research article the design method of axial flow...

Research ArticleThe Design Method of Axial Flow Runners Focusing onAxial Flow Velocity Uniformization and Its Application toan Ultra-Small Axial Flow Hydraulic Turbine

Yasuyuki Nishi1 Yutaka Kobayashi2 Terumi Inagaki1 and Norio Kikuchi3

1Department of Mechanical Engineering Ibaraki University 4-12-1 Nakanarusawa-cho Hitachi-shi Ibaraki 316-8511 Japan2Graduate School of Science and Engineering Ibaraki University 4-12-1 Nakanarusawa-cho Hitachi-shi Ibaraki 316-8511 Japan3Ibasei Ltd 4-7-10 Kamine-cho Hitachi-shi Ibaraki 317-0064 Japan

Correspondence should be addressed to Yasuyuki Nishi yasuyukinishifevcibarakiacjp

Received 28 June 2016 Revised 21 October 2016 Accepted 3 November 2016

Academic Editor Jechin Han

Copyright copy 2016 Yasuyuki Nishi et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We proposed a portable and ultra-small axial flow hydraulic turbine that can generate electric power comparatively easily usingthe low head of open channels such as existing pipe conduits or small rivers In addition we proposed a simple design methodfor axial flow runners in combination with the conventional one-dimensional design method and the design method of axial flowvelocity uniformization with the support of three-dimensional flow analysis Applying our design method to the runner of anultra-small axial flow hydraulic turbine the performance and internal flow of the designed runner were investigated using CFDanalysis and experiment (performance test and PIVmeasurement) As a result the runners designed with our design method weresignificantly improved in turbine efficiency compared to the original runner Specifically in the experiment a new design of therunner achieved a turbine efficiency of 0768 This reason was that the axial component of absolute velocity of the new design ofthe runner was relatively uniform at the runner outlet in comparison with that of the original runner and as a result the negativerotational flow was improved Thus the validity of our design method has been verified

1 Introduction

Conventionally hydropower generation has been used inlarge-scale facilities to generate electric power efficiently byutilizing high or medium hydraulic head However the num-ber of locations where enough head is available is decreasingIn addition installation of large-scale facilities requires large-scale civil engineering projects which have a significantimpact on the environment Therefore it is thought thatsmall hydraulic turbines show promise in generating powerin situations of low available head such turbines woulduse water in open channels such as existing pipe conduitsor small rivers [1ndash4] It is also expected that because axialflow hydraulic turbines are particularly suited for low headapplications they will be widely implemented if they aredecreased in size and made portable [5ndash8] However smallaxial flow hydraulic turbines have extremely low Reynoldsnumbers (approximately 1 times 105) thus very few airfoils

are applicable Furthermore design methods are not wellestablished

Incidentally in hydraulic turbines the design of theFrancis hydraulic turbine has been optimized in recent yearsusing a design of experiments and an optimization algorithm[9ndash11] However a large amount of sample data needs tobe acquired and obtaining the most feasible solution istime consuming thus the computational load increasesTherefore it is important to establish a simple designmethodfor designing reliable and highly efficient axial flow runnersfrom the null state without sample data

In light of this background in this study we propose aportable and ultra-small axial flow hydraulic turbine that cangenerate electric power using the low head of open channelssuch as existing pipe conduits or small rivers The runnersand guide vanes of this hydraulic turbine are designed usinga conventional one-dimensional design method [12 13]and their performance and internal flows are investigated

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 5390360 13 pageshttpdxdoiorg10115520165390360

2 International Journal of Rotating Machinery

by numerical analysis In addition we propose a simpledesign method for axial flow runners in combination withthe conventional one-dimensional design method and thedesign method of axial flow velocity uniformization withthe support of three-dimensional flow analysis This designmethod can decide the unique formof the runner on the basisof the quantitative data of the velocity distributions at therunner inlet and outlet using three-dimensional flow analysisTherefore we believe that our method can provide reliableand highly efficient performance for a runner in comparisonwith the method wherein designers empirically repeat thechanges of shapes by examining the analytical results fromcomplicated three-dimensional internal flows Applying ourdesign method to the runner of an ultra-small axial flowhydraulic turbine the performance and internal flow of thedesigned runner are investigated using numerical analysisIn addition as verification we conducted an experimentusing an actual device and verified the validity of this designmethod

2 Simple Design Method forAxial Flow Runners

In this study we propose a simple design method for axialflow runners focusing on axial flow velocity uniformizationThis designmethod is a combination of the conventional one-dimensional design method [12 13] and the design methodof axial flow velocity uniformization with the support ofa three-dimensional flow analysis The design flowchartis shown in Figure 1 First a runner is designed on thebasis of the conventional one-dimensional design methodVelocity distributions at the inlet and outlet of the runner areexamined on the basis of the three-dimensional flow analysisNext the axial flow velocity uniformization is performedand the blade angle and chord length of the runner aremodified The performance of the runner is verified usingthree-dimensional flow analysis If it does not achieve thetarget performance the axial flow velocity uniformization isperformed again Through iterations of this procedure thedesign process is complete when the performance achieves itstarget We have assumed that this design method is effectivein cases wherein factors such as a low Reynolds number orcharacteristic data of the airfoil are unclear and the assumedflow by the one-dimensional designmethod strongly deviatesfrom the actual three-dimensional flowThe following are thedetails of the conventional design method [12 13] and thedesign method of axial flow velocity uniformization

21 One-Dimensional Design Method The specific speed 119899119904is calculated using the following design parameters effectivehead119867 turbine output 119871 and rotational speed 119899

119899119904 = 119899 (1198711000)1211986754 (1)

Using the specific speed 119899119904 obtained from (1) and adesign diagram [12] the circumferential velocity coefficient119896119906 hub ratio ] and the axial velocity coefficient 119896119886 arecalculated In addition the circumferential velocity 119906119905 of a tip

Yes

No

Axial flow velocity uniformization

Check velocity at runner inlet and outlet

Three-dimensional flow analysis

One-dimensional design method

Check performance

Design specification

Finish the design


Design method of axial flow velocity

uniformizationH n L

Figure 1 Design flow

the outer diameter 119863119905 of a runner and the hub diameter 119863ℎare obtained with the following formulae

119906119905 = 119896119906radic2119892119867119863119905 = 60119906119905120587119899 ] = 119863ℎ119863119905

(2)

Furthermore the axial component V119886 of the absolutevelocity and the flow rate 119876 are obtained with the followingformulae

V119886 = 119896119886radic2119892119867119876 = 120587 (1 minus ]2)1198632119905 V1198864

(3)

Next dividing the blade into several parts fromhub to tipvortex design is determined Referencing specific speed 119899119904the number of blades 119911 is determined and then the pitch 119905 ateach radial point 120593 is calculated by the following expression

119905 = 120587119863119911 (4)

The velocity triangle of this runner is illustrated inFigure 2 [13] At each radial point 120593 the airfoil and attackangle 120575 are selected By estimating hydraulic efficiency 120578ℎchord length 119897 and mean relative flow angle 120573 between therunner inlet and outlet are calculated using the followingexpression [13]

119908 = V119886sin120573

120578ℎ119867 = 12119892 119897119905119862119871119906119908 (1 minus 120576 cot120573) (5)

International Journal of Rotating Machinery 3

a = a1 = a2

u = u1 = u2

12

w1

w2

w

Figure 2 Velocity triangle

In this study the blade is divided into four parts from hubto tip and the calculation is performed at five radial pointsThis vortex design type is a free vortex At each radial point120593 the airfoil selects MEL031 [14] in which characteristic dataexist for low Reynolds numbers The attack angle is 120575 = 2∘However considering that the Reynolds number based onchord length and relative velocity is as low as approximately1 times 105 hydraulic efficiency is estimated to be 120578ℎ = 07 (120578 =0659)

In addition the blade angle 120579 is obtained from thefollowing formula

120579 = 120573 minus 120575 (6)

Finally taking into account the leakage loss the blade tipclearance is determined

The one-dimensional design method for the guide vaneis also shown below The outer diameter of the guide vane isthe size of the outer diameter of the runner plus the bladetip clearance and the hub diameter is the same as that of therunner Dividing the blade into several parts from hub to tipvortex design is determined Referencing specific speed 119899119904the number of blades 119911119892 of the guide vane is determined andthen the pitch 119905119892 of the guide vane at each radial point 120593119892 iscalculated by the following expression

119905119892 = 120587119863119892119911119892 (7)

At each radial point 120593119892 the airfoil and attack angle 120575119892 ofthe guide vane are selected It is assumed that prerotation at aguide vane inlet is zero (V1199063 = 0) and that V1199064 = V1199061 at a guidevane outlet Mean absolute flow angle 120572119892 between the guidevane inlet and outlet and blade angle 120579119892 are calculated usingthe following expression [15]

tan120572119892 = V119886119892((V1199063 + V1199064) 2) 120579119892 = 120572119892 minus 120575119892

(8)

where V119886119892 is the axial component of the mean absolutevelocity between the guide vane inlet and outlet

In addition the chord length 119897119892 of the guide vane isobtained from the following formula [15]

119862119871119892 119897119892119905119892 =2V1199064V119886119892

cos 120576119892 sin2120572119892sin (120572119892 + 120576119892) (9)

In this study the blade of the guide vane is divided intofour parts from hub to tip and the calculation is performedat five radial points This vortex design type is a free vortexAt each radial point 120593119892 the airfoil selects MEL031 [14] andthe attack angle is 120575119892 = 8∘

22 DesignMethod of Axial Flow Velocity Uniformization Byperforming a three-dimensional flow analysis for the runnerdesigned with the one-dimensional design method shown inSection 21 the distributions of the axial component of theabsolute velocity at the runner inlet and outlet are calculatedUsing these velocity distributions axial flow velocity uni-formization is performed Specifically the axial componentsV119886119888 of the mean absolute velocities between the runner inletand outlet are calculated on the basis of the values analyzedat each radial point 120593 Then after the axial flow velocityuniformization is performed the axial components V1015840119886 of themean absolute velocities between the runner inlet and outletare obtained from the following expression

V1015840119886 = V119886119889 + (V119886119889 minus V119886119888) (10)

Here V119886119889 is the axial component of the mean absolutevelocity between the runner inlet and outlet based on thedesign values using the one-dimensional design method

Accordingly after performing the axial flow velocityuniformization the chord length 1198971015840 and the blade angle 1205791015840 areobtained from formulae (11)

1205731015840 = tanminus1( V1015840119886119908119889 cos120573119889) 1198971015840 = 2119892119867120578ℎ119905119862119871119906119908119889 (1 minus 120576 cot1205731015840) 1205791015840 = 1205731015840 minus 120575

(11)

Here119908119889 is the mean relative velocity between the runnerinlet and outlet based on the design values using the one-dimensional design method

In addition120573119889 is themean relative flow angle between therunner inlet and outlet based on the design values using theone-dimensional design method

As shown above the chord length 1198971015840 and the bladeangle 1205791015840 at each radial point 120593 are modified and then thethree-dimensional flow analysis of the modified runner isperformed The verification of performance and the axialflow velocity uniformization are iterated until the targetperformance is obtained In this study the target performancefor the turbine efficiency is 120578 = 075


Guide vane

Runner

Generator

Flow703

691

Figure 3 Ultra-small axial flow hydraulic turbine

3 Test Hydraulic Turbine

An overview of the ultra-small axial flow hydraulic turbineproposed in this study is shown in Figure 3 This hydraulicturbine is easily portable The targets are set as followseffective head 119867 = 15m turbine output 119871 = 100W at arotational speed of 119899 = 2460minminus1 and a turbine efficiencyof 120578 = 075 so that it is possible to obtain a practical turbineoutput when the turbine is implemented at low head valuesThe specific speed 119899119904 shown in formula (1) is 469 [minminus1 kWm] Considering that the Reynolds number based on chordlength and relative velocity is as low as approximately 1 times105 the design values in the one-dimensional design methodare set as follows effective head H = 15m turbine output L= 755W at rotational speed 119899 = 2460minminus1 and turbineefficiency 120578 = 0659

An overview of the sample runners is shown in Figures4(a)ndash4(d) and the dimensions are shown in Table 1 Here theoriginal runner is designed using only the conventional one-dimensional design method shown in Section 21 The outerdiameter of the runner is 119863119905 = 681mm the hub diameter is119863ℎ = 302mm the number of blades is 119911 = 4 and the bladetip clearance is 05mm In addition MEL031 [11] is selectedfor an airfoil at any radial point and the attack angle is 120575 = 2∘The design flow rate isQ = 00078m3s Case 1 runner Case 2runner and Case 3 runner were all designed using the designmethodproposed in this study andwere created after the axialflow velocity uniformization was performed once twice andthree times respectively

An overview of the sample guide vane is shown inFigure 5 and the dimensions are shown in Table 2The guidevane is designed using the conventional one-dimensionaldesign method shown in Section 21 The outer diameter is119863119905119892 = 691mm the hub diameter is 119863ℎ119892 = 302mm andthe number of blades is 119911119892 = 5 In addition MEL031 [14] isselected for an airfoil at any radial point and the attack angleis 120575119892 = 8∘

Table 1 Specifications of test runners

Hub Mid Tip

Original

Radius 119903 [mm] 151 246 341Solidity 119897119905 104 072 057

Blade angle 120579 [∘] 169 210 247Airfoil MEL031

Blade number 119911 4

Case 1




Case 2




Case 3




Table 2 Specifications of guide vane

Hub Mid TipRadius 119903119892 [mm] 151 248 346Solidity 119897119892119905119892 153 101 074Blade angle 120579119892 [∘] 548 646 693Airfoil MEL031Blade number 119911119892 5

4 Numerical Analysis Methodsand Conditions

The computational model is shown in Figure 6 As shown inFigure 3 a bent pipe was installed in the upper flow of theguide vane in the case of a real hydraulic turbine However tosimplify the analytical model and remove the influence of thebent pipe we used a computational model comprising only adirect pipe when we applied our design method We believethat the tendency of the qualitative performance of thishydraulic turbine does not change depending on the presenceof the bent pipe We used the general-purpose thermal fluidanalysis code ANSYS CFX150 for the numerical analysesand conducted three-dimensional steady flow analyses Thegoverning equations are the conservation of mass equation[16] and the conservation of momentum equation [16] TheSST (Shear Stress Transport) model [16] was adopted as theturbulence model Water was used for the working fluidFor boundary conditions the mass flow rate 7793 kgs (Q =00078m3s) was applied to the inlet boundary static pressure(gauge pressure) 0 Pa was applied to the outlet boundaryand arbitrary rotational speed was applied to the runner


(a) Original (b) Case 1

(c) Case 2 (d) Case 3

Figure 4 Test runners

Figure 5 Guide vane

Inlet OutletGuide vane Runner

195 130 130 520

Figure 6 Computational domain

region Nonslip conditions were applied to all the wallsMoreover the boundaries between the rotating and staticsystems were joined using the frozen rotor [17] For examplethe computational grids of the original runner and the guidevane are shown in Figures 7(a) and 7(b) The computationalgrid of each runner was a tetrahedron and the face sizeof the blade surface was 04mm There were five prismlayers of the blade surface and the size of the first layerwas 003mm The numbers of computational elements fororiginal runner Case 1 runner Case 2 runner and Case 3runner were approximately 2070000 2130000 2600000and 2810000 elements respectively The computational gridof the guide vane was a tetrahedron and the face size ofthe blade surface was 06mm There were five prism layers

of the blade surface and the size of the first layer was003mm The number of computational elements for theguide vane was approximately 1280000 The total numbersof computational elements for original runner Case 1 runnerCase 2 runner and Case 3 runner were approximately5060000 5110000 5580000 and 5800000 elementsrespectively To study the grid dependence we performed ananalysis after increasing the computational elements for theoriginal runner and guide vane to approximately 3170000and 1990000 respectively then we performed an analysisafter increasing the computational elements to approximately4250000 and 2550000 respectively Consequently it wasconfirmed that the effect of the number of computationalelements in the grids was relatively low even though theeffective head and turbine output changed by approximately+30 and minus09 respectively in the former analysis andby approximately +26 and minus12 respectively in the latteranalysis Moreover we performed an unsteady flow analysisfor the original runner using the transient rotor-stator [17]As a result it was confirmed that the difference between thesteady and unsteady flow analyses was relatively small eventhough the effective head and turbine output changed byapproximately +25 and +33 respectively compared withthe results presented in the paper

5 Analysis Results and Discussion

51 Comparison of Turbine Performance The turbine per-formance of each runner obtained by numerical analysis isdepicted in Figures 8(a)ndash8(c) In the figures the design valueof the turbine output (755W) is also illustrated For theoriginal runner the maximum value of turbine efficiency 120578is 0662 at the design rotational speed 119899 = 2460 and is almostequal to the design value (0659) However the turbine output


(a) Runner (original) (b) Guide vane

Figure 7 Computational grids

0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000

OriginalCase 1Case 2

Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)

(c) Turbine efficiency

Figure 8 Turbine performances (Cal)


0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value

(b) Circumferential component

Figure 9 Absolute velocity at runner inlet (119899 = 2460minminus1 Cal)

119871 and the effective head 119867 are significantly larger than theirdesign values By contrast for Cases 1ndash3 runners designedusing our design method the turbine output L decreases inall the rotational speed regions more than that of the originalrunner However at the same time the effective head Hdecreases Therefore the turbine efficiency 120578 of Cases 1ndash3runners except at 119899 = 3690 have all significantly improvedwhen compared to that of the original runner It is noted thatin particular Case 2 runner achieves a turbine efficiency of120578 = 0752 at 119899 = 2460 which surpasses the design valueHowever 120578 value of Case 3 runner is slightly lower than thatof Case 2 runner This appears to be because the hydraulicefficiency 120578ℎ that was assumed in the design of the axial flowvelocity uniformization is different from actual values

52 Comparison of Internal Flow The axial component V1198861and the circumferential component V1199061 of the absolute veloc-ity at the runner inlet at each radial point 120593 of each runner areillustrated in Figures 9(a) and 9(b) Here V1198861 and V1199061 are thecircumferential average values of the axial component and thecircumferential component respectively at the 1mm upperpoint of the stream from the blade Rotational speed is 119899 =2460The value 120593 = 0 represents the hub and 120593 = 1 representsthe tip The value V1198861 of each runner decreases significantlyon the hub side This phenomenon can be explained by theReynolds number decreasing on the hub side a boundarylayer developing on the hub surfacewhen flowpasses througha guide vane and other related effects Therefore V1198861 isslightly larger than the design value from the mid-point tothe tip-point but it is close to the design value as a wholeIn particular Cases 1ndash3 runners unlike the original runnerdecrease nonuniformity and have a similar distribution ofdesign values The value V1199061 is in relatively good agreementwith the design value although for each runner the valuedecreases on the hub side In particular in Cases 1ndash3 runnersthe diminution of V1199061 near the hub is smaller compared to theoriginal runner and thus the distribution gets closer to that

of the design Based on the discussion in the preceding textthe design of the guide vane is appropriate to some extent

The axial component V1198862 and the circumferential com-ponent V1199062 of the absolute velocity at the runner outlet ateach radial point 120593 of each runner are illustrated in Figures10(a) and 10(b) Here V1198862 and V1199062 are the circumferentialaverage values of the axial component and the circumferentialcomponent respectively at the 1mm lower point of thestream from the blade Rotational speed is 119899 = 2460 Thevalue 120593 = 0 represents the hub and 120593 = 1 represents thetip In the case of the original runner V1198862 is smaller on thehub side and becomes larger toward the tip In additionV1199062 has negative values except for the values on the tip sidethereby indicating a negative rotation that is in the directionopposite to the direction of flow into the runner Causes ofthis might be that the Reynolds number of this runner is lowwhich becomes even lower for locations closer to the hub orthat an axial flow velocity at the runner inlet was not uniformpreviously or that the boundary layer develops on the hubsurface among other reasons This negative rotation flowappears to increase the effective head and the turbine outputIn contrast Cases 1ndash3 runners designed with our designmethod have a value of V1198862 that in comparison to that of theoriginal runner is uniform and close to the design value theyalso have a value of V1199062 that is also close to the design valueCase 2 runner is particularly noteworthy As shown in Figures11(a) and 11(b) if the absolute velocity vectors are comparedbetween the original runner and Case 2 runner the reverseflow is created at the runner outlet of the original runner butis eliminated in Case 2 runner Accordingly it is apparentthat the turbine efficiency of Case 2 runner is significantlyimproved compared to the original runner

6 Verification by Experiment

61 Experimental Apparatus and Methods To verify the highperformance of the hydraulic turbine described in Section 5


0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u2 (ms)minus10minus20minus30minus40minus50


Case 3Design value


Figure 10 Absolute velocity at runner outlet (119899 = 2460minminus1 Cal)


Figure 11 Absolute velocity vector (120593 = 0125 119899 = 2460minminus1 Cal)

an actual device was used for a verification test An overviewof the experimental apparatus is shown in Figure 12 Actualdevices of the runners are shown in Figures 13(a) and 13(b)and an actual device of the guide vane is shown in Figure 14Water was used for the working fluid and the experimentwas conducted with a constant flow rate 119876 = 00078m3sThe flow rate was measured using an electromagnetic flowmeter (TOSHIBACORPORATIONGF630 Accuracyplusmn05of rate) The load of the hydraulic turbine was controlledusing a motor and an inverter and the rotational speed 119899was set up arbitrarily The rotational speed 119899 and torque 119879weremeasured with amagnetoelectric-type rotation detector(Ono Sokki Co Ltd MP-981 accuracy plusmn002 of full scale)and a torque detector (Ono Sokki Co Ltd SS-005 accuracyplusmn02 of full scale) respectively From these values theturbine output 119871 was obtained

119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump

Figure 12 Experimental apparatus



Figure 13 Actual device of the runner

Figure 14 Actual device of the guide vane

Note that the torque obtainedwas corrected bymeasuringthe torque without a runner The static pressures at the inletand outlet of a hydraulic turbine weremeasuredwith a strain-gauge pressure transducer (Kyowa Electronic InstrumentsCo Ltd PGMC-A-200KP-F nonlinearity plusmn15 rated out-put)The effective headH was calculated using the differencebetween the static pressures and the difference between thedynamic pressures obtained from the flow rate

119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)

Here 119875119894 and 119875119900 are the static pressure of the turbine inletand outlet In addition V119894 and V119900 are the average flow velocityof the turbine inlet and outlet

Furthermore the turbine efficiency 120578 was obtained withthe following formula

120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109


For themeasurement errors for the original runner at 119899 =2460 the total errors of the turbine output L effective headHand turbine efficiency 120578were approximately plusmn47 (plusmn012m)plusmn27 (plusmn36W) and plusmn54 (plusmn0038) respectively

To measure the internal flow of the hydraulic turbineusing a PIV system a solid-state laser (PIV Laser G6000output 6W and wavelength 532 nm) with continuous oscil-lation was used as a light source The light of the laser-sheetilluminated the central and vertical sections of the runnerfrom a position vertically below the runner During thisoperation the laser-sheet light was reflected 90∘ by a mirrorThe thickness of the laser-sheet was about 1mm Nylon12 with a diameter of around 55120583m and a specific gravityof 102 was used as tracer particles A high-speed camera(Vision Research Inc PHANTOM Miro M110) was used tophotograph images in chronological order at a photographyspeed of 10000 fps The resolution is 448 times 360 pixels Basedon these images with reference to the two two-dimensionalcomponents of the internal flow of the hydraulic turbinePIV analysis was conducted by the direct cross-correlationmethod using a PIV analysis software from Flow Expert(Katokoken Co Ltd Ver 129)

62 Numerical Analysis Methods and Conditions Along withthis experiment the actual turbine was analyzed usingnumerical analysis The computational model of the actualturbine is shown in Figure 15 The analysis code used ANSYSCFX150 used in Section 4 and conducted three-dimensional


020406080

100120140160180

0 1000 2000 3000 4000 5000

Exp (original) Exp (Case 2)Cal (original) Cal (Case 2)Design value

n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)


Figure 16 Turbine performances

steady flow analysesThe governing equations the turbulencemodel the working fluid the boundary conditions and soforth are the same as those of Section 4 The computationalgrid of each runner was a tetrahedron and the face size of theblade surface was 04mmThere were ten prism layers of theblade surface and the size of the first layer was 0007mmThenumbers of computational elements for original runner andCase 2 runner were approximately 2530000 and 3150000elements respectively The computational grids of the guidevane used the same thing as Section 4 The total numbers ofcomputational elements for original runner and Case 2 run-ner were approximately 5810000 and 6430000 elementsrespectively

63 Results and Discussion The comparison of the perfor-mances of the original runner and Case 2 runner with regardto experimental values and calculated values is shown in Fig-ures 16(a)ndash16(c)The turbine output 119871 and the effective head

119867 from the experimental values of the original runner andCase 2 runner are all slightly larger than the calculated valuesWith regard to the turbine efficiency 120578 the experimentaland calculated values show qualitative agreement althoughthere is a slight difference in the high rotational speed regionIt is apparent that the turbine efficiency of Case 2 runneris significantly improved compared to that of the originalrunner and thatCase 2 runner achieves an experimental valueof 120578 = 0768 for turbine efficiency which is better than thetarget value

With regard to the original runner and the Case 2 runnerthe PIVmeasurement results of the absolute velocity vector inthe central and vertical sections of the runners are illustratedin Figures 17(a) and 17(b) with the respective calculationresults in Figures 18(a) and 18(b) Here the rotational speedis 119899 = 2460 In addition the PIV measurement resultsare obtained using time-averaged processing on the basisof the 12196 images photographed (for approximately 50


40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2

Figure 17 Absolute velocity vector (119899 = 2460minminus1 Exp)

10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2

Figure 18 Absolute velocity vector (119899 = 2460minminus1 Cal)

rotations of the runner) The flow at the outlet of theoriginal runner in both the PIV measurement results andthe calculation results is rapid on the tip side and slow onthe hub side which indicates nonuniformity In additionlarge-scale reverse flow is generated on the hub side Incontrast Case 2 runner has no reverse flow at the outletand is thus relatively uniform Our design method is nowvalidated

As described above using this design method an axialflow runner with relatively high efficiency can be easilydesigned by altering the form of the runner only two orthree times after producing a runner in a null state Atthat time we decide the unique form of the runner usingquantitative data of the velocity distributions at the runnerinlet and outlet (Figures 9(a) and 10(a)) Therefore this is asimple method with a smaller calculation load in comparisonwith the optimized design method that uses a design ofexperiments and an optimization algorithm In addition ourmethod can yield reliable results in comparison with themethod wherein designers empirically repeat the changesof shapes by examining the analytical results from three-dimensional internal flows

7 Conclusions

We proposed a simple design method for axial flow runnersusing a combination of the conventional one-dimensionaldesign method and the design method of axial flow velocityuniformization with the support of three-dimensional flowanalysis We applied our design method to the runners of anultra-small axial flowhydraulic turbineTheperformance andinternal flow of the hydraulic runner were investigated usingnumerical analysis and with an experiment The conclusionsare the following

(1) For the original runner designed using a conventionalone-dimensional design method turbine efficiencyis almost equal to the design values at a designrotational speed but turbine output and effective headare significantly larger than their design values

(2) Cases 1ndash3 runners designed with our design methodare significantly improved in turbine efficiency com-pared to the original runner Specifically in the exper-iment Case 2 runner achieves a turbine efficiency of0768 which surpasses the target value


(3) The reason that the turbine efficiency of Case 2 runnershows a significant improvement in comparison withthat of the original runner is that the axial componentof absolute velocity is relatively uniform at the runneroutlet and as a result the negative rotational flow isimprovedThus the validity of our designmethod hasbeen verified

Nomenclature

119862119871 Lift coefficient119863 Runner diameter m119892 Gravitational acceleration ms2119867 Effective head m119897 Chord length m119871 Turbine output W119899 Rotational speed minminus1119899119904 Specific speed minminus1 kW m119875 Static pressure Pa119876 Flow rate m3s119903 Runner radius m119905 Pitch m119879 Torque Nsdotm119906 Circumferential velocity msV Absolute velocity ms119908 Relative velocity ms119911 Number of blades

Greek Letters

120575 Attack angle ∘120578 Turbine efficiency = 119871120588119892119876119867120579 Blade angle ∘120593 Dimensionless radial point = (119903 minus 119903ℎ)(119903119905 minus 119903ℎ)] Hub ratio = 119863ℎ119863119905120576 Drag-lift ratio120588 Fluid density kgm3

SubscriptsSuperscripts

1 Runner inlet2 Runner outlet3 Guide vane inlet4 Guide vane outlet119886 Axial component119889 Design value119892 Guide vaneℎ Hub119894 Turbine inlet119899 Numerical analysis value119900 Turbine outlet119905 Tip119906 Circumferential component1015840 After the axial flow velocity uniformizationmdash Mean value between the runner inlet and outlet

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge that a part of the study hasbeen subsidized by JST A-STEP High-risk Challenge Type(Revitalization Promotion Type) and express their gratitudehere

References

[1] C S Kaunda C Z Kimambo and T K Nielsen ldquoA technicaldiscussion on microhydropower technology and its turbinesrdquoRenewable and Sustainable Energy Reviews vol 35 pp 445ndash4592014

[2] A Furukawa S Watanabe D Matsushita and K OkumaldquoDevelopment of ducted Darrieus turbine for low headhydropower utilizationrdquo Current Applied Physics vol 10 no 2pp S128ndashS132 2010

[3] T Ikeda S Iio andK Tatsuno ldquoPerformance of nano-hydraulicturbine utilizing waterfallsrdquo Renewable Energy vol 35 no 1 pp293ndash300 2010

[4] AMuis andP Sutikno ldquoDesign and simulation of very lowheadaxial hydraulic turbinewith variation of swirl velocity criterionrdquoInternational Journal of Fluid Machinery and Systems vol 7 no2 pp 68ndash79 2014

[5] H M Ramos M Simao and K N Kenov ldquoLow-head energyconversion a conceptual design and laboratory investigation ofa microtubular hydro propellerrdquo ISRN Mechanical Engineeringvol 2012 Article ID 846206 10 pages 2012

[6] R Sonohata J Fukutomi and T Shigemitsu ldquoStudy on contra-rotating small-sized axial flow hydro turbinerdquo Open Journal ofFluid Dynamics vol 2 pp 318ndash323 2012

[7] T Shigemitsu Y Takesihma and J Fukutomi ldquoInfluence ofspoke geometry on performance and internal flow of contra-rotating small-sized hydroturbinerdquoTurbomachinery vol 44 no2 pp 89ndash97 2016

[8] E Chica S Agudelo and N Sierra ldquoLost wax casting process ofthe runner of a propeller turbine for small hydroelectric powerplantsrdquo Renewable Energy vol 60 pp 739ndash745 2013

[9] T Nakamura K Sugishita N Ohtake and N TakasuldquoImprovement of cavitation performance of francis turbinerunnerrdquo Turbomachinery vol 33 no 2 pp 85ndash90 2005

[10] Y Enomoto S Kurosawa and T Suzuki ldquoDesign optimizationof a francis turbine runner using multi-objective genetic algo-rithmrdquo Turbomachinery vol 33 no 12 pp 732ndash737 2005

[11] Y Enomoto T Nakamura and S Kurosawa ldquoDesign optimiza-tion for francis turbine runnersrdquo Turbomachinery vol 41 no 9pp 570ndash576 2013

[12] S Tsuji ldquoExample exercises fluid machineryrdquo Jitsugyotosyo pp189ndash190 1970

[13] The Japan Society of Mechanical Engineers Mechanical Engi-neersrsquo Handbook Applications 1205742 Fluid Machinery MaruzenTokyo Japan 2007

[14] H Matsumiya T Kogaki M Iida and K Kieda ldquoDevelopmentof a high performance airfoilrdquo Turbomachinery vol 29 no 9pp 519ndash524 2001


[15] K Imaichi Y Murakami and H Tsurusaki The Foundation ofthe Pump Design with a Personal Computer Japan IndustrialPublishing 1989

[16] ANSYS Inc ANSYS CFX-Solver Theoretical Guide 2010[17] ANSYS ANSYS CFX-Solver Modeling Guide 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



by numerical analysis In addition we propose a simpledesign method for axial flow runners in combination withthe conventional one-dimensional design method and thedesign method of axial flow velocity uniformization withthe support of three-dimensional flow analysis This designmethod can decide the unique formof the runner on the basisof the quantitative data of the velocity distributions at therunner inlet and outlet using three-dimensional flow analysisTherefore we believe that our method can provide reliableand highly efficient performance for a runner in comparisonwith the method wherein designers empirically repeat thechanges of shapes by examining the analytical results fromcomplicated three-dimensional internal flows Applying ourdesign method to the runner of an ultra-small axial flowhydraulic turbine the performance and internal flow of thedesigned runner are investigated using numerical analysisIn addition as verification we conducted an experimentusing an actual device and verified the validity of this designmethod

2 Simple Design Method forAxial Flow Runners

In this study we propose a simple design method for axialflow runners focusing on axial flow velocity uniformizationThis designmethod is a combination of the conventional one-dimensional design method [12 13] and the design methodof axial flow velocity uniformization with the support ofa three-dimensional flow analysis The design flowchartis shown in Figure 1 First a runner is designed on thebasis of the conventional one-dimensional design methodVelocity distributions at the inlet and outlet of the runner areexamined on the basis of the three-dimensional flow analysisNext the axial flow velocity uniformization is performedand the blade angle and chord length of the runner aremodified The performance of the runner is verified usingthree-dimensional flow analysis If it does not achieve thetarget performance the axial flow velocity uniformization isperformed again Through iterations of this procedure thedesign process is complete when the performance achieves itstarget We have assumed that this design method is effectivein cases wherein factors such as a low Reynolds number orcharacteristic data of the airfoil are unclear and the assumedflow by the one-dimensional designmethod strongly deviatesfrom the actual three-dimensional flowThe following are thedetails of the conventional design method [12 13] and thedesign method of axial flow velocity uniformization

21 One-Dimensional Design Method The specific speed 119899119904is calculated using the following design parameters effectivehead119867 turbine output 119871 and rotational speed 119899

119899119904 = 119899 (1198711000)1211986754 (1)

Using the specific speed 119899119904 obtained from (1) and adesign diagram [12] the circumferential velocity coefficient119896119906 hub ratio ] and the axial velocity coefficient 119896119886 arecalculated In addition the circumferential velocity 119906119905 of a tip

Yes

No

Axial flow velocity uniformization

Check velocity at runner inlet and outlet


One-dimensional design method

Check performance

Design specification

Finish the design


Design method of axial flow velocity

uniformizationH n L

Figure 1 Design flow

the outer diameter 119863119905 of a runner and the hub diameter 119863ℎare obtained with the following formulae

119906119905 = 119896119906radic2119892119867119863119905 = 60119906119905120587119899 ] = 119863ℎ119863119905

(2)

Furthermore the axial component V119886 of the absolutevelocity and the flow rate 119876 are obtained with the followingformulae

V119886 = 119896119886radic2119892119867119876 = 120587 (1 minus ]2)1198632119905 V1198864

(3)

Next dividing the blade into several parts fromhub to tipvortex design is determined Referencing specific speed 119899119904the number of blades 119911 is determined and then the pitch 119905 ateach radial point 120593 is calculated by the following expression

119905 = 120587119863119911 (4)

The velocity triangle of this runner is illustrated inFigure 2 [13] At each radial point 120593 the airfoil and attackangle 120575 are selected By estimating hydraulic efficiency 120578ℎchord length 119897 and mean relative flow angle 120573 between therunner inlet and outlet are calculated using the followingexpression [13]

119908 = V119886sin120573

120578ℎ119867 = 12119892 119897119905119862119871119906119908 (1 minus 120576 cot120573) (5)


a = a1 = a2

u = u1 = u2

12

w1

w2

w




120579 = 120573 minus 120575 (6)



119905119892 = 120587119863119892119911119892 (7)


tan120572119892 = V119886119892((V1199063 + V1199064) 2) 120579119892 = 120572119892 minus 120575119892

(8)



119862119871119892 119897119892119905119892 =2V1199064V119886119892

cos 120576119892 sin2120572119892sin (120572119892 + 120576119892) (9)



V1015840119886 = V119886119889 + (V119886119889 minus V119886119888) (10)




(11)





Guide vane

Runner

Generator

Flow703

691







Hub Mid Tip

Original




Case 1




Case 2




Case 3












Figure 5 Guide vane


195 130 130 520









0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)




0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










a = a1 = a2

u = u1 = u2

12

w1

w2

w




120579 = 120573 minus 120575 (6)



119905119892 = 120587119863119892119911119892 (7)


tan120572119892 = V119886119892((V1199063 + V1199064) 2) 120579119892 = 120572119892 minus 120575119892

(8)



119862119871119892 119897119892119905119892 =2V1199064V119886119892

cos 120576119892 sin2120572119892sin (120572119892 + 120576119892) (9)



V1015840119886 = V119886119889 + (V119886119889 minus V119886119888) (10)




(11)





Guide vane

Runner

Generator

Flow703

691







Hub Mid Tip

Original




Case 1




Case 2




Case 3












Figure 5 Guide vane


195 130 130 520









0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)




0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Guide vane

Runner

Generator

Flow703

691







Hub Mid Tip

Original




Case 1




Case 2




Case 3












Figure 5 Guide vane


195 130 130 520









0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)




0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Figure 5 Guide vane


195 130 130 520









0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)




0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Case 3Design value

L(W

)

n (minminus1)

(a) Turbine output


Case 3Design value

00

05

10

15

20

25

30

35

0 1000 2000 3000 4000 5000

H(m

)

n (minminus1)

(b) Effective head


Case 3Design value

040

045

050

055

060

065

070

075

080

0 1000 2000 3000 4000 5000

(mdash

)

n (minminus1)




0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a1 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)

u1 (ms)


Case 3Design value










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0001020304050607080910

00 10 20 30 40 50 60 70

(mdash

)

a2 (ms)


Case 3Design value

(a) Axial component

0001020304050607080910

00 10 20 30 40 50

(mdash

)



Case 3Design value






119871 = 212058711989911987960 (12)

Motor

Test turbine

Tachometer

Tank

Torque meter

Pressure taps

Flow meter

Valve Pump







119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119867 = 119875119894 minus 119875119900120588119892 + V1198942 minus V119900

2

2119892 (13)



120578 = 119871120588119892119876119867 (14)

Inlet

Outlet

Guide vane

Runner

1382 5528

1406

2109






020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










020406080

100120140160180

0 1000 2000 3000 4000 5000


n (minminus1)

L(W

)

(a) Turbine output

00

05

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000


n (minminus1)

H(m

)

(b) Effective head

04

05

06

07

08

09

0 1000 2000 3000 4000 5000


n (minminus1)

(mdash

)








40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










40

20

00

(m

s)

(a) Original

40

20

00

(m

s)

(b) Case 2


10

00

20

30

40

(m

s)

(a) Original

10

00

20

30

40

(m

s)

(b) Case 2




7 Conclusions






Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Nomenclature


Greek Letters




Competing Interests


Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article the design method of axial flow...

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