US20130022473A1
2013-01-24
13/189,045
2011-07-22
An axial rotor includes a plurality of blades extending from a hub that is rotatable about an axis of rotation. Each of the plurality of blades includes a blade body that extends over a span from a base to a tip. The plurality of blades defines an exit flow angle relative to a plane that is perpendicular to the axis of rotation. The exit flow angle decreases along the span from the base to the tip.
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F04D29/181 » CPC main
Details, component parts, or accessories; Rotors Axial flow rotors
F04D29/384 » CPC further
Details, component parts, or accessories; Rotors specially for elastic fluids for axial flow pumps; Blades characterised by form
F04D29/00 IPC
Details, component parts, or accessories
This disclosure relates to blades, such as rotor blades or stator vane blades. Rotor and stator blades are known and used in engines, pumps, turbines and the like to propel a vehicle, move a fluid or extract work from a fluid. As fluid flows around the blades, the flow can separate and decrease the operating efficiency of the blades.
FIG. 1 schematically illustrates an example desalination system.
FIG. 2 illustrates an example turbopump machine.
FIG. 3 illustrates an example turbine blade of a rotor.
FIG. 4 illustrates a cross-section through a plurality of blades of a rotor showing an exit flow angle from between the blades.
FIG. 1 schematically illustrates selected portions of an example desalination system 20, which provides an example operating environment for a turbopump machine 22, blade 46 and vane 47 that will be described in more detail below. It is to be understood that the desalination system 20 is only an exemplary end use environment and that other systems, such as but not limited to aircraft or aerospace systems and turbine engines, will also benefit from the disclosed turbopump machine 22, blade 46 or vane 47.
In the illustrated example, the turbopump machine 22 includes a pump section 24 and a turbine section 26. The turbopump machine 22 is fluidly connected with a reverse osmosis device 28 of known construction, for the desalination of water.
In the illustrated example, feed water is received into the pump section 24, which pressurizes the feed water and moves the feed water to the reverse osmosis device 28. As an example, the reverse osmosis device 28 includes one or more membranes to separate the feed water into a low-salinity stream 30 and a saline stream 32. The saline stream 32 is fed into the turbine section 26 of the turbopump machine 22, for energy recovery.
FIG. 2 illustrates a portion of an example of the turbopump machine 22. The pump section 24 and the turbine section 26 are coupled with a rotatable shaft 40 for rotation about axis A. The pump section 24 includes an impeller 42 that is coupled to rotate with the rotatable shaft 40.
The turbine section 26 is coupled to drive the rotatable shaft 40. The turbine section 26 includes an axial rotor 44 (e.g., turbine) having a plurality of blades 46 (one shown). In this example, the turbine section 26 also includes a plurality of fixed stator vanes 47 located upstream from the axial rotor 44. The turbine section 26 may have one or more stages of blades 46, vanes 47 or both.
The turbine section 26 includes a turbine nozzle 48 upstream from the blades 46 and in communication with an inlet 50 of the turbine section 26. An outlet 52 is located downstream from the blades 46. In the example shown, the outlet 52 is an annular outlet that extends between an outer wall 54 and an inner wall 56.
For the purpose of description, FIG. 3 shows one of the blades 46 of the axial rotor 44, however, it is to be understood that the blade 46 is also representative of the vanes 47 with regard to the salient features described herein. As can be appreciated, the vanes 47 may be fixed at their radially outer tips, whereas the blades 46 are designed to rotate. Each of the blades 46 extends from a hub 58 that is rotatable about the axis A (FIG. 2). Each of the blades 46 includes a blade body 60 (e.g., airfoil-shaped body) that extends over a span S from a base 62 at the hub 58 to a tip 64. The blade body 60 also extends between a leading end 66 and a trailing end 68 and between a pressure side surface 70 and a suction side surface 72 (FIG. 4).
The blade body 60 also defines a mean camber line C (FIG. 4) that extends from the leading end 66 to the trailing end 68. The mean camber line C is the mid-thickness of the blade 46 such that, normal to the mean camber line C, there is an equal amount of blade body distance above and below the mean camber line C.
Each of the blades 46 receives a fluid flow F that splits at the nose of the leading end 66 and flows over the pressure side surface 70 and the suction side surface 72. The flow F exits from between adjacent blades 46 at an angle relative to a plane 74 that is perpendicular to the axis of rotation A or, for the vanes 47, axis around which the vanes 47 are arranged. The direction of the exit flow F can be determined through computer simulation or experimental data, for example.
In the illustrated example, the exit flow F forms an angle 76 with regard to the plane 74. Alternatively, the angle 76 can be represented as an angle to the axis A (i.e., 90Β° minus angle 76). The exit flow angle 76 decreases along the span S from the base 62 to the tip 64 of the blade 46. The feature of the decreasing exit flow angle 76 facilitates the control of flow through the axial rotor to reduce or eliminate flow separation near the hub 58, for example.
The reduction or elimination of flow separation near the hub 58 enhances the efficiency of the blade 46 and the turbine section 26 of the turbopump machine 22 can be operated at speeds that are more beneficial for enhancing the efficiency of the pump section 24 of the turbopump machine 22. For instance, the turbine section 26 is operated at a speed of approximately 3500-4500 revolutions per minute, such as at 4000 revolutions per minute, to drive the pump section 24 at the same speed through the common coupling with the shaft 40. At such speeds, the pump section 24 operates in a more efficient speed regime to thereby enhance the overall efficiency performance of the turbopump machine 22.
In one example, the average exit flow angle 76 over the span S is less than 12Β°. For example, the average exit flow angle is an integrated average over the span S.
In a further example, the decreasing exit flow angle 76 is represented as a proportional ratio of a maximum exit flow angle at the base 62 to a minimum exit flow angle at the tip 64. For instance, the proportional ratio is no greater than 2.33. The βproportional ratioβ refers to the quotient of the maximum exit flow angle divided by the minimum exit flow angle, as a scalable value.
In a further example, the proportional ratio is greater than 1 and is less than or equal to 4. In other examples, the proportional ratio is 4, 2.4 or 1.67.
The above exemplary proportional ratios are achieved by establishing the exit flow angle at the base 62 to be between 12Β° and 20Β° and the exit flow angle at the tip 64 to be between 5Β° and 12Β°.
In a further embodiment, the decreasing exit flow angle 76 has a rate of decrease over the span S from the base 62 to the tip 64 that is non-linear.
In one example, the exit flow angle 76 is controlled by the geometry of the blades 46 with regard to the shape of the pressure side surface 70 and the suction side surface 72. The shape of the pressure side surface 70 and the suction side surface 72 is represented by a set of coordinates and a radii of curvature at each respective coordinate. For example, the coordinate system is a cylindrical coordinate system that includes X-coordinates along a direction that is parallel to the axis of rotation A and radial coordinates that are a function of radial distance and angle relative to a reference point in space.
Table I below shows an exemplary set of coordinates and radii of curvature at each coordinate for the blade 46 having a decreasing exit flow angle as described herein. It is to be understood that the exemplary coordinates and radii of curvature are scalable such that the given values are relative to each other for a given scale factor. By defining the coordinate values and radii at selected locations, the surfaces of the blades 46 are ascertained.
The Table values present actual blade 46 profiles in ambient, non-operating or non-hot conditions for an end use blade.
| TABLE I | |||||
| Co- | |||||
| ordi- | |||||
| Sec- | nate | Radial | |||
| tion | Description | # | X-Coord. | Coord. | Radii |
| 1 | suction | 1 | 0.065000318 | β0.112583481 | 5.618000031 |
| side from | 2 | 0.069693290 | β0.115220830 | 5.618000031 | |
| LE - curve 0 | 3 | 0.074823737 | β0.117943175 | 5.618000031 | |
| 4 | 0.080434263 | β0.120724402 | 5.618000031 | ||
| 5 | 0.086569928 | β0.123532899 | 5.618000031 | ||
| 6 | 0.093278728 | β0.126325026 | 5.618000031 | ||
| 7 | 0.100611016 | β0.129043564 | 5.618000031 | ||
| 8 | 0.108617760 | β0.131614670 | 5.618000031 | ||
| 9 | 0.117348216 | β0.133945093 | 5.618000031 | ||
| 10 | 0.126846194 | β0.135919631 | 5.618000031 | ||
| 11 | 0.137145326 | β0.137400031 | 5.618000031 | ||
| 12 | 0.148265779 | β0.138226330 | 5.618000031 | ||
| 13 | 0.160200313 | β0.138220698 | 5.618000031 | ||
| 14 | 0.172921583 | β0.137196854 | 5.618000031 | ||
| 15 | 0.186368138 | β0.134972095 | 5.618000031 | ||
| 16 | 0.200455457 | β0.131381154 | 5.618000031 | ||
| 17 | 0.215079650 | β0.126288310 | 5.618000031 | ||
| 18 | 0.230129391 | β0.119594432 | 5.618000031 | ||
| 19 | 0.245496839 | β0.111237586 | 5.618000031 | ||
| 20 | 0.261085689 | β0.101188287 | 5.618000031 | ||
| 21 | 0.276815355 | β0.089442305 | 5.618000031 | ||
| 22 | 0.292621374 | β0.076013222 | 5.618000031 | ||
| 23 | 0.308453947 | β0.060926266 | 5.618000031 | ||
| 24 | 0.324275166 | β0.044214074 | 5.618000031 | ||
| 25 | 0.340055823 | β0.025914336 | 5.618000031 | ||
| 26 | 0.355772793 | β0.006068866 | 5.618000031 | ||
| 27 | 0.371406823 | 0.015276501 | 5.618000031 | ||
| 28 | 0.386940688 | 0.038071387 | 5.618000031 | ||
| 29 | 0.402358174 | 0.062260009 | 5.618000031 | ||
| 30 | 0.417643368 | 0.087780744 | 5.618000031 | ||
| 31 | 0.432779819 | 0.114564918 | 5.618000031 | ||
| 32 | 0.447750360 | 0.142536327 | 5.618000031 | ||
| 33 | 0.462537318 | 0.171611324 | 5.618000031 | ||
| 34 | 0.477122128 | 0.201698154 | 5.618000031 | ||
| 35 | 0.491485506 | 0.232697010 | 5.618000031 | ||
| 36 | 0.505607843 | 0.264500797 | 5.618000031 | ||
| 37 | 0.519469440 | 0.296996117 | 5.618000031 | ||
| 38 | 0.533065021 | 0.330059648 | 5.618000031 | ||
| 39 | 0.546459556 | 0.363532424 | 5.618000031 | ||
| 40 | 0.559657156 | 0.397278816 | 5.618000031 | ||
| 41 | 0.572605133 | 0.431189537 | 5.618000031 | ||
| 42 | 0.585260093 | 0.465146542 | 5.618000031 | ||
| 43 | 0.597582281 | 0.499029756 | 5.618000031 | ||
| 44 | 0.609536648 | 0.532720149 | 5.618000031 | ||
| 45 | 0.621092856 | 0.566102803 | 5.618000031 | ||
| 46 | 0.632225990 | 0.599073410 | 5.618000031 | ||
| 47 | 0.642915845 | 0.631525517 | 5.618000031 | ||
| 48 | 0.653147221 | 0.663357437 | 5.618000031 | ||
| 49 | 0.662909985 | 0.694477797 | 5.618000031 | ||
| 50 | 0.672198832 | 0.724815845 | 5.618000031 | ||
| 51 | 0.681012392 | 0.754294515 | 5.618000031 | ||
| 52 | 0.689353466 | 0.782845497 | 5.618000031 | ||
| 53 | 0.697228253 | 0.810431600 | 5.618000031 | ||
| 54 | 0.704645991 | 0.837001979 | 5.618000031 | ||
| 55 | 0.711618304 | 0.862523258 | 5.618000031 | ||
| 56 | 0.718159318 | 0.886984587 | 5.618000031 | ||
| 57 | 0.724284470 | 0.910355806 | 5.618000031 | ||
| 58 | 0.730010867 | 0.932652533 | 5.618000031 | ||
| 59 | 0.735356152 | 0.953855932 | 5.618000031 | ||
| 60 | 0.740338922 | 0.973996639 | 5.618000031 | ||
| 61 | 0.744977653 | 0.993071556 | 5.618000031 | ||
| 62 | 0.749291241 | 1.011112213 | 5.618000031 | ||
| 63 | 0.753298342 | 1.028147936 | 5.618000031 | ||
| 64 | 0.757017136 | 1.044191718 | 5.618000031 | ||
| 65 | 0.760465503 | 1.059294343 | 5.618000031 | ||
| 66 | 0.763660669 | 1.073483109 | 5.618000031 | ||
| 67 | 0.766619086 | 1.086785316 | 5.618000031 | ||
| 68 | 0.769356787 | 1.099251032 | 5.618000031 | ||
| 69 | 0.771889031 | 1.110924363 | 5.618000031 | ||
| 70 | 0.774229586 | 1.121825933 | 5.618000031 | ||
| 71 | 0.776392400 | 1.132000685 | 5.618000031 | ||
| 72 | 0.778390110 | 1.141491771 | 5.618000031 | ||
| 73 | 0.780234754 | 1.150341392 | 5.618000031 | ||
| 74 | 0.781908453 | 1.158583283 | 5.618000031 | ||
| 75 | 0.783462167 | 1.166247129 | 5.618000031 | ||
| 76 | 0.784905970 | 1.173368812 | 5.618000031 | ||
| 77 | 0.786246657 | 1.179981947 | 5.618000031 | ||
| 78 | 0.787490845 | 1.186118960 | 5.618000031 | ||
| 79 | 0.788644731 | 1.191810608 | 5.618000031 | ||
| 80 | 0.789714336 | 1.197086573 | 5.618000031 | ||
| trailing | 1 | 0.789714336 | 1.197086573 | 5.618000031 | |
| edge - | 2 | 0.789917886 | 1.201568007 | 5.618000031 | |
| curve 1 | 3 | 0.788787067 | 1.205909133 | 5.618000031 | |
| 4 | 0.786423087 | 1.209721804 | 5.618000031 | ||
| 5 | 0.783037424 | 1.212664962 | 5.618000031 | ||
| 6 | 0.778932869 | 1.214475274 | 5.618000031 | ||
| 7 | 0.774476528 | 1.214990854 | 5.618000031 | ||
| 8 | 0.770067036 | 1.214165688 | 5.618000031 | ||
| 9 | 0.766098738 | 1.212073445 | 5.618000031 | ||
| 10 | 0.762926638 | 1.208901286 | 5.618000031 | ||
| 11 | 0.760834396 | 1.204933047 | 5.618000031 | ||
| pressure | 1 | 0.760834396 | 1.204933047 | 5.618000031 | |
| side - | 2 | 0.758890986 | 1.199366808 | 5.618000031 | |
| curve 2 | 3 | 0.756731153 | 1.193209171 | 5.618000031 | |
| 4 | 0.754332125 | 1.186405063 | 5.618000031 | ||
| 5 | 0.751668751 | 1.178895593 | 5.618000031 | ||
| 6 | 0.748714447 | 1.170621157 | 5.618000031 | ||
| 7 | 0.745439947 | 1.161515594 | 5.618000031 | ||
| 8 | 0.741813719 | 1.151509404 | 5.618000031 | ||
| 9 | 0.737802327 | 1.140536427 | 5.618000031 | ||
| 10 | 0.733369470 | 1.128522754 | 5.618000031 | ||
| 11 | 0.728477359 | 1.115400434 | 5.618000031 | ||
| 12 | 0.723085821 | 1.101097465 | 5.618000031 | ||
| 13 | 0.717153311 | 1.085549712 | 5.618000031 | ||
| 14 | 0.710636795 | 1.068693519 | 5.618000031 | ||
| 15 | 0.703492701 | 1.050473332 | 5.618000031 | ||
| 16 | 0.695677280 | 1.030842900 | 5.618000031 | ||
| 17 | 0.687147677 | 1.009767294 | 5.618000031 | ||
| 18 | 0.677862585 | 0.987224758 | 5.618000031 | ||
| 19 | 0.667784035 | 0.963210702 | 5.618000031 | ||
| 20 | 0.656877935 | 0.937739253 | 5.618000031 | ||
| 21 | 0.645116150 | 0.910846651 | 5.618000031 | ||
| 22 | 0.632477641 | 0.882591307 | 5.618000031 | ||
| 23 | 0.618950009 | 0.853056550 | 5.618000031 | ||
| 24 | 0.604531646 | 0.822353303 | 5.618000031 | ||
| 25 | 0.589231968 | 0.790614545 | 5.618000031 | ||
| 26 | 0.573073685 | 0.758000076 | 5.618000031 | ||
| 27 | 0.556092620 | 0.724689305 | 5.618000031 | ||
| 28 | 0.538339317 | 0.690882921 | 5.618000031 | ||
| 29 | 0.519877613 | 0.656794429 | 5.618000031 | ||
| 30 | 0.500785053 | 0.622647643 | 5.618000031 | ||
| 31 | 0.481151491 | 0.588670969 | 5.618000031 | ||
| 32 | 0.461077690 | 0.555092037 | 5.618000031 | ||
| 33 | 0.440672696 | 0.522130072 | 5.618000031 | ||
| 34 | 0.420052171 | 0.489992142 | 5.618000031 | ||
| 35 | 0.399335384 | 0.458867610 | 5.618000031 | ||
| 36 | 0.378642440 | 0.428924143 | 5.618000031 | ||
| 37 | 0.358092219 | 0.400304586 | 5.618000031 | ||
| 38 | 0.337798953 | 0.373124361 | 5.618000031 | ||
| 39 | 0.317870677 | 0.347470969 | 5.618000031 | ||
| 40 | 0.298406631 | 0.323403537 | 5.618000031 | ||
| 41 | 0.279496312 | 0.300954282 | 5.618000031 | ||
| 42 | 0.261218518 | 0.280130506 | 5.618000031 | ||
| 43 | 0.243638873 | 0.260915518 | 5.618000031 | ||
| 44 | 0.226812482 | 0.243273884 | 5.618000031 | ||
| 45 | 0.210780546 | 0.227152109 | 5.618000031 | ||
| 46 | 0.195573643 | 0.212483868 | 5.618000031 | ||
| 47 | 0.181210056 | 0.199191704 | 5.618000031 | ||
| 48 | 0.167697757 | 0.187191188 | 5.618000031 | ||
| 49 | 0.155035138 | 0.176393047 | 5.618000031 | ||
| 50 | 0.143211976 | 0.166705981 | 5.618000031 | ||
| 51 | 0.132210836 | 0.158038929 | 5.618000031 | ||
| 52 | 0.122007556 | 0.150302216 | 5.618000031 | ||
| 53 | 0.112572968 | 0.143409699 | 5.618000031 | ||
| 54 | 0.103873782 | 0.137279347 | 5.618000031 | ||
| 55 | 0.095873952 | 0.131834269 | 5.618000031 | ||
| 56 | 0.088535376 | 0.127002731 | 5.618000031 | ||
| 57 | 0.081818417 | 0.122719280 | 5.618000031 | ||
| 58 | 0.075679705 | 0.118929714 | 5.618000031 | ||
| 59 | 0.070069723 | 0.115595981 | 5.618000031 | ||
| 60 | 0.065000318 | 0.112583481 | 5.618000031 | ||
| leading | 1 | 0.065000318 | 0.112583481 | 5.618000031 | |
| edge - | 2 | 0.043013237 | 0.096609026 | 5.618000031 | |
| curve 3 | 3 | 0.024827920 | 0.076412261 | 5.618000031 | |
| 4 | 0.011239149 | 0.052875906 | 5.618000031 | ||
| 5 | 0.002840832 | 0.027028596 | 5.618000031 | ||
| 6 | 0.000000000 | 0.000000004 | 5.618000031 | ||
| 7 | 0.002840832 | β0.027028589 | 5.618000031 | ||
| 8 | 0.011239149 | β0.052875891 | 5.618000031 | ||
| 9 | 0.024827920 | β0.076412261 | 5.618000031 | ||
| 10 | 0.043013237 | β0.096609026 | 5.618000031 | ||
| 11 | 0.065000325 | β0.112583496 | 5.618000031 | ||
| 2 | suction | 1 | 0.065000318 | β0.112583481 | 5.848999977 |
| side from | 2 | 0.069683179 | β0.115239047 | 5.848999977 | |
| LE - curve 0 | 3 | 0.074791476 | β0.118028820 | 5.848999977 | |
| 4 | 0.080364786 | β0.120941833 | 5.848999977 | ||
| 5 | 0.086445890 | β0.123964138 | 5.848999977 | ||
| 6 | 0.093081519 | β0.127075091 | 5.848999977 | ||
| 7 | 0.100321889 | β0.130244657 | 5.848999977 | ||
| 8 | 0.108220577 | β0.133432060 | 5.848999977 | ||
| 9 | 0.116834305 | β0.136583164 | 5.848999977 | ||
| 10 | 0.126221716 | β0.139626786 | 5.848999977 | ||
| 11 | 0.136441514 | β0.142471209 | 5.848999977 | ||
| 12 | 0.147549480 | β0.145000294 | 5.848999977 | ||
| 13 | 0.159593701 | β0.147069812 | 5.848999977 | ||
| 14 | 0.172610804 | β0.148506343 | 5.848999977 | ||
| 15 | 0.186613724 | β0.149105951 | 5.848999977 | ||
| 16 | 0.201587886 | β0.148640454 | 5.848999977 | ||
| 17 | 0.217480972 | β0.146867111 | 5.848999977 | ||
| 18 | 0.234199509 | β0.143546104 | 5.848999977 | ||
| 19 | 0.251611769 | β0.138459995 | 5.848999977 | ||
| 20 | 0.269558102 | β0.131433159 | 5.848999977 | ||
| 21 | 0.287867129 | β0.122344099 | 5.848999977 | ||
| 22 | 0.306372851 | β0.111128107 | 5.848999977 | ||
| 23 | 0.324927896 | β0.097771138 | 5.848999977 | ||
| 24 | 0.343411207 | β0.082298227 | 5.848999977 | ||
| 25 | 0.361728609 | β0.064761654 | 5.848999977 | ||
| 26 | 0.379809737 | β0.045231745 | 5.848999977 | ||
| 27 | 0.397604167 | β0.023788195 | 5.848999977 | ||
| 28 | 0.415076017 | β0.000517053 | 5.848999977 | ||
| 29 | 0.432199448 | 0.024491007 | 5.848999977 | ||
| 30 | 0.448955536 | 0.051141378 | 5.848999977 | ||
| 31 | 0.465329200 | 0.079334021 | 5.848999977 | ||
| 32 | 0.481308073 | 0.108963713 | 5.848999977 | ||
| 33 | 0.496881396 | 0.139919445 | 5.848999977 | ||
| 34 | 0.512039185 | 0.172083616 | 5.848999977 | ||
| 35 | 0.526772141 | 0.205332130 | 5.848999977 | ||
| 36 | 0.541071355 | 0.239534006 | 5.848999977 | ||
| 37 | 0.554928243 | 0.274552137 | 5.848999977 | ||
| 38 | 0.568339825 | 0.310243130 | 5.848999977 | ||
| 39 | 0.581320465 | 0.346456289 | 5.848999977 | ||
| 40 | 0.593860745 | 0.383038938 | 5.848999977 | ||
| 41 | 0.605945051 | 0.419847518 | 5.848999977 | ||
| 42 | 0.617561340 | 0.456734419 | 5.848999977 | ||
| 43 | 0.628701091 | 0.493553251 | 5.848999977 | ||
| 44 | 0.639358640 | 0.530159593 | 5.848999977 | ||
| 45 | 0.649532020 | 0.566416740 | 5.848999977 | ||
| 46 | 0.659222603 | 0.602199256 | 5.848999977 | ||
| 47 | 0.668433666 | 0.637384236 | 5.848999977 | ||
| 48 | 0.677170455 | 0.671854734 | 5.848999977 | ||
| 49 | 0.685440183 | 0.705501199 | 5.848999977 | ||
| 50 | 0.693254590 | 0.738245428 | 5.848999977 | ||
| 51 | 0.700625658 | 0.770009995 | 5.848999977 | ||
| 52 | 0.707564712 | 0.800711870 | 5.848999977 | ||
| 53 | 0.714088321 | 0.830313981 | 5.848999977 | ||
| 54 | 0.720211267 | 0.858767986 | 5.848999977 | ||
| 55 | 0.725948811 | 0.886033893 | 5.848999977 | ||
| 56 | 0.731319785 | 0.912110388 | 5.848999977 | ||
| 57 | 0.736338675 | 0.936964154 | 5.848999977 | ||
| 58 | 0.741025090 | 0.960617185 | 5.848999977 | ||
| 59 | 0.745394588 | 0.983061492 | 5.848999977 | ||
| 60 | 0.749464512 | 1.004315853 | 5.848999977 | ||
| 61 | 0.753252745 | 1.024414659 | 5.848999977 | ||
| 62 | 0.756773591 | 1.043362498 | 5.848999977 | ||
| 63 | 0.760044515 | 1.061209202 | 5.848999977 | ||
| 64 | 0.763080955 | 1.077992082 | 5.848999977 | ||
| 65 | 0.765896201 | 1.093732715 | 5.848999977 | ||
| 66 | 0.768505454 | 1.108484030 | 5.848999977 | ||
| 67 | 0.770922959 | 1.122297406 | 5.848999977 | ||
| 68 | 0.773160458 | 1.135204315 | 5.848999977 | ||
| 69 | 0.775230050 | 1.147246361 | 5.848999977 | ||
| 70 | 0.777143657 | 1.158472896 | 5.848999977 | ||
| 71 | 0.778912544 | 1.168931961 | 5.848999977 | ||
| 72 | 0.780542612 | 1.178668857 | 5.848999977 | ||
| 73 | 0.782028496 | 1.187719941 | 5.848999977 | ||
| 74 | 0.783408284 | 1.196124673 | 5.848999977 | ||
| 75 | 0.784688652 | 1.203923821 | 5.848999977 | ||
| 76 | 0.785875857 | 1.211155534 | 5.848999977 | ||
| 77 | 0.786975920 | 1.217856407 | 5.848999977 | ||
| 78 | 0.787994623 | 1.224061608 | 5.848999977 | ||
| 79 | 0.788937449 | 1.229804754 | 5.848999977 | ||
| 80 | 0.789809585 | 1.235117197 | 5.848999977 | ||
| trailing | 1 | 0.789809585 | 1.235117197 | 5.848999977 | |
| edge - | 2 | 0.789851844 | 1.239603162 | 5.848999977 | |
| curve 1 | 3 | 0.788565755 | 1.243900895 | 5.848999977 | |
| 4 | 0.786066294 | 1.247626066 | 5.848999977 | ||
| 5 | 0.782576978 | 1.250445604 | 5.848999977 | ||
| 6 | 0.778410017 | 1.252107263 | 5.848999977 | ||
| 7 | 0.773938000 | 1.252462268 | 5.848999977 | ||
| 8 | 0.769561052 | 1.251479149 | 5.848999977 | ||
| 9 | 0.765670538 | 1.249245644 | 5.848999977 | ||
| 10 | 0.762614489 | 1.245961547 | 5.848999977 | ||
| 11 | 0.760666251 | 1.241920590 | 5.848999977 | ||
| pressure | 1 | 0.760666251 | 1.241920590 | 5.848999977 | |
| side - | 2 | 0.758962274 | 1.236412764 | 5.848999977 | |
| curve 2 | 3 | 0.757061601 | 1.230301976 | 5.848999977 | |
| 4 | 0.754942298 | 1.223529577 | 5.848999977 | ||
| 5 | 0.752580404 | 1.216033340 | 5.848999977 | ||
| 6 | 0.749949753 | 1.207750082 | 5.848999977 | ||
| 7 | 0.747021735 | 1.198608875 | 5.848999977 | ||
| 8 | 0.743765056 | 1.188533425 | 5.848999977 | ||
| 9 | 0.740146101 | 1.177452326 | 5.848999977 | ||
| 10 | 0.736128330 | 1.165284634 | 5.848999977 | ||
| 11 | 0.731672883 | 1.151955128 | 5.848999977 | ||
| 12 | 0.726738095 | 1.137383938 | 5.848999977 | ||
| 13 | 0.721280158 | 1.121499419 | 5.848999977 | ||
| 14 | 0.715253115 | 1.104227901 | 5.848999977 | ||
| 15 | 0.708609581 | 1.085506320 | 5.848999977 | ||
| 16 | 0.701301098 | 1.065280199 | 5.848999977 | ||
| 17 | 0.693279028 | 1.043506384 | 5.848999977 | ||
| 18 | 0.684495747 | 1.020156741 | 5.848999977 | ||
| 19 | 0.674905539 | 0.995220661 | 5.848999977 | ||
| 20 | 0.664466023 | 0.968708754 | 5.848999977 | ||
| 21 | 0.653140068 | 0.940655589 | 5.848999977 | ||
| 22 | 0.640897214 | 0.911120534 | 5.848999977 | ||
| 23 | 0.627715528 | 0.880191028 | 5.848999977 | ||
| 24 | 0.613583982 | 0.847985506 | 5.848999977 | ||
| 25 | 0.598503053 | 0.814647019 | 5.848999977 | ||
| 26 | 0.582487822 | 0.780350626 | 5.848999977 | ||
| 27 | 0.565567613 | 0.745291889 | 5.848999977 | ||
| 28 | 0.547788203 | 0.709691703 | 5.848999977 | ||
| 29 | 0.529211164 | 0.673786879 | 5.848999977 | ||
| 30 | 0.509913921 | 0.637824357 | 5.848999977 | ||
| 31 | 0.489988685 | 0.602056742 | 5.848999977 | ||
| 32 | 0.469541043 | 0.566735506 | 5.848999977 | ||
| 33 | 0.448687464 | 0.532102704 | 5.848999977 | ||
| 34 | 0.427553087 | 0.498386234 | 5.848999977 | ||
| 35 | 0.406268507 | 0.465792984 | 5.848999977 | ||
| 36 | 0.384966493 | 0.434504390 | 5.848999977 | ||
| 37 | 0.363779098 | 0.404673189 | 5.848999977 | ||
| 38 | 0.342834175 | 0.376420200 | 5.848999977 | ||
| 39 | 0.322253317 | 0.349835038 | 5.848999977 | ||
| 40 | 0.302148938 | 0.324975252 | 5.848999977 | ||
| 41 | 0.282622218 | 0.301867664 | 5.848999977 | ||
| 42 | 0.263761491 | 0.280510485 | 5.848999977 | ||
| 43 | 0.245642006 | 0.260877669 | 5.848999977 | ||
| 44 | 0.228324383 | 0.242920816 | 5.848999977 | ||
| 45 | 0.211855575 | 0.226574376 | 5.848999977 | ||
| 46 | 0.196267828 | 0.211757958 | 5.848999977 | ||
| 47 | 0.181581303 | 0.198381931 | 5.848999977 | ||
| 48 | 0.167803183 | 0.186349347 | 5.848999977 | ||
| 49 | 0.154929906 | 0.175559789 | 5.848999977 | ||
| 50 | 0.142948002 | 0.165911973 | 5.848999977 | ||
| 51 | 0.131835893 | 0.157306030 | 5.848999977 | ||
| 52 | 0.121564880 | 0.149645180 | 5.848999977 | ||
| 53 | 0.112101071 | 0.142837375 | 5.848999977 | ||
| 54 | 0.103406280 | 0.136795953 | 5.848999977 | ||
| 55 | 0.095439196 | 0.131440535 | 5.848999977 | ||
| 56 | 0.088156857 | 0.126696929 | 5.848999977 | ||
| 57 | 0.081515469 | 0.122497544 | 5.848999977 | ||
| 58 | 0.075461298 | 0.118797369 | 5.848999977 | ||
| 59 | 0.069958746 | 0.115528814 | 5.848999977 | ||
| 60 | 0.065000318 | 0.112583481 | 5.848999977 | ||
| leading | 1 | 0.065000318 | 0.112583481 | 5.848999977 | |
| edge - | 2 | 0.043013237 | 0.096609026 | 5.848999977 | |
| curve 3 | 3 | 0.024827920 | 0.076412261 | 5.848999977 | |
| 4 | 0.011239149 | 0.052875906 | 5.848999977 | ||
| 5 | 0.002840832 | 0.027028598 | 5.848999977 | ||
| 6 | 0.000000000 | 0.000000004 | 5.848999977 | ||
| 7 | 0.002840832 | β0.027028589 | 5.848999977 | ||
| 8 | 0.011239149 | β0.052875891 | 5.848999977 | ||
| 9 | 0.024827920 | β0.076412261 | 5.848999977 | ||
| 10 | 0.043013237 | β0.096609026 | 5.848999977 | ||
| 11 | 0.065000325 | β0.112583488 | 5.848999977 | ||
| 3 | suction | 1 | 0.065000318 | β0.112583473 | 6.079999924 |
| side from | 2 | 0.069678701 | β0.115246922 | 6.079999924 | |
| LE - curve 0 | 3 | 0.074781358 | β0.118067861 | 6.079999924 | |
| 4 | 0.080347024 | β0.121041872 | 6.079999924 | ||
| 5 | 0.086417839 | β0.124163195 | 6.079999924 | ||
| 6 | 0.093039975 | β0.127420321 | 6.079999924 | ||
| 7 | 0.100263201 | β0.130795091 | 6.079999924 | ||
| 8 | 0.108141482 | β0.134261981 | 6.079999924 | ||
| 9 | 0.116732806 | β0.137784272 | 6.079999924 | ||
| 10 | 0.126098558 | β0.141311899 | 6.079999924 | ||
| 11 | 0.136303216 | β0.144778520 | 6.079999924 | ||
| 12 | 0.147412822 | β0.148097008 | 6.079999924 | ||
| 13 | 0.159492433 | β0.151154816 | 6.079999924 | ||
| 14 | 0.172602654 | β0.153809309 | 6.079999924 | ||
| 15 | 0.186794519 | β0.155883938 | 6.079999924 | ||
| 16 | 0.202098608 | β0.157162815 | 6.079999924 | ||
| 17 | 0.218519196 | β0.157395437 | 6.079999924 | ||
| 18 | 0.236019224 | β0.156299055 | 6.079999924 | ||
| 19 | 0.254512638 | β0.153576583 | 6.079999924 | ||
| 20 | 0.273858577 | β0.148938581 | 6.079999924 | ||
| 21 | 0.293867439 | β0.142131463 | 6.079999924 | ||
| 22 | 0.314317286 | β0.132962912 | 6.079999924 | ||
| 23 | 0.334977984 | β0.121317156 | 6.079999924 | ||
| 24 | 0.355635315 | β0.107155696 | 6.079999924 | ||
| 25 | 0.376107305 | β0.090504102 | 6.079999924 | ||
| 26 | 0.396252424 | β0.071434222 | 6.079999924 | ||
| 27 | 0.415966898 | β0.050050274 | 6.079999924 | ||
| 28 | 0.435180366 | β0.026470426 | 6.079999924 | ||
| 29 | 0.453847528 | β0.000820583 | 6.079999924 | ||
| 30 | 0.471939504 | 0.026766026 | 6.079999924 | ||
| 31 | 0.489440113 | 0.056155618 | 6.079999924 | ||
| 32 | 0.506340981 | 0.087212466 | 6.079999924 | ||
| 33 | 0.522638381 | 0.119797148 | 6.079999924 | ||
| 34 | 0.538331449 | 0.153765604 | 6.079999924 | ||
| 35 | 0.553420424 | 0.188967407 | 6.079999924 | ||
| 36 | 0.567907870 | 0.225249484 | 6.079999924 | ||
| 37 | 0.581797004 | 0.262452513 | 6.079999924 | ||
| 38 | 0.595058441 | 0.300418377 | 6.079999924 | ||
| 39 | 0.607599795 | 0.339024514 | 6.079999924 | ||
| 40 | 0.619455040 | 0.378082097 | 6.079999924 | ||
| 41 | 0.630673885 | 0.417405099 | 6.079999924 | ||
| 42 | 0.641295195 | 0.456814915 | 6.079999924 | ||
| 43 | 0.651351035 | 0.496140510 | 6.079999924 | ||
| 44 | 0.660869122 | 0.535219252 | 6.079999924 | ||
| 45 | 0.669873714 | 0.573898256 | 6.079999924 | ||
| 46 | 0.678386271 | 0.612032056 | 6.079999924 | ||
| 47 | 0.686426103 | 0.649483085 | 6.079999924 | ||
| 48 | 0.694010615 | 0.686120212 | 6.079999924 | ||
| 49 | 0.701159060 | 0.721841574 | 6.079999924 | ||
| 50 | 0.707890451 | 0.756561875 | 6.079999924 | ||
| 51 | 0.714218855 | 0.790177643 | 6.079999924 | ||
| 52 | 0.720162153 | 0.822626352 | 6.079999924 | ||
| 53 | 0.725738764 | 0.853865266 | 6.079999924 | ||
| 54 | 0.730961800 | 0.883825183 | 6.079999924 | ||
| 55 | 0.735851884 | 0.912509620 | 6.079999924 | ||
| 56 | 0.740420938 | 0.939865828 | 6.079999924 | ||
| 57 | 0.744689226 | 0.965921819 | 6.079999924 | ||
| 58 | 0.748668790 | 0.990649462 | 6.079999924 | ||
| 59 | 0.752377391 | 1.014080763 | 6.079999924 | ||
| 60 | 0.755830228 | 1.036236644 | 6.079999924 | ||
| 61 | 0.759039819 | 1.057124853 | 6.079999924 | ||
| 62 | 0.762023091 | 1.076802135 | 6.079999924 | ||
| 63 | 0.764792919 | 1.095298290 | 6.079999924 | ||
| 64 | 0.767361164 | 1.112641692 | 6.079999924 | ||
| 65 | 0.769741833 | 1.128889203 | 6.079999924 | ||
| 66 | 0.771947920 | 1.144095778 | 6.079999924 | ||
| 67 | 0.773989558 | 1.158295393 | 6.079999924 | ||
| 68 | 0.775877595 | 1.171534777 | 6.079999924 | ||
| 69 | 0.777623057 | 1.183868885 | 6.079999924 | ||
| 70 | 0.779236138 | 1.195349813 | 6.079999924 | ||
| 71 | 0.780726433 | 1.206028104 | 6.079999924 | ||
| 72 | 0.782080114 | 1.215944052 | 6.079999924 | ||
| 73 | 0.783335567 | 1.225144029 | 6.079999924 | ||
| 74 | 0.784499288 | 1.233671904 | 6.079999924 | ||
| 75 | 0.785577297 | 1.241571546 | 6.079999924 | ||
| 76 | 0.786575079 | 1.248883367 | 6.079999924 | ||
| 77 | 0.787497997 | 1.255646586 | 6.079999924 | ||
| 78 | 0.788351238 | 1.261899114 | 6.079999924 | ||
| 79 | 0.789139509 | 1.267675638 | 6.079999924 | ||
| 80 | 0.789867401 | 1.273009658 | 6.079999924 | ||
| trailing | 1 | 0.789867401 | 1.273009658 | 6.079999924 | |
| edge - | 2 | 0.789791048 | 1.277495027 | 6.079999924 | |
| curve 1 | 3 | 0.788391769 | 1.281757355 | 6.079999924 | |
| 4 | 0.785794675 | 1.285415173 | 6.079999924 | ||
| 5 | 0.782232046 | 1.288141370 | 6.079999924 | ||
| 6 | 0.778022587 | 1.289692283 | 6.079999924 | ||
| 7 | 0.773542821 | 1.289929032 | 6.079999924 | ||
| 8 | 0.769193351 | 1.288830400 | 6.079999924 | ||
| 9 | 0.765363216 | 1.286494851 | 6.079999924 | ||
| 10 | 0.762395084 | 1.283131123 | 6.079999924 | ||
| 11 | 0.760554373 | 1.279040098 | 6.079999924 | ||
| pressure | 1 | 0.760554373 | 1.279040098 | 6.079999924 | |
| side - | 2 | 0.759019971 | 1.273573279 | 6.079999924 | |
| curve 2 | 3 | 0.757303357 | 1.267492414 | 6.079999924 | |
| 4 | 0.755383790 | 1.260737538 | 6.079999924 | ||
| 5 | 0.753237665 | 1.253242135 | 6.079999924 | ||
| 6 | 0.750839770 | 1.244939923 | 6.079999924 | ||
| 7 | 0.748161912 | 1.235756278 | 6.079999924 | ||
| 8 | 0.745173335 | 1.225608826 | 6.079999924 | ||
| 9 | 0.741840601 | 1.214421272 | 6.079999924 | ||
| 10 | 0.738127112 | 1.202107310 | 6.079999924 | ||
| 11 | 0.733993292 | 1.188583016 | 6.079999924 | ||
| 12 | 0.729396880 | 1.173763156 | 6.079999924 | ||
| 13 | 0.724292696 | 1.157568216 | 6.079999924 | ||
| 14 | 0.718632758 | 1.139915109 | 6.079999924 | ||
| 15 | 0.712367117 | 1.120734453 | 6.079999924 | ||
| 16 | 0.705444157 | 1.099963784 | 6.079999924 | ||
| 17 | 0.697811067 | 1.077551723 | 6.079999924 | ||
| 18 | 0.689415336 | 1.053462625 | 6.079999924 | ||
| 19 | 0.680205762 | 1.027680516 | 6.079999924 | ||
| 20 | 0.670133531 | 1.000211954 | 6.079999924 | ||
| 21 | 0.659154654 | 0.971089005 | 6.079999924 | ||
| 22 | 0.647231221 | 0.940371633 | 6.079999924 | ||
| 23 | 0.634333551 | 0.908148289 | 6.079999924 | ||
| 24 | 0.620442986 | 0.874544621 | 6.079999924 | ||
| 25 | 0.605552733 | 0.839711368 | 6.079999924 | ||
| 26 | 0.589671075 | 0.803836286 | 6.079999924 | ||
| 27 | 0.572821915 | 0.767129958 | 6.079999924 | ||
| 28 | 0.555046558 | 0.729830921 | 6.079999924 | ||
| 29 | 0.536404133 | 0.692196429 | 6.079999924 | ||
| 30 | 0.516971469 | 0.654495180 | 6.079999924 | ||
| 31 | 0.496841967 | 0.617002189 | 6.079999924 | ||
| 32 | 0.476124763 | 0.579991043 | 6.079999924 | ||
| 33 | 0.454941630 | 0.543725371 | 6.079999924 | ||
| 34 | 0.433424950 | 0.508452415 | 6.079999924 | ||
| 35 | 0.411713898 | 0.474396139 | 6.079999924 | ||
| 36 | 0.389951080 | 0.441751510 | 6.079999924 | ||
| 37 | 0.368279248 | 0.410681933 | 6.079999924 | ||
| 38 | 0.346837282 | 0.381315202 | 6.079999924 | ||
| 39 | 0.325756997 | 0.353742868 | 6.079999924 | ||
| 40 | 0.305161119 | 0.328022093 | 6.079999924 | ||
| 41 | 0.285159975 | 0.304175973 | 6.079999924 | ||
| 42 | 0.265850484 | 0.282197267 | 6.079999924 | ||
| 43 | 0.247313693 | 0.262050122 | 6.079999924 | ||
| 44 | 0.229616284 | 0.243677661 | 6.079999924 | ||
| 45 | 0.212808073 | 0.227002621 | 6.079999924 | ||
| 46 | 0.196924165 | 0.211934239 | 6.079999924 | ||
| 47 | 0.181985036 | 0.198371589 | 6.079999924 | ||
| 48 | 0.167997345 | 0.186207101 | 6.079999924 | ||
| 49 | 0.154955938 | 0.175330713 | 6.079999924 | ||
| 50 | 0.142845050 | 0.165632367 | 6.079999924 | ||
| 51 | 0.131639972 | 0.157004431 | 6.079999924 | ||
| 52 | 0.121308580 | 0.149343535 | 6.079999924 | ||
| 53 | 0.111813135 | 0.142551973 | 6.079999924 | ||
| 54 | 0.103111841 | 0.136538640 | 6.079999924 | ||
| 55 | 0.095159508 | 0.131219208 | 6.079999924 | ||
| 56 | 0.087909691 | 0.126516834 | 6.079999924 | ||
| 57 | 0.081315503 | 0.122361720 | 6.079999924 | ||
| 58 | 0.075316474 | 0.118712917 | 6.079999924 | ||
| 59 | 0.069884099 | 0.115485221 | 6.079999924 | ||
| 60 | 0.065000318 | 0.112583473 | 6.079999924 | ||
| leading | 1 | 0.065000318 | 0.112583473 | 6.079999924 | |
| edge - | 2 | 0.043013237 | 0.096609026 | 6.079999924 | |
| curve 3 | 3 | 0.024827920 | 0.076412261 | 6.079999924 | |
| 4 | 0.011239149 | 0.052875903 | 6.079999924 | ||
| 5 | 0.002840832 | 0.027028598 | 6.079999924 | ||
| 6 | 0.000000000 | 0.000000004 | 6.079999924 | ||
| 7 | 0.002840832 | β0.027028589 | 6.079999924 | ||
| 8 | 0.011239149 | β0.052875895 | 6.079999924 | ||
| 9 | 0.024827920 | β0.076412261 | 6.079999924 | ||
| 10 | 0.043013237 | β0.096609026 | 6.079999924 | ||
| 11 | 0.065000325 | β0.112583488 | 6.079999924 | ||
| 4 | suction | 1 | 0.065000318 | β0.112583481 | 6.310999870 |
| side side | 2 | 0.069677077 | β0.115250342 | 6.310999870 | |
| from LE - | 3 | 0.074780613 | β0.118086010 | 6.310999870 | |
| curve 0 | 4 | 0.080349930 | β0.121089011 | 6.310999870 | |
| 5 | 0.086427353 | β0.124257222 | 6.310999870 | ||
| 6 | 0.093059547 | β0.127582669 | 6.310999870 | ||
| 7 | 0.100296699 | β0.131052852 | 6.310999870 | ||
| 8 | 0.108193561 | β0.134648085 | 6.310999870 | ||
| 9 | 0.116808996 | β0.138338462 | 6.310999870 | ||
| 10 | 0.126206130 | β0.142083257 | 6.310999870 | ||
| 11 | 0.136452019 | β0.145826668 | 6.310999870 | ||
| 12 | 0.147616684 | β0.149493843 | 6.310999870 | ||
| 13 | 0.159771621 | β0.152986437 | 6.310999870 | ||
| 14 | 0.172986686 | β0.156177133 | 6.310999870 | ||
| 15 | 0.187325358 | β0.158903480 | 6.310999870 | ||
| 16 | 0.202840179 | β0.160964578 | 6.310999870 | ||
| 17 | 0.219559103 | β0.162114322 | 6.310999870 | ||
| 18 | 0.237475678 | β0.162065834 | 6.310999870 | ||
| 19 | 0.256538033 | β0.160496533 | 6.310999870 | ||
| 20 | 0.276630133 | β0.157069609 | 6.310999870 | ||
| 21 | 0.297573745 | β0.151461750 | 6.310999870 | ||
| 22 | 0.319134593 | β0.143398061 | 6.310999870 | ||
| 23 | 0.341046154 | β0.132682756 | 6.310999870 | ||
| 24 | 0.363038272 | β0.119213216 | 6.310999870 | ||
| 25 | 0.384867936 | β0.102976881 | 6.310999870 | ||
| 26 | 0.406336814 | β0.084035933 | 6.310999870 | ||
| 27 | 0.427298248 | β0.062497687 | 6.310999870 | ||
| 28 | 0.447650105 | β0.038502797 | 6.310999870 | ||
| 29 | 0.467328876 | β0.012201693 | 6.310999870 | ||
| 30 | 0.486298025 | 0.016249288 | 6.310999870 | ||
| 31 | 0.504538178 | 0.046688329 | 6.310999870 | ||
| 32 | 0.522043705 | 0.078958042 | 6.310999870 | ||
| 33 | 0.538816154 | 0.112898774 | 6.310999870 | ||
| 34 | 0.554860055 | 0.148343891 | 6.310999870 | ||
| 35 | 0.570183933 | 0.185127541 | 6.310999870 | ||
| 36 | 0.584797919 | 0.223079354 | 6.310999870 | ||
| 37 | 0.598716736 | 0.262021601 | 6.310999870 | ||
| 38 | 0.611813962 | 0.301830232 | 6.310999870 | ||
| 39 | 0.623954952 | 0.342352360 | 6.310999870 | ||
| 40 | 0.635265768 | 0.383356214 | 6.310999870 | ||
| 41 | 0.645848155 | 0.424637556 | 6.310999870 | ||
| 42 | 0.655776978 | 0.466000676 | 6.310999870 | ||
| 43 | 0.665109396 | 0.507258594 | 6.310999870 | ||
| 44 | 0.673890531 | 0.548233747 | 6.310999870 | ||
| 45 | 0.682156801 | 0.588757455 | 6.310999870 | ||
| 46 | 0.689938307 | 0.628669441 | 6.310999870 | ||
| 47 | 0.697262883 | 0.667833924 | 6.310999870 | ||
| 48 | 0.704155743 | 0.706133187 | 6.310999870 | ||
| 49 | 0.710636258 | 0.743439436 | 6.310999870 | ||
| 50 | 0.716721952 | 0.779635012 | 6.310999870 | ||
| 51 | 0.722435832 | 0.814667225 | 6.310999870 | ||
| 52 | 0.727792740 | 0.848443270 | 6.310999870 | ||
| 53 | 0.732809663 | 0.880905509 | 6.310999870 | ||
| 54 | 0.737505198 | 0.912029028 | 6.310999870 | ||
| 55 | 0.741892278 | 0.941759408 | 6.310999870 | ||
| 56 | 0.745989621 | 0.970106244 | 6.310999870 | ||
| 57 | 0.749810457 | 0.997047961 | 6.310999870 | ||
| 58 | 0.753369927 | 1.022592187 | 6.310999870 | ||
| 59 | 0.756684661 | 1.046775103 | 6.310999870 | ||
| 60 | 0.759765208 | 1.069587588 | 6.310999870 | ||
| 61 | 0.762627661 | 1.091083765 | 6.310999870 | ||
| 62 | 0.765285730 | 1.111306667 | 6.310999870 | ||
| 63 | 0.767749548 | 1.130273104 | 6.310999870 | ||
| 64 | 0.770032525 | 1.148041368 | 6.310999870 | ||
| 65 | 0.772147417 | 1.164671302 | 6.310999870 | ||
| 66 | 0.774104714 | 1.180207729 | 6.310999870 | ||
| 67 | 0.775913656 | 1.194689035 | 6.310999870 | ||
| 68 | 0.777585089 | 1.208175898 | 6.310999870 | ||
| 69 | 0.779128909 | 1.220725060 | 6.310999870 | ||
| 70 | 0.780554414 | 1.232392073 | 6.310999870 | ||
| 71 | 0.781857789 | 1.243225217 | 6.310999870 | ||
| 72 | 0.783053756 | 1.253269911 | 6.310999870 | ||
| 73 | 0.784161866 | 1.262576699 | 6.310999870 | ||
| 74 | 0.785187662 | 1.271192193 | 6.310999870 | ||
| 75 | 0.786136568 | 1.279161930 | 6.310999870 | ||
| 76 | 0.787013710 | 1.286528945 | 6.310999870 | ||
| 77 | 0.787824035 | 1.293334723 | 6.310999870 | ||
| 78 | 0.788572073 | 1.299617290 | 6.310999870 | ||
| 79 | 0.789262295 | 1.305414319 | 6.310999870 | ||
| 80 | 0.789898813 | 1.310760379 | 6.310999870 | ||
| trailing | 1 | 0.789898813 | 1.310760379 | 6.310999870 | |
| edge - | 2 | 0.789746940 | 1.315243840 | 6.310999870 | |
| curve 1 | 3 | 0.788276076 | 1.319481850 | 6.310999870 | |
| 4 | 0.785617769 | 1.323095441 | 6.310999870 | ||
| 5 | 0.782009721 | 1.325761437 | 6.310999870 | ||
| 6 | 0.777774751 | 1.327241182 | 6.310999870 | ||
| 7 | 0.773291588 | 1.327402353 | 6.310999870 | ||
| 8 | 0.768961251 | 1.326230764 | 6.310999870 | ||
| 9 | 0.765170991 | 1.323830962 | 6.310999870 | ||
| 10 | 0.762259960 | 1.320417643 | 6.310999870 | ||
| 11 | 0.760488391 | 1.316296220 | 6.310999870 | ||
| pressure | 1 | 0.760488391 | 1.316296220 | 6.310999870 | |
| side - | 2 | 0.759056151 | 1.310841560 | 6.310999870 | |
| curve 2 | 3 | 0.757450759 | 1.304763317 | 6.310999870 | |
| 4 | 0.755651832 | 1.297998428 | 6.310999870 | ||
| 5 | 0.753636658 | 1.290478468 | 6.310999870 | ||
| 6 | 0.751380086 | 1.282132626 | 6.310999870 | ||
| 7 | 0.748854756 | 1.272884846 | 6.310999870 | ||
| 8 | 0.746030152 | 1.262647629 | 6.310999870 | ||
| 9 | 0.742873013 | 1.251338124 | 6.310999870 | ||
| 10 | 0.739346802 | 1.238867760 | 6.310999870 | ||
| 11 | 0.735412061 | 1.225143790 | 6.310999870 | ||
| 12 | 0.731026113 | 1.210078239 | 6.310999870 | ||
| 13 | 0.726143062 | 1.193581581 | 6.310999870 | ||
| 14 | 0.720714092 | 1.175565600 | 6.310999870 | ||
| 15 | 0.714687943 | 1.155954123 | 6.310999870 | ||
| 16 | 0.708011150 | 1.134677410 | 6.310999870 | ||
| 17 | 0.700628638 | 1.111675858 | 6.310999870 | ||
| 18 | 0.692485273 | 1.086908221 | 6.310999870 | ||
| 19 | 0.683526278 | 1.060353160 | 6.310999870 | ||
| 20 | 0.673699200 | 1.032011628 | 6.310999870 | ||
| 21 | 0.662955761 | 1.001913667 | 6.310999870 | ||
| 22 | 0.651253462 | 0.970119119 | 6.310999870 | ||
| 23 | 0.638557792 | 0.936718285 | 6.310999870 | ||
| 24 | 0.624844790 | 0.901837111 | 6.310999870 | ||
| 25 | 0.610103130 | 0.865637481 | 6.310999870 | ||
| 26 | 0.594336033 | 0.828312993 | 6.310999870 | ||
| 27 | 0.577563703 | 0.790088177 | 6.310999870 | ||
| 28 | 0.559824109 | 0.751217008 | 6.310999870 | ||
| 29 | 0.541174054 | 0.711972237 | 6.310999870 | ||
| 30 | 0.521688998 | 0.672641098 | 6.310999870 | ||
| 31 | 0.501462698 | 0.633518398 | 6.310999870 | ||
| 32 | 0.480605513 | 0.594897389 | 6.310999870 | ||
| 33 | 0.459242046 | 0.557060599 | 6.310999870 | ||
| 34 | 0.437508464 | 0.520273089 | 6.310999870 | ||
| 35 | 0.415548891 | 0.484774530 | 6.310999870 | ||
| 36 | 0.393511653 | 0.450773597 | 6.310999870 | ||
| 37 | 0.371545762 | 0.418443978 | 6.310999870 | ||
| 38 | 0.349796653 | 0.387921125 | 6.310999870 | ||
| 39 | 0.328403026 | 0.359301597 | 6.310999870 | ||
| 40 | 0.307493716 | 0.332643479 | 6.310999870 | ||
| 41 | 0.287185103 | 0.307968974 | 6.310999870 | ||
| 42 | 0.267579705 | 0.285267830 | 6.310999870 | ||
| 43 | 0.248762965 | 0.264498383 | 6.310999870 | ||
| 44 | 0.230805591 | 0.245597258 | 6.310999870 | ||
| 45 | 0.213760048 | 0.228478938 | 6.310999870 | ||
| 46 | 0.197663710 | 0.213044584 | 6.310999870 | ||
| 47 | 0.182537928 | 0.199184150 | 6.310999870 | ||
| 48 | 0.168389589 | 0.186781377 | 6.310999870 | ||
| 49 | 0.155213460 | 0.175718114 | 6.310999870 | ||
| 50 | 0.142992556 | 0.165876299 | 6.310999870 | ||
| 51 | 0.131700754 | 0.157141253 | 6.310999870 | ||
| 52 | 0.121304184 | 0.149403259 | 6.310999870 | ||
| 53 | 0.111763082 | 0.142559007 | 6.310999870 | ||
| 54 | 0.103033490 | 0.136512637 | 6.310999870 | ||
| 55 | 0.095068179 | 0.131175697 | 6.310999870 | ||
| 56 | 0.087818384 | 0.126467824 | 6.310999870 | ||
| 57 | 0.081234992 | 0.122316346 | 6.310999870 | ||
| 58 | 0.075254180 | 0.118681192 | 6.310999870 | ||
| 59 | 0.069850191 | 0.115467578 | 6.310999870 | ||
| 60 | 0.065000318 | 0.112583481 | 6.310999870 | ||
| leading | 1 | 0.065000318 | 0.112583481 | 6.310999870 | |
| edge - | 2 | 0.043013237 | 0.096609026 | 6.310999870 | |
| curve 3 | 3 | 0.024827920 | 0.076412261 | 6.310999870 | |
| 4 | 0.011239149 | 0.052875903 | 6.310999870 | ||
| 5 | 0.002840832 | 0.027028596 | 6.310999870 | ||
| 6 | 0.000000000 | 0.000000004 | 6.310999870 | ||
| 7 | 0.002840832 | β0.027028589 | 6.310999870 | ||
| 8 | 0.011239149 | β0.052875895 | 6.310999870 | ||
| 9 | 0.024827920 | β0.076412261 | 6.310999870 | ||
| 10 | 0.043013237 | β0.096609026 | 6.310999870 | ||
| 11 | 0.065000325 | β0.112583481 | 6.310999870 | ||
| 5 | suction | 1 | 0.065000318 | β0.112583481 | 6.541999817 |
| side from | 2 | 0.069677249 | β0.115250915 | 6.541999817 | |
| LE - curve 0 | 3 | 0.074785046 | β0.118090384 | 6.541999817 | |
| 4 | 0.080363460 | β0.121100970 | 6.541999817 | ||
| 5 | 0.086455747 | β0.124281093 | 6.541999817 | ||
| 6 | 0.093109585 | β0.127623260 | 6.541999817 | ||
| 7 | 0.100376360 | β0.131115541 | 6.541999817 | ||
| 8 | 0.108312190 | β0.134738699 | 6.541999817 | ||
| 9 | 0.116977543 | β0.138463199 | 6.541999817 | ||
| 10 | 0.126437366 | β0.142248616 | 6.541999817 | ||
| 11 | 0.136760846 | β0.146039009 | 6.541999817 | ||
| 12 | 0.148020461 | β0.149759114 | 6.541999817 | ||
| 13 | 0.160290346 | β0.153309450 | 6.541999817 | ||
| 14 | 0.173643559 | β0.156560704 | 6.541999817 | ||
| 15 | 0.188146830 | β0.159346998 | 6.541999817 | ||
| 16 | 0.203856081 | β0.161462322 | 6.541999817 | ||
| 17 | 0.220802367 | β0.162652895 | 6.541999817 | ||
| 18 | 0.238980681 | β0.162621543 | 6.541999817 | ||
| 19 | 0.258338809 | β0.161032796 | 6.541999817 | ||
| 20 | 0.278757930 | β0.157534346 | 6.541999817 | ||
| 21 | 0.300052285 | β0.151787356 | 6.541999817 | ||
| 22 | 0.321977884 | β0.143503800 | 6.541999817 | ||
| 23 | 0.344254673 | β0.132478371 | 6.541999817 | ||
| 24 | 0.366600215 | β0.118604265 | 6.541999817 | ||
| 25 | 0.388762027 | β0.101872034 | 6.541999817 | ||
| 26 | 0.410535634 | β0.082345054 | 6.541999817 | ||
| 27 | 0.431769937 | β0.060140345 | 6.541999817 | ||
| 28 | 0.452363402 | β0.035400555 | 6.541999817 | ||
| 29 | 0.472252280 | β0.008283799 | 6.541999817 | ||
| 30 | 0.491400898 | 0.021047115 | 6.541999817 | ||
| 31 | 0.509793520 | 0.052431632 | 6.541999817 | ||
| 32 | 0.527423978 | 0.085701466 | 6.541999817 | ||
| 33 | 0.544295728 | 0.120693207 | 6.541999817 | ||
| 34 | 0.560416162 | 0.157240450 | 6.541999817 | ||
| 35 | 0.575793982 | 0.195168555 | 6.541999817 | ||
| 36 | 0.590440452 | 0.234300911 | 6.541999817 | ||
| 37 | 0.604348719 | 0.274465650 | 6.541999817 | ||
| 38 | 0.617275417 | 0.315548867 | 6.541999817 | ||
| 39 | 0.629218042 | 0.357358843 | 6.541999817 | ||
| 40 | 0.640328526 | 0.399663031 | 6.541999817 | ||
| 41 | 0.650708079 | 0.442240119 | 6.541999817 | ||
| 42 | 0.660432279 | 0.484884381 | 6.541999817 | ||
| 43 | 0.669559658 | 0.527402937 | 6.541999817 | ||
| 44 | 0.678137004 | 0.569616377 | 6.541999817 | ||
| 45 | 0.686201930 | 0.611352801 | 6.541999817 | ||
| 46 | 0.693785787 | 0.652450442 | 6.541999817 | ||
| 47 | 0.700914264 | 0.692751646 | 6.541999817 | ||
| 48 | 0.707611084 | 0.732119381 | 6.541999817 | ||
| 49 | 0.713902175 | 0.770464182 | 6.541999817 | ||
| 50 | 0.719804406 | 0.807658553 | 6.541999817 | ||
| 51 | 0.725335240 | 0.843601882 | 6.541999817 | ||
| 52 | 0.730517566 | 0.878261030 | 6.541999817 | ||
| 53 | 0.735362947 | 0.911529899 | 6.541999817 | ||
| 54 | 0.739893794 | 0.943415642 | 6.541999817 | ||
| 55 | 0.744120955 | 0.973841250 | 6.541999817 | ||
| 56 | 0.748065472 | 1.002840281 | 6.541999817 | ||
| 57 | 0.751737773 | 1.030362606 | 6.541999817 | ||
| 58 | 0.755156755 | 1.056454539 | 6.541999817 | ||
| 59 | 0.758335233 | 1.081117511 | 6.541999817 | ||
| 60 | 0.761286259 | 1.104367375 | 6.541999817 | ||
| 61 | 0.764026284 | 1.126267076 | 6.541999817 | ||
| 62 | 0.766566396 | 1.146836996 | 6.541999817 | ||
| 63 | 0.768918455 | 1.166113257 | 6.541999817 | ||
| 64 | 0.771096051 | 1.184160948 | 6.541999817 | ||
| 65 | 0.773111284 | 1.201039433 | 6.541999817 | ||
| 66 | 0.774973631 | 1.216785312 | 6.541999817 | ||
| 67 | 0.776693165 | 1.231449723 | 6.541999817 | ||
| 68 | 0.778280377 | 1.245095134 | 6.541999817 | ||
| 69 | 0.779745102 | 1.257782340 | 6.541999817 | ||
| 70 | 0.781096280 | 1.269567847 | 6.541999817 | ||
| 71 | 0.782323360 | 1.280498266 | 6.541999817 | ||
| 72 | 0.783455431 | 1.290624499 | 6.541999817 | ||
| 73 | 0.784503341 | 1.299997807 | 6.541999817 | ||
| 74 | 0.785472572 | 1.308667421 | 6.541999817 | ||
| 75 | 0.786368310 | 1.316679597 | 6.541999817 | ||
| 76 | 0.787195563 | 1.324079275 | 6.541999817 | ||
| 77 | 0.787959099 | 1.330908895 | 6.541999817 | ||
| 78 | 0.788663387 | 1.337208629 | 6.541999817 | ||
| 79 | 0.789312661 | 1.343016267 | 6.541999817 | ||
| 80 | 0.789910853 | 1.348366976 | 6.541999817 | ||
| trailing | 1 | 0.789910853 | 1.348366976 | 6.541999817 | |
| edge - | 2 | 0.789726913 | 1.352849364 | 6.541999817 | |
| curve 1 | 3 | 0.788225770 | 1.357076764 | 6.541999817 | |
| 4 | 0.785541654 | 1.360671163 | 6.541999817 | ||
| 5 | 0.781914651 | 1.363311172 | 6.541999817 | ||
| 6 | 0.777669191 | 1.364760637 | 6.541999817 | ||
| 7 | 0.773185015 | 1.364889860 | 6.541999817 | ||
| 8 | 0.768863142 | 1.363687158 | 6.541999817 | ||
| 9 | 0.765090168 | 1.361260295 | 6.541999817 | ||
| 10 | 0.762203574 | 1.357826352 | 6.541999817 | ||
| 11 | 0.760461569 | 1.353692293 | 6.541999817 | ||
| pressure | 1 | 0.760461569 | 1.353692293 | 6.541999817 | |
| side - | 2 | 0.759065628 | 1.348215222 | 6.541999817 | |
| curve 2 | 3 | 0.757499516 | 1.342105031 | 6.541999817 | |
| 4 | 0.755742967 | 1.335296154 | 6.541999817 | ||
| 5 | 0.753773510 | 1.327717662 | 6.541999817 | ||
| 6 | 0.751566172 | 1.319296122 | 6.541999817 | ||
| 7 | 0.749093711 | 1.309952497 | 6.541999817 | ||
| 8 | 0.746325791 | 1.299597025 | 6.541999817 | ||
| 9 | 0.743229210 | 1.288140059 | 6.541999817 | ||
| 10 | 0.739767849 | 1.275492668 | 6.541999817 | ||
| 11 | 0.735902011 | 1.261554003 | 6.541999817 | ||
| 12 | 0.731589198 | 1.246234059 | 6.541999817 | ||
| 13 | 0.726783395 | 1.229434133 | 6.541999817 | ||
| 14 | 0.721435785 | 1.211063981 | 6.541999817 | ||
| 15 | 0.715494931 | 1.191041470 | 6.541999817 | ||
| 16 | 0.708906829 | 1.169287562 | 6.541999817 | ||
| 17 | 0.701616347 | 1.145739198 | 6.541999817 | ||
| 18 | 0.693567395 | 1.120350003 | 6.541999817 | ||
| 19 | 0.684704661 | 1.093093038 | 6.541999817 | ||
| 20 | 0.674974918 | 1.063966632 | 6.541999817 | ||
| 21 | 0.664328396 | 1.032995462 | 6.541999817 | ||
| 22 | 0.652721524 | 1.000238061 | 6.541999817 | ||
| 23 | 0.640118599 | 0.965788066 | 6.541999817 | ||
| 24 | 0.626493633 | 0.929770052 | 6.541999817 | ||
| 25 | 0.611834168 | 0.892353058 | 6.541999817 | ||
| 26 | 0.596141517 | 0.853734076 | 6.541999817 | ||
| 27 | 0.579434335 | 0.814150035 | 6.541999817 | ||
| 28 | 0.561749101 | 0.773862839 | 6.541999817 | ||
| 29 | 0.543140948 | 0.733157754 | 6.541999817 | ||
| 30 | 0.523684502 | 0.692337573 | 6.541999817 | ||
| 31 | 0.503472567 | 0.651712239 | 6.541999817 | ||
| 32 | 0.482615024 | 0.611590266 | 6.541999817 | ||
| 33 | 0.461236149 | 0.572270215 | 6.541999817 | ||
| 34 | 0.439472109 | 0.534031808 | 6.541999817 | ||
| 35 | 0.417467535 | 0.497129112 | 6.541999817 | ||
| 36 | 0.395371377 | 0.461783081 | 6.541999817 | ||
| 37 | 0.373333603 | 0.428178221 | 6.541999817 | ||
| 38 | 0.351500660 | 0.396458298 | 6.541999817 | ||
| 39 | 0.330012947 | 0.366726816 | 6.541999817 | ||
| 40 | 0.309000880 | 0.339046419 | 6.541999817 | ||
| 41 | 0.288582951 | 0.313441962 | 6.541999817 | ||
| 42 | 0.268863022 | 0.289902329 | 6.541999817 | ||
| 43 | 0.249928936 | 0.268385261 | 6.541999817 | ||
| 44 | 0.231853381 | 0.248824358 | 6.541999817 | ||
| 45 | 0.214690611 | 0.231129527 | 6.541999817 | ||
| 46 | 0.198479787 | 0.215196654 | 6.541999817 | ||
| 47 | 0.183244258 | 0.200910151 | 6.541999817 | ||
| 48 | 0.168992221 | 0.188147098 | 6.541999817 | ||
| 49 | 0.155719474 | 0.176782593 | 6.541999817 | ||
| 50 | 0.143410191 | 0.166692078 | 6.541999817 | ||
| 51 | 0.132038772 | 0.157754347 | 6.541999817 | ||
| 52 | 0.121571653 | 0.149853483 | 6.541999817 | ||
| 53 | 0.111969233 | 0.142880529 | 6.541999817 | ||
| 54 | 0.103187338 | 0.136734247 | 6.541999817 | ||
| 55 | 0.095178157 | 0.131321386 | 6.541999817 | ||
| 56 | 0.087892756 | 0.126557618 | 6.541999817 | ||
| 57 | 0.081281371 | 0.122366585 | 6.541999817 | ||
| 58 | 0.075279035 | 0.118705392 | 6.541999817 | ||
| 59 | 0.069858894 | 0.115477197 | 6.541999817 | ||
| 60 | 0.065000318 | 0.112583481 | 6.541999817 | ||
| leading | 1 | 0.065000318 | 0.112583481 | 6.541999817 | |
| edge - | 2 | 0.043013237 | 0.096609026 | 6.541999817 | |
| curve 3 | 3 | 0.024827920 | 0.076412261 | 6.541999817 | |
| 4 | 0.011239149 | 0.052875903 | 6.541999817 | ||
| 5 | 0.002840832 | 0.027028596 | 6.541999817 | ||
| 6 | 0.000000000 | 0.000000004 | 6.541999817 | ||
| 7 | 0.002840832 | β0.027028589 | 6.541999817 | ||
| 8 | 0.011239149 | β0.052875895 | 6.541999817 | ||
| 9 | 0.024827920 | β0.076412261 | 6.541999817 | ||
| 10 | 0.043013237 | β0.096609026 | 6.541999817 | ||
| 11 | 0.065000325 | β0.112583488 | 6.541999817 | ||
In another example, the exit flow angle 76 is a camber angle between the mean camber line C at the trailing end 68 (as shown by extended mean camber line 77) relative to the plane 74. In one example, the flow angle 76 approaches approximately 5Β° and approximately 12Β° near the tip 64 and approaches approximately 12Β° and approximately 20Β° at the base 62 near the hub 58.
Although a combination of features is shown in the illustrated examples, not all of them need to be combined to realize the benefits of various embodiments of this disclosure. In other words, a system designed according to an embodiment of this disclosure will not necessarily include all of the features shown in any one of the Figures or all of the portions schematically shown in the Figures. Moreover, selected features of one example embodiment may be combined with selected features of other example embodiments.
The preceding description is exemplary rather than limiting in nature. Variations and modifications to the disclosed examples may become apparent to those skilled in the art that do not necessarily depart from the essence of this disclosure. The scope of legal protection given to this disclosure can only be determined by studying the following claims.
1. An axial rotor comprising:
a plurality of blades extending from a hub and arranged about an axis, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, the exit flow angle decreasing along the span from the base to the tip.
2. The axial rotor as recited in claim 1, wherein an average exit flow angle over the span is less than 12Β°.
3. The axial rotor as recited in claim 1, wherein a proportional ratio of a maximum exit flow angle along the span to a minimum exit flow angle along the span is no greater than 2.33.
4. The axial rotor as recited in claim 1, wherein the rate of decrease of the exit flow angle along the span from the base to the tip is non-linear.
5. The axial rotor as recited in claim 1, wherein the exit flow angle at the tip is 5-12Β° and the exit flow angle at the base is 12-20Β°.
6. The axial rotor as recited in claim 1, wherein a proportional ratio of a maximum exit flow angle at the base and a minimum exit flow angle at the tip is greater than 1 and less than or equal to 4.
7. The axial rotor as recited in claim 1, wherein the blade body extends between a leading edge and a trailing edge and a suction side surface and a pressure side surface, the suction side surface and the pressure side surface being defined by a set of coordinates and a radii of curvature at each coordinate as set forth in Table I and scaled by a desirable factor.
8. The axial rotor of claim 1, wherein under normal operating conditions, a fluid flow about each of the plurality of blades does not separate near the trailing edge near the hub and wherein the fluid flow about each of the plurality of blades does not separate near the trailing edge near the tip.
9. A turbopump machine comprising:
a rotatable shaft;
a pump coupled to rotate with the rotatable shaft;
a turbine coupled to drive the rotatable shaft, the turbine including an axial rotor having a plurality of blades extending from a hub that is rotatable about an axis of rotation, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, the exit flow angle decreasing along the span from the base to the tip.
10. A method of controlling flow over an axial rotor, the method comprising:
for an axial rotor that includes a plurality of blades extending from a hub that is rotatable about an axis of rotation, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, establishing a decreasing exit flow angle along the span from the base to the tip.
11. The method as recited in claim 9, including establishing an average exit flow angle of less than 12Β° over the span from the base to the tip.
12. The method as recited in claim 9, including establishing a proportional ratio of a maximum exit flow angle along the span to a minimum exit flow angle along the span that is no greater than 2.33.
13. The method as recited in claim 9, including establishing the rate of decrease of the exit flow angle along the span from the base to the tip to be non-linear.
14. The method as recited in claim 9, including establishing the exit flow angle at the tip to be 5-12Β° and the exit flow angle at the base to be 12-20Β°.
15. The method as recited in claim 9, including establishing a proportional ratio of a maximum exit flow angle along the span at the base and a minimum exit flow angle at the tip to be greater than 1 and less than or equal to 4.
16. The method as recited in claim 9, wherein the blade body extends between a leading edge and a trailing edge and a suction side surface and a pressure side surface, the suction side surface and the pressure side surface being defined by a set of coordinates and a radius of curvature at each coordinate as set forth in Table I and scaled by a desirable factor.
17. The method as recited in claim 9, including operating the axial rotor at a speed of 3500-4500 revolutions per minute to drive a pump that coupled with the axial rotor at the same speed.
18. An axial turbine comprising:
a plurality of airfoils that extend from a hub, each of the plurality of airfoils including an airfoil body extending between a leading end, a trailing end, a base at the hub, and a tip and defining a mean camber line, wherein a camber angle of the mean camber line at the trailing end relative to a plane that is perpendicular to an axis about which the plurality of airfoils are arranged is between approximately 5Β° and approximately 12Β° near the tip and is between approximately 12Β° and approximately 20Β° near the hub.
19. The axial turbine of claim 18, wherein under normal operating conditions, a fluid flow about each of the plurality of airfoils does not separate near the trailing edge near the hub and wherein the fluid flow about each of the plurality of airfoils does not separate near the trailing edge near the tip.