Research Article Flow Pattern Analysis and Performance...

Research ArticleFlow Pattern Analysis and Performance Improvement ofRegenerative Flow Pump Using Blade Geometry Modification

J Nejadrajabali A Riasi and S A Nourbakhsh

Department of Mechanical Engineering University of Tehran PO Box 115554563 Tehran 14174 66191 Iran

Correspondence should be addressed to A Riasi ariasiutacir

Received 24 December 2015 Revised 24 January 2016 Accepted 26 January 2016

Academic Editor Tariq Iqbal

Copyright copy 2016 J Nejadrajabali 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

Regenerative pump is a low specific speed and rotor-dynamic turbomachine capable of developing high heads at low flow ratesIn this paper a numerical study has been carried out in order to investigate the effect of blade angle on the performance of aregenerative pump Two groups of impellers were employed The first type has symmetric angle blades with identical inletoutletangles of plusmn10∘ plusmn30∘ and plusmn50∘ and the second group has nonsymmetric angle blades in which the inlet angle was set to 0∘ andsix different angles of plusmn10∘ plusmn30∘ and plusmn50∘ were designed for the outlet of the blades A total of 12 impellers as well as primaryradial blades impeller were investigated in this studyThe results showed that all forward blades have higher head coefficients thanradial blades impeller at design flow coefficient It was found that regenerative pumps with symmetric angle forward blades havebetter performance than other types Also it is worth mentioning that the highest head coefficient and efficiency occur at angle+10 lt 120573 lt +30 of symmetric angle blades It was found that the maximum efficiency occurs at angle of +155∘ by curve fitting tothe data obtained from numerical simulations for symmetric angle forward blades

1 Introduction

Regenerative flow pumps are placed in the category of dyna-mic pumps The ability to produce high heads at low flowrates is the main characteristic of these pumps The specificspeed of regenerative pumps is very low and they share someof the characteristics of positive displacement pumps withoutany wear and lubrication problems The fluid in regenerativepump moves spirally in flow channel and reenters the bladesof impeller several times in its peripheral path from inlet tooutlet Because of this repetitive treatment of impeller bladingon fluid regenerative pumps have the ability to generate ahead equivalent to that of several centrifugal stages with com-parable tip speeds The regenerative pumps are less likely tocause cavitation because of its smaller pressure gradient thancentrifugal pumps Therefore regenerative pumps typicallyrequire lower net positive suction head than centrifugalpumps [1] Typically regenerative pumps have a disadvantageof having a low hydraulic efficiency (between 30 and 50)

Regenerative pumps have found applications in manyindustrial areas which require high heads at low flow ratesincluding automotive and aerospace fuel pumping booster

systems water supply agricultural industries shipping andmining and chemical and food processing systems [2]

In 1955 Wilson et al offered a mathematical analysisfor regenerative pumps with radial blades that have alreadybeen used They considered helical flow and made variousallowances for losses and provided experimental corrob-orations of their results The calculated and experimentalperformance curves were compared and excellent agreementwas observed [3] Song et al modified Wilsonrsquos theory Theyintroduced loss models in a manner that does not requireempirical coefficients and experimental results But their ana-lysis was just accurate at design point [4] Yoo et al in 2005presented equations to calculate the geometry of rotatingflows They attempted to develop an improved mathematicalmodel to suggest systematic methods to find the circulatoryflow rate mean inlet and outlet radii of the impeller andslip factor [1] Based on this improved momentum exchangetheory they studied the design of a regenerative flow pumpfor artificial heart pump application [5]Thesemodels requireexperimental support to determine a number of empiricalcoefficients in the proposedmodels In particular these mod-els do not take account of the influence of blade angle on the

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 8628467 16 pageshttpdxdoiorg10115520168628467

2 International Journal of Rotating Machinery

performance and hence they have limited applicability as adesign tool [6]

There are few articles that studied the effect of geometricvariables of the regenerative pumps Shimosaka andYamazakistudied the changes in the number of blades clearance andchannel area in a regenerative pump In the experiments theflow channel was fixed and in each test change in one param-eter was examined They introduced a parameter namedldquocharacteristic dimension of flow channelrdquo to define thelimit value for clearance and channel area Another param-eter called ldquowidth ratio of vanerdquo was applied to determinenumber of blades [7] Yamazaki and Tomita studied regen-erative pumps with nonradial blades with different sidechannel areas They proposed some correlation coefficientsand empirical equations for efficiency torque and headcoefficient as functions of Reynolds number blade angle sidechannel area and flow coefficient [8ndash10] Grabow studied theeffects of the blade angle for both radial and semicircularblades He tested the pump in both cases with different bladeangles in the range of plusmn60∘ He found from the theoreticalstudy that the optimum shut-off head was reached for theblade angle in the range of 40∘ndash55∘ but the experimentalresults showed the optimal blade angle in the range of 40∘ndash45∘[11] Sixsmith andAltmann studied the regenerative compres-sor with airfoil blades They added a core in the flow channelto direct the circulating flow together with the provision ofairfoil blades It resulted in significant improvements in theperformance They found that the airfoil blades producedmore pressure rise than any other blade shapes [12] Badamiinvestigated the effect of clearances number of blades bladeangles and channel area on the performance of regenerativepumps He presented a newmodel of regenerative pumpwithaxial inlet and outlet port [13] Choi et al carried out anexperimental study to investigate the influence of blade angleon the performance of regenerative pump The influenceof the impeller blade angle and its shape on regenerativepump performance has been experimentally investigatedStraight blades with inclined blade angles of 0∘ plusmn15∘ plusmn30∘and plusmn45∘ were tested In addition radial chevron impellerswith chevron angles of 15∘ 30∘ and 45∘ were also includedin their experiments It was found that the head and theefficiency strongly depend on the blade angles as well as theblade geometry Among all blade configurations tested inthis study the chevron blade exhibited the highest head withreasonably good efficiencyThe results showed that there wasan optimum chevron angle of around 30∘ [6]

In recent years computational fluid dynamics (CFD) hasbeen widely used for the analysis of fluid flow in turboma-chinery But the number of articles in the field of numericalmethods for the study of flow in the regenerative turboma-chines is very low

Meakhail et al in 2003 used CFX software to study theswirling flow in a regenerative pump with radial blades Theyfound that in addition to the tip of blades the flow exits fromthe side edge [14] Teshome and Dribsa used a commercialcode to investigate the effect of aerodynamic blades on theperformance of regenerative pump They extracted the per-formance curves for pump from CFD simulations Theyfound out that significant improvement of performance has

been obtained in using aerodynamic blades with semiellipticprofile [2] Quail et al used FLUENT software to investigatethe fluid flow in a regenerative pump The results of CFDsimulations were validated by the experimental data Theyalso used a novel method of manufacturing to evaluate theeffect of change in blade geometry on the efficiency of pump[15 16] Vasudeva Karanth et al used CFD analysis in order toenhance the performance of regenerative pump It was seenas a significant effect on the pump performance by varyingthe number of blades and changing the geometry of theinlet and outlet passage of the regenerative pump [17] Maityet al used CFD to study regenerative pumps They foundout that a curvature in the outlet flow domain increases thenet pressure head by minimizing the vortex flow Also thesemicircular static fluid on the sides of the impeller enhancesthe circulatory fluidmotion thereby increasing the efficiencyof the pump Positioning of the blades on either side of theimpeller by offsetting enhances the fluidmotion and results inthe net increase in static and net pressure head The differentnumber of impeller vanes on either side of impeller will alsocontribute to the increase in net pressure head [18]

In this paper a numerical study has been carried outin order to investigate the effect of blade angle on the per-formance of a regenerative pump Also an analysis of flowpattern in regenerative pump at different flow coefficientswas done The objective of this work is to improve the per-formance of regenerative pumps by modifications of bladesgeometry Two types of impeller were designed The first onehas symmetric angle blades and the second onewith nonsym-metric angle blades The blades inlet and outlet of the firstgroup were designed in six different angles of plusmn10∘ plusmn30∘ andplusmn50∘ For the second group the inlet angle was set to 0∘ and sixdifferent angles of plusmn10∘ plusmn30∘ and plusmn50∘ were designed for theoutlet of the blades The results of CFD were validated withexperimental results of a regenerative pump The results ofnumerical investigation are used to improve the performanceof regenerative pump

2 Experiments

21 Specifics of Regenerative Pump Components of theregenerative pump are shown in Figure 1 Typically a regener-ative pump consists of an impeller with blades at its peripheryinlet port discharge port stripper to isolate the high-pressuredischarge from the low-pressure inlet flowpassage and a cas-ingThemain geometric parameters of the tested regenerativepump are presented in Table 1 and Figure 2

22 Experiments Apparatus and Procedure Figure 3 showsthe arrangement of test rig A reservoir tank with the capacityof 200 liters was employed in order to store and ultimatelyreceive water A control valve was installed in the return lineto the reservoir tank to adjust the flow rate The flow rate wasmeasured using a rotameter which was calibrated Results ofcalibration test are presented in Table 2

The pump was driven by a 500-watt induction motoroperating at a constant speed of 2900 rpm A watt meter isused to measure the power consumption of the electropump

International Journal of Rotating Machinery 3

Casing

ImpellerInlet portStripper Outlet port

Figure 1 Schematic of the regenerative pump

Table 1 Geometric specifications of regenerative pump

Parameters Unit ValueNumber of blades in each side119873 mdash 36Tip radius of casing 119903

119878

(mm) 36Tip radius of blade 119903

119879

(mm) 325Hub radius of blade 119903

119867

(mm) 235Height of blade ℎ (mm) 9Width of the blade 119887 (mm) 31Width of the channel 119889 (mm) 43Angle of stripper 120579

119904

(∘) 16Blade angle 120573 (∘) 0 plusmn10 plusmn30 plusmn50

Table 2 Results of calibration test for rotameter

Rotameter flowrate (litmin)

Calibration(litmin) Correction coefficient

40 39999 099935 35145 100430 29849 099525 24064 096320 19842 099215 15291 101910 11100 1110

The performance curve of the electromotor is shown in Fig-ure 4 which was obtained using a dynamometer separately

The angular speed was measured using a proximity sen-sor The inlet and outlet pressures were measured using twoanalog pressure gauges

The uncertainty in the measurement of flow rate wasabout plusmn3 And the pressures weremeasured with the uncer-tainty of plusmn1

3 Numerical Simulation andModel Description

The commercial software CFX-13 was used to solve the fullthree-dimensional Reynolds-averaged Navier-Stokes equa-tions in this numerical study The basic tool required for the

b d

h

Impeller

Casing

rH rT rS

A0

Figure 2 Regenerative pump geometric parameters

derivation of the RANS equations from the instantaneousNavier-Stokes equations is the Reynolds decompositionReynolds decomposition refers to separation of the flowvariable (like velocity 119906) into the mean (time-averaged) com-ponent (119906) and the fluctuating component (1199061015840) The Navier-Stokes equations of motion for an incompressible Newtonianfluid expressed in tensor notation are as follows

120597119906119894

120597119909119894

= 0

120597119906119894

120597119905

+ 119906119895

120597119906119894

120597119909119895

+ 1199061015840

119895

1205971199061015840

119894

120597119909119895

= 119891119894

minus1

120588

120597119901

120597119909119894

+ V1205972

119906119894

120597119909119895120597119909119894

(1)

where 119891119894is a vector representing external forces Using the

equation of conservation of mass with slight variationsmomentum equation becomes as follows

120588120597119906119894

120597119905

+ 120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (2)

where 119878119894119895= (12)(120597119906

119894120597119909119895+ 120597119906119895120597119909119894) is the mean rate of

strain tensor Finally since integration in time removes thetime dependence of the resultant terms the time derivativemust be eliminated leaving

120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (3)

The solver was a 3D CFD code The governing equationsare discretized using the finite element finite volume methodin this code To achieve high accuracy the high resolutionscheme was applied for discretization of momentum equa-tion pressure turbulent kinetic energy and turbulent dissi-pation rate

For grid generation the computing space is divided intotwo parts consisting of flow channel and impeller The 3Dmodels of them were generated and meshed separately Sincegenerating mesh for whole impeller causes a lack of precise


Electromotor

Watt meter

Reservoir tank

Flow

met

er

Globe valve

Regenerative pump

Rota

met

er

Gate valve

P1

P2

Figure 3 Schematic of regenerative pump test rig

01020304050607080

Effici

ency

P1 (W)

150

200

250

300

350

400

450

500

550

600

650

700

750

800

Figure 4 Performance curve of electromotor (efficiency versus power consumption)

control and prolongs the grid generation one blade fromeach side of impeller was selected for grid generation Finallythis part was rotated 35 times to have a complete impellerDuring mesh generation orthogonal quality skewness andaspect ratio are assured to be in desirable range Skewnesswas held below 09 and aspect ratios of greater than 5 1were not applied Hexahedral cells were used for importantregions with curvature and strong gradients and tetrahedralcells for other regions Figure 5 shows the generated grids forthe blades and flow channel Due to existence of intensivegradients in blades region and also complex spiral flowpattern in them structured grids were used for the regionbetween blades Mesh clustering was applied for importantregions such as interface between flow channel and impellerExcessive expansion of cells in the direction normal to thewalls was avoided At least a few cells should be consideredinside the boundary layer and for the pump this was keptto a minimum of 5 cells Five layers were considered for theinterface between impeller and flow channel

For numerical simulation the convergence criteria wereset at maximum residuals of 1 times 10minus4 Water at 25∘C was

selected as the working fluid A constant total pressureboundary condition was applied for inlet region of pumpwhile a constantmass flow rate (normal to the boundary) wasimplemented for outlet region of flow channel

The flow channel domain was stationary and the impellerdomain was rotating at constant speed For quasi-steadysimulation the grids between impeller and flow channel areconnected by means of a frozen rotor interface In the caseof transient simulation transient rotor stator was selected forconnection between impeller and flow channel grids

As shown in Figure 6 for grid independency studieseight adapted grid sizes were assessed It was found that byincreasing the number of cells from 252 times 10

6 to 335 times 106changes in hydraulic efficiency are about 0019 and furthergrid refinement from 335 times 10

6 cells to 386 times 106 cellsdecreases the hydraulic efficiency about 0016 So gridindependence was established at around 335 times 106 cells

31 CFD Results Validation For validation of CFD resultsthe performance curve of regenerative pump obtained fromnumerical simulations was compared with the experimental


Figure 5 CFD grids of geometries

35701

40479

4166941781

42163

4174941741

41734

353637383940414243

0 1000000 2000000 3000000 4000000

Hyd

raul

ic effi

cien

cy

Number of cells

Figure 6 Hydraulic efficiency versus number of cells

data In this study three well-known turbulence models(standard 119896-120576 low-Reynolds 119896-120596 and SST) were examinedStandard 119896-120576 is a high-Re turbulence model that is able topredict inviscid flow regime properly So this model needswall function approximation to solve viscous region nearwalls The low-Re 119896-120596 turbulence model could be used forentire flow region even near walls The low-Re 119896-120596 modelwould typically require a near wall resolution of 119910+ lt 2 Inturbomachinery flows even119910+ lt 2 cannot be guaranteed andfor this reason a new near wall treatment was developed forthe 119896-120596models It allows for smooth shift from 119896-120596model to awall function formulation regarding local 119910+ value [19] TheSST turbulence model combines the 119896-120596 turbulence modeland 119896-120576 turbulence model such that 119896-120596 is used in the innerregion of the boundary layer and switches to 119896-120576 in the freeshear flow

Since the regenerative pump complies with the sameaffinity laws as centrifugal and axial pumps the performancecurves are presented using dimensionless flow coefficient (120601)head coefficient (120595) and efficiency (120578) which is defined as theratio between the hydraulic power transferred to the workingfluid and the mechanical power (119875) introduced into thesystemby the impeller Pumpcharacteristic flow head power

and efficiency coefficients can be expressed in conventionaldimensionless terms (4)ndash(7) [6]

120595 =119892119867

1198802

119892

(4)

120601 =119876

119860119900119880119892

(5)

120591 =119875

1205881198601199001198803

119892

(6)

120578 =120588119876119892119867

119875

=120601120595

120591

(7)

The performance curves of numerical simulationsobtained from three turbulence models are compared withthe experimental data in Figure 7

As it can be seen in Figure 7(a) the 119896-120596 turbulencemodelhas better agreement with experimental data than 119896-120576 andSST turbulence models However because of very complexflow in regenerative pump at low flow coefficients the levelof agreement with the measured data is not as close as thosefor higher flow coefficients Although all three turbulence


005

115

225

335

445

5

0 01 02 03 04 05 06Flow coefficient (120601)

Hea

d co

effici

ent(120595)

Experiment SSTk-120596 k-120576

(a) Head coefficient versus flow coefficient

05

101520253035404550

0 01 02 03 04 05 06

Effici

ency

Flow coefficient (120601)


(b) Efficiency versus flow coefficient

Figure 7 Comparison of regenerative pump performance curves obtained from numerical simulations with experimental data

minus300minus250minus200minus150minus100minus50

050

100150200250300

Hyd

raul

ic effi

cien

cy

Accumulated time step

TransientSteady state

(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)

Figure 8 Variations in hydraulic efficiency of the pump and torque on impeller during accumulated time steps

models have good trends in high flow coefficients results ofCFD simulations showed that unlike 119896-120596 turbulence modelthe 119896-120576 and SST turbulence models were not acceptablefor prediction of the performance of regenerative pumps atlower flow coefficients So the 119896-120596 turbulence model withautomatic near wall treatments was carried out for numericalstudy The low-Reynolds 119896-120596 turbulence model is developedbyWilcox [20]The kinematic eddy viscosity is obtained fromthe following equation

120592119905=119896

120596

(8)

The evolution of 119896 and 120596 is modelled with two transportequations

120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)

where constants 120573 1205731015840 120590119896 120590120596 and 120572 are presented in Table 3

Table 3 Constants for the low-Reynolds 119896-120596 turbulence model

120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results

41 Analysis of Flow Pattern in Regenerative Pump Accord-ing to results of other researchers steady-state approximationfor numerical simulations of regenerative pumps wouldrepresent good results [15 16] But since the nature of theflow in regenerative pump is unsteady a transient simulationwas accomplished just for main geometry of the pump toevaluate the results of quasi-steady simulationsThe time stepselected to update the relative position between impeller andcasing is 568119890 minus 05 This time step provides 1∘ rotation of therotor between iterations at rotational speed of 2900 rpmThenumerical solutions were carried out until the transient fluc-tuations of the flow variables became periodic About threecomplete rotations of impeller are required to achieve conver-gence Figures 8(a) and 8(b) show the variations in hydraulic


120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12

Figure 9 Fluid particle path lines at four different flow coefficients

minus04minus02

002040608

112

0 02 04 06 08 1Fluid particle path

PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12

Figure 10 Comparison of pressure variation along a particle path line for four flow coefficients

efficiency of the pump and torque on impeller during accu-mulated time steps for steady and transient numerical sim-ulations at design point As it can be seen the differencebetween the final results is not considerable The differencebetween the hydraulic efficiencies and torques obtained fromthese two methods is about 26 and 17 respectively Sothe results obtained from quasi-steady simulations would bereliable Since the unsteady simulations are time-consumingand due to high number of simulations in this study the flowin regenerative pump was assumed steady state and validatedwith experimental results as mentioned before

Figure 9 shows the fluid particle path line in regenerativepump for four flow coefficients As it can be seen the numberof rotations of fluid increases by reduction in flow coefficientPressure variation along a streamline at design point (120601

119899) and

three other flow coefficients is shown in Figure 10As it can be seen in Figure 10 there are some fluctuations

in the curves that increase with reduction in flow coefficientThenumber of fluctuations in these curves indicates the num-ber of rotations of fluid in regenerative pumpThe minimumpoints in fluctuations of the curves in Figure 10 are related toentry of blades and the maximum ones are related to exit ofblades The head of pump decreases during passing throughthe channel of the pump because of rotational losses It can beseen that by reducing flow coefficient while increasing the

number of fluid rotations (Figure 9) in the pump the head ofpump increases The growth in pressure by reduction of flowcoefficient is also shown in pressure contours of Figure 11Thegradual growth in pressure is clearly obvious in these pressurecontours (Figure 11)

The space between inlet and outlet regions of casing isoccupied with stripper to separate low-pressure inlet fromhigh-pressure outlet The stripper helps the fluid to go outfrom discharge port But despite the existence of stripperthe amount of high-pressure fluid trapped between bladescollides with the low-pressure fluid at inlet region of pumpSo there is a loss at the inlet port of regenerative pump As canbe seen in Figure 10 there is a pressure drop at the beginningof the curves

Figure 12 indicates the velocity distribution along the fluidparticle path for different flow coefficients

The amplitude of fluctuations of velocity curves reducesby reduction in flow coefficient Figure 13 shows the velocitycontours at design flow coefficient The vortex at the inletregion because of mixture of high-pressure outlet with low-pressure inlet is obvious in Figure 13

Two groups of impellers were employed in this study toinvestigate the effects of blade geometry modifications onthe performance of a regenerative pump The first type hassymmetric angle blades and the second group nonsymmetric


PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12

Figure 11 Pressure contours at 120601120601119899

= 06 120601120601119899

= 1 and 120601120601119899

= 12

Table 4 Definition of symmetric and nonsymmetric angle blades

(1) Symmetric angle blades 1205731

= 1205732

= 120573 = plusmn10 plusmn30 plusmn50(2) Nonsymmetric angle blades 120573

1

= 0 and 1205732

= plusmn10 plusmn30 plusmn50

angle blades The results obtained for these two groups ofblades are presented and discussed

42 Effect of Blade Geometry Modification As presented inTable 4 and shown in Figure 14 the first group is namedsymmetric angle blades which have identical inletoutletangle And the second group is nonsymmetric angle bladesIn this group the inlet angle is constant and set to 0∘

A total of 12 impellers as well as primary radial bladesimpeller consist of symmetric forward blades (120573

1= 1205732=

+10∘

+30∘

+50∘) symmetric backward blades (120573

1= 1205732=

minus10∘

minus30∘

minus50∘) nonsymmetric forward blades (120573

2=

+10∘

+30∘

+50∘) and nonsymmetric backward blades (120573

2=

minus10∘

minus30∘

minus50∘) which were investigated in this numerical

study

The blade angle 120573 is defined as shown in Figure 14 Thepositive sign of 120573 represents the forward blade and the neg-ative sign indicates backward blade The 3D geometries andschematics of impellers are shown in Figure 15

As mentioned before the regenerative pumps have con-formance with the affinity laws So the flow coefficient (120601)and the head coefficient (120595) and also hydraulic efficiency (120578)defined by (4) (5) and (7) were applied for presenting thecharacteristic curves of the pump

Figure 16 shows the performance curves 120595 versus 120601 forradial blade forward and backward symmetric angle bladeand also forward and backward nonsymmetric angle bladeimpellers

As it can be seen in the case of symmetric angle withbackward blades the heads of pump are lower than those ofradial blades impeller But the condition for the case of sym-metric angle with forward blades is different It is observedthat the head coefficients are increased at blades angle of+10∘ and +30∘ and reduced at angle of +50∘ So there is anoptimum angle in this range Generally it is obvious thatincreasing 120573 or in other words forwarding blades in cen-trifugal turbomachines augments the Eulerian head But in


0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)

Figure 12 Velocity distribution along fluid particle path (a) 120601120601119899

= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12

regenerative pumps the number of crock-screw circulationsbetween blades and channel is an important parameter whichcan affect the total head By increasing 120573 the number ofcrock-screw rotations will decrease because of the fastermovement of fluid in the side channel So the outcome ofthese two parameters will affect the final total head

It can be seen in Figure 16(b) that in both cases of secondgroup blades the head coefficients are reduced by increasingthe absolute value of 120573 However at angles of 120573

2= plusmn10

∘ forflow coefficients higher than 035 it is observed that thereare not any considerable differences relative to those of radialblades in the head coefficients Both cases of nonsymmetricangle blades have not better performance than radial bladesimpeller But it is obvious that the performance of backwardblades is better than forward ones at lower flow coefficientsAt shut-off condition (120601 = 0) the head coefficient ofnonsymmetric angle forward blade with 120573

2= +30

∘ is about275 while at the same condition the head coefficient forbackward blade with 120573

2= minus30

∘ is about 325 Also for 1205732=

+50∘ and 120573

2= minus50

∘ the head coefficients are respectivelyequal to 18 and 225 at shut-off condition

The comparison of efficiency curves is shown in Figure 17It is worth noting that the best efficiency point of theregenerative pump with radial blades impeller is found at120601119899= 047 with about 425 As it can be seen in Figure 17(a)

there is not any considerable change in efficiency at 120601 lt 035for the case of forward blades It is observed that at designflow coefficient (120601

119899= 047) the maximum efficiency of

the 10∘ forward blades is about 447 which is about 22

higher than that of radial blades The maximum efficiencyfor the case of 30∘ forward blades is about 1 higher thanbest efficiency of radial blades But by increasing 120573 to 50∘the maximum efficiency is decreased about 3 In the caseof backward blades at angle of minus10∘ there is not significantchange in efficiency curves relative to radial blades But itseems that in the range of 03 lt 120601 lt 045 the radial bladeshave better efficiencyWith decreasing120573 the efficiency curvesdecline except at very low flow coefficients A significantfalling is observed at angle of minus50∘ And it was seen that thebest efficiency point is changed at angle of minus50∘

For nonsymmetric angle blades as it can be seen inFigure 17(b) at angle of +10∘ forward case there is not anysignificant change in efficiency curve relative to that of radialblades in whole range of flow coefficients It was found thatthemore the blades angle120573 increases themore the efficienciesdecrease The same conditions occur for nonsymmetricbackward blades The efficiency curve at angle of minus10∘ isalmost coincident on that of radial blades By decreasing 120573 tominus30∘ the efficiency decreases in whole range of flow ratesThesame as symmetric angle backward blades the best efficiencypoint is shifted to lower flow coefficient at angle of minus50∘ andalso a significant falling is observed

For better comparison between these types of blades andeffect of changing angles on the performance of regenerativepump Figure 18 is drawn

It is obvious from Figure 18 that symmetric angle withforward blades has better performance than nonsymmetricangle blades It is observed that the performance of both


Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00

Figure 13 Velocity contour at design flow coefficient

symmetric and nonsymmetric angle with backward blades isthe same at 120601120601

119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12

nonsymmetric angle blades have higher head coefficientsAlso it should be noted that the highest head coefficientoccurs at angle +10 lt 120573 lt +30 of symmetric angle bladesSo there is an optimum angle in this range of 120573 Figure 19 isdrawn to compare the effect of the blades angle on efficiencyat design flow coefficient As it is observed symmetric angleblades have better efficiency than radial blades at angles ofplusmn10∘ and +30∘ or in other words the curve exhibits thatfor minus10 lt 120573 lt +40 the symmetric angle blades havehigher efficiency relative to radial blades In the case ofnonsymmetric angle blades it was found that only the bladesangle between 0 and about 10∘ has better efficiency than radialblades But a significant improvement is not observed

Results at design flow coefficient for all blades are pre-sented in Table 5

Generally it was found out from curves of Figures 18 and19 that regenerative pumps with symmetric angle forward

blades have better performance than other types As can beseen in Figure 20 a polynomial curve was fitted to the dataobtained from numerical simulations to find the angle whichhas the best efficiencyThemaximum efficiency takes place atangle of +155∘ as shown in Figure 20

5 Conclusions

In this study a numerical investigation has been carried out inorder to study the effect of blade angle on the performance ofa regenerative pumpA total of 12 impellers aswell as primaryradial blades impeller consist of symmetric forward andbackward blades (120573

1= 1205732= 120573 = plusmn10

∘

plusmn30∘

plusmn50∘) nonsym-

metric forward and backward blades (1205732= plusmn10

∘

plusmn30∘

plusmn50∘)

which were investigated in this numerical study The resultsshowed that in the case of symmetric angle with backwardblades the head coefficients of the pump are lower thanthose of radial blades impeller It is observed in the caseof symmetric angle with forward blades that the head


Rotation direction (forward blades)

1205731

1205732

Rotation direction (backward blades)

1205731

1205732

(a) Symmetric blades


1205732


1205732

(b) Nonsymmetric blades

Figure 14 Schematic of blades (a) symmetric blades and (b) nonsymmetric blades

coefficients are increased at blades angle of +10∘ and +30∘and reduced at angle of +50∘ relative to radial blades Bothcases (backwardforward) of nonsymmetric angle bladeshave not better performance than radial blades impellerResults showed that for symmetric angle blades there arenot any significant changes in efficiency at 120601 lt 035 for thecase of forward blades Also the maximum efficiency of the10∘ symmetric angle forward blades is about 447 whichis about 22 higher than that of radial blades In the caseof symmetric angle backward blades with decreasing 120573 theefficiency curves decline except at very low flow coefficients

For nonsymmetric angle blades at angles of plusmn10∘ there arenot any significant changes in efficiency curves relative to thatof radial blades in whole range of flow coefficients Generallyit was found that regenerative pumps with symmetric angleforward blades have better performance than other typesAlso it should be noted that the highest head coefficientoccurs at angle +10 lt 120573 lt +30 of symmetric angle bladesTo obtain the angle which has the best efficiency a polyno-mial curve was fitted to the data obtained from numericalsimulations for symmetric angle forward blades It was foundthat the maximum efficiency occurs at angle of +155∘


Forbackward 12057312 = plusmn10 Forbackward 12057312 = plusmn30 Forbackward 12057312 = plusmn50



(b) Nonsymmetric blades (1205731= 0

∘)

Figure 15 Geometry of impellers (a) symmetric blades and (b) nonsymmetric blades

Nomenclatures

1198600 Cross section area (m2)

119887 Width of blade (mm)119889 Width of channel (mm)119891119894 External forces (N)

119892 Gravity (msminus2)119867 Pump head (m)ℎ Height of blade (mm)119896 Turbulence kinetic energy (m2sminus2)119873 Number of blades


0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601

Forward 50degForward 30deg

Forward 10degNumerical (radial blades) Numerical (radial blades)

Backward minus50degBackward minus30deg

Backward minus10deg

(a) Symmetric angle blades

0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg

(b) Nonsymmetric angle blades

Figure 16 Characteristics curves of the regenerative pump (a) symmetric blades and (b) nonsymmetric blades

Table 5 Results of numerical study at design flow coefficient

Angles Efficiency Ψ (head coefficient)

Symmetric angle blades

1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044

Nonsymmetric angle blades (1205731

= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

Forward 50degForward 30degForward 10deg

Numerical (radial blades)Backward minus50deg


Numerical (radial blades)


0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






Figure 17 Efficiency curves of the regenerative pump (a) symmetric blades and (b) nonsymmetric blades

1198751 Power consumption of electromotor (watt)

119875119896 Production rate of the turbulent kineticEnergy (m2sminus3)

119901 Pressure (Pa)119876 Volume flow rate (m3sminus1)119903119904 Tip radius of casing (mm)119903119879 Tip radius of blade (mm)

119903119867 Hub radius of blade (mm)

119878119894119895 Strain rate tensor

119880119892 Tangential speed (msminus1)

119880119895 [119880 119881119882] mean velocity vector in tensornotation (msminus1)

119906119894 [119906 V 119908] instantaneous velocity vector in

tensor notation (msminus1)119906119894 [119906 V 119908] mean velocity vector in tensor

notation (msminus1)1199061015840

119894

[1199061015840

V1015840 1199081015840] fluctuating velocity vector intensor notation (msminus1)

119881 Velocity (msminus1)119881max Maximum velocity (msminus1)119909119894 [119883 119884 119885] Cartesian coordinates in tensor

notation (m)119910+ Exp[(119906+ minus 55)25] distance from the wall

(nondimensional)


0

05

1

15

2

25

minus50 minus30 minus10 10 30 50

Backward ForwardRadial

120595

120573

Symmetric bladesNonsymmetric blades

120601120601n = 12

120601120601n = 10

120601120601n = 07

Figure 18 Comparison of head coefficients between all types ofimpellers with different blade angles at 120601120601

119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial

minus50 minus30 minus10

Figure 19 Comparison of efficiency between types of impeller atdesign flow coefficient

Greek Symbols

120572 120573 1205731015840

120590119896 120590120596 119896-120596 turbulence model coefficients

120573 Blade angle (∘)120576 Dissipation rate (m2sminus3)120578 Hydraulic efficiency

40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419

Figure 20 Curve fitting to the data of symmetric angle forwardblades at design flow coefficient

120579119904 Stripper angle (∘)

120588 Density (kgmminus3)120592 Kinematic viscosity (m2sminus1)120592119905 Kinematic turbulent viscosity (m2sminus1)

120583 Dynamic viscosity (kgmminus1sminus1)120601 Flow coefficient120601119899 Flow coefficient at design point

120595 Head coefficient120591 Power coefficient120596 Specific dissipation rate

Conflict of Interests

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

References

[1] I S Yoo M R Park and M K Chung ldquoImproved momentumexchange theory for incompressible regenerative turboma-chinesrdquo Proceedings of the Institution of Mechanical EngineersPart A Journal of Power and Energy vol 219 no 7 Article IDA09704 pp 567ndash581 2005

[2] Y Teshome and E Dribsa CFD study of the performance ofregenerative flow pump (RFP) with aerodynamic blade geometry[MS thesis] University of Addis Ababa Addis Ababa Ethiopia2007

[3] W A Wilson M A Santalo and J A Oelrich ldquoA theory of thefluid dynamic mechanism of regenerative pumpsrdquo Transactionsof ASME vol 77 pp 1303ndash1316 1955

[4] JW Song A Engeda andM K Chung ldquoAmodified theory forthe flowmechanism in a regenerative flowpumprdquoProceedings ofthe Institution of Mechanical Engineers Part A Journal of Powerand Energy vol 217 no 3 pp 311ndash322 2003

[5] I S Yoo M R Park and M K Chung ldquoHydraulic design ofa regenerative flow pump for an artificial heart pumprdquo Proceed-ings of the Institution ofMechanical Engineers A Journal of Powerand Energy vol 220 no 7 pp 699ndash706 2006

[6] W C Choi I S Yoo M R Park and M K Chung ldquoExper-imental study on the effect of blade angle on regenerativepump performancerdquo Proceedings of the Institution ofMechanical


Engineers Part A Journal of Power and Energy vol 227 no 5 pp585ndash592 2013

[7] M Shimosaka and S Yamazaki ldquoResearch on the characteristicsof regenerative pump 1st report influences of flow channel andimpellerrdquo Bulletin of JSME vol 3 no 10 pp 185ndash190 1960

[8] S Yamazaki andY Tomita ldquoResearch on the performance of theregenerative pump with non-radial vanesrdquo Bulletin of the JSMEvol 14 no 77 pp 1178ndash1186 1971

[9] S Yamazaki Y Tomita and T Sasahara ldquoResearch on theperformance of the regenerative pump with nonradial vanesrdquoBulletin of the JSME vol 15 no 81 pp 337ndash343 1972

[10] Y Tomita S Yamazaki and T Sasahara ldquoThe scale effect anddesign method of the regenerative pump with nonradial vanesrdquoBulletin of the JSME vol 16 no 98 pp 1176ndash1183 1973

[11] G Grabow ldquoInfluence of the number of vanes and vane angleon the suction behaviour of regenerative pumpsrdquo in Proceedingsof the 5th Conference on Fluid Machinery vol 1 pp 351ndash364Budapest Hungry September 1975

[12] H Sixsmith and H Altmann ldquoA regenerative compressorrdquoJournal of Engineering for Industry vol 99 no 3 pp 637ndash6471977

[13] M Badami ldquoTheoretical and experimental analysis of tradi-tional and new periphery pumpsrdquo SAE Technical Paper Series971074 1997

[14] T Meakhail O P Seung D A Lee and S Mikhail ldquoA studyof circulating flow in regenerative pumprdquo in Proceedings of theKSAS 1st International Session pp 19ndash26 Gyeongju Republic ofKorea 2003

[15] F Quail T Scanlon and M Stickland ldquoDesign optimisation ofa regenerative pump using numerical and experimental tech-niquesrdquo International Journal of Numerical Methods for Heat ampFluid Flow vol 21 no 1 pp 95ndash111 2011

[16] F J Quail T H Scanlon and A Baumgartner ldquoDesignstudy of a regenerative pump using one-dimensional andthree-dimensional numerical techniquesrdquo European Journal ofMechanics BFluids vol 31 no 1 pp 181ndash187 2012

[17] K Vasudeva Karanth M S Manjunath S Kumar and NYagnesh Sharma ldquoNumerical study of a self priming regener-ative pump for improved performance using geometric mod-ificationsrdquo International Journal of Current Engineering andTechnology vol 5 no 1 pp 104ndash109 2015

[18] A Maity V Chandrashekharan and M W Afzal ldquoExperi-mental and numerical investigation of regenerative centrifugalpump using CFD for performance enhancementrdquo InternationalJournal of Current Engineering and Technology vol 5 no 4 pp2898ndash2903 2015

[19] H Alemi S A NourbakhshM Raisee andA F Najafi ldquoEffectsof volute curvature on performance of a low specific-speedcentrifugal pump at design and off-design conditionsrdquo Journalof Turbomachinery vol 137 no 4 pp 041009-1ndash041009-10 2015

[20] DCWilcox ldquoMultiscalemodel for turbulent flowsrdquo inProceed-ings of the AIAA 24th Aerospace Sciences Meeting AIAA Paperno 86-0029 Reno Nev USA January 1986

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



performance and hence they have limited applicability as adesign tool [6]

There are few articles that studied the effect of geometricvariables of the regenerative pumps Shimosaka andYamazakistudied the changes in the number of blades clearance andchannel area in a regenerative pump In the experiments theflow channel was fixed and in each test change in one param-eter was examined They introduced a parameter namedldquocharacteristic dimension of flow channelrdquo to define thelimit value for clearance and channel area Another param-eter called ldquowidth ratio of vanerdquo was applied to determinenumber of blades [7] Yamazaki and Tomita studied regen-erative pumps with nonradial blades with different sidechannel areas They proposed some correlation coefficientsand empirical equations for efficiency torque and headcoefficient as functions of Reynolds number blade angle sidechannel area and flow coefficient [8ndash10] Grabow studied theeffects of the blade angle for both radial and semicircularblades He tested the pump in both cases with different bladeangles in the range of plusmn60∘ He found from the theoreticalstudy that the optimum shut-off head was reached for theblade angle in the range of 40∘ndash55∘ but the experimentalresults showed the optimal blade angle in the range of 40∘ndash45∘[11] Sixsmith andAltmann studied the regenerative compres-sor with airfoil blades They added a core in the flow channelto direct the circulating flow together with the provision ofairfoil blades It resulted in significant improvements in theperformance They found that the airfoil blades producedmore pressure rise than any other blade shapes [12] Badamiinvestigated the effect of clearances number of blades bladeangles and channel area on the performance of regenerativepumps He presented a newmodel of regenerative pumpwithaxial inlet and outlet port [13] Choi et al carried out anexperimental study to investigate the influence of blade angleon the performance of regenerative pump The influenceof the impeller blade angle and its shape on regenerativepump performance has been experimentally investigatedStraight blades with inclined blade angles of 0∘ plusmn15∘ plusmn30∘and plusmn45∘ were tested In addition radial chevron impellerswith chevron angles of 15∘ 30∘ and 45∘ were also includedin their experiments It was found that the head and theefficiency strongly depend on the blade angles as well as theblade geometry Among all blade configurations tested inthis study the chevron blade exhibited the highest head withreasonably good efficiencyThe results showed that there wasan optimum chevron angle of around 30∘ [6]

In recent years computational fluid dynamics (CFD) hasbeen widely used for the analysis of fluid flow in turboma-chinery But the number of articles in the field of numericalmethods for the study of flow in the regenerative turboma-chines is very low

Meakhail et al in 2003 used CFX software to study theswirling flow in a regenerative pump with radial blades Theyfound that in addition to the tip of blades the flow exits fromthe side edge [14] Teshome and Dribsa used a commercialcode to investigate the effect of aerodynamic blades on theperformance of regenerative pump They extracted the per-formance curves for pump from CFD simulations Theyfound out that significant improvement of performance has

been obtained in using aerodynamic blades with semiellipticprofile [2] Quail et al used FLUENT software to investigatethe fluid flow in a regenerative pump The results of CFDsimulations were validated by the experimental data Theyalso used a novel method of manufacturing to evaluate theeffect of change in blade geometry on the efficiency of pump[15 16] Vasudeva Karanth et al used CFD analysis in order toenhance the performance of regenerative pump It was seenas a significant effect on the pump performance by varyingthe number of blades and changing the geometry of theinlet and outlet passage of the regenerative pump [17] Maityet al used CFD to study regenerative pumps They foundout that a curvature in the outlet flow domain increases thenet pressure head by minimizing the vortex flow Also thesemicircular static fluid on the sides of the impeller enhancesthe circulatory fluidmotion thereby increasing the efficiencyof the pump Positioning of the blades on either side of theimpeller by offsetting enhances the fluidmotion and results inthe net increase in static and net pressure head The differentnumber of impeller vanes on either side of impeller will alsocontribute to the increase in net pressure head [18]

In this paper a numerical study has been carried outin order to investigate the effect of blade angle on the per-formance of a regenerative pump Also an analysis of flowpattern in regenerative pump at different flow coefficientswas done The objective of this work is to improve the per-formance of regenerative pumps by modifications of bladesgeometry Two types of impeller were designed The first onehas symmetric angle blades and the second onewith nonsym-metric angle blades The blades inlet and outlet of the firstgroup were designed in six different angles of plusmn10∘ plusmn30∘ andplusmn50∘ For the second group the inlet angle was set to 0∘ and sixdifferent angles of plusmn10∘ plusmn30∘ and plusmn50∘ were designed for theoutlet of the blades The results of CFD were validated withexperimental results of a regenerative pump The results ofnumerical investigation are used to improve the performanceof regenerative pump

2 Experiments

21 Specifics of Regenerative Pump Components of theregenerative pump are shown in Figure 1 Typically a regener-ative pump consists of an impeller with blades at its peripheryinlet port discharge port stripper to isolate the high-pressuredischarge from the low-pressure inlet flowpassage and a cas-ingThemain geometric parameters of the tested regenerativepump are presented in Table 1 and Figure 2

22 Experiments Apparatus and Procedure Figure 3 showsthe arrangement of test rig A reservoir tank with the capacityof 200 liters was employed in order to store and ultimatelyreceive water A control valve was installed in the return lineto the reservoir tank to adjust the flow rate The flow rate wasmeasured using a rotameter which was calibrated Results ofcalibration test are presented in Table 2

The pump was driven by a 500-watt induction motoroperating at a constant speed of 2900 rpm A watt meter isused to measure the power consumption of the electropump


Casing





119878


119879


119867


119904





40 39999 099935 35145 100430 29849 099525 24064 096320 19842 099215 15291 101910 11100 1110






b d

h

Impeller

Casing

rH rT rS

A0



120597119906119894

120597119909119894

= 0

120597119906119894

120597119905

+ 119906119895

120597119906119894

120597119909119895

+ 1199061015840

119895

1205971199061015840

119894

120597119909119895

= 119891119894

minus1

120588

120597119901

120597119909119894

+ V1205972

119906119894

120597119909119895120597119909119894

(1)



120588120597119906119894

120597119905

+ 120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (2)

where 119878119894119895= (12)(120597119906



120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (3)




Electromotor

Watt meter

Reservoir tank

Flow

met

er

Globe valve

Regenerative pump

Rota

met

er

Gate valve

P1

P2


01020304050607080

Effici

ency

P1 (W)

150

200

250

300

350

400

450

500

550

600

650

700

750

800












35701

40479

4166941781

42163

4174941741

41734

353637383940414243

0 1000000 2000000 3000000 4000000

Hyd

raul

ic effi

cien

cy

Number of cells





120595 =119892119867

1198802

119892

(4)

120601 =119876

119860119900119880119892

(5)

120591 =119875

1205881198601199001198803

119892

(6)

120578 =120588119876119892119867

119875

=120601120595

120591

(7)




005

115

225

335

445

5


Hea

d co

effici

ent(120595)



05

101520253035404550

0 01 02 03 04 05 06

Effici

ency






050

100150200250300

Hyd

raul

ic effi

cien

cy



(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)



120592119905=119896

120596

(8)


120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)



120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results



120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Casing





119878


119879


119867


119904





40 39999 099935 35145 100430 29849 099525 24064 096320 19842 099215 15291 101910 11100 1110






b d

h

Impeller

Casing

rH rT rS

A0



120597119906119894

120597119909119894

= 0

120597119906119894

120597119905

+ 119906119895

120597119906119894

120597119909119895

+ 1199061015840

119895

1205971199061015840

119894

120597119909119895

= 119891119894

minus1

120588

120597119901

120597119909119894

+ V1205972

119906119894

120597119909119895120597119909119894

(1)



120588120597119906119894

120597119905

+ 120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (2)

where 119878119894119895= (12)(120597119906



120588119906119895

120597119906119894

120597119909119895

= 120588119891119894

+120597

120597119909119894

[minus119901120575119894119895+ 2120583119878

119894119895minus 1205881199061015840

119894

1199061015840

119895

] (3)




Electromotor

Watt meter

Reservoir tank

Flow

met

er

Globe valve

Regenerative pump

Rota

met

er

Gate valve

P1

P2


01020304050607080

Effici

ency

P1 (W)

150

200

250

300

350

400

450

500

550

600

650

700

750

800












35701

40479

4166941781

42163

4174941741

41734

353637383940414243

0 1000000 2000000 3000000 4000000

Hyd

raul

ic effi

cien

cy

Number of cells





120595 =119892119867

1198802

119892

(4)

120601 =119876

119860119900119880119892

(5)

120591 =119875

1205881198601199001198803

119892

(6)

120578 =120588119876119892119867

119875

=120601120595

120591

(7)




005

115

225

335

445

5


Hea

d co

effici

ent(120595)



05

101520253035404550

0 01 02 03 04 05 06

Effici

ency






050

100150200250300

Hyd

raul

ic effi

cien

cy



(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)



120592119905=119896

120596

(8)


120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)



120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results



120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Electromotor

Watt meter

Reservoir tank

Flow

met

er

Globe valve

Regenerative pump

Rota

met

er

Gate valve

P1

P2


01020304050607080

Effici

ency

P1 (W)

150

200

250

300

350

400

450

500

550

600

650

700

750

800












35701

40479

4166941781

42163

4174941741

41734

353637383940414243

0 1000000 2000000 3000000 4000000

Hyd

raul

ic effi

cien

cy

Number of cells





120595 =119892119867

1198802

119892

(4)

120601 =119876

119860119900119880119892

(5)

120591 =119875

1205881198601199001198803

119892

(6)

120578 =120588119876119892119867

119875

=120601120595

120591

(7)




005

115

225

335

445

5


Hea

d co

effici

ent(120595)



05

101520253035404550

0 01 02 03 04 05 06

Effici

ency






050

100150200250300

Hyd

raul

ic effi

cien

cy



(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)



120592119905=119896

120596

(8)


120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)



120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results



120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











35701

40479

4166941781

42163

4174941741

41734

353637383940414243

0 1000000 2000000 3000000 4000000

Hyd

raul

ic effi

cien

cy

Number of cells





120595 =119892119867

1198802

119892

(4)

120601 =119876

119860119900119880119892

(5)

120591 =119875

1205881198601199001198803

119892

(6)

120578 =120588119876119892119867

119875

=120601120595

120591

(7)




005

115

225

335

445

5


Hea

d co

effici

ent(120595)



05

101520253035404550

0 01 02 03 04 05 06

Effici

ency






050

100150200250300

Hyd

raul

ic effi

cien

cy



(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)



120592119905=119896

120596

(8)


120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)



120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results



120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










005

115

225

335

445

5


Hea

d co

effici

ent(120595)



05

101520253035404550

0 01 02 03 04 05 06

Effici

ency






050

100150200250300

Hyd

raul

ic effi

cien

cy



(a)

005

115

225

335

445

555

6


Torq

ue (N

middotm)


(b)



120592119905=119896

120596

(8)


120597

120597119909119895

(119880119895119896) =

120597

120597119909119895

[(] +]119905

120590119896

)120597119896

120597119909119895

] + 119875119896minus 1205731015840

119896120596 (9)

120597

120597119909119895

(119880119895120596) =

120597

120597119909119895

[(] +]119905

120590120596

)120597120596

120597119909119895

] + 120572120596

119896

119875119896minus 1205731205962

(10)



120573 1205731015840

120590119896

120590120596

120572

340 009 2 20 59

4 Results



120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120601120601n = 03 120601120601n = 06 120601120601n = 1 120601120601n = 12


minus04minus02

002040608

112


PP

max

120601120601n = 03

120601120601n = 06

120601120601n = 10

120601120601n = 12




119899) and









PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PPmax

10 08 06 04 02 00 minus02

120601120601n = 06 120601120601n = 10 120601120601n = 12


= 06 120601120601119899

= 1 and 120601120601119899

= 12



= 1205732


1

= 0 and 1205732





1= 1205732=

+10∘

+30∘


1= 1205732=

minus10∘

minus30∘


2=

+10∘

+30∘


2=

minus10∘

minus30∘


study






0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

12


Mean = 0406

VV

max

(a)

0

02

04

06

08

1

12


VV

max

Mean = 0463

(b)

002040608

112


VV

max

Mean = 0505

(c)

002040608

112


VV

max

Mean = 0641

(d)


= 03 (b) 120601120601119899

= 06 (c) 120601120601119899

= 10 and (d) 120601120601119899

= 12



2= plusmn10


2= +30


2= minus30


+50∘ and 120573

2= minus50











Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Section A-A

A

A

VVmax

10 09 08 07 06 05 04 03 02 01 00



119899= 07 and 120601120601

119899= 1 but at 120601120601

119899= 12





5 Conclusions


1= 1205732= 120573 = plusmn10

∘

plusmn30∘



∘

plusmn30∘

plusmn50∘)




1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1205731

1205732


1205731

1205732



1205732


1205732










∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














∘)


Nomenclatures





0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

05

1

15

2

25

3

35

4

45

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601120601




Backward minus10deg


0

05

1

15

2

25

3

35

4

01 02 03 04 05 060

05

1

15

2

25

3

35

4

01 02 03 04 05 06

120595120595

120601 120601




Backward minus10deg






1205731

= 1205732

= minus50 2997 04121205731

= 1205732

= minus30 3995 07371205731

= 1205732

= minus10 4252 09631205731

= 1205732

= 0 4242 10351205731

= 1205732

= +10 4470 11601205731

= 1205732

= +30 4366 12031205731

= 1205732

= +50 4101 1044


= 0)

1205732

= minus50 3307 04221205732

= minus30 3910 07331205732

= minus10 4197 09811205732

= 0 4242 10351205732

= +10 4295 10691205732

= +30 4071 09471205732

= +50 3796 0759


0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30

35

40

45

50

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601






0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

0

5

10

15

20

25

30

35

40

45

0 01 02 03 04 05 06

Effici

ency

120601120601

















119894

[1199061015840




(nondimensional)


0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

05

1

15

2

25



120595

120573


120601120601n = 12

120601120601n = 10

120601120601n = 07


119899

= 07 120601120601119899

= 1 and120601120601119899

= 12

30

32

34

36

38

40

42

44

46

10 30 50

Effici

ency

120573 (deg)


Backward Forward

Radial



Greek Symbols

120572 120573 1205731015840



40

41

42

43

44

45

46

0 5 10 15 20 25 30 35 40 45 50 55

Effici

ency Max = 155

120573 (∘)

y = 00001x3 minus 00152x2 + 03656x + 42419








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 Flow Pattern Analysis and Performance...

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