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CN1312380C - Strong curved wing section of sea temperature difference energy-solar energy reboil circulation power generating steam turbine - Google Patents

Strong curved wing section of sea temperature difference energy-solar energy reboil circulation power generating steam turbine Download PDF

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CN1312380C
CN1312380C CNB2005100307716A CN200510030771A CN1312380C CN 1312380 C CN1312380 C CN 1312380C CN B2005100307716 A CNB2005100307716 A CN B2005100307716A CN 200510030771 A CN200510030771 A CN 200510030771A CN 1312380 C CN1312380 C CN 1312380C
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airfoil
aerofoil profile
steam turbine
ratio
chord length
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CN1757883A (en
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王彤
杨波
谷传纲
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Shanghai Jiao Tong University
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Shanghai Jiao Tong University
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Abstract

本发明涉及一种用于海洋温差能—太阳能重热循环发电的蒸汽透平的翼型,针对工质气体的流量小,蒸汽透平的转速较高的特点,尽量减小翼型前端的压力面曲率,翼型的最大厚度d与翼型的弦长c之比为:d/c=0.3,最大厚度位置与翼型的弦长之比为:xd/c=0.25;最大弯度f与翼型的弦长c之比为:f/c=0.1457,最大弯度位置与翼型的弦长之比为:xf/c=0.47,虽然在翼型前端为了避免较大的冲角牺牲了一部分翼型的做功能力,但是通过大厚度、强弯的设计,足以弥补前者对于蒸汽透平性能带来的损失。翼型在后缘xR/c=0.97处以圆弧过渡,过渡圆弧的半径R与弦长之比c之比为:R/c=0.02,较钝的外缘使外物对翼型的损伤降至最小,且易于加工。

The invention relates to an airfoil of a steam turbine used for ocean temperature difference energy-solar reheat cycle power generation, aiming at the characteristics of small flow rate of working medium gas and high speed of steam turbine, the pressure at the front end of the airfoil is reduced as much as possible Surface curvature, the ratio of the maximum thickness d of the airfoil to the chord length c of the airfoil is: d/c=0.3, the ratio of the maximum thickness position to the chord length of the airfoil is: x d /c=0.25; the maximum camber f and The ratio of the chord length c of the airfoil is: f/c=0.1457, and the ratio of the maximum camber position to the chord length of the airfoil is: x f /c=0.47, although at the front end of the airfoil it is sacrificed to avoid a large angle of attack Part of the airfoil's working ability, but through the large thickness and strong bending design, it is enough to make up for the loss caused by the former to the performance of the steam turbine. The airfoil transitions in a circular arc at the trailing edge x R /c=0.97, the ratio of the radius R of the transition arc to the chord length c ratio is: R/c=0.02, and the blunt outer edge makes the foreign object affect the airfoil Damage is minimized and easy to process.

Description

Be used for the reheat aerofoil profile of steam turbine of circulating generation of ocean thermal energy-solar energy
Technical field
The present invention relates to a kind of aerofoil profile, relate in particular to a kind of reheat aerofoil profile of steam turbine of circulating generation of ocean thermal energy-solar energy that is used for, belong to field of energy source developing technology.
Background technique
Ocean thermal energy-solar energy circulating generation of reheating is a kind of mode of the novel acquisition energy.Being used for the reheat steam turbine of circulating generation of ocean thermal energy-solar energy is by a Working medium gas that flows out from solar thermal collector is imported in the steam turbine, promote the rotation of steam turbine, thereby the kinetic energy of working medium is converted into the mechanical energy of steam turbine and is converted into the purpose that electric power is exported or directly output realizes obtaining the energy by generator, is the mode of obtaining electric power a kind of complete environmental protection, cleaning.The blade of steam turbine is the most critical parts of such steam turbine.And for the blade of steam turbine, the aerofoil profile of leaf cross-section is selected and research is the direct factor that influence the mechanical efficient of steam turbine.
Owing to the flow of the Working medium gas that flows out from solar thermal collector is little, and the rotating speed of steam turbine is higher, so when utilizing ocean thermal energy-solar energy to reheat circulating generation, steam turbine is had special requirement.For general steam turbine, often adopt the measure of inlet whirl, promptly add a nozzle at the steam turbine inlet, improve the inlet angle of steam flow, but the adding of nozzle brings extra complexity not only for the steam turbine structure, but also can lose energy greatly, reduce cycle efficiency greatly.Therefore, not only simple in structure for such steam turbine, and for the requirement of vane airfoil profile, also different with general steam turbine.The steam turbine blade is met stream with inevasible with the bigger angle of attack in a lot of operating times.If select aerofoil profile commonly used (as NACA aerofoil profile, RAF-6 aerofoil profile, CLARK aerofoil profile, LS aerofoil profile, Gottingen aerofoil profile, FAGE﹠amp during the design blade; COLLINS aerofoil profile, RHODE GENESE aerofoil profile, COANDA aerofoil profile, EPPLER aerofoil profile etc.), tend to because the bigger pressure side curvature of aerofoil profile front end commonly used, make aerofoil profile under more abominable operating conditions (the big steam flow angle of attack), steam flow will separate at blade surface very soon.At this moment, the lift coefficient of aerofoil profile will descend significantly, the rapid increase of resistance coefficient, and turbine efficiency will reduce greatly, be difficult to reach designing requirement.At present, be used for the aerofoil profile of steam turbine design, often be limited in the less operating mode scope, in the operating mode scope, aerofoil profile has bigger lift coefficient and less resistance coefficient, still, in case leave this operating mode scope, aerofoil profile generation stall, performance worsens rapidly.Therefore, must design a kind of aerofoil profile that is specifically designed to such steam turbine.
Summary of the invention
The objective of the invention is at the deficiencies in the prior art, design provides a kind of reheat aerofoil profile of steam turbine of circulating generation of ocean thermal energy-solar energy that is used for, and the flow that can adapt to Working medium gas fully is little, the characteristic that the rotating speed of steam turbine is higher.By the design of new aerofoil profile, reduce the inlet angle of attack that working medium flows into steam turbine on the one hand as far as possible, even make aerofoil profile under the bigger angle of attack on the one hand, can guarantee that also blade has bigger lift coefficient and less resistance coefficient.
For realizing this purpose, the maximum ga(u)ge d of the aerofoil profile of the present invention's design is about with the ratio of the chord length c of aerofoil profile: d/c=0.3, maximum ga(u)ge position x dWith the ratio of the chord length c of aerofoil profile be: x d/ c=0.25; Aerofoil profile maximum camber f with the ratio of the chord length c of aerofoil profile is: f/c=0.1457, maximum ga(u)ge position x fBe about x with the ratio of the chord length c of aerofoil profile f/ c=0.47.Consider the hydraulic performance of the big angle of attack of aerofoil profile, aerofoil profile is at trailing edge x R/ c=0.97 sentences arc transition, and transition arc radius R is R/c=0.02 with the ratio of the chord length c of aerofoil profile.
Wherein, X dBe the abscissa value of aerofoil profile maximum ga(u)ge place aerofoil profile, X fBe the abscissa value of aerofoil profile maximum camber place aerofoil profile, X RAbscissa value for aerofoil profile arc transition place aerofoil profile.
The flow that the present invention is directed to Working medium gas is little, and the higher characteristics of the rotating speed of steam turbine are the steam flow angle of attack of avoiding entering the mouth bigger, reduce the pressure side curvature of aerofoil profile front end as far as possible, when striving for that steam flow flows into steam turbine, has less steam flow to separate and energy loss.
By increasing maximum ga(u)ge and camber is a kind of the most effectively means that will obtain bigger lift coefficient.Reducing of the pressure side curvature of aerofoil profile front end will certainly influence the acting ability of whole aerofoil profile, so by the method that the control adverse pressure gradient slows down nearly wall fluid, increase camber and thickness.Like this, though sacrificed the acting ability of a part of aerofoil profile for fear of the bigger angle of attack,, be enough to remedy the loss that the former brings for the steam turbine performance by big thickness, strong curved design at the aerofoil profile front end.
Big thickness and strong curved aerofoil profile are the most worrying to be mobile performance under the off-design condition of aerofoil profile, and the angle of attack increases a little, the resistance increase and the loss of lift that will cause airflow breakaway and bring thus.Compare with common Airfoil Design, consider the off design performance of aerofoil profile, in design during this aerofoil profile, have a mind to move behind the position with maximum ga(u)ge, enlarge the envelope curve of aerofoil profile as far as possible, with the acting ability of the off design performance that improves aerofoil profile.From flowing angle, point of maximum thickness also is difficult for too close leading edge.This mainly be because, after the too close leading edge of point of maximum thickness, " point " leading edge to walk around aerofoil profile of flowing and sharply quickening, the reach of pressure minimum point, the corresponding deterioration of adverse pressure gradient, and cause too early generation commentaries on classics to be twisted and corresponding loss of lift, after moving after the point of maximum thickness, the position of pressure minimum value can be pushed as far as possible to the rear portion of aerofoil profile, make aerofoil profile leading portion boundary layer stable, separation point is postponed, and helps the acting of aerofoil profile leading portion convex surface, thereby the performance of aerofoil profile can be improved on the whole.
In addition, because trailing edge is with arc transition, therefore more blunt outer rim makes foreign object reduce to minimum to the damage of aerofoil profile, and is easy to processing.
In sum, the reheat novel aerofoil profile of circulating generation steam turbine of ocean thermal energy-solar energy that is used for of the present invention has following characteristics:
1, this aerofoil profile front end reduces pressure side curvature as far as possible, with the steam flow angle of attack that reduces to enter the mouth.
2, the maximum ga(u)ge d of aerofoil profile is about with the ratio of the chord length c of aerofoil profile: d/c=0.3, aerofoil profile maximum camber f with the ratio of the chord length c of aerofoil profile is: f/c=0.1457, improve the acting ability of aerofoil profile, to remedy owing to the aerofoil profile forefront pressure curvature of face reduces to the influence of steam turbine acting ability.
3, the maximum ga(u)ge position of this aerofoil profile is: x d/ c=0.25 compares with other aerofoil profiles, and maximum ga(u)ge moves behind the position, thereby the performance of aerofoil profile can be improved on the whole.
4, during this Airfoil Design, at trailing edge x R/ c=0.97 sentences arc transition, and the radius R of transition arc with the ratio of the ratio c of chord length is: R/c=0.02, and more blunt outer rim makes foreign object reduce to minimum to the damage of aerofoil profile, and more blunt outer rim also makes the processing of aerofoil profile reduce to minimum.
Description of drawings
Fig. 1 is an airfoil structure schematic representation of the present invention.
Among Fig. 1, the upper surface of 1 expression aerofoil profile, the lower surface of 2 expression aerofoil profiles, 3 is the mean camber line of aerofoil profile.
C is the chord length of aerofoil profile, and d is the maximum ga(u)ge of aerofoil profile, X dBe the abscissa value of aerofoil profile maximum ga(u)ge place aerofoil profile, f is the maximum camber of aerofoil profile, X fAbscissa value for aerofoil profile maximum camber place aerofoil profile.
Fig. 2 is aerofoil profile liter of the present invention, resistance coefficient plotted curve.
Among Fig. 2, α is the air-flow angle of attack, C yBe wing section lift coefficient, C xBe the profile drag coefficient.
Embodiment
Below be unit 1 with the aerofoil profile chord length, the specific embodiment of the present invention is further described.
Get after the aerofoil profile chord length is unit 1, the coordinate such as the table 1 of blade are listed.
Table 1 blade coordinate
Upper surface Lower surface
X Y X Y
0 0 0.01 0.039917724 0.02 0.062667844 0.03 0.081184363 0.04 0.096981359 0.05 0.111737581 0.06 0.125557549 0.07 0.138469859 0.08 0.150507051 0.09 0.161702157 0.1 0.172089196 0.11 0.181703173 0.12 0.190576134 0.13 0.198740618 0.14 0.206227688 0.15 0.213086151 0.16 0.219379608 0.17 0.225162291 0.18 0.230480053 0.19 0.235368883 0.2 0.239861815 0.21 0.243984486 0.22 0.24776056 0.23 0.251209266 0.24 0.254347859 0.25 0.257190638 0.26 0.259750421 0.27 0.262038055 0.28 0.264062413 0.29 0.265832371 0.3 0.267354337 0.31 0.268636201 0.32 0.26968585 0.33 0.270510187 0.34 0.271116114 0.35 0.271510533 0.36 0.271699362 0.37 0.271689501 0 0 0.01 -0.027018233 0.02 -0.035546076 0.03 -0.041214871 0.04 -0.045386351 0.05 -0.048586573 0.06 -0.051085221 0.07 -0.053040556 0.08 -0.05455562 0.09 -0.055700916 0.1 -0.056526732 0.11 -0.057070044 0.12 -0.057357478 0.13 -0.057409738 0.14 -0.057241124 0.15 -0.056861988 0.16 -0.056277754 0.17 -0.055490394 0.18 -0.054497443 0.19 -0.053294956 0.2 -0.051879483 0.21 -0.050249544 0.22 -0.048403661 0.23 -0.04634134 0.24 -0.04406406 0.25 -0.041575765 0.26 -0.038881387 0.27 -0.035988319 0.28 -0.032906916 0.29 -0.02965049 0.3 -0.026234817 0.31 -0.022679617 0.32 -0.019007078 0.33 -0.015243823 0.34 -0.011416967 0.35 -0.007559051 0.36 -0.003701628 0.37 0.000119805
0.38 0.271487361 0.39 0.271097872 0.4 0.270526949 0.41 0.26978051 0.42 0.268863978 0.43 0.267782775 0.44 0.266541833 0.45 0.265146081 0.46 0.263600449 0.47 0.261910361 0.48 0.260080255 0.49 0.258115059 0.5 0.256019212 0.51 0.253797151 0.52 0.251453806 0.53 0.248993614 0.54 0.246421012 0.55 0.243740438 0.56 0.240955836 0.57 0.238068685 0.58 0.235078492 0.59 0.231983778 0.6 0.228785035 0.61 0.225481278 0.62 0.222072014 0.63 0.21855675 0.64 0.214934499 0.65 0.211204276 0.66 0.207366574 0.67 0.20341942 0.68 0.199362815 0.69 0.195195773 0.7 0.1909178 0.71 0.186527417 0.72 0.182024625 0.73 0.177407944 0.74 0.172676388 0.75 0.167829465 0.76 0.162866188 0.77 0.157783599 0.78 0.152585149 0.79 0.147265908 0.8 0.141825877 0.81 0.136264068 0.38 0.003871721 0.39 0.007519609 0.4 0.011029943 0.41 0.014372156 0.42 0.017518145 0.43 0.020441779 0.44 0.02312186 0.45 0.025540638 0.46 0.027689732 0.47 0.029587383 0.48 0.031254299 0.49 0.032709214 0.5 0.033968398 0.51 0.035047136 0.52 0.035959231 0.53 0.036716023 0.54 0.037329839 0.55 0.037810045 0.56 0.038166994 0.57 0.038409562 0.58 0.038545637 0.59 0.038584093 0.6 0.038531339 0.61 0.038395758 0.62 0.038183757 0.63 0.037901747 0.64 0.037553179 0.65 0.037139038 0.66 0.036658833 0.67 0.036113054 0.68 0.035502197 0.69 0.034826261 0.7 0.034086231 0.71 0.033282108 0.72 0.032414878 0.73 0.031484541 0.74 0.030492083 0.75 0.029437503 0.76 0.028322282 0.77 0.027146912 0.78 0.025911886 0.79 0.024618683 0.8 0.02326681 0.81 0.021858732
0.82 0.13057851 0.83 0.124770189 0.84 0.118839598 0.85 0.112786737 0.86 0.106613578 0.87 0.100320121 0.88 0.093907845 0.89 0.087377736 0.9 0.080731274 0.91 0.073968457 0.92 0.067091752 0.93 0.060101652 0.94 0.052999635 0.95 0.04578718 0.96 0.03846626 0.97 0.031037861 0.98 0.023503954 0.99 0.01586602 1 0 0.82 0.020394449 0.83 0.018874948 0.84 0.017301214 0.85 0.015676205 0.86 0.014001401 0.87 0.01227976 0.88 0.010513746 0.89 0.008706812 0.9 0.006860435 0.91 0.004978068 0.92 0.003061682 0.93 0.001114235 0.94 -0.000861314 0.95 -0.0028625 0.96 -0.004887351 0.97 -0.006931924 0.98 -0.008995231 0.99 -0.01016715 1 0
The maximum ga(u)ge of this aerofoil profile is about: d=0.3, the maximum ga(u)ge position is: x d=0.25; Camber is: f=0.1457, x f=0.47.Trailing edge x=0.97 place is the arc transition of R=0.02 with the radius.
1, at this aerofoil profile front end, reduces pressure side curvature, with the steam flow angle of attack that reduces to enter the mouth as far as possible.
2, the maximum ga(u)ge of this aerofoil profile is about: d=0.3, and camber is: f=0.1457, improve the acting ability of aerofoil profile.
3, the maximum ga(u)ge position of this aerofoil profile is: x d=0.25, to compare with other aerofoil profiles, maximum ga(u)ge moves behind the position, thereby the performance of aerofoil profile can be improved on the whole.
4, during this Airfoil Design, at trailing edge x=0.97 place, be the arc transition of R=0.02 with the radius, more blunt outer rim makes foreign object reduce to minimum to the damage of aerofoil profile, and more blunt outer rim also makes the processing of aerofoil profile reduce to minimum.
When reynolds' number is 3 * 10 5The time, the liter of this aerofoil profile, resistance coefficient are as shown in Figure 2.Can find that from Fig. 2 though the pressure side curvature of aerofoil profile front end reduces, because the thickness of aerofoil profile increases, the acting ability of aerofoil profile is not subjected to very big influence, maximum lift coefficient is: C Ymax=1.185; Owing to move behind the maximum ga(u)ge position, stall angle increased:
Figure C20051003077100101

Claims (2)

1、一种用于海洋温差能-太阳能重热循环发电的蒸汽透平的翼型,其特征在于翼型的最大厚度d与翼型的弦长c之比为:d/c=0.3,最大厚度位置为:xd/c=0.25;最大弯度f与翼型的弦长c之比为:f/c=0.1457,最大弯度位置为:xf/c=0.47;翼型在后缘xR/c=0.97处以圆弧过渡,过渡圆弧的半径R与弦长c之比为:R/c=0.02;其中Xd为翼型最大厚度处翼型的横坐标值,Xf为翼型最大弯度处翼型的横坐标值,XR为翼型圆弧过渡处翼型的横坐标值。1. A steam turbine airfoil used for ocean temperature difference energy-solar reheat cycle power generation, characterized in that the ratio of the maximum thickness d of the airfoil to the chord length c of the airfoil is: d/c=0.3, the maximum The thickness position is: x d /c=0.25; the ratio of the maximum camber f to the chord length c of the airfoil is: f/c=0.1457, the maximum camber position is: x f /c=0.47; the airfoil is at the trailing edge x R /c=0.97 is a circular arc transition, the ratio of the radius R of the transition arc to the chord length c is: R/c=0.02; where X d is the abscissa value of the airfoil at the maximum thickness of the airfoil, and X f is the airfoil The abscissa value of the airfoil at the maximum camber, and X R is the abscissa value of the airfoil at the arc transition of the airfoil. 2、根据权利要求1的用于海洋温差能—太阳能重热循环发电的蒸汽透平的翼型,其特征在于所述翼型弦长c取为单位1后,叶片坐标为:2. According to claim 1, the steam turbine airfoil used for ocean temperature difference energy-solar reheat cycle power generation is characterized in that after the airfoil chord length c is taken as unit 1, the blade coordinates are:          上表面 upper surface             下表面 lower surface      X X          Y Y      X X          Y Y     00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.21 00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.21     00.0399177240.0626678440.0811843630.0969813590.1117375810.1255575490.1384698590.1505070510.1617021570.1720891960.1817031730.1905761340.1987406180.2062276880.2130861510.2193796080.2251622910.2304800530.2353688830.2398618150.243984486     00.0399177240.0626678440.0811843630.0969813590.1117375810.1255575490.1384698590.1505070510.1617021570.1720891960.1817031730.1905761340.1987406180.2062276880.2130861510.2193796080.2251622910.2304800530.2353688830.2398618150.243984486     00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.21 00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.21     0-0.027018233-0.035546076-0.041214871-0.045386351-0.048586573-0.051085221-0.053040556-0.05455562-0.055700916-0.056526732-0.057070044-0.057357478-0.057409738-0.057241124-0.056861988-0.056277754-0.055490394-0.054497443-0.053294956-0.051879483-0.050249544     0-0.027018233-0.035546076-0.041214871-0.045386351-0.048586573-0.051085221-0.053040556-0.05455562-0.055700916-0.056526732-0.057070044-0.057357478-0.057409738-0.057241124-0.056861988-0.056277754-0.055490394-0.054497443-0.053294956-0.051879483-0.050249544
  0.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.65   0.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.65   0.247760560.2512092660.2543478590.2571906380.2597504210.2620380550.2640624130.2658323710.2673543370.2686362010.269685850.2705101870.2711161140.2715105330.2716993620.2716895010.2714873610.2710978720.2705269490.269780510.2688639780.2677827750.2665418330.2651460810.2636004490.2619103610.2600802550.2581150590.2560192120.2537971510.2514538060.2489936140.2464210120.2437404380.2409558360.2380686850.2350784920.2319837780.2287850350.2254812780.2220720140.218556750.2149344990.211204276   0.247760560.2512092660.2543478590.2571906380.2597504210.2620380550.2640624130.2658323710.2673543370.2686362010.269685850.2705101870.2711161140.2715105330.2716993620.2716895010.2714873610.2710978720.2705269490.269780510.2688639780.2677827750.2665418330.2651460810.2636004490.2619103610.2600802550.2581150590.2560192120.2537971510.2514538060.2489936140.2464210120.2437404380.2409558360.2380686850.2350784920.2319837780.2287850350.2254812780.2220720140.218556750.2149344990.211204276   0.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.65   0.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.65   -0.048403661-0.04634134-0.04406406-0.041575765-0.038881387-0.035988319-0.032906916-0.02965049-0.026234817-0.022679617-0.019007078-0.015243823-0.011416967-0.007559051-0.0037016280.0001198050.0038717210.0075196090.0110299430.0143721560.0175181450.0204417790.023121860.0255406380.0276897320.0295873830.0312542990.0327092140.0339683980.0350471360.0359592310.0367160230.0373298390.0378100450.0381669940.0384095620.0385456370.0385840930.0385313390.0383957580.0381837570.0379017470.0375531790.037139038 -0.048403661-0.04634134-0.04406406-0.041575765-0.038881387-0.035988319-0.032906916-0.02965049-0.026234817-0.022679617-0.019007078-0.015243823-0.011416967-0.007559051-0.0037016280.0001198050.0038717210.0075196090.0110299430.0143721560.0175181450.0204417790.023121860.0255406380.0276897320.0295873830.0312542990.0327092140.0339683980.0350471360.0359592310.0367160230.0373298390.0378100450.0381669940 .0384095620.0385456370.0385840930.0385313390.0383957580.0381837570.0379017470.0375531790.037139038
  0.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991 0.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.970.9180.9   0.2073665740.203419420.1993628150.1951957730.19091780.1865274170.1820246250.1774079440.1726763880.1678294650.1628661880.1577835990.1525851490.1472659080.1418258770.1362640680.130578510.1247701890.1188395980.1127867370.1066135780.1003201210.0939078450.0873777360.0807312740.0739684570.0670917520.0601016520.0529996350.045787180.038466260.0310378610.0235039540.015866020   0.2073665740.203419420.1993628150.1951957730.19091780.1865274170.1820246250.1774079440.1726763880.1678294650.1628661880.1577835990.1525851490.1472659080.1418258770.1362640680.130578510.1247701890.1188395980.1127867370.1066135780.1003201210.0939078450.0873777360.0807312740.0739684570.0670917520.0601016520.0529996350.045787180.038466260.0310378610.0235039540.015866020   0.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991 0.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.970.9180.9   0.0366588330.0361130540.0355021970.0348262610.0340862310.0332821080.0324148780.0314845410.0304920830.0294375030.0283222820.0271469120.0259118860.0246186830.023266810.0218587320.0203944490.0188749480.0173012140.0156762050.0140014010.012279760.0105137460.0087068120.0068604350.0049780680.0030616820.001114235-0.000861314-0.0028625-0.004887351-0.006931924-0.008995231-0.010167150   0.0366588330.0361130540.0355021970.0348262610.0340862310.0332821080.0324148780.0314845410.0304920830.0294375030.0283222820.0271469120.0259118860.0246186830.023266810.0218587320.0203944490.0188749480.0173012140.0156762050.0140014010.012279760.0105137460.0087068120.0068604350.0049780680.0030616820.001114235-0.000861314-0.0028625-0.004887351-0.006931924-0.008995231-0.010167150
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