)的单位为英寸的距离，Z距离上的轮廓截面相互平滑连接以便形成完整的翼面形状。
2.如权利要求1所述的涡轮叶片，其特征在于，其形成涡轮第一级的一部分。
3.如权利要求1所述的涡轮叶片，其特征在于，所述翼面形状在垂直于任何翼面表面位置的方向上位于±0.055英寸的范围内。
4.如权利要求1所述的涡轮叶片，其特征在于，其包括平台(30)，从平台中心的根部(31)到翼面尖端(33)的涡轮翼面的高度是4.3英寸。
5.如权利要求1所述的涡轮叶片，其特征在于，X、Y和Z距离可作为同一常数或数字的函数进行缩放以便提供放大或缩小的翼面。
6.一种涡轮，其包括具有如权利要求1所述的涡轮叶片(16)的涡轮叶轮(19)。
7.如权利要求6所述的涡轮，其特征在于，涡轮叶轮包括涡轮的第一级。
8.如权利要求6所述的涡轮，其特征在于，其包括用于所述叶片的平台(30)，所述涡轮叶轮的轴向中心线和平台中心处的每个翼面的根部(31)之间的径向高度是28英寸，并与0.000处的无量纲Z值相对应。
9.如权利要求8所述的涡轮，其特征在于，从平台中心的根部(31)到翼面尖端(33)的涡轮翼面的高度是4.3英寸。
10.如权利要求6所述的涡轮，其特征在于，X、Y和Z距离可作为同一常数或数字的函数进行缩放以便提供放大或缩小的翼面。
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