USPatent applicationPatented

Fuel system centrifugal boost pump impeller

Granted 3 Feb 2015 · no office action yet

Assignee: Collins Aerospace

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Attorney: Attorney · Log in to unlock

Inventors: Adrian L. Stoicescu, Steven A. Heitz · Examiner: Nathaniel Wiehe · AU 3745 · TC 3700

Life of the application

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Abstract

A centrifugal boost pump inducer section includes a plurality of inducer main blades, and a plurality of splitter blades, each of which includes normal to the blade mean line cross sectional surfaces distributed over the length of the blades, the cross sectional surfaces defined as a set of R-coordinates, theta-coordinates and Z-coordinates relative to an impeller outer diameter set out in one set of tables. A centrifugal boost pump impeller section includes a plurality of impeller main blades, a plurality of primary splitter blades, and a plurality of secondary splitter blades, each of which includes normal to the blade mean line cross sectional surfaces distributed over the length of the blades, the cross sectional surfaces defined as a set of R-coordinates, theta-coordinates and Z-coordinates relative to an impeller outer diameter set out in another set of tables.

Description

5 parts
›BACKGROUND

This disclosure relates to an aircraft jet engine mounted centrifugal fuel boost pump, for example, in particular to the impeller blades.

The boost pump is commonly packaged together with the main fuel pump, which is usually of a positive displacement gear pump type, both being driven by a common shaft. The fuel leaving the boost stage goes through a filter and a fuel oil heat exchanger before entering the main pump. Pressure losses are introduced by these components and the associated plumbing, while heat is also added to the fuel. The fuel feeding the boost pump comes from the main frame fuel tanks through the main frame plumbing. The tanks are usually vented to the ambient atmospheric pressure, or, in some cases, are pressurized a couple of psi above that. The tanks are provided with immersed pumping devices, which are in some cases axial flow pumps driven by electric motors or turbines, or in other cases ejector pumps, collectively referred to as main frame boost pumps.

During flight, the pressure in the tank decreases with altitude following the natural depression in the ambient atmospheric pressure. Under normal operating conditions, industry standards require the main frame boost pumps to provide uninterrupted flow to the engine mounted boost pumps at a minimum of 5 psi above the true vapor pressure of the fuel and with no V/L (vapor liquid ratio) or no vapor present as a secondary phase. Under abnormal operation, which amounts to inoperable main frame boost pumps, the pressure at the inlet of the boost stage pumps can be only 2, or 3 psi above the fuel true vapor pressure, while vapor can be present up to a V/L ratio of 0.45, or more. Definition of terms, recommended testing practices, and fuel physical characteristics are outlined in industry specifications and standards like Coordinating Research Council Report 635, AIR 1326, SAE ARP 492, SAE ARP 4024, ASTM D 2779, and ASTM D 3827, for example.

During normal or abnormal operation, the boost pump is required to maintain enough pressure at the main pump inlet under all the operating conditions encountered in a full flight mission such as the main pump can maintain the demanded output flow and pressure to the fuel control and metering unit for continuous and uninterrupted engine operation. There are also limitations in the maximum pressure rise the engine mounted boost pump is allowed to deliver such not to exceed the mechanical pressure rating of the fuel oil heat exchanger, or limitations pertaining to minimum impeller blade spacing such as a large contaminant like a bolt lost from maintenance interventions would pass through and be trapped safely in the downstream filter. All these requirements along with satisfying a full flow operating range from large flows during takeoff to a trickle of flow during flight idle descent, and fuel temperature swings from −40 F to 300 F, makes the aerodynamic design of the engine mounted fuel pumps a serious challenge.

In order to achieve the pressure rise demanded by the downstream main fuel pump and fuel metering system and to also be capable of operating with extreme low suction conditions encountered during the abnormal operation, the boost pump impellers are provided with a radial blade section and with an axial blade section upstream there from. The radial blade section is commonly referred to as the impeller blade section, while the axial blade section is referred to as the inducer blade section. The inducer's primary function is to sustain good pressure and flow conditions at the inlet of the impeller radial section even under the low suction conditions imposed by the abnormal operation, where the main frame boost pumps are inoperable.

The gap between the minimum required supply pressure for normal engine operation and the maximum allowed discharge pressure demanded by pressure rating limitations of the inter-stage fuel oil heat exchanger are often so narrow, that the final design is determined only after the first unit went through design and development testing. The impeller diameter, which primarily controls the pump pressure rise, is intentionally set to a slightly larger value in the initial design, the unit built and tested, and ultimately the impeller diameter is trimmed to its final value such to match all the constraints imposed by the requirements.

›SUMMARY

A disclosed boost pump inducer section includes a plurality of main blades, and a plurality of splitter blades, that each includes normal to the blade mean line cross sectional surfaces distributed over the length of the blades. The cross sectional surfaces are defined as a set of cylindrical R-coordinates, theta-coordinates and Z-coordinates relative to an impeller outer diameter set out in one set of tables, TABLE N-1, and TABLE N-2, where N is the same value.

A disclosed boost pump impeller section includes a plurality of main blades, a plurality of primary splitter blades, and a plurality of secondary splitter blades, that each includes normal to the blade mean line cross sectional surfaces distributed over the length of the blades. The cross sectional surfaces are defined as a set of cylindrical R-coordinates, theta-coordinates and Z-coordinates relative to an impeller outer diameter set out in one set of tables, TABLE N-3, TABLE N-4, and TABLE N-5, where N is the same value.

›BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be further understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

FIG. 1 is a schematic of an example fuel delivery system.

FIG. 2 is a cross-sectional view of the engine mounted boost pump.

FIG. 3 is a perspective view of the boost stage impeller.

FIG. 4 is a front view of the boost stage impeller with front shroud removed.

FIG. 5 is a perspective view of the boost stage impeller with front shroud removed.

FIG. 6 is a side view of the boost stage impeller.

FIG. 7 is a side cross-sectional view of the boost stage impeller.

FIG. 8 is a front view of the impeller blades showing geometry defining cross sections.

FIG. 9 is a cross-sectional view through a blade, which illustrates the coordinate system of the disclosure.

›DETAILED DESCRIPTION · 1 of 2

A schematic of an example of engine mounted fuel delivery system, for example, for an aircraft, is illustrated in FIG. 1 . The system 10 includes a fuel inlet 12 that is fluidly connected to airframe plumbing at engine airframe interface. Fuel is delivered to this interface from the aircraft fuel tanks by means of airframe mounted fuel pumps. A boost pump 14 pressurizes the fuel before providing the fuel to the main pump 18 . Typically, a filter 17 and a heat exchanger 16 are installed in between the boost pump 14 and the main pump 18 . Fuel from the main pump 18 is regulated by a fuel metering unit 20 , which supplies pressure regulated fuel to the engine 22 .

FIG. 2 shows a cross-sectional view of an example engine-mounted boost and main fuel pump having the longitudinal axis, which corresponds to an axis Z. Only the boost pump 14 is illustrated in FIG. 2 . The boost pump 14 includes a shrouded impeller 24 rotationally driven by a shaft 23 , which is typically driven by a gearbox mounted on the engine. The impeller 24 is arranged between a boost housing cover 26 and a center plate 28 . Front and rear labyrinth seals 30 , 32 respectively seal between the impeller 24 and the boost housing cover 26 and center plate 28 . A rear side face seal 46 is also provided between the center plate 28 and the impeller 24 in the example shown.

The shaft 23 is splined to a drive gear 34 , which is couple to and rotationally drives a driven gear 36 . A drive gear floating bearing 38 and a drive gear fixed bearing 40 support the drive gear 34 . A driven gear floating bearing 42 and a driven gear fixed bearing 44 support the driven gear 36 .

During operation, fuel flow enters through the inlet from the far right side opening 45 of the boost pump housing cover 26 flowing axially from left to right. The fuel flow then enters first the inducer section 53 of the rotating impeller 24 where the pressure is raised and the eventual air and vapor phase present in the mixture are compressed back in to solution such by the time the fuel flow reaches the impeller section 51 most of the mixture is in the liquid phase. The fuel flow then enters the impeller section 51 where the majority of the pressure rise takes place, while the fluid absolute velocity is greatly increased. The fuel flow leaves the impeller 24 at its outside diameter exit port, or perimeter 62 , under significantly larger pressure and with large velocity in an almost tangential direction. At this location, the flow stream contains potential energy based on the actual static pressure and a good amount of kinetic energy due to the high flow velocity.

FIGS. 3-6 show various views of the impeller 24 , which is cast or machined. Typically, machined impellers are provided by two components in the example, a hub 50 and a shroud 48 . The inducer and impeller blades are machined directly in the hub as one piece. The shroud 48 is machined separately and attached by brazing to the hub 50 . In case the impeller 24 is mounted on the drive shaft by means of a thread, the shroud 48 is provided with a couple of notches as a wrenching feature.

The impeller section 51 has three sets of blades, a set of main blades 52 , a set of primary splitter blades 54 , and a set of secondary splitter blades 56 . In one example, there are five main blades 52 , five primary splitter blades 54 , and ten secondary splitter blades 56 . The outer ends of these blades are evenly circumferentially spaced from one another at the perimeter 62 , in the example.

A typical impeller blade works by engaging the incoming flow at the leading edge of the blade with some incidence and by guiding the flow along its length all the way to impeller exit port at the perimeter 62 efficiently and without generating eddies or flow separation. The fluid stream is forced by the cascade of blades into a complex rotational motion combined with a longitudinal and radial motion. The inertial effects of the centrifugal and Coriolis forces introduced by the forced fluid motion impart pressure into the fluid. The impeller section 51 achieves the desired fluid characteristics, in part, by the geometry of the three regions, R 1 , R 2 , R 3 as shown in FIG. 4 , where R 1 is provided circumferentially between the main blades 52 upstream from the primary splitter blades 54 , R 2 is provided circumferentially between the main blades 52 and the primary splitter blades 54 , and R 3 is provided circumferentially between the primary splitter blades 54 and the secondary splitter blades 56 . The blade surface running against the fluid develops higher pressures at the pressure side, while on the opposite side of the blade a depression is created on the suction side. The blade shape and length impart the required amount of work into the fluid with minimum viscous drag and without introducing eddies, or flow separation.

The inducer section 53 has two sets of blades, a set of inducer main blades 58 , and a set of inducer splitter blades 60 . The inducer section 53 is axial as opposed to mostly radial, as in the impeller section 51 . The fluid stream guidance and energy transfer mechanism between the inducer section blades and the fluid are similar to those encountered in the impeller section 51 , except for the fact that the calculations are based on a two phase mixture. The mixture contains a liquid phase and a gaseous phase, where the gaseous phase contains air and vapor of the fuel. Staring from the opening 45 , the pressure is progressively rising due to the work imposed by the inducer section blades, and consequently the vapor and air present in the gaseous phase are compressed back into solution. The hub shape in the inducer section is designed to provide larger volume towards inlet where the specific volume of the two-phase mixture is the smallest.

Referring to FIG. 7 , the first inducer main blade 58 begins at an inner diameter D 1 and extends radially outwardly to an outer diameter D 4 . The impeller main blade 52 begins at an inner diameter D 3 , as shown in FIG. 8 , and extends radially outwardly to an outer diameter D 2 , which corresponds to the perimeter 62 . In one example, D 4 and D 3 are approximately equal to one another.

›DETAILED DESCRIPTION · 2 of 2

FIG. 8 shows a front view of the impeller blades along with the cross section defining the blade geometry. The blade thickness varies along the blade as well as from hub to shroud in a linear progression. As a result, each cross section has a rectangular shape and is defined by means of numerical coordinates of the four corner points, as explained below with reference to FIG. 9 . Generally, sections through each blade correspond to the “station numbers” located at a particular angle “theta,” referred to in the Tables. The stations for the impeller main blade 52 for the data in Table 1-3 are shown in FIG. 8 . The first set of data corresponds to section Mi and continues to the last set of data, Mo, for the impeller main blade 52 . Similarly, the first set of data corresponds to section Pi and continues to the last set of data, Po, for the primary splitter blade 54 ; the first set of data corresponds to section Si and continues to the last set of data, So, for the secondary splitter blade 56 . A various number of sections may be used to define a given blade, as is evident by the data in the Tables.

The coordinates of all the cross sections used to generate the geometry of the blades are listed in a cylindrical coordinate system, which lines up with the impeller and pump axis. The four corner points of each cross section are the hub pressure side, hub suction side, shroud pressure side, and shroud suction side based on their physical location. The final shape of the blade is obtained by cubic spline interpolation between the corresponding points of all the cross section composing a blade. The blade coordinate tables defining the inducer blades and the impeller blades are listed under TABLE N-1 through N-5, where N represents a value and the same values represent a set of data for a given impeller 24 . That is, Tables 1-1, 1-2, 1-3, 1-4, 1-5 represent data for one example impeller; Tables 2-1, 2-2, 2-3, 2-4, 2-5 represent data for another example impeller; Tables 3-1, 3-2, 3-3, 3-4, 3-5 represent data for yet another example impeller.

Tables N-1 through N-5 defining the inducer and impeller blade geometries are shown in a cylindrical coordinate system for R, theta, and Z, in inches, of each blade surface. Tables N-1 is a cylindrical coordinate table defining the inducer main blade 58 geometry. Tables N-2 is a cylindrical coordinate table defining the inducer splitter blade 60 geometry. Tables N-3 is a cylindrical coordinate table defining the impeller main blade 52 geometry. Tables N-4 is a cylindrical coordinate table defining the impeller primary splitter blade 54 geometry. Tables N-5 is a cylindrical coordinate table defining the impeller secondary splitter blade 56 geometry. Referring to FIG. 9 with reference to the Tables, the “shroud pressure side” corresponds to point A, the “shroud suction side” corresponds to point B, the “hub suction side” corresponds to point C, and the “hub pressure side” corresponds to point D. Together points A-D define a quadrilateral cross-section through the respective blade.

The cylindrical coordinate system Z axis aligns with the impeller 24 axis of rotation, with the Z zero coordinate in the axial plane corresponding with where the main, primary splitter and secondary splitter impeller blades 52 , 54 , 56 intersect the perimeter 62 . The positive direction of the Z axis points towards the pump opening 45 . The R coordinate corresponds to the distance from the Z axis, and theta is the relative angular position. One example impeller 24 includes diameters as follows: D 1 ≈0.5 in (12.7 mm), D 3 ≈D 4 ≈2.0 in (50.8 mm), D 2 ≈4.0 in (101.6 mm). The data in the Tables corresponds to a ratio between the given R and Z coordinate and the impeller outer diameter D 2 .

The Table values are shown to four decimal places. However, in view of manufacturing constraints, actual values useful for manufacture of the component are considered to be the values to determine the claimed profile. There are typical manufacturing tolerances, which must be accounted for in the profile. Accordingly, the Table coordinate values are for nominal component. It will therefore be appreciated that plus or minus typical manufacturing tolerances are applicable to the Table coordinate values and that a component having a profile substantially in accordance with those values includes tolerances. For example, a manufacturing tolerance of about +/−0.010 inches on surface profile should be considered within the design limits for the component. Thus, the mechanical and aerodynamic functions of the component are not impaired by manufacturing imperfections and tolerances, which in different embodiments may be greater or lesser than the values set forth in the disclosed Tables. As appreciated by those skilled in the art, manufacturing tolerances may be determined to achieve a desired mean and standard deviation of manufactured components in relation to the ideal component profile points set forth in the disclosed Tables.

Although example embodiments have been disclosed, a worker of ordinary skill in this art would recognize that certain modifications would come within the scope of the claims. For that reason, the following claims should be studied to determine their true scope and content.

›Tables in the description — 15
TABLE 1
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.2533359.87340.44280.25330.12660.44810.0800357.79330.44080.08002.20670.4504
20.25330.41150.44220.25330.67730.44780.0800358.19980.44000.08002.88890.4501
30.25331.69170.44090.25331.97020.44680.0800359.34850.43840.08004.31350.4492
40.25333.57700.43910.25333.86810.44520.08001.10220.43630.08006.34300.4477
50.25336.00680.43670.25336.31050.44310.08003.40030.43370.08008.91700.4456
60.25338.94250.43390.25339.25900.44060.08006.20450.43060.080011.99700.4431
70.253312.35660.43070.253312.68570.43770.08009.48700.42700.080015.55530.4401
80.253316.22750.42710.253316.56930.43430.080013.22630.42290.080019.57050.4367
90.253320.53790.42310.253320.89230.43050.080017.40510.41850.080024.02510.4328
100.253325.27330.41870.253325.64030.42640.080022.00950.41360.080028.90420.4286
110.253330.42130.41390.253330.80100.42190.080127.03030.40840.079934.19210.4239
120.253335.97120.40880.253336.36360.41700.080332.45880.40280.079939.87600.4189
130.253341.91350.40330.253342.31850.41180.080538.28730.39670.079945.94470.4135
140.253348.23970.39750.253348.65740.40620.080944.50910.39040.080052.38800.4077
150.253354.94220.39130.253355.37260.40030.081451.11860.38360.080259.19620.4015
160.253362.01420.38480.253362.45720.39410.082058.24260.37680.080566.22870.3947
170.253369.44920.37790.253369.90490.38750.082765.74060.36960.080973.61350.3876
180.253377.24150.37080.253377.70980.38060.083673.60750.36210.081581.34390.3801
190.253385.38570.36330.253385.86670.37340.084781.83820.35430.082389.41420.3723
200.253393.88310.35570.253394.36410.36570.086090.42810.34610.083297.81920.3641
210.2533102.72280.34770.2533103.20370.35780.087599.37240.33760.0844106.55410.3556
220.2533111.90030.33950.2533112.38130.34950.0893108.66650.32880.0857115.61510.3468
230.2533121.41160.33090.2533121.89260.34090.0913118.30540.31970.0873124.99870.3377
240.2533131.25210.32210.2533131.73350.33200.0936128.28200.31020.0892134.70360.3283
250.2533141.40880.31290.2533141.89120.32290.0962138.58140.30040.0913144.71870.3185
260.2533151.86410.30350.2533152.34820.31340.0991149.18460.29040.0938155.02770.3084
270.2533162.59810.29380.2533163.08470.30360.1024160.07060.28000.0966165.61220.2980
280.2533173.58880.28370.2533174.07850.29360.1060171.30050.26960.0999176.36680.2870
290.2533184.81200.27350.2533185.30580.28320.1100182.75410.25900.1036187.36360.2756
300.2533196.24160.26290.2533196.74030.27260.1144194.40410.24800.1078198.57780.2640
310.2533207.84960.25200.2533208.35420.26170.1193206.22130.23680.1125209.98240.2521
320.2533219.60640.24090.2533220.11790.25050.1247218.17560.22530.1177221.54860.2398
330.2533231.48120.22950.2533232.00060.23910.1307230.23560.21350.1235233.24610.2273
340.2533243.44200.21790.2533243.97050.22730.1373242.36920.20140.1299245.04330.2145
350.2533255.45640.20600.2533255.99520.21530.1445254.54350.18900.1371256.90810.2014
360.2533267.49160.19380.2533268.04200.20320.1520266.72250.17610.1452268.81110.1882
370.2533279.51510.18130.2533280.07830.19080.1591278.86690.16300.1530280.72650.1747
380.2533291.49470.16860.2533292.07210.17810.1658290.94870.14950.1604292.61810.1609
390.2533303.39930.15560.2533303.99250.16520.1721302.94120.13590.1673304.45050.1469
400.2533315.19900.14240.2533315.80940.15200.1779314.81780.12200.1738316.19060.1325
410.2533326.86550.12890.2533327.49480.13860.1833326.55260.10780.1797327.80770.1178
420.2533338.37240.11510.2533339.02200.12510.1851338.11150.09340.1882339.28290.1028
TABLE 1
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
11000000000000
12000000000000
13000000000000
14000000000000
15000000000000
16000000000000
17000000000000
18000000000000
19000000000000
20000000000000
21000000000000
22000000000000
23000000000000
24000000000000
250.253381.52940.31550.253381.77060.32050.095080.09620.30490.092683.20390.3140
260.253391.97410.30590.253392.23820.31130.097990.49300.29450.095093.71930.3043
270.2533102.69760.29590.2533102.98510.30170.1012101.18500.28370.0978104.49780.2943
280.2533113.67780.28560.2533113.98950.29190.1050112.14960.27260.1010115.51770.2840
290.2533124.89050.27510.2533125.22720.28180.1091123.36200.26120.1045126.75570.2734
300.2533136.30960.26430.2533136.67230.27140.1138134.79520.24960.1084138.18670.2625
310.2533147.90690.25320.2533148.29680.26070.1189146.41990.23760.1128149.78380.2512
320.2533159.65290.24190.2533160.07140.24970.1247158.20540.22540.1177161.51880.2397
330.2533171.51660.23020.2533171.96520.23850.1310170.11950.21290.1232173.36230.2279
340.2533183.46600.21840.2533183.94650.22690.1380182.12870.20020.1292185.28380.2157
350.2533195.46860.20620.2533195.98300.21510.1456194.19870.18710.1360197.25290.2033
360.2533207.49160.19380.2533208.04200.20320.1534206.28910.17350.1437209.24450.1908
370.2533219.51510.18130.2533220.07830.19080.1606218.41520.16000.1515221.17810.1777
380.2533231.49470.16860.2533232.07210.17810.1674230.47780.14620.1588233.08900.1642
390.2533243.39930.15560.2533243.99250.16520.1737242.44960.13220.1657244.94210.1505
400.2533255.19900.14240.2533255.80940.15200.1795254.30350.11790.1722256.70490.1365
410.2533266.86550.12890.2533267.49480.13860.1848266.01330.10340.1782268.34700.1222
420.2533278.37240.11510.2533279.02200.12510.1835277.51570.08860.1898279.87870.1076
TABLE 1
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.27303.32930.08930.26893.47850.09260.23810.11470.04070.2427359.88530.0382
20.284223.42820.08230.279023.65570.08570.254223.35640.03370.259923.03510.0314
30.296738.75170.07580.290439.05860.07920.270139.65990.02820.276839.25310.0260
40.309750.87330.07010.302451.26330.07340.285552.02600.02370.293151.53310.0216
50.322660.52360.06510.314461.00050.06840.300161.66080.02010.308661.08030.0181
60.335368.24580.06080.326168.81320.06410.313969.29540.01720.323268.62500.0153
70.347374.46240.05720.337375.12390.06040.326775.42530.01470.336874.66290.0129
80.358779.50170.05410.347980.26100.05720.338680.40450.01270.349579.54740.0110
90.369483.61710.05150.357884.47770.05450.349684.49250.01110.361283.53790.0094
100.379587.00350.04930.367187.96890.05220.359887.88250.00960.372186.82800.0080
110.388889.81090.04740.375890.88460.05020.369290.72070.00840.382289.56350.0069
120.397692.15500.04570.383993.34030.04850.377993.11840.00740.391591.85590.0060
130.405794.12560.04430.391495.42560.04700.386195.16110.00660.400293.79090.0052
140.413395.79270.04310.398597.21040.04570.393696.91550.00580.408395.43510.0045
150.420597.21130.04210.405198.74950.04450.400798.43360.00520.415896.84100.0039
160.427298.42480.04120.4114100.08620.04350.407399.75680.00460.422998.04970.0034
170.433599.46800.04040.4173101.25480.04260.4135100.91760.00410.429599.09420.0029
180.4394100.36860.03970.4229102.28300.04180.4194101.94260.00370.4357100.00110.0026
190.4450101.14920.03920.4282103.19300.04110.4250102.85280.00330.4416100.79170.0022
200.4503101.82790.03860.4332104.00280.04050.4303103.66570.00290.4472101.48350.0019
210.4550102.47230.03820.4383104.67140.03990.4356104.35100.00260.4521102.13540.0017
220.4595103.05280.03790.4432105.27540.03940.4407104.95440.00230.4568102.72510.0015
230.4638103.57870.03760.4478105.82210.03890.4455105.50280.00200.4614103.26430.0013
240.4680104.05800.03730.4523106.31910.03850.4502106.00600.00180.4657103.76070.0011
250.4719104.49750.03700.4566106.77340.03820.4546106.47030.00160.4699104.22010.0010
260.4758104.90300.03680.4608107.19060.03780.4589106.90120.00140.4740104.64790.0008
270.4795105.27960.03670.4648107.57600.03760.4630107.30300.00120.4779105.04810.0007
280.4831105.63150.03650.4686107.93380.03730.4670107.67950.00110.4817105.42460.0006
290.4867105.96250.03640.4724108.26780.03710.4709108.03400.00090.4854105.78050.0005
300.4901106.27570.03630.4760108.58150.03690.4746108.36930.00080.4890106.11850.0004
310.4935106.57400.03620.4796108.87770.03670.4783108.68800.00070.4925106.44120.0003
320.4968106.85990.03610.4830109.15890.03660.4819108.99210.00060.4960106.75070.0002
330.5001107.13560.03600.4864109.42750.03640.4854109.28370.00050.4994107.04890.0002
340.5033107.40320.03600.4897109.68560.03630.4888109.56450.00040.5028107.33760.0001
350.5065107.66440.03600.4930109.93490.03620.4922109.83630.00030.5061107.61840.0000
360.5097107.92090.03600.4961110.17720.03610.4956110.10040.00020.5094107.89280.0000
370.5128108.17400.03600.4993110.41370.03610.4989110.35860.00020.5126108.16250.0000
380.5160108.42290.03600.5023110.64370.03600.5022110.61460.00010.5159108.43120.0000
390.5192108.68460.03600.5055110.88350.03600.5053110.85430.00010.5191108.6842−0.0001
400.5859113.25600.03600.5721115.20920.03600.5720115.23480.00010.5857113.3040−0.0001
TABLE 1
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
50.320996.62270.06580.316296.89730.06770.301997.53870.01970.306897.20250.0186
60.3334104.35940.06150.3280104.69450.06340.3158105.15930.01680.3213104.76110.0157
70.3453110.59070.05780.3393110.98950.05980.3287111.27530.01440.3348110.81290.0133
80.3566115.64500.05470.3500116.11050.05660.3407116.24030.01240.3474115.71160.0113
90.3672119.77560.05210.3600120.31080.05390.3518120.31380.01070.3590119.71660.0097
100.3772123.17760.04980.3694123.78520.05170.3620123.68920.00930.3698123.02130.0083
110.3864126.00090.04790.3781126.68370.04970.3716126.51240.00820.3798125.77180.0072
120.3951128.36120.04620.3863129.12180.04800.3804128.89480.00720.3891128.07950.0062
130.4032130.34840.04480.3939131.18920.04650.3886130.92200.00630.3977130.03000.0054
140.4108132.03240.04360.4011132.95580.04520.3962132.66050.00560.4057131.69010.0047
150.4178133.46810.04250.4078134.47630.04410.4033134.16260.00490.4132133.11200.0041
160.4245134.69920.04160.4141135.79410.04310.4100135.46940.00440.4202134.33700.0036
170.4307135.76010.04080.4200136.94370.04230.4162136.61380.00390.4268135.39800.0031
180.4366136.67860.04010.4256137.95260.04150.4221137.62200.00350.4330136.32160.0027
190.4422137.47730.03950.4309138.84310.04080.4277138.51540.00310.4388137.12910.0024
200.4475138.17430.03900.4360139.63330.04020.4330139.31130.00280.4444137.83800.0021
210.4525138.79090.03850.4408140.33190.03970.4381140.02380.00250.4496138.46260.0018
220.4573139.34280.03810.4454140.96670.03920.4429140.65820.00220.4547139.02130.0016
230.4619139.83900.03770.4498141.54530.03880.4474141.23850.00200.4595139.52870.0014
240.4663140.28760.03740.4540142.07510.03840.4518141.77400.00170.4641139.99260.0012
250.4706140.69570.03710.4580142.56290.03810.4560142.27110.00150.4686140.41940.0010
260.4747141.06910.03690.4619143.01440.03780.4600142.73500.00140.4729140.81410.0009
270.4786141.41300.03670.4657143.43450.03750.4639143.16990.00120.4770141.18120.0007
280.4825141.73180.03650.4693143.82740.03730.4677143.57970.00110.4810141.52440.0006
290.4862142.02950.03640.4728144.19690.03710.4713143.96750.00090.4850141.84690.0005
300.4899142.30920.03630.4763144.54600.03690.4749144.33610.00080.4888142.15170.0004
310.4935142.57400.03620.4796144.87770.03670.4783144.68800.00070.4925142.44120.0003
320.4968142.85990.03610.4830145.15890.03660.4819144.99210.00060.4960142.75070.0002
330.5001143.13560.03600.4864145.42750.03640.4854145.28370.00050.4994143.04890.0002
340.5033143.40320.03600.4897145.68560.03630.4888145.56450.00040.5028143.33760.0001
350.5065143.66440.03600.4930145.93490.03620.4922145.83630.00030.5061143.61840.0000
360.5097143.92090.03600.4961146.17720.03610.4956146.10040.00020.5094143.89280.0000
370.5128144.17400.03600.4993146.41370.03610.4989146.35860.00020.5126144.16250.0000
380.5160144.42290.03600.5023146.64370.03600.5022146.61460.00010.5159144.43120.0000
390.5192144.68460.03600.5055146.88350.03600.5053146.85430.00010.5191144.6842−0.0001
400.5859149.25600.03600.5721151.20920.03600.5720151.23480.00010.5857149.3040−0.0001
TABLE 1
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
110.3846108.15080.04830.3800108.52850.04930.3734108.34800.00790.3780107.93630.0074
120.3933110.51180.04660.3881110.96570.04760.3821110.73150.00700.3873110.24270.0064
130.4015112.49910.04510.3956113.03270.04620.3902112.76020.00610.3960112.19170.0056
140.4091114.18260.04380.4027114.79940.04500.3978114.50070.00540.4041113.84990.0048
150.4163115.61750.04280.4093116.32060.04390.4048116.00500.00480.4117115.26960.0042
160.4230116.84720.04180.4155117.63960.04290.4114117.31440.00430.4188116.49200.0037
170.4294117.90630.04100.4214118.79080.04210.4176118.46160.00380.4255117.55020.0032
180.4354118.82270.04030.4269119.80180.04130.4234119.47300.00340.4318118.47060.0028
190.4410119.61880.03960.4321120.69480.04070.4289120.36980.00300.4377119.27460.0025
200.4464120.31300.03910.4371121.48800.04010.4342121.16940.00270.4433119.97980.0022
210.4515120.92520.03860.4418122.19110.03960.4391121.88590.00240.4486120.60040.0019
220.4563121.47250.03820.4464122.83050.03910.4438122.52560.00210.4537121.15390.0016
230.4610121.96400.03780.4507123.41400.03870.4483123.11160.00190.4586121.65560.0014
240.4655122.40750.03750.4548123.94900.03830.4526123.65290.00170.4633122.11380.0012
250.4698122.81030.03720.4588124.44230.03800.4568124.15590.00150.4678122.53460.0010
260.4739123.17820.03700.4626124.89950.03770.4607124.62570.00130.4721122.92330.0009
270.4780123.51640.03680.4663125.32550.03750.4646125.06680.00120.4763123.28430.0007
280.4819123.82940.03660.4699125.72460.03720.4683125.48270.00100.4804123.62140.0006
290.4857124.12100.03640.4734126.10030.03700.4719125.87670.00090.4844123.93780.0005
300.4894124.39460.03630.4768126.45580.03680.4754126.25150.00080.4883124.23630.0004
310.4930124.65320.03620.4801126.79390.03670.4788126.60960.00070.4920124.51960.0003
320.4966124.89940.03610.4833127.11710.03650.4821126.95300.00060.4958124.78980.0002
330.5001125.13560.03600.4864127.42750.03640.4854127.28370.00050.4994125.04890.0002
340.5033125.40320.03600.4897127.68560.03630.4888127.56450.00040.5028125.33760.0001
350.5065125.66440.03600.4930127.93490.03620.4922127.83630.00030.5061125.61840.0000
360.5097125.92090.03600.4961128.17720.03610.4956128.10040.00020.5094125.89280.0000
370.5128126.17400.03600.4993128.41370.03610.4989128.35860.00020.5126126.16250.0000
380.5160126.42290.03600.5023128.64370.03600.5022128.61460.00010.5159126.43120.0000
390.5192126.68460.03600.5055128.88350.03600.5053128.85430.00010.5191126.6842−0.0001
400.5859131.25600.03600.5721133.20920.03600.5720133.23480.00010.5857131.3040−0.0001
TABLE 2
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.20550.08430.41030.2055359.91570.41320.08281.03350.40880.0828358.96650.4147
20.2055358.94620.40930.2055358.76220.41250.08280.06000.40740.0828357.64850.4143
30.2055356.24570.40720.2055356.04640.41060.0828357.52400.40480.0828354.76800.4127
40.2055352.27180.40420.2055352.05710.40780.0828353.71470.40130.0828350.61420.4101
50.2055347.15180.40030.2055346.92180.40420.0828348.75930.39680.0828345.31430.4066
60.2055340.96670.39560.2055340.72140.39980.0828342.73880.39150.0828338.94930.4023
70.2055333.77480.39020.2055333.51420.39470.0828335.71150.38540.0828331.57750.3972
80.2055325.62140.38420.2055325.34540.38890.0828327.72270.37850.0828323.24410.3913
90.2055316.54290.37740.2055316.25160.38240.0828318.80870.37100.0828313.98570.3848
100.2055306.56980.37000.2055306.26320.37520.0828309.00030.36270.0828303.83280.3775
110.2055295.72830.36190.2055295.40630.36740.0828298.32330.35380.0828292.81130.3695
120.2055284.04080.35320.2055283.70350.35900.0828286.79870.34420.0827280.94550.3609
130.2055271.52740.34400.2055271.17470.35000.0831274.43870.33400.0826268.26330.3517
140.2055258.20580.33410.2055257.83780.34040.0836261.25150.32310.0826254.79210.3418
150.2055244.09210.32370.2055243.70880.33020.0844247.24720.31160.0829240.55360.3313
160.2055229.19320.31280.2055228.80990.31930.0856232.27390.30010.0835225.72920.3197
170.2055213.53000.30140.2055213.14670.30790.0872216.51260.28790.0845210.16410.3075
180.2055197.11510.28940.2055196.73140.29590.0892199.97830.27510.0860193.86810.2948
190.2055179.97930.27690.2055179.59210.28340.0918182.71950.26180.0879176.85180.2814
200.2055162.28770.26380.2055161.89280.27030.0949164.90550.24790.0903159.27510.2674
210.2055144.25860.25020.2055143.85140.25670.0986146.75510.23360.0933141.35490.2529
220.2055126.13120.23620.2055125.70670.24250.1030128.50770.21860.0971123.33010.2377
230.2055108.15000.22160.2055107.70270.22790.1081110.40910.20320.1016105.44360.2221
240.205590.54810.20650.205590.07200.21280.113492.70680.18700.107487.91330.2060
250.205573.53250.19090.205573.02100.19720.118175.63420.17030.113070.91930.1894
260.205557.27350.17480.205556.72000.18110.122359.36010.15310.118054.63330.1723
270.205541.90030.15820.205541.29740.16470.126144.00470.13550.122239.19290.1545
TABLE 2
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
11000000000000
12000000000000
13000000000000
14000000000000
15000000000000
16000000000000
17000000000000
18000000000000
19000000000000
20000000000000
21000000000000
220.2055186.00380.23820.2055185.83400.24070.1011186.90750.22460.0989184.93030.2318
230.2055168.04940.22310.2055167.80330.22650.1066169.26410.20760.1031166.58860.2176
240.2055150.47670.20750.2055150.14340.21190.1124151.97140.19000.1084148.64870.2030
250.2055133.49410.19140.2055133.05940.19670.1177135.27260.17180.1134131.28090.1879
260.2055117.27350.17480.2055116.72000.18110.1223119.36010.15310.1180114.63330.1723
270.2055101.90030.15820.2055101.29740.16470.1261104.00470.13550.122299.19290.1545
TABLE 2
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.2261109.65030.11190.2224109.38130.11590.1808111.72090.06070.1853112.21970.0579
20.234895.18570.10460.230394.85480.10860.195294.72460.05300.200495.27950.0504
30.244782.14970.09750.239481.75200.10150.209680.66030.04660.215581.27370.0441
40.255370.76000.09090.249370.29260.09480.223868.97560.04110.230369.64890.0387
50.266460.96640.08470.259660.42690.08860.237759.21790.03640.244859.95250.0340
60.277752.61970.07920.270352.00620.08300.251151.03180.03230.258851.82930.0300
70.288945.53800.07420.280944.84830.07790.264144.13430.02870.272444.99640.0266
80.300039.53840.06980.291438.77060.07340.276638.29740.02560.285339.22590.0235
90.310834.45360.06590.301633.60570.06930.288433.33630.02290.297734.33320.0209
100.321230.13680.06240.311629.20670.06570.299829.10070.02050.309430.16780.0186
110.331326.46280.05920.321125.44860.06250.310525.46800.01840.320626.60720.0165
120.340923.32650.05650.330422.22630.05960.320722.33840.01660.331223.55160.0147
130.350120.64080.05410.339219.45250.05710.330519.62990.01490.341320.91900.0131
140.358918.33340.05190.347717.05530.05480.339717.27560.01340.350818.64230.0117
150.367316.34450.05000.355814.97490.05280.348415.22040.01210.359916.66630.0105
160.375414.62480.04830.363513.16230.05090.356813.41870.01100.368514.94550.0094
170.383013.13370.04670.370911.57680.04930.364711.83310.00990.376713.44210.0084
180.390311.83720.04540.378110.18470.04780.372310.43220.00900.384412.12470.0075
190.397310.70730.04420.38498.95820.04640.37959.19010.00810.391810.96730.0067
200.40409.71330.04310.39147.88110.04520.38658.08120.00740.39889.95180.0060
210.41048.83010.04210.39776.91070.04420.39317.10280.00670.40569.06010.0054
220.41658.04560.04120.40376.03810.04320.39956.22870.00600.41208.27030.0048
230.42217.31430.04050.40985.28760.04220.40585.47730.00540.41807.53250.0043
240.42766.65800.03980.41564.61370.04140.41194.80200.00490.42376.86870.0039
250.43286.06700.03920.42124.00720.04060.41784.19270.00440.42926.26890.0035
260.43795.53340.03860.42663.45980.04000.42353.64070.00390.43455.72480.0031
270.44285.04980.03820.43192.96450.03930.42893.13910.00350.43975.22960.0027
280.44754.61030.03770.43702.51520.03880.43422.68160.00310.44464.77720.0024
290.45214.20940.03730.44192.10630.03830.43942.26330.00280.44944.36260.0021
300.45653.84270.03700.44681.73340.03780.44441.87950.00250.45413.98150.0019
310.46093.50620.03660.45141.39220.03740.44921.52650.00220.45873.63010.0016
320.46513.19630.03640.45601.07940.03700.45401.20100.00190.46313.30510.0014
330.46932.91000.03610.46050.79160.03670.45860.90000.00160.46743.00370.0012
340.47332.64470.03590.46480.52620.03640.46310.62100.00140.47172.72340.0010
350.47732.39800.03570.46910.28070.03610.46750.36170.00120.47582.46200.0008
360.48122.16780.03550.47330.05300.03590.47190.12010.00100.47992.21760.0006
370.48501.95240.03540.4773359.84120.03570.4761359.89440.00080.48391.98830.0005
380.48881.75010.03520.4814359.64360.03550.4803359.68300.00060.48781.77260.0003
390.49251.55960.03510.4853359.45860.03540.4845359.48450.00050.49171.56910.0002
400.49611.37990.03510.4892359.28530.03520.4886359.29720.00030.49561.37620.0001
410.49971.21100.03500.4930359.12350.03510.4927359.11880.00020.49951.19140.0000
420.50371.03210.03490.4971358.95420.03510.4963358.96640.00010.50291.0336−0.0001
430.5726358.32710.03490.5660356.50140.03510.5653356.48520.00010.5719358.3076−0.0001
TABLE 2
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
60.276388.50780.07990.271688.12320.08230.252687.17920.03190.257487.68190.0305
70.287481.41570.07490.282380.97620.07720.265680.28910.02840.270980.84160.0270
80.298475.40590.07040.292974.90960.07270.278174.45990.02530.283875.06340.0239
90.309270.31070.06650.303269.75590.06870.290069.50680.02260.296170.16270.0212
100.319665.98340.06290.313265.36820.06510.301465.27940.02020.307865.98910.0189
110.329662.29860.05980.322861.62140.06200.312261.65520.01810.318962.42010.0168
120.339259.15160.05700.332158.41060.05910.322558.53430.01630.329559.35570.0150
130.348456.45490.05450.341055.64860.05660.332255.83480.01460.339656.71410.0134
140.357254.13630.05240.349553.26320.05430.341453.48970.01320.349154.42830.0120
150.365552.13620.05040.357651.19480.05230.350251.44380.01190.358152.44290.0108
160.373550.40520.04870.365349.39420.05050.358649.65170.01070.366750.71250.0096
170.381248.90260.04710.372847.82080.04890.366548.07580.00970.374849.19930.0086
180.388547.59450.04570.379946.44090.04740.374146.68480.00880.382647.87210.0078
190.395446.45290.04450.386745.22660.04610.381445.45270.00790.390046.70470.0070
200.402145.44940.04340.393344.15970.04490.388344.35500.00720.397045.67800.0062
210.408544.55590.04240.399543.19990.04390.395043.38680.00650.403744.77610.0056
220.414643.76120.04150.405642.33800.04290.401342.52250.00580.410243.97640.0050
230.420543.05310.04070.411441.56260.04200.407441.74620.00530.416443.26360.0045
240.426242.42060.04000.417040.86320.04120.413341.04540.00480.422342.62530.0040
250.431641.85430.03930.422440.23050.04050.419040.41010.00430.428042.05150.0036
260.436841.34590.03880.427739.65640.03980.424539.83170.00380.433541.53390.0032
270.441940.88810.03820.432839.13390.03920.429839.30330.00350.438841.06540.0028
280.446840.47470.03780.437738.65680.03870.434938.81880.00310.443940.64000.0025
290.451540.10050.03740.442538.22000.03820.439938.37320.00270.448940.25270.0022
300.456239.76070.03700.447137.81880.03780.444737.96210.00240.453739.89890.0019
310.460639.45130.03670.451737.44930.03740.449537.58160.00210.458439.57500.0016
320.465039.16880.03640.456137.10790.03700.454137.22860.00190.463039.27760.0014
330.469338.91000.03610.460536.79160.03670.458636.90000.00160.467439.00370.0012
340.473338.64470.03590.464836.52620.03640.463136.62100.00140.471738.72340.0010
350.477338.39800.03570.469136.28070.03610.467536.36170.00120.475838.46200.0008
360.481238.16780.03550.473336.05300.03590.471936.12010.00100.479938.21760.0006
370.485037.95240.03540.477335.84120.03570.476135.89440.00080.483937.98830.0005
380.488837.75010.03520.481435.64360.03550.480335.68300.00060.487837.77260.0003
390.492537.55960.03510.485335.45860.03540.484535.48450.00050.491737.56910.0002
400.496137.37990.03510.489235.28530.03520.488635.29720.00030.495637.37620.0001
410.499737.21100.03500.493035.12350.03510.492735.11880.00020.499537.19140.0000
420.503737.03210.03490.497134.95420.03510.496334.96640.00010.502937.0336−0.0001
430.572634.32710.03490.566032.50140.03510.565332.48520.00010.571934.3076−0.0001
TABLE 2
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
11000000000000
120.337941.02160.05740.333440.54530.05870.323740.68000.01600.328341.21000.0152
130.347138.32420.05490.342237.78410.05630.333437.97890.01440.338338.57010.0136
140.356036.00530.05270.350635.39920.05400.342635.63210.01300.347936.28580.0122
150.364434.00500.05070.358733.33100.05200.351333.58460.01170.357034.30210.0109
160.372532.27410.04890.366431.53040.05030.359731.79080.01060.365632.57340.0098
170.380130.77180.04730.373829.95680.04870.367630.21320.00960.373831.06200.0088
180.387529.46430.04590.380928.57640.04720.375128.82030.00860.381629.73660.0079
190.394528.32350.04470.387727.36130.04590.382327.58630.00780.389128.57110.0071
200.401227.32190.04350.394226.29230.04480.389226.48720.00710.396127.54580.0063
210.407626.43040.04250.400425.33060.04370.395825.51690.00640.402926.64600.0057
220.413825.63760.04160.406424.46670.04280.402124.65020.00580.409425.84870.0051
230.419724.93160.04080.412123.68910.04190.408223.87130.00520.415625.13850.0045
240.425424.30140.04010.417722.98740.04110.414023.16770.00470.421624.50290.0041
250.430923.73750.03940.423122.35210.04040.419722.52950.00420.427323.93210.0036
260.436223.23160.03880.428321.77530.03980.425121.94810.00380.432923.41750.0032
270.441322.77650.03830.433321.24990.03920.430421.41650.00340.438222.95210.0028
280.446222.36600.03780.438220.76980.03870.435520.92890.00300.443422.53000.0025
290.451021.99480.03740.443020.32990.03820.440420.48000.00270.448422.14590.0022
300.455721.65810.03700.447619.92550.03770.445220.06550.00240.453221.79550.0019
310.460221.35190.03670.452119.55260.03730.449919.68170.00210.458021.47500.0017
320.464621.07260.03640.456619.20770.03700.454519.32520.00190.462521.18100.0014
330.468920.81710.03610.460918.88790.03670.459018.99310.00160.467020.91060.0012
340.473020.58270.03590.465118.59040.03640.463418.68300.00140.471420.66140.0010
350.477120.36700.03570.469218.31280.03610.467618.39260.00120.475720.43100.0008
360.481220.16780.03550.473318.05300.03590.471918.12010.00100.479920.21760.0006
370.485019.95240.03540.477317.84120.03570.476117.89440.00080.483919.98830.0005
380.488819.75010.03520.481417.64360.03550.480317.68300.00060.487819.77260.0003
390.492519.55960.03510.485317.45860.03540.484517.48450.00050.491719.56910.0002
400.496119.37990.03510.489217.28530.03520.488617.29720.00030.495619.37620.0001
410.499719.21100.03500.493017.12350.03510.492717.11880.00020.499519.19140.0000
420.503719.03210.03490.497116.95420.03510.496316.96640.00010.502919.0336−0.0001
430.572616.32710.03490.566014.50140.03510.565314.48520.00010.571916.3076−0.0001
TABLE 3
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.2014359.91960.39920.20140.08040.40220.0888359.14630.39780.08880.85370.4038
20.20140.77740.39860.20140.93280.40160.0888359.88050.39670.08881.93850.4036
30.20162.87400.39700.20143.03320.40030.08881.76240.39450.08874.06050.4027
40.20165.91150.39480.20146.07410.39840.08884.76360.39180.08877.25640.4008
50.20169.83250.39210.20149.99900.39590.08908.47860.38850.088911.34450.3986
60.201514.52610.38880.201514.77120.39260.088913.13970.38470.088816.26020.3956
70.201620.05610.38500.201620.30160.38910.089018.43490.38010.088921.83410.3921
80.201526.32180.38060.201526.49560.38470.089324.60360.37510.088828.30080.3880
90.201533.21600.37570.201533.49610.38010.089331.35470.36940.089035.25140.3836
100.201540.82040.37020.201641.09830.37510.089638.93280.36340.089143.13640.3784
110.201549.17960.36450.201549.39870.36940.089947.09380.35680.089351.58670.3730
120.201558.07700.35820.201558.35690.36340.090555.83010.35000.089460.53740.3669
130.201467.67900.35160.201667.95350.35710.090865.28500.34230.089770.24050.3604
140.201577.86730.34450.201578.18740.35030.091575.46550.33440.090080.56630.3536
150.201488.67860.33720.201488.98950.34290.092386.09570.32620.090591.48330.3462
160.2015100.07550.32920.2014100.39520.33520.093297.58350.31780.0911102.82710.3380
170.2015111.97450.32080.2015112.39280.32700.0940109.69860.30930.0918114.81090.3292
180.2016124.50850.31200.2015124.89660.31860.0953122.23180.30000.0928127.34230.3199
190.2015137.52770.30330.2014137.91460.30960.0966135.22920.29040.0939140.19440.3104
200.2016150.96800.29370.2014151.38330.30030.0978148.70700.28060.0951153.72950.3005
210.2016164.83340.28420.2015165.22880.29040.0996162.60850.27020.0963167.38300.2902
220.2014178.91170.27400.2014179.32480.28030.1015176.76030.25960.0981181.51140.2795
230.2015193.24500.26340.2016193.64070.26990.1036191.10240.24840.1000195.85940.2683
240.2015207.71150.25270.2014208.16390.25900.1061205.64100.23690.1019210.27860.2566
250.2015222.25280.24150.2015222.69180.24780.1086220.30410.22510.1043224.78780.2448
260.2015236.78400.23010.2014237.23680.23630.1114234.78920.21280.1068239.23730.2322
270.2015251.17190.21800.2015251.66330.22430.1146249.18810.20030.1096253.64270.2197
280.2015265.41060.20570.2016265.88120.21200.1180263.48400.18740.1129267.78140.2066
290.2015279.28360.19320.2016279.83250.19950.1218277.47570.17400.1167281.75730.1932
300.2014292.91280.18030.2014293.50480.18660.1251291.12740.16010.1204295.40180.1795
310.2014306.17030.16690.2015306.73000.17320.1284304.33270.14620.1240308.56130.1653
320.2016319.01130.15360.2016319.61770.15980.1315317.18970.13170.1275321.43600.1508
TABLE 3
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10123456789100
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
11000000000000
12000000000000
13000000000000
14000000000000
15000000000000
16000000000000
17000000000000
18000000000000
19000000000000
20000000000000
21000000000000
220.2016119.03200.27600.2016119.20550.27870.1005118.23740.26580.0992120.09730.2732
230.2014133.35090.26530.2014133.57070.26830.1025132.40720.25380.1009134.56100.2628
240.2015147.79700.25410.2015148.07700.25770.1050146.68220.24130.1027149.27160.2522
250.2016162.32630.24260.2015162.64600.24670.1077161.05960.22870.1049163.97260.2413
260.2014176.81150.23090.2016177.20350.23550.1108175.33030.21560.1074178.65360.2298
270.2014191.18800.21860.2014191.58440.22380.1142189.64260.20190.1100193.20790.2180
280.2014205.38310.20600.2015205.80070.21170.1178203.65220.18830.1132207.61680.2057
290.2015219.27850.19320.2014219.82550.19950.1218217.43540.17400.1167221.67810.1932
300.2015232.99030.18030.2016233.48730.18660.1251231.02750.16010.1204235.26370.1795
310.2016246.17940.16690.2016246.77080.17320.1284244.41610.14620.1242248.57320.1653
320.2015258.97950.15360.2014259.60480.15980.1317257.17470.13170.1274261.36590.1508
TABLE 3
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
10.22464.11540.11150.22094.39870.11530.18200.21740.06340.1863359.78260.0607
20.233618.90110.10440.229219.21270.10820.196019.29380.05550.201118.77950.0527
30.243733.01310.09750.238533.36240.10140.209935.57230.04890.216035.05730.0462
40.254546.08750.09100.248346.47110.09480.224149.64880.04320.230749.08220.0407
50.265857.89470.08500.259158.32120.08880.237661.72600.03830.244961.11920.0358
60.277368.43970.07950.269768.92080.08330.251272.13660.03390.259071.48860.0317
70.288677.70070.07490.280578.25220.07840.263881.12300.03030.272380.47150.0279
80.299785.86970.07050.291086.44720.07400.276388.92340.02700.285488.18950.0246
90.310893.02340.06670.301293.64120.07020.288095.66190.02400.297894.94700.0219
100.321299.30210.06310.311099.96720.06670.2993101.58690.02160.3096100.78430.0194
110.3315104.80370.06010.3206105.46920.06370.3099106.75730.01940.3208105.91860.0172
120.3411109.61060.05770.3299110.35610.06090.3202111.26570.01750.3315110.40680.0153
130.3505113.86720.05520.3385114.66210.05850.3296115.26940.01580.3415114.33020.0137
140.3595117.61660.05300.3468118.46280.05630.3390118.81690.01420.3513117.82080.0123
150.3679120.92730.05110.3550121.81840.05410.3475121.95280.01280.3605120.91910.0109
160.3761123.86320.04950.3625124.83990.05250.3558124.73970.01150.3690123.67830.0096
170.3841126.49490.04810.3700127.52990.05080.3635127.24030.01040.3774126.10670.0087
180.3915128.85340.04670.3767129.93860.04950.3711129.50310.00960.3852128.31700.0077
190.3986130.94210.04560.3834132.11160.04840.3782131.54420.00850.3929130.29020.0068
200.4054132.84250.04450.3899134.09150.04700.3848133.36010.00790.4001132.06570.0060
210.4119134.57000.04370.3961135.83840.04620.3914135.05660.00710.4070133.69430.0055
220.4182136.11190.04260.4020137.45130.04510.3974136.61590.00630.4136135.24080.0046
230.4241137.53260.04210.4076138.88630.04430.4036138.01860.00570.4198136.63510.0041
240.4297138.84150.04130.4136140.19930.04340.4096139.32820.00520.4256137.96630.0038
250.4350140.01930.04070.4190141.43360.04260.4154140.55150.00460.4314139.18620.0033
260.4403141.14590.04020.4244142.53260.04210.4210141.69450.00410.4368140.30460.0030
270.4451142.18050.03990.4295143.58940.04150.4261142.79210.00380.4421141.42310.0025
280.4501143.14400.03930.4343144.55030.04100.4313143.81250.00330.4471142.42290.0022
290.4549144.06620.03910.4393145.44010.04040.4366144.75830.00300.4521143.37940.0019
300.4595144.90190.03880.4439146.31970.03990.4414145.67050.00260.4569144.29500.0016
310.4639145.72960.03830.4484147.11370.03960.4460146.54360.00230.4615145.19970.0013
320.4682146.49540.03800.4529147.89200.03930.4506147.37960.00200.4661146.03980.0011
330.4725147.22890.03800.4572148.63700.03880.4550148.18060.00170.4706146.84500.0009
340.4768147.94940.03770.4612149.33310.03850.4595148.96610.00150.4750147.61730.0007
350.4809148.63990.03740.4656150.00490.03830.4637149.67310.00130.4794148.37540.0006
360.4849149.30200.03720.4695150.66040.03800.4681150.41270.00110.4837149.10290.0004
370.4889149.95330.03720.4734151.30510.03770.4722151.10640.00090.4878149.80130.0003
380.4928150.57820.03690.4774151.93910.03770.4762151.78830.00070.4918150.51570.0002
390.4966151.22100.03690.4812152.54750.03740.4804152.45850.00050.4959151.17540.0000
400.5006151.82630.03690.4849153.13170.03740.4842153.13130.00040.4998151.85200.0000
410.5042152.43520.03660.4885153.70720.03720.4883153.76470.00030.5039152.5178−0.0001
420.5082153.11810.03660.4925154.35900.03720.4916154.34640.00020.5073153.1038−0.0002
430.5765161.94290.03660.5609163.06550.03720.5601163.15620.00020.5757162.0036−0.0002
TABLE 3
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
60.2759113.51890.08030.2711113.77490.08250.2525117.03650.03360.2573116.61950.0320
70.2870122.79750.07540.2819123.13560.07790.2654125.99700.02980.2708125.59820.0284
80.2983130.98840.07100.2925131.32690.07350.2779133.80490.02650.2837133.36120.0251
90.3090138.11820.06720.3027138.51250.06940.2898140.54720.02380.2962140.05230.0224
100.3196144.39400.06370.3128144.85220.06610.3010146.43980.02130.3077145.92900.0199
110.3297149.90760.06070.3224150.39360.06310.3119151.59390.01910.3191151.06450.0178
120.3393154.73500.05820.3315155.25120.06040.3221156.13130.01720.3296155.51670.0158
130.3486158.96570.05570.3406159.53000.05790.3315160.10160.01530.3396159.46550.0139
140.3573162.74270.05360.3488163.33940.05570.3408163.65710.01390.3492162.98300.0126
150.3660166.04670.05160.3569166.67660.05380.3494166.80050.01260.3584166.05910.0112
160.3741169.01020.05000.3646169.68360.05190.3578169.57380.01120.3670168.84060.0101
170.3819171.64960.04860.3722172.36370.05050.3658172.09990.01010.3754171.29190.0090
180.3893173.99730.04730.3792174.79060.04920.3731174.32700.00930.3831173.48830.0079
190.3963176.12550.04590.3858176.91470.04780.3803176.37490.00850.3906175.46600.0071
200.4032178.01970.04480.3922178.88220.04670.3871178.17980.00770.3977177.28310.0063
210.4096179.74800.04400.3984180.62870.04560.3937179.86700.00680.4047178.91690.0057
220.4160181.27970.04320.4041182.24730.04480.3998181.40960.00630.4112180.41880.0049
230.4218182.71040.04230.4099183.70740.04400.4057182.85660.00550.4177181.79930.0044
240.4278183.99180.04150.4155185.01710.04320.4115184.18860.00490.4238183.10400.0038
250.4332185.17480.04100.4208186.26210.04260.4172185.41190.00440.4296184.30370.0036
260.4387186.25740.04040.4257187.41240.04180.4224186.57340.00410.4353185.43860.0030
270.4440187.28240.03990.4306188.46430.04130.4273187.67940.00360.4408186.51270.0026
280.4491188.21880.03960.4354189.46230.04070.4323188.72410.00330.4462187.52970.0023
290.4541189.10530.03910.4400190.37490.04040.4371189.68020.00300.4514188.45870.0019
300.4588189.94470.03880.4446191.23400.03990.4420190.61530.00260.4564189.37210.0016
310.4636190.76690.03850.4488192.08990.03960.4464191.50940.00230.4612190.23810.0014
320.4682191.51320.03800.4532192.85480.03910.4509192.35180.00200.4660191.05300.0011
330.4725192.21970.03800.4571193.62090.03880.4552193.18540.00170.4706191.82530.0009
340.4769192.94540.03770.4614194.33250.03850.4594193.93710.00150.4751192.62170.0007
350.4808193.64140.03740.4656194.99860.03830.4638194.67480.00130.4794193.37890.0006
360.4849194.28680.03720.4696195.66150.03800.4679195.40770.00110.4837194.09120.0004
370.4890194.96030.03720.4735196.32240.03770.4721196.09570.00090.4878194.79910.0003
380.4927195.60060.03690.4773196.94120.03770.4763196.80310.00070.4919195.49520.0002
390.4966196.23120.03690.4811197.55010.03740.4803197.44540.00050.4959196.18820.0000
400.5004196.82210.03690.4850198.11850.03740.4844198.10790.00040.4999196.84020.0000
410.5041197.44300.03660.4887198.71860.03720.4883198.76950.00030.5040197.5115−0.0001
420.5082198.10380.03660.4926199.36950.03720.4917199.34110.00020.5074198.1032−0.0002
430.5765206.94150.03660.5608208.07580.03720.5602208.13990.00020.5757207.0150−0.0002
TABLE 3
stationR/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2R/D2ThetaZ/D2
numbershroud pressure sideshroud suction sidehub suction sidehub pressure side
1000000000000
2000000000000
3000000000000
4000000000000
5000000000000
6000000000000
7000000000000
8000000000000
9000000000000
10000000000000
11000000000000
12000000000000
13000000000000
14000000000000
150.3640143.73230.05220.3590144.07200.05330.3516144.13630.01230.3565143.72730.0115
160.3721146.68330.05050.3666147.04410.05160.3597146.90130.01090.3651146.47640.0104
170.3798149.28370.04890.3740149.72550.05000.3675149.43080.00980.3735148.95000.0093
180.3874151.66370.04750.3808152.11130.04860.3749151.67940.00900.3813151.12090.0082
190.3944153.77220.04620.3875154.30220.04750.3821153.72810.00820.3889153.14690.0074
200.4015155.68510.04510.3940156.24320.04640.3887155.54270.00740.3961154.90190.0066
210.4079157.38600.04430.4001158.02420.04540.3953157.22780.00660.4030156.54640.0057
220.4143158.93540.04340.4058159.58840.04450.4013158.76360.00600.4097158.07090.0052
230.4204160.32860.04260.4116161.05990.04370.4074160.20400.00550.4161159.43510.0046
240.4261161.61150.04180.4168162.40840.04290.4130161.56510.00490.4223160.73270.0041
250.4319162.78000.04130.4220163.64190.04230.4185162.79550.00440.4282161.93500.0036
260.4374163.89730.04070.4270164.78990.04180.4236163.97340.00380.4338163.08300.0030
270.4426164.90000.04020.4320165.83190.04130.4287165.07800.00360.4394164.12310.0027
280.4478165.83660.03960.4366166.83340.04070.4337166.11260.00330.4450165.12750.0023
290.4528166.71000.03910.4412167.77140.04020.4384167.07230.00270.4501166.05650.0020
300.4577167.55650.03880.4456168.64870.03990.4430168.03850.00250.4552166.95640.0017
310.4625168.34490.03850.4499169.46800.03930.4474168.90960.00220.4601167.82920.0014
320.4672169.11070.03830.4541170.26560.03910.4520169.76330.00190.4648168.64380.0012
330.4716169.82280.03800.4580171.04340.03880.4561170.58850.00170.4697169.44180.0010
340.4759170.51600.03770.4621171.77410.03850.4601171.39350.00150.4744170.18510.0008
350.4803171.16460.03740.4661172.45420.03830.4642172.15130.00120.4790170.90840.0006
360.4847171.83340.03720.4697173.15190.03800.4683172.89570.00100.4833171.61340.0004
370.4889172.45400.03720.4735173.80580.03770.4720173.61950.00090.4877172.30570.0003
380.4927173.08780.03690.4774174.41670.03770.4761174.30250.00070.4919173.01310.0002
390.4967173.71550.03690.4810175.04720.03740.4803174.97380.00050.4959173.67380.0000
400.5005174.32990.03690.4850175.63840.03740.4842175.59880.00040.5000174.35480.0000
410.5042174.93210.03660.4885176.21580.03720.4882176.27760.00030.5038175.0222−0.0001
420.5083175.59180.03660.4925176.85190.03720.4917176.84670.00020.5075175.6155−0.0002
430.5766184.42990.03660.5608185.56340.03720.5601185.65500.00020.5758184.5176−0.0002

Claims as granted

6 claims

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Classifications

8 codes
IPC · International Patent Classification
Section F — Mechanical engineering; lighting; heating; weapons
  • F04D1/02
  • F04D9/04
  • F04D13/12
  • F04D29/22
USPC · US Patent Classification
416/175416/177416/176416/198.R

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File wrapper

⤢ drag to zoomJan 2012Jul 2012Jan 2013Jul 2013Jan 2014Jul 2014Jan 2015USPTOApplicantExaminer-initiated interview
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Pendency
3.0 y
1,113 days filing → grant
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0
none on record
Interviews
1
examiner interview summaries
Examiner
Nathaniel Wiehe
art unit 3745 · TC 3700
Citations: 17 back · 7 forward

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Chain of title

⤢ drag to zoom20122014201620182020202220242026202820302032Owner 1
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