viscous flow analysis a mixed flow pump...

International Journal of Rotating Machinery2001, Vol. 7, No. l, pp. 53--63Reprints available directly from the publisherPhotocopying permitted by license only

2001 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach SciencePublishers imprint.

Printed in Malaysia.

3-D Viscous Flow Analysis of a Mixed FlowPump ImpellerSTEVEN M. MINER*

Mechanical Engineering Department, United States Naval Academy, Annapolis, MD 21402, USA

(Received 30 July 1999," In finalform 27 August 1999)

This paper presents the results ofa study using a coarse grid to analyze the flow in the impellerof a mixed flow pump. A commercial computational fluid dynamics code (FLOTRAN) isused to solve the 3-D Reynolds Averaged Navier Stokes equations in a rotating cylindricalcoordinate system. The standard k-e turbulence model is used. The mesh for this study uses26,000 nodes and the model is run on a SPARCstation 20. This is in contrast to typicalanalyses using in excess of 100,000 nodes that are run on a super computer platform. Thesmaller mesh size has advantages in the design environment. Stage design parameters are,rotational speed l185rpm, flow coefficient 4:0.116, head coefficient t:0.094, andspecific speed 2.01 (5475 US). Results for the model include circumferentially averagedresults at the leading and trailing edges ofthe impeller, and analysis ofthe flow field within theimpeller passage. Circumferentially averaged results include axial and tangential velocities,static pressure, and total pressure. Within the impeller passage the static pressure andvelocity results are presented on surfaces from the leading edge to the trailing edge, the hub tothe shroud, and the pressure surface to the suction surface. Results of this study are consistentwith the expected flow characteristics of mixed flow impellers, indicating that small CFDmodels can be used to evaluate impeller performance in the design environment.

Keywords." Pump, Mixed flow, 3-D, Viscous, Impeller

INTRODUCTION

Designers are continually being challenged to pro-vide pumps that operate more efficiently, quietly,and reliably at lower cost. Key to building thesemachines is a better understanding of, and ability topredict their hydraulic and dynamic characteristics.Understanding and predicting these characteristics

requires a detailed knowledge of the flow fieldswithin the stationary and rotating passages of thepump. With the advent of more powerful compu-ters, computational fluid dynamics (CFD) is seeingmore and more use in predicting the flow fieldsin both the stationary and rotating passages ofturbomachines. Lakshminarayana (1991) pro-vides a review of the techniques that are currently

Tel.: 410 293 6527. Fax" 410 293 2591. E-mail: [email protected].

53

54 S.M. MINER

being used, as well as, an assessment of the state ofthe art.Most of the previous work in this area has been

for compressible flow, and was driven by the gasturbine industry. Adamczyk et al. (1989), andFurukawa et al. (1991) are typical examples.Examples of incompressible studies are Yu et al.(1995), and Yang (1995). In both cases, compres-sible and incompressible flow, the solutions havebeen obtained using codes that are developed inhouse, using meshes that have in excess of 100,000nodes, and are run on super computer platforms.The hardware and time requirements for models ofthis size are not suitable for use in day to day designapplications.The present work uses FLOTRAN to obtain

solutions for the flow field and pressure field withinthe impeller of a mixed flow pump. The code is runon a Sun SPARCstation 20, and the model size isapproximately 26,000 nodes. Turn around time forgeometry update and solution is one day, whichmakes the use of the code in the design processfeasible. Results presented here include circumfer-entially averaged velocity and pressure profiles atthe leading and trailing edges of the impeller. Inaddition, velocity and static pressure distributiondata are presented on surfaces from the leadingedge to the trailing edge, the hub to the shroud, andthe pressure surface to the suction surface. Thisstudy is a continuation ofwork performed by Whiteet al. (1993), and Miner (1996), which consideredan axial flow impeller. The mixed flow geometry isbeing evaluated because of its increase in headcoefficient.

CFD FORMULATION

FLOTRAN is a finite element based code whichsolves the Reynolds Averaged Navier Stokes equa-tions in primitive variable form. Turbulence ismodeled using the k-c turbulence model, with thelog law of the wall to simulate the boundary layers.The formulation of the code is based on theSIMPLER method of Patankar (1980). For the

impeller analysis discussed in this paper the equa-tions governing the turbulent incompressible floware formulated in a rotating reference frame. Thecontinuity and momentum equations become:

Opv. (pu) +N- 0,

D(pU)+2po x U + po) x o) x rDtpg- VP + #evZu, (2)

where P is modified to account for effects dueto rotation, and #o the linear combination of thekinematic viscosity and the turbulent viscosityderived from the k-c model. These equations alongwith the appropriate boundary conditions aresolved for the three components of velocity andthe pressure. Boundary conditions used for thisanalysis include stationary and moving walls,specified inlet velocities, specified outlet pressure,and periodic boundaries.

GEOMETRY

Figure shows a cross section view of the pump,which is described in detail by White et al. (1993),the only difference being that the axial flow impel-lers have been replaced by mixed flow impellers.The pump is a two stage design with an impellerand stator making up each stage. The impellers arecontra-rotating. The analysis presented in thispaper is for the first stage impeller only. Designparameters for the stage are rotational speed1185 rpm, flow rate 0.38 m3/s, and head rise 13.1 m.These result in the following nondimensionalparameters, flow coefficient 4 0.116, head coeffi-cient = 0.094, and specific speed 2.01 (5475 US).Figure 2 shows a perspective view of the impeller.This particular impeller has the shroud attachedto the blade tips, which eliminates the blade tipleakage flow. The hub radius varies from 0.037 mat the leading edge to 0.107 m at the trailing edge.

3-D VISCOUS FLOW ANALYSIS

FIGURE Pump cross-section.

55

FIGURE 2 Pump impeller.

The shroud radius varies from 0.126 m at the lead-ing edge to 0.149m at the trailing edge. TheReynold’s number based on the blade tip speed atthe trailing edge is 1.7 x 106.Due to symmetry, only one of the blade passages

needs to be analyzed. Figure 3 illustrates thisblade passage with the appropriate upstream and.

downstream extensions. This becomes the geometrythat is modeled in the rotating reference frame.At the inlet to the domain the axial velocity is aconstant based on the through flow for the pump.The absolute tangential velocity at the inlet is zero,which implies in the rotating frame the relativevelocity is -ra, and the radial velocity is zero. Theinlet to the solution domain is located approx-imately twelve chord lengths upstream of theblade leading edge. The only specification made atthe outlet is that the static pressure in the absoluteframe is uniform and set to zero. This absolutecondition is converted into the appropriate rela-tive pressure in the rotating frame. This condition isapplied roughly sixteen chord lengths downstreamof the blade trailing edge. Periodic boundaries areused upstream and downstream of the blade lead-ing and trailing edges, respectively. For the rotat-ing solid surfaces all of the velocity componentsare set to zero. This includes all the surfaces withinthe blade passage, the nose cone portion of thehub upstream of the blade leading edge, and ashort section of the hub, 40% of chord length,downstream of the trailing edge. The shroud sur-faces upstream and downstream of the blade pas-sage, and the remaining hub surface downstreamare stationary in the absolute reference frame.

56 S.M. MINER

PERIODIC

OUTLET

INLET

FIGURE 3 Solution domain.

In the rotating frame they are treated as movingboundaries with the axial and radial componentsofvelocity set to zero and the tangential componentset equal to -r0c for the shroud, and -r.a forthe hub.The selection of an appropriate mesh density for

this study is based on the previous analysis of anaxial flow impeller by Miner (1996). In that studytwo meshes were considered, one with 22,176 nodesand the other with 40,131 nodes. Comparison ofthe velocity profiles from the two meshes showedno significant differences. Therefore, it was deter-mined that the coarse mesh provided sufficientresolution. In addition, the computational resultsfor the coarse mesh were compared to measureddata for the axial flow impeller. The largest dif-ference between the measured and computed datawas 15% in the tangential velocity profile. Thisdifference was due primarily to a difference in thedownstream boundary condition used in the modeland the conditions downstream of the measuredimpeller. The computational model considered only

the first stage impeller, whereas the measured datawas collected with both of the impellers in place.The experience gained in the analysis of the axialflow impeller was used as the basis for establishingthe mesh density in the present analysis, which has26,299 nodes. There are 17 nodes blade to blade, 17nodes hub to shroud, and 91 nodes inlet to outlet,of which 31 are in the blade passage. The nodes arespaced more closely near the hub, shroud, andblade surfaces, as well as, near the leading andtrailing edges. The value for y+ is between 400and 600 throughout the blade passage. This valueindicates that the near wall nodes are not withinthe laminar sublayer but are within the overlaplayer of the turbulent boundary layer. Therefore,the application of the log law of the wall formula-tion is appropriate.The time required to generate the completed

FEA model was approximately 8 h, the solution forthe initial geometry required 500 iterations and 85 hof CPU time. Subsequent updates to the geometryand an updated solution could be obtained within

3-D VISCOUS FLOW ANALYSIS 57

24 h, 8 h to modify the model and 15 h to update thesolution. Updated solutions were always startedfrom the previous converged solution. Having a oneday turn around time allows CFD analysis to beused in the design process.

RESULTS

The results presented in this paper include circum-ferentially averaged velocity and pressure profilesat the leading and trailing edges of the impeller. Theaveraged velocity results are absolute and nondi-mensionalized by the trailing edge blade tip velocityUt, the pressures are nondimensionalized by pUff/2,and the radius is nondimensionalized by the shroudradius at the trailing edge r0. In addition, velocityand static pressure distribution data are presented

on surfaces from the leading edge to the trailingedge, the hub to the shroud, and the pressure sur-face to the suction surface.

Figure 4 shows the circumferentially averagedresults at the leading edge. These results are taken0.1 chord lengths upstream of the leading edge. Atthis upstream location the shroud is not rotatingwith the impeller. The axial velocity shows a slightdeficit at the hub relative to the shroud. This is dueto flow having to come up over the nose cone of theimpeller. The effect of the nose is also evident in theradial velocity profile, which shows positive velo-city from the hub towards the shroud. The tan-gential profile is nearly zero from the hub to theshroud, with slight preswirl at the shroud surfacedue to the extension of the shroud upstream of theleading edge. The preswirl is less than 5% of the tipspeed at the leading edge. The static pressure profile

0.9

0.8

0.7

0.4

0.3

0.20 0.2

Axial Velocity

0.9

0.9, 0.9

0.8 0.8

0.7 0.7

0.6 0.6

O.S O.,0.4 0.4

0.3 0.

0.21 0.20.3 0.4 0.5 0.2 0.4 0.6 -0.05 0 0.05

Radial Velocity

0.9.

0.15Tangential Velocity

Static Pressure Total Pressure

FIGURE 4 Leading edge results.

0.25

58 S.M. MINER

shows a drop in pressure from the hub to the shroudsurface. This can be understood in terms ofthe axialand tangential velocity profiles. At the hub both theaxial and tangential velocities were lower than thevelocities at the shroud, this reduction in velocityproduces the rise in static pressure at the hub. Themajority of this effect is due to the reduction in theaxial velocity.

Figure 5 shows circumferentially averaged resultsat the trailing edge. These results are taken 0.1chord lengths downstream of the trailing edge. Atthis downstream location the shroud is not rotatingwith the impeller. At the trailing edge the axialvelocity profile shows the opposite trend from theleading edge, with the peak velocity shifted downtoward the hub. This shift in the axial velocity pro-file is consistent with the balance between the cen-trifugal and pressure forces acting on the fluid, thatarises through the concept of radial equilibrium.

The radial velocity profile shows larger values at thehub than the shroud, which is due to the shape ofthe hub. The hub radius changes by a factor of 2.9from the leading edge to the trailing edge, while theradius of the shroud changes by only a factor of 1.2.At the trailing edge the variation in the tangentialvelocity from the hub to the shroud is :t:8% aboutthe mean. The tangential velocity plot also indicatesthat the boundary layers at the hub and shroudsurfaces are thin compared to the passage height.The static pressure at the trailing edge increasesfrom the hub to the shroud. This variation in theprofile relates primarily to the axial velocity profilewith its higher velocity at the hub compared to theshroud. The tangential velocity makes a smallercontribution to the change in pressure from the hubto the shroud. The total pressure at the trailing edgeis uniform to within +4% of the mean value fromthe hub to the shroud.

1.0 1.0,

0.9

0.8

0.70.1 0.2 0.3

Axial Velocity

0.9

0.9

0.8

0.8

0.70.4 0.5 0

0’.65 075Static Pressure

0.1 0’.2Radial Velocity

0.3

1.0

0.9

0’.8 0’.9 1’.0

012’ 0’.4’ 0’.6Tangential Velocity

1L.1Total Pressure

FIGURE 5 Trailing edge results.


Figures 6 and 7 show axial velocity distributionsand static pressure distributions within the impellerpassage, respectively. At the leading edge the veloc-ity distribution shows the deficit in flow that was

evident in the circumferentially averaged profile,but it also shows that the velocity at the pressuresurface is reduced compared to the velocity at thesuction surface. The corresponding pressure plot in

PS

H

Trailing Edge

Mid-Chord

PS S

H

SS

SS

SS

380

900

864

828

796

756

720

684

648

612

576

540

504

468

432

396

360

324

288

252

216

180

144

108

72

36

0

Leading Edge

PS

H

H

H

Trailing Edge

Mid-Chord

SS

SS

SS 10.0

8.4

6.8

5.2

3.6

2.0

0.4

-1.2

-2.8

-4.4

-6.0

-7.6

-9.2

-10.8

-12.4

-14.0

-15.6

-17.2

-18.8

-20.4

,-22.0

-23.6

-25.2

-26.8

-28.4

-30.0

Leading Edge

FIGUIRE 6 Axial velocity distributions, L.E. to T.E. FIGURE 7 Pressure distributions, L.E. to T.E.

60 S.M. MINER

Fig. 7 shows the pressure contours being alignedwith the blade surfaces. At the mid-chord locationthe formation of a jet-wake structure is becomingevident. The lower velocity fluid is accumulatingnear intersection of the pressure and hub surfaces,with a corresponding high velocity region at theintersection of the suction and shroud surfaces. Thepressure plot at mid-chord shows the contourslosing alignment with the blade surfaces and beingmore heavily influenced by the presence of thedeveloping jet-wake structure. At the trailing edgelocation the development of the jet-wake structurehas continued. The low velocity fluid continues toaccumulate along the pressure and shroud surfaces,with the high velocity fluid accumulating at theintersection of the hub and suction surfaces. Thecontours on the pressure plot show that the direc-tion of the gradient is from the pressure/shroudintersection towards the suction/hub intersection,and not directed from the pressure surface to thesuction surface. These results are consistent withthe jet-wake phenomena and previously publishedresults.

Figures 8 and 9 show relative velocity vectors andpressure contours on surfaces from the hub to theshroud. The velocity results for the hub and shroudsurfaces are for the first layer of nodes off of thesurfaces. On all three surfaces the high velocity fluidtravels along the suction surface, with the velocitybeing higher at the shroud than the hub. All threesurfaces show a low pressure region on the suctionsurface at about mid-chord where the fluid travelsover a convex portion of the blade. Again, thepressure contours show the gradient in pressure atthe trailing edge going from the pressure/shroudsurface intersection to the suction/hub surfaceintersection.

Figures 10 and 11 show relative velocity vectorsand pressure contours on surfaces from the suctionsurface to the pressure surface. As with Fig. 8, thevelocity results for the pressure and suction surfacesare for the first layer of nodes off of the surface.Here again, the results show the formation of thejet-wake structure.

780

Shroud

Mid-Height

PS

Hub

TE

FIGURE 8 Velocity vectors, hub to shroud.

900

864

828

796

756

720

684

648

612

576

540

504

468

432

396

360

324

288

252

216

180

144

108

72

36


LE

LE

LE

PSTE

SS

Shroud

PS

SS

Mid-Height

PS

TE

10.0

8.4

6.8

5.2

3.6

2.0

0.4

-1.2

-2.8

-4.4

-6.0

-7.6

-9.2

-10.8

-12.4

-14.0

-15.6

-17.2

-18.8

-20.4

-25.2

-26.8

-28.4

SS

Hub

FIGURE 9 Pressure distributions, hub to shroud.

540

Pressure

S680

H

Mid-Span

Suction

FIGURE l0 Velocity vectors, S.S. to P.S.

9O0

864

828

796

756

720

684

648

612

576

540

5O4

468

432

396

360

324

288

252

216

180

144

108

72

36

62 S.M. MINER

LE

LE

LE

H

Pressure

H

Mid-Span

H

TE

4.4

10.0

8.4

6.8

5.2

3.6

2.0

0.4

-1.2

-2.8

-4.4

-6.0

-7.6

-9.2

-10.8

-12.4

-14.0

-15.6

-17.2

-18.8

-20.4

-22.0

-23.6

-25.2

-26.8

-28.4

-30.0

Suction

FIGURE 11 Pressure distributions, S.S. to P.S.

CONCLUSIONS

The following conclusions are based on the resultsof this study:

(1) Results of this study are consistent with theexpected flow characteristics of mixed flowimpellers.

(2) Both the circumferentially averaged data andthe blade passage results provide sufficientdetail to evaluate the performance of theimpeller.

(3) Using small models, CFD can be used effec-tively in the design process. Turn around timesof one day are possible using a work station.

Acknowledgements

This work was supported by the Naval SurfaceWarfare Center, Carderock Division, AnnapolisDetachment, and the Naval Academy ResearchCouncil.

NOMENCLATURE

g gravitational vectorP modified static pressurer radius vector

ri hub radius

r0 shroud radiusU velocity vectorUt blade tip speed#e effective viscosityp density

b flow coefficientb head coefficiento angular velocity vector

References

Adamczyk, J.J., Celestina, M.L., Beach, T.A. and Barnett, M.(1989) Simulation of 3-D viscous flow within a multi-stageturbine, ASME Paper 89-GT-152.

Furukawa, M., Yamasaki, M. and Inoue, M. (1991) A zonalapproach for Navier-Stokes computations of compressiblecascade flow fields using a TVD finite volume method, ASMEJournal of Turbomachinery, 113(4), 573-582.


Lakshminarayana, B. (1991) An assessment of computationalfluid dynamic techniques in the analysis and design ofturbomachinery The 1990 Freeman Scholar Lecture, ASMEJournal ofFluids Engineering, 113(3), 315-352.

Miner, S.M. (1996) 3D viscous flow analysis of an axial flowpump impeller, Proc. 6th Int’l Syrup. on Transport Phenomenaand Dynamics of Rotating Machinery, ISROMAC-6, Vol. II,pp. 336-344.

Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow,Hemisphere, New York, NY.

White, J.W., Purnell, J.G. and Stricker, J.G. (1993) In-linesubmersible pump, Proceedings of the 2nd ASME PumpingMachinery Symposium, ASME, FED-Vol. 154, pp. 369-375.

Yang, C.I. (1995) A simulation of viscous incompressible flowthrough a multiple-blade-row turbomachinery with a high-resolution upwind finite differencing scheme, NumericalSimulations in Turbomachinery, ASME, FED-227, 11-18.

Yu, W.S., Lakshminarayana, B. and Thompson, D.E. (1995)Computation of three-dimensional viscous flow in highReynolds number pump guide vane, Numerical Simulationsin Turbomachinery, ASME, FED-227, 117-122.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


viscous flow analysis a mixed flow pump...

Documents