Investigation of di�erent design methods of volutes

with circular cross sections for a single-stage

centrifugal pump

Axel Knapp1*, Martin Bohle1, Harald Roclawski1

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

International

Symposium on

Transport Phenomena

and

Dynamics of Rotating

Machinery

Maui, Hawaii

December 16-21, 2017

AbstractIn the open literature di�erent methods to design a volute geometry have been described wellsince several years, for example Eckert [1], Pfleiderer [2], Stepanoff [3] or Troskolanski[4]. Nevertheless, there are only few comparisons of those design methods with respect to thepump performance (e.g. Rutschi [5] or Yang et al. [6]) known at the moment. In this paper, thedesign methods of volute geometries with circular cross sections for a single-stage centrifugalpump according to Pfleiderer and Stepanoff are compared to each other according to the pumpperformance.

�e di�erent volute geometries have been investigated numerically by means of 3D-CFD(Computational Fluid Dynamics) tools. For validation, the volute geometries have been investigatedexperimentally as well. To ensure the comparability of the di�erent design methods, every volutehas circular cross sections, is used with the same impeller geometry and in addition the design ofthe tongue region is the same.Keywordscentrifugal pump — volute casing — design methods1Institute of Fluid Mechanics and Fluid Machinery (SAM), Department of Mechanical and Process Engineering, TechnicalUniversity of Kaiserslautern, Kaiserslautern, Germany*Corresponding author: axel.knapp@mv.uni-kl.de

NOMENCLATURE

Aϑ cross section area(mm2)

a radius of the center of gravity (mm)b chord (mm)c velocity

(m s−1)

cin velocity at pin(m s−1)

cout velocity at pout(m s−1)

cu velocity in circumferential direction(m s−1)

c0 velocity at cross section 0(m s−1)

D diameter (mm)Da diameter of the discharge pipe (mm)Di diameter of the inlet pipe (mm)dZ diameter of the tongue tip (mm)g gravitational constant

(m s−2)

H head (m)∆h height di�erence between pin and pout (m)η e�ciency (−)ISG impeller sidewall gapϑ design angle (◦)Kcm Stepanoff-coe�cient (−)M torque (N m)Ûm mass fow rate

(kg s−1)

n nominal speed(min−1)

nq speci�c speed(min−1)

Ph hydraulic power (W)Pm mechanical power (W)pin evaluation plane at the in�ow domainpout evaluation plane at the out�ow domainpst static pressure (bar)ptot total pressure (bar)P� PfleidererQ �ow rate

(m3 h−1)

Q080 numerical results for Q = 80 m3 h−1

Q100 numerical results for Q = 100 m3 h−1

Q120 numerical results for Q = 120 m3 h−1

R radius of the cross section area (mm)r radius (mm)ra outer radius of the volute (mm)ri inner radius of the volute (mm)r2 outer radius of the impeller (mm)ρ density

(kg m−3)

Ste Stepanoff

INTRODUCTION

In radial and semi-axial single-stage centrifugal pumps the�uid is collected in the stator region a�er leaving the impeller.In case of standardized chemical pumps or standardized waterpumps this stator region is designed as a volute casing. Sev-

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 2/8

Figure 1. Sketch

eral pump manufacturers are producing those single-stagecentrifugal pumps in di�erent sizes for several design points.To improve the pump performance, pump manufacturersnormally change the design of the impellers, they vary thecross-sectional shape or they redesign the tongue region atthe volute. However, the proceed of designing the volutecasing of a single-stage centrifugal pump is normally notbeing changed by a pump manufacturer.

K. Rutschi [5] discovered that the throat area has anin�uence on the best e�ciency point of a pump. He tested oneimpeller geometry with three di�erent volute casings withtrapezoidal cross-section shapes designed with the designmethod according to Pfleiderer.

S. Yang et al. [6] investigated the in�uence of di�erentdesign rules, volute throat areas and cross-section shapes onthe performance of a single-stage centrifugal pump with aspeci�c speed nq = 22.9 min−1 using CFD. Highest e�ciencywas found with circular cross-section shape. Furthermore,the simulation study showed that a large volute throat areacould o�set the e�ciency curve to larger �ow rates.

R. Dong et al. [7] had experimentally investigated thee�ect of the tongue shape on the performance, pressure �uc-tuation and noise in a centrifugal pump. One result was, thatthe head of the pump can be increased by retracting androunding the tongue.

R.C. Worster [8] concluded that it is the volute ratherthan the impeller which determines the point of best e�-ciency.

O. Litfin and A. Delgado [9] investigated three di�erentvolute casings designed with the design method accordingto Stepanoff. One of the results is that the design �ow ratehas an in�uence on the point of best e�ciency. With a risingdesign �ow rate the head curve becomes �a�er and the pointof best e�ciency is shi�ed towards higher �ow rates.

�e research presented in this paper can be consideredas a �rst step in comparing the e�ect of di�erent designmethods of volutes with circular cross sections on the overallpump performance.

1. DESIGN METHODS

�e �rst step in designing a volute is to calculate the �owrate at each cross section. �e �ow rate Qϑ can be calculatedgenerally by means of equation (1) for a random design angleϑ.

Qϑ =

∫ ra

ri

cϑ b dr (1)

Furthermore the �ow rate Qϑ can be described by the total�ow rate Q and the circular arc segment depending on thedesign angle ϑ.

Qϑ =ϑ

360◦Q (2)

Equating the previous two equations delivers

ϑ =360◦

Q

∫ ra

ri

cϑ b dr (3)

Equation (3) is generally valid for every kind of cross-sectionalshape.

1.1 C. PLeiderer [2]

�e design method according to Pfleiderer is based onthe assumption that the �ow inside the volute satis�es theprinciple of the conversation of momentum.

cϑ = cu,ϑ · r = cu,i · ri = const. (4)

In that case equation (3) can be wri�en as

ϑ =360◦ cu,i ri

Q

∫ ra

ri

b drr

(5)

for every kind of cross-section shape. �e volutes, investi-gated in this paper, have circular cross sections (Figure 1).�is fact leads to equation (6).

ϑ =720◦ cu,i

Qπ ri

[ri + R −

√ri (ri + 2 R)

](6)

In the design of a volute the design angle ϑ is normally setand the radius R of the cross section area has to be calculated.�is leads to equation (7) for the radius R of the circular crosssection area.

R =ϑQ

720◦ π cu,i ri+

√ϑQ

360◦ π cu,i(7)

1.2 A. J. Stepanoff [3]

�e design method according to Stepanoff is based on theprinciple of the conversation of kinetic energy.

cϑ = Kcm

√2 g H = const . (8)

�e coe�cient Kcm is a function of the speci�c speed nq .

nq = n√

QH0.75 (9)

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 3/8

Figure 2. Coe�cient Kcm according to Stepanoff

�e course of the coe�cient Kcm is shown in Figure 2. �evelocity cϑ is assumed to be constant at every single crosssection at the whole volute.

�e cross section area Aϑ can be calculated by means ofthe continuity equation.

Aϑ =Qϑ

cϑ=

ϑQ360◦ cϑ

(10)

Equation (10) leads to the equation for the radius R of thecircular cross section area.

R =12

√ϑQ

90◦ π cϑ(11)

1.3 Comparison

Both volutes have been calculated by means of equation (7)and equation (11), respectively. �e number of cross sectionareas is chosen to Nϑ = 39. Furthermore, the design point ofthe pump is:

Q = 100 m3 h−1

H = 30 m → nq = 39 min−1

n = 3000 min−1

A comparison of both designed volutes is shown in Figure3 in a two-dimensional view. �e Stepanoff-volute has alarger cross section area Aϑ at every single cross sectioncompared to the Pfleiderer-volute.

�e design of the tongue region is the same for bothdesigns. �e tongue has a circular tip and the position is�xed for both design methods. �e diameter of the tonguetip is dZ = 3 mm.

To ensure comparability of the design methods the tonguetip geometry is the same and in addition no di�usor is con-nected. �e discharge pipe has a constant area that is the

Figure 3. Comparison of the designed volutes (2D)

same as the last cross section area and is arranged radiallyto the volute.

�e course of the cross section area Aϑ is plo�ed versusthe design angle ϑ in Figure 4. �e blue line represents thecourse according to Stepanoff. �e course according toPfleiderer is represented by the red do�ed line. �e lastcross section area according to Stepanoff is 18% larger thanthe cross section area according to Pfleiderer.

Figure 4. Course of the cross section area Aϑ

2. NUMERICAL SETUP

�e numerical model includes the in�ow of the pump, the im-peller with both impeller sidewall gaps and the volute with aconstant cylindrical out�ow. All meshes of the �uid regionsare generated in ANSYS ICEM CFD and are meshed withblock-structured meshes with only hex-volume elements.

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 4/8

�e Impeller consists of 1 million elements, the in�ow andthe impeller sidewall gaps are meshed with 400.000 elements.Both volutes are meshed with 1.2 million elements. �e nu-merical calculations have been done by means of ANSYS CFXusing the SST (Shear Stress Transport) turbulence model anda sliding mesh at the impeller region. At the inlet domain astatic pressure is set as boundary condition. �e mass �owrate is set as boundary condition at the outlet domain andis being varied in steps of 0.2 Ûm for calculating the charac-teristic curves of the pump. Wall regions are set as no slipwall whether the region is stationary or rotating. All �uiddomains are connected via general grid interfaces. If a sta-tionary region is connected with a rotating region, transientrotor stator is de�ned as frame change option. All numericalresults have been averaged over 60◦ a�er two calculated revo-lutions of the impeller. To ensure the comparability betweenexperimental and numerical results, the evaluation planespin and pout of the numerical model are placed just like at thetest rig (Figure 5).

Figure 5. Numerical setup

3. TEST RIG

�e experimental tests have been done at a new test facility atthe Institute of Fluid Mechanics and Fluid Machinery (SAM)at the Technical University of Kaiserslautern. �is test rigallows to perform experiments with a rotational speed up to3000 min−1 with water as working �uid.

�e test bench is equipped with pressure sensors to de-termine the pressures on the suction and the pressure sideof the pump as well as the pressure at the tank. �e pressure

measuring points are arranged at 2 D ahead and a�er thepump, respectively. �e tank is connected to a compressedair line for varying the tank pressure. �e �ow rate is deter-mined by a magnetic-inductive �ow meter which is installedat the ascending line. At the ascending line the temperatureis determined by a PT-100 sensor. �e torque to calculate thee�ciency can be measured by means of a torque meter. Dif-ferent operating points can be adjusted by means of a controlvalve to reduce the �ow rate and a variable speed drive tovary the speed of the asynchronous motor. In addition theloop can be vented at its highest point. �e volute casing ofeach design variant has been manufactured from polymethylmethacrylate (PMMA) and thus o�ers an optical access tothe �ow at the volute. All casings are designed keeping amodular design in mind to allow short set-up times.

4. RESULTS AND DISCUSSION

4.1 Numerical results

In Figure 6 characteristic curves determined numerically areshown. �e head H and the e�ciency η are plo�ed versusthe �ow rate Q. �e red line with red circles representsthe head curve of the volute according to Pfleiderer (P�).�e head curve of the volute according to Stepanoff (Ste)is represented by the blue line with blue open squares. Atpartial load a higher head can be received by a volute casingaccording to Pfleiderer whereas at overload conditions theopposite is true. Both head curves intersect at the designpoint. �e head curves are calculated with respect to equation(12).

H =∆ptotρ g

=ptot,out − ptot,in

ρ g(12)

�e total pressure ptot,out is an area averaged value at theevaluation plane pout and the total pressure ptot,in is an areaaveraged value at the evaluation plane pin, respectively.

Figure 6. Characteristic curves (numerical)

�e e�ciency curve of the volute according to Pflei-derer is represented by the red dashed line with red dotsin Figure 6. �e blue dashed line with blue �lled squares

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 5/8

Figure 7. Test rig

represents the e�ciency curve of the volute according toStepanoff. At partial load a higher e�ciency can be re-ceived by a volute casing according to Pfleiderer whereasat overload conditions the opposite is true. �e volute cas-ing according to Pfleiderer receives its highest e�ciencyalready at a �ow rate of Q = 80 m3 h−1. In the further coursetowards the design point the e�ciency is decreasing. �ee�ciency curves are calculated with respect to equation (13).

η =Ph

Pm=ρ g H Q2 π n M

(13)

�e torque M is de�ned as the torque at the rotating regionsdepending on the rotational axis.

4.2 Experimental results

In Figure 8 characteristic curves determined experimentallyare shown. �e head H and the e�ciency η are plo�ed versusthe �ow rate Q. �e red line with red circles represents thehead curve of the volute according to Pfleiderer. �e headcurve of the volute according to Stepanoff is representedby the blue line with blue open squares. At partial load ahigher head can be received by a volute casing according toPfleiderer whereas in the range of the design point and atoverload conditions the opposite is true. Both head curvesintersect at partial load. �e head curves are calculated with

respect to equation (14).

H =∆ptotρ g

=pst,out − pst,in

ρ g+

cout2 − cin

2

2 g+ ∆h (14)

�e velocities c at the measuring points of the static pres-sure pst are calculated by means of the continuity equation.�e value ∆h describes the height di�erence between bothmeasuring points.

Figure 8. Characteristic curves (experimental)

�e e�ciency curve of the volute according to Pflei-

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 6/8

derer is represented by the red dashed line with red dotsin Figure 8. �e blue dashed line with blue �lled squaresrepresents the e�ciency curve of the volute according toStepanoff. At partial load a higher e�ciency can be re-ceived by a volute casing according to Pfleiderer whereasin the range of the design point and at overload conditionsthe opposite is true. �e volute casing according to Pflei-derer receives its highest e�ciency already at a �ow rate ofapproximately Q = 80 m3 h−1. In the further course towardsthe design point the e�ciency is decreasing and the pumpis already working at overload conditions. �e e�ciencycurves are calculated with respect to equation (13).

4.3 Comparison and discussion

Figure 9. Characteristic curves (Comparison)

In Figure 9 numerical and experimental results are com-pared to each other. �e red lines and circles represent theresults of the volute according to Pfleiderer. �e results ofthe volute according to Stepanoff are represented by theblue lines and squares. �e head curves are represented bythe line and the do�ed one as well as the open symbols. �edashed lines and the �lled symbols represent the e�ciencycurves. Numerical and experimental results �t quite well.�e numerical results could be validated by the experimentalresults. �e e�ciency curves determined numerically are ata higher level than the ones determined experimentally. �iscan be explained by the non-consideration of the bearingfriction at the numerical simulation.

�e gradient of the head curves decreases in the rangeof strong partial load. �is fact is caused by a strong vortexthat occurs at the in�ow domain at strong partial load. �isvortex is shown in Figure 12 with a volute casing accordingto Pfleiderer above and with a volute casing according toStepanoff below on the le�-hand side. In addition in bothcases a strong vortex occurs at the discharge line.

In Figure 12 the velocity is plo�ed as streamlines at strongpartial load on the le�-hand and at the design point on theright-hand side with a volute casing according to Pfleidererabove and with a volute casing according to Stepanoff be-low. At the design point there is a light vortex at the evalua-tion plane pout in case of Pfleiderer. �e pump is working

at overload conditions and the head curve drops. At thebest e�ciency point no vortex occurs (Figure 13). In caseof Stepanoff (Figure 12 on le�-hand side below) the �uidat the in�ow domain is swirling stronger and faster than inthe case of Pfleider (Figure 12 on le�-hand side above) atstrong partial load. �is causes the lower level of the headcurve with a Stepanoff-casing at partial load.

Figure 10. Averaged velocity c at each cross section

Figure 11. Velocity ratio cϑ/c0 at each cross section

In Figure 10 the area averaged velocity c at each crosssection is plo�ed versus the design angle ϑ. �e cross sectionarea at the tongue is described by the design angle ϑ = 0◦.�e red crosses represent the course of the velocity c for the�ow rate Q = 80 m3 h−1 with a volute casing according toPfleiderer. �e �uid is being decelerated gradually at thevolute. �at is also shown in Figure 11 by the red dashedline P� Q080. In Figure 11 the velocity ratio cϑ/c0 is plo�edversus the design angle ϑ.

At the design point (Q100) the �uid is being accelerateda�er the tongue at the volute according to Pfleiderer. Inthe further course the velocity c rises slightly. �at case isrepresented by the red dots in Figure 10 and the red lineP� Q100 in Figure 11. In consequence, the pump is alreadyworking at overload conditions.

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 7/8

Figure 12. Streamlines at strong partial load (le�) and design point (right)

�e red circles in Figure 10 represent the results for the�ow rate Q = 120 m3 h−1 with a volute casing according toPfleiderer. In that case the rate of change of the velocityis very high at the beginning of the volute. In the furthercourse the velocity is still rising. �e gradient of the velocityratio cϑ/c0 is very high, too. �at is represented by the reddo�ed line P� Q120 in Figure 11.

For the �ow rate Q = 80 m3 h−1 with a volute casing ac-cording to Stepanoff the �uid is being decelerated stronglyat the whole volute. �at case is represented by the bluetriangles in Figure 10 and the blue do�ed line Ste Q080 inFigure 11.

At the design point (Q100) the deceleration of the �uidis much smoother than at partial load (Q080) for a volute

Investigation of di�erent design methods of volutes with circular cross sections for a single-stage centrifugal pump — 8/8

Figure 13. Streamlines at best e�ciency point (Pfleiderer)

casing according to Stepanoff (blue �lled squares). �at iscon�rmed by the blue dashed line Ste Q100 in Figure 11.

�e blue open squares in Figure 10 represent the course ofthe velocity c for the �ow rate Q = 120 m3 h−1 with a volutecasing according to Stepanoff. �e �uid is being acceler-ated very slightly at the whole volute. �e gradient of thevelocity ratio cϑ/c0 is rising. �e course of the velocity ratiois represented by the blue dashed line Ste Q120 in Figure 11.In consequence, the pump is working at overload conditions.

5. SUMMARY AND OUTLOOK

In this paper, the in�uence of the design methods on theperformance of a single-stage centrifugal pump is shownfor the nominal speed of 3000 min−1. Diagrams showingthro�le curves and e�ciency curves that have been evaluatednumerically as well as experimentally are discussed. �eresults shown o�er the opportunity to increase the e�ciencyof a single-stage centrifugal pump by varying the designmethod of the volute geometry.

At the Institute of Fluid Mechanics and Fluid Machinery(SAM) at the Technical University of Kaiserslautern furtherinvestigations on design methods of volutes with circularcross sections for a single-stage centrifugal pump will bedone.

In the next steps volute geometries designed according toa given parabolic distribution of the entry �ow angle α4 anddi�erent given linear courses of the relation Aϑ/R will beinvestigated. �e �nal step will be detailed investigations onthe production of losses at each volute. �erefore there willbe a discussion about the di�erent internal �ow structures.

ACKNOWLEDGMENTS

We acknowledge the AHRP (Alliance for High-PerformanceComputing Rheinland-Pfalz) for the support during the nu-merical investigations. All numerical investigations are per-formed on the High-Performance Computer “Elwetritsch”.

REFERENCES

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[7] R. Dong, S. Chu, and J. Katz. E�ect of modi�cation totongue and impeller geometry on unsteady �ow, pressure�uctuation and noise in a centrifugal pump. Transaction ofAMSE, Journal of Turbomachinery, Vol. 119, pp. 506-515,1997.

[8] R. C. Worster. �e �ow in volutes and its e�ect on centrifu-gal pump performance. Proceedings of the Institution ofMechanical Engineers, Vol. 177 No. 31, pp. 843-875, 1963.

[9] Oliver Lit�n and Antonio Delgado. On the E�ect of VoluteDesign on Unsteady Flow and Impeller–Volute Interactionin a Centrifugal Pump. Proceedings of the ASME 2014 4thJoint US-European Fluids Engineering Division SummerMeeting, FEDSM2014-21533, 2014.