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Steady and Unsteady Radial Forces for a

Centrifugal Pump With Impeller to

Tongue Gap Variation

Jos Gonzlez Prez

Jorge Parrondo

Carlos Santolaria

Eduardo Blanco

ASME Journal of Fluids Engineering.

Mayo 2006.

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Jos Gonzleze-mail: [email protected]

Jorge Parrondo

Carlos Santolaria

Eduardo Blanco

Universidad de Oviedo,rea de Mecnica de Fluidos,

Campus de Viesques,33271 Gijn (Asturias), Spain

Steady and Unsteady RadialForces for a Centrifugal PumpWith Impeller to Tongue GapVariation

Experimental and numerical studies are presented on the steady and unsteady radialforces produced in a single volute vaneless centrifugal pump. Experimentally, the un-steady pressure distributions were obtained using fast response pressure transducers.These measurements were compared with equivalent numerical results from a URANScalculation, using the commercial code FLUENT. Two impellers with different outlet diam-eters were tested for the same volute, with radial gaps between the blade and tongue of10.0% and 15.8% of the impeller radius, for the bigger and smaller impeller diameters,respectively. Very often, pump manufacturers apply the similarity laws to this situation,but the measured specific speeds in this case were found to be slightly different. Thesteady radial forces for the two impellers were calculated from both the measured aver-age pressure field and the model over a wide range of flow rates in order to fullycharacterize the pump behavior. Again, a deviation from the expected values applying thesimilarity laws was found. The data from the pressure fluctuation measurements were

processed to obtain the dynamic forces at the blade passing frequency, also over a wide

range of flow rates. Afterwards, these results were used to check the predictions from thenumerical simulations. For some flow rates, the bigger diameter produced higher radial

forces, but this was not to be a general rule for all the operating points. This paperdescribes the work carried out and summarizes the experimental and the numericalresults, for both radial gaps. The steady and unsteady forces at the blade passing fre-quency were calculated by radial integration of the pressure distributions on the shroudside of the pump volute. For the unsteady forces, the numerical model allowed a separateanalysis of the terms due to the pressure pulsations and terms related to the momentumexchange in the impeller. In this way, the whole operating range of the pump was studiedand analyzed to account for the static and dynamic flow effects. The unsteady forces arevery important when designing the pump shaft as they can produce a fatigue collapse ifthey are not kept under a proper working value. DOI: 10.1115/1.2173294

Introduction

Knowledge of the radial forces is fundamental to understanding

the dynamic working conditions of a centrifugal pump. The main

goal of this paper is to determine such forces both on a steady and

unsteady basis. The flow inside a centrifugal pump is quite com-

plex and it is always dominated by the geometrical constraints

which impose a strongly 3D structure.

The fluid flow inside a centrifugal pump is characterized by a

circumferentially nonuniform unsteady pattern, mostly associated

with the rotation frequency and, especially, the blade-passing fre-

quency 1 . Fluctuations at the blade-passing frequency are theresult of the hydraulic disturbances that follow the trailing edge of

the impeller blades and the fluid-dynamic interaction of the blades

with the volute of the pump. This phenomenon can be an impor-

tant source for hydraulic noise and vibration 2 .The magnitude of these flow fluctuations for a given pump is

very dependent on the operating point 3 . Besides this flow ratedependence, there are geometrical features that affect flow fluc-

tuations, not only within the pump, but also over the hydraulic

circuit. One such feature is the radial gap between the exit of the

impeller and the volute at the tongue region, 4,5 . The effect ofthe radial gap on the fluid-dynamic perturbations produced in the

pump is particularly interesting, because pump manufacturers usu-ally offer to equip each volute with several impellers of slightly

different outlet diameter and thus different blade-tongue gap. This

is so because these impellers can be conveniently obtained from a

progressive cut-back of the blades, and manufacturers can offer a

wide range of operating specifications without an important incre-

ment of production costs 6 .The main goal of this work was to evaluate the influence of the

radial gap between the impeller exit and the volute tongue on the

unsteady radial forces produced on the impeller of a centrifugal

pump with volute casing. For such purpose, two different impel-

lers were tested for one single volute, with outlet diameters of 190

and 200 mm, respectively the former is a cut-back of the latter .The resulting radial gaps were 15.8% and 10% of the impeller

radius and the respective specific speeds were s =0.52, 0.53, for

the smaller and bigger impellers, respectively.Both experimental and numerical studies were performed. Mea-

surements were carried out with pressure transducers installed on

the shroud of the pump volute, at every 10 deg. Both static and

fluctuating blade-passing frequency pressure values were ob-tained for both impellers over a wide range of flow rates. The

experimental data were compared to the predictions from the nu-

merical simulations of the flow using the commercial CFD code

FLUENT. This comparison focused on both the steady and unsteady

radial forces produced on the impeller of the pump due to the

pressure distribution along the volute, as a preparatory step to the

validation of the total radial forces predicted by the simulations.

Contributed by the Fluids Engineering Division of ASME for publication in theJOURNAL OF FLUIDS ENGINEERING. Manuscript received May 18, 2004; final manuscript

received September 29, 2005. Review conducted by Joseph Katz.

454 / Vol. 128, MAY 2006 Copyright 2006 by ASME Transactions of the ASME

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Experimental Facility

In the hydraulic setup used for the experiments, water was

pumped from and returned to a 100 m 3 reservoir Fig. 1 . Thetested pump had a single axial suction duct and a vaneless spiralvolute casing. This pump could be equipped with a shrouded

seven-bladed impeller of either 190 or 200 mm outside diameter.The main parameters of this pump have been already described in

previous studies 3,7,8 . The rotational speed was =169.65 rad/s and, therefore, the blade passing frequency is fBP=189 Hz. In this setup, measurement uncertainties were found to

be less than 2.5% for the flow rate and 1.5% for the head.For both impellers, 36 pressure taps were located, one at every

10 deg, on the volute shroud along a circumference with R=107 mm see Fig. 2 . Fast-response pressure transducers Kistler7031 were placed on these taps. After proper amplification, theresulting pressure signals and the signal from an optical tachom-eter were digitized and recorded in a PC equipped with a multi-channel analog-to-digital conversion card. The signals were fastFourier transform processed to obtain the pressure fluctuation dataat the dominant frequencies, in particular the blade-passing fre-

quency fBP. Measurement uncertainty for the pressure fluctuations

at fBP was 1.5%. A more detailed description of the test facility

and the experimental procedure can be found elsewhere 3,7 .Tests were conducted at 17 flow rates, from 0% to 160% of the

nominal flow rate, for both impellers. The result was the static

pressure and the pressure fluctuation at the blade-passing fre-quency amplitude and phase delay for each of the 36 measure-ment positions, for each different operating condition. As an ex-ample, Fig. 3 shows the power spectra of the pressure at one

position in the tongue region, 20 deg from the tongue edge, as a

function of the flow rate for the impeller 200 mm in diameter. Asexpected, the unsteady content of the pressure is mostly associatedwith the blade-passing frequency. The amplitude is high for flowrates at the extremes, but at a minimum when the flow rate is nearnominal. Further details on these results and discussion can befound in Ref. 3 or 8 .

In this experimental facility, no velocity measurements wereavailable. Therefore when studying the radial forces, only thepressure component of such forces could be calculated from theexperimental data.

Numerical Model

The meshing details for the 3D model of the pump are dis-cussed in Ref. 9 . The most relevant features of the model are thegrid refinement in the volute tongue region and the sliding meshtechnique, apart from the fully unsteady calculation with theblades changing relative positions for each time step. An example

of the grid generated for one of the impellers is shown in Fig. 4.The numerical code used FLUENT solves the fully 3D incom-pressible Navier-Stokes equations, including the centrifugal forcesource in the impeller and the unsteady terms. Turbulence was

simulated with the standard k- model. Although the grid sizeused was not adequate to investigate local boundary layer vari-ables, global values were well captured and the details of the flownear the tongue for the two impellers follow the usual trends

Fig. 1 Experimental setup for the pump measurements di-mensions in m

Fig. 2 View of the piezoelectric transducers mounted on theshroud side of the pump

Fig. 3 Pressure spectrum as a function of flow rate D2=0.2 m. Position: 20 deg from volute tongue in the rotatingdirection.

Fig. 4 Sketch of the pump unstructured mesh. Inlet and outletpipe portions are added.

Journal of Fluids Engineering MAY 2006, Vol. 128 / 455

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found in the literature for example, 1 . For such calculations,wall functions based on the logarithmic law were used. The time-

dependent term scheme was second order and implicit. The

pressure-velocity coupling was calculated by means of the SIM-

PLEC algorithm. Second order, upwind discretizations for the

convection terms and central difference schemes for the diffusion

terms were used.

The type of boundary conditions at both the inlet and outlet

were selected based on convergence criteria and a good simulationof the flow feature through a real machine. In pumping systems,

the flow rate can be controlled by modifying the circuit hydraulic

resistance for instance, by the opening or closing of a valve . Thiscan be modeled by imposing a pressure drop at the exit as afunction of the flow rate. On the other hand, a constant pressure

level can be considered at the inlet side for all flow rates. There-fore, total pressure at the inlet and a pressure drop proportional tothe kinetic energy at the outlet were imposed throughout the simu-

lations. These boundary conditions avoid the definition of a uni-form and constant velocity profile at the inlet or outlet, which, ingeneral, would not be so realistic.

At the inlet and exit pipes, there is an unavoidable effect on the

final flow solution as a result of the boundary conditions. A rea-sonable length must be added to the real machine geometry toavoid this effect as much as possible and to better simulate thepumping circuit influence. Previous models were developed with

a similar technique and defined a preliminary approach to the

problem, with less inlet and outlet lengths 10 . The comparisonof results between the old and present models leads to the conclu-sion that the most recent model, presented here, provides assur-

ance of a reasonable geometrical independence from the imposedboundary conditions.

A cluster with 12 Athlon-K7 nodes was used for the calcula-

tions. The time step used in the unsteady calculation was set to

2.94104 s in order to get enough time resolution for the dy-

namic analysis. The Courant number was kept below 2, whichassures very good time accuracy and numerical stability.

The number of iterations was adjusted to reduce the residualsbelow acceptable values in each time step. In particular, the ratio

of the sum of the residuals and the sum of the fluxes for a given

variable in all the cells was reduced down to the value of 10 5

five orders of magnitude . After initializing the unsteady calcula-

tion with the steady solution, about five impeller revolutions werenecessary to achieve the periodic unsteady solution convergence.

A final grid with about 335,000 cells was used in the presentstudy. A comparison of the performance prediction curve for oneof the impellers with this numerical model was previously pre-sented 9 . The grid size dependence was studied through inten-sive tests for the bigger impeller 9 . As a conclusion, the overallperformance of the pump was kept the same for the definitivegrids, whose results are presented here. Particularly, even withless than half of the cells finally used for the computations, the

variations observed in flow rate, head, and efficiency were keptunder very reasonable values always less than 1.2% . Besidesthese static value changes, a better and more detailed flow pattern,especially near the walls, could be observed with increasing cell

numbers and this fact conditioned the selection of the finer grid asfinal, to proceed with the study.

The numerical accuracy of both steady and fluctuating results

was estimated to be on the order of 2% and 1%, respectively.During the numerical study, the guidelines proposed in 11 wereused and the numerical uncertainty was related to the change incertain reference values when different mesh refinements were

considered. In other words, the values obtained for accuracy canbe considered reasonable enough as to validate the numerical re-sults.

The developed numerical model considers neither the leakage

flows between the impeller and the casing walls nor the resultingdisk friction. This would lead to an unavoidable growth in thenumber of cells, difficult to handle with existing calculation re-

sources. Nevertheless, the influence of these physical volumes be-tween the impeller shroud or hub and the exterior sidewalls on theunsteady radial forces can be assumed to be small. The effects ofthese volumes are mostly in a plane perpendicular to the rotationalshaft, and then its major force would result in an axial direction.

On the other hand, the magnitude of the flow rate circulatingthrough these small volumes for commercial pumps with similarspecific speed does not usually exceed 4% for the nominal flowrate 12 .

Steady Radial Forces for Both Impellers

The fluid dynamic interaction between the flow leaving the im-peller and the static solid boundary that forms the casing of acentrifugal pump has been widely studied in the literature; see forexample 6 for a general idea or 13 for a more specific problem.In particular, the effect of the radial gap was pointed out as animportant parameter by many authors.

In order to show the static effect of the radial gap, first the staticpressure fields on the shroud side around the volute were mea-sured and calculated. Different flow rates were tested, ranging

from 0% to 160% of the nominal flow rate, in steps of 10%. Theexperimental and numerical results for three of these flow rates

are compared in Fig. 5 as a function of the angular position ,which is measured from the line formed by the center of rotationand the position of the volute tongue edge.

For all the studied flow rates, the numerical results follow thetrends of the experimental data, but some significant differencesappear. At low flow rates, the predicted pressure values appear tobe greater than the experimental ones. On the other hand, at high

flow rates, at angular positions above 200 deg, the predictedvalues are smaller Fig. 5 . These differences can be attributed tonot including the interstitial regions between the impeller hub andshroud and the corresponding lateral sides of the casing in thenumerical model.

The effects of such interstitial regions are twofold. On onehand, some flow rate leakage circulates from the volute to theimpeller inlet through the gap of the shroud side, so that the netflow rate through the impeller is greater than the external flowrate. According to the guidelines 12 , the leakage flow at designoperating conditions may be established at about 4% of the nomi-nal flow rate, but its relative magnitude increases at lower flowrates. Consequently, for a given external flow rate, the predictionsactually correspond to a somewhat smaller flow rate through theimpeller than in the real pump, and, hence, the static pressurepredictions can be expected to be greater than the experimentalvalues. This is what can be observed in Fig. 5 for the low flowrate, or even for the high flow rate in the narrow zone of the

volute 150 deg .

Fig. 5 Static pressure around the volute for three flow ratescomparison of the numerical and experimental results

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On the other hand, the presence of the interstitial gaps betweenthe impeller sides and the lateral walls of the casing means thatthe effective cross section of the volute in the real pump is some-

what greater than in the numerical model. This increment is par-ticularly relevant at the tongue region, since it facilitates either thepositive for low flow rates or negative for high flow rates flowexchange through the radial gap, i.e., it contributes to the attenu-ation of the static pressure difference across that tongue gap. Forthis reason, the experimental static pressure values for the high

flow rate and angular position above 200 deg are greater thanthe corresponding numerical predictions.

From these results, and keeping in mind the existing differ-ences, an integration to obtain the total force on the shaft wasperformed. For the numerical model a full integration over differ-ent axial positions is possible, whereas for the experimental mea-surements, only the pressure on the shroud is available. Therefore,for the experimental measurements a constant pressure distribu-tion over the whole axial span was imposed. However, in the

experimental data, the momentum due to the non-axisymmetricvelocity field was not included because it was not measured.The forces were calculated in the absolute coordinate system

where the reference for the angle is the tongue position. The posi-tive angular direction is the counter-rotating one same referenceas for the angle in Fig. 5 .

In Fig. 6, the experimental results of the integration are shownfor both impellers. An expected trend with a V shape was ob-tained, with a minimum force close to the nominal flow rate. If thesimilarity laws were applied, the same curve would be obtainedbecause the plot is generated using nondimensional values. On thecontrary, a shift of the minimum force value at higher flow ratesfor the bigger impeller was found. Similarity laws seem to be

applicable for flow rates in the range of zero to 0.7QN. Neverthe-less, significant differences were found for higher flow rates. For

the lowest flow range, 0 to 0.5QN

, the nondimensional static forceis slightly higher for the smaller impeller. On the other hand, in itsdimensional values and due to the bigger impeller diameter, theforce is higher for the higher diameter up to the nominal flow rate.At higher flow rates, the static force is much higher for the smallerimpeller, due to the lack of similarity and to the nominal flow rateshift. There is no data available to check possible differences for

flow rates above 1.5QN, but the trend indicates that this effectremains there and the smaller impeller produces higher static ra-dial forces even in the nondimensional values.

Besides the difference in the calculation procedure, the numeri-cal model captures satisfactorily the global trend for the angle ofthe obtained force, as shown in Fig. 7. A bigger difference in the

value of the total radial force is obtained, but only for a reducedrange of the flow rate, that is, for the highest flows Fig. 8 .

A shift in the minimum force position of about 10% of thenominal flow rate is seen when comparing numerical and experi-

mental results. This could be a result of the disk friction forcesinduced by the leakage flows, which are not included in the nu-merical model yet exist in the real machine. The effect of suchsimplification on the calculated performance curves has been dis-cussed in previous papers 9,14 with the conclusion that the ef-ficiency at the nominal flow rate was overestimated. Nevertheless,the flow patterns numerically obtained were in agreement with theexpected trends, for example, the location of the stagnation pointin the volute tongue as a function of the flow rate, separation, andso forth.

Therefore, both static pressure and force are well captured forthe bigger impeller and for the smaller one produced as a cut-back of the bigger one . These results show a minimum force atflow rates slightly higher than the nominal one for both impellers.The non-axisymmetric flow leaving the impeller has a very small

influence on the static radial force at any flow rate.

Comparison of the Fluctuations in the Shroud Side

Plane for Both Impellers

After the static values of the simulation were compared with themeasurements for both impellers, the pressure fluctuations at thebladepassing frequency were examined. A circumferential integra-

Fig. 6 Experimental comparison of the static pressure forcefor the two impellers

Fig. 7 Comparison of the static contribution for the forceangle around the volute angles referred to the rotation centerto volute tongue direction. Impeller with D2 =200 mm.

Fig. 8 Comparison of the static contribution for the force mag-nitude around the volute. Impeller with D2 =200 mm.


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Fig. 9 a Comparison of the pressure fluctuations at the blade-passing frequency for the two impellers Q

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tion of the pressure component at the blade-passing frequency wasperformed around the impeller exit position. This procedure isequivalent to performing a filtering of the pressure distribution on

the volute at the blade-passing frequency for the different studiedflow rates.

For this pump and under the selected operating conditions, nocavitation effects in the performance curve were found. The con-tribution of the dynamic effects, particularly the pressure values inthe volute except at the blade-passing frequency, can be consid-ered negligible see Fig. 3, taken from the measurements . Andthis is also the case for any circumferential position. The previousstatement does not mean that in other parts of the impeller or atthe inlet or outlet pipes, other frequencies could show their ef-fects. Therefore, the predominant effect is observed at the bladepassing frequency. Before a full numerical to experimental com-parison is performed, a comparison of the experimental results forthe two impellers is analyzed Fig. 9 .

The experimental results for the two impellers are compared inFigs. 9

a

and 9

b

, where six different flow rates are plotted. Inthese figures, the effect of the radial gap on the pressure distribu-tions can be clearly seen.

For flow rates below the nominal Fig. 9 a , the differences inthe amplitude of the pressure amplitude are quite small and lim-ited to a region near and downstream of the volute tongue posi-

tion, that is, angular positions with between 0 and 150 deg.For flow rates higher than the nominal Fig. 9 b , the three

different graphs show pressure amplitude differences for the twoimpellers are even higher and extend to all the circumferentialpositions.

These pressure fluctuations are also very well predicted for allflow rates by the numerical model for the bigger impeller. Oneexample for 150% of the nominal flow rate is shown in Fig. 10.For the smaller impeller, similar conclusions can be drawn, al-though this study did not cover this case.

Radial Force Due to Blade-Passing-Frequency Effects

The numerically calculated pressure fluctuations at the blade-passing frequency can be used to compare different axial planes not available in the experiments . Figure 11 shows how the un-steady pressure peak at the blade-passing frequency is not uniformover the whole axial span of the volute. This analysis for differentplanes was already mentioned in previous publications, but isshown and analyzed here for the sake of completeness 9 .

For almost all the studied flows, a similar behavior was found.The values of the pressure fluctuations in both side planes shroudand hub are quite similar, but for the central plane a maximum

value was obtained. This higher pressure in the center plane couldbe an explanation for the pair of counter-rotating vortices found inall circumferential positions, explained in more detail in 9 .

In the figures that follow, the resulting radial force from the

unsteady pressure fluctuations at the blade passing frequency areplotted. The horizontal component corresponds to the component

of the unsteady radial force in the X direction see Fig. 4 . Thisdirection is defined by two geometrical points: the rotational cen-

ter and the volute tongue position. The vertical component Ydirection is perpendicular in the counter-rotating direction. Theresults shown in the following figures trace an envelope for aforce vector which rotates at the blade passing frequency. There-

fore, the force completes Z rotations for each impeller one. Inaddition, for each force rotation, if the vector is placed in theorigin of coordinates, the vector end evolves enclosed by theellipse-like curves and would trace them. The rotation directionand the value of the nondimensionalization parameter are alsoadded to these and following figures.

An integration procedure for the pressure fluctuations is defined

taking into account the value and angular phase at the blade-passing frequency. Then, this integration will produce estimates ofthe radial forces at the blade-passing frequency. The integrationwas performed by assigning to each chosen measurement locationa corresponding surface point in the impeller exit section. Thespatial resolution is fixed by the 36 measurement positions. Thevalue for the unsteady force is obtained following a procedureequivalent to that used for the static pressure, but takes into ac-count the relative angle at this frequency for each flow rate andeach impeller. Figures 12 and 13 show the results of the calcula-tion for the two impellers based on the experimental values of thepressure fluctuations.

The integration procedure gives a force that resembles the totalunsteady force, which rotates around the impeller with a complexand wide frequency range, at the blade-passing frequency. In otherwords, it is a calculation which filters the total unsteady force atsuch particular frequency. In other words, it corresponds to thecomponent of the unsteady force at the blade passing frequency,which performs a rotation for each blade-passing period. When

the force is aligned with the Xaxis, it would produce a radial forcedirected towards the volute tongue position.

For each blade-passing rotation 2/Z rad the projected forcefor a given flow rate completes one of the elliptical shaped figures.The maximum force and angle vary with the flow rate for thesmaller impeller, whereas the angle remains almost constant forthe bigger impeller.

The comparison of Figs. 12 and 13 shows that the bigger im-peller does not always produce a higher dynamic force. For low

Fig. 10 Comparison of the pressure fluctuations at the blade-passing frequency for Q=1.5QN on a shroud plane z=0.0.Tongue at =0 deg and D2 =200 mm.

Fig. 11 Nondimensional pressure fluctuation at the blade-passing frequency for three axial positions at the volute nu-merical values. The tongue is at =0 deg and Q=0.5QN.


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flow rates the trend was as expected the bigger impeller gives riseto higher forces . For the higher flow rates, the opposite trend wasfound. From the available data, no absolute conclusion can bedrawn about the origin of this difference. The extremely complexflow pattern appearing at flow rates higher than nominal couldhave different interactions with the external geometry and producethe measured behavior.

Using the developed numerical model, a full integration overthe axial span is possible. The resulting unsteady forces for twooff-design conditions of the bigger impeller are shown in Fig. 14.

Although the shape of the curve enclosing the vector forces isalso elliptical, the minimum values and angles differ from the

values experimentally observed. These differences can be attrib-uted to the nonuniform axial distribution of the unsteady force atthe blade-passing frequency, shown in Fig. 11.

Another effect on the force due to pressure fluctuations at theblade-passing frequency could be a result of momentum flux fluc-tuations. This effect might be important and has been reported inother existing studies 15 . Therefore, any comparison with thenumerical results would be limited to the pressure component ofsuch fluctuations.

If both axial span variations and velocity influence are dis-

counted, and the calculated values are integrated following thesame procedure as for the experimental results, different conclu-sions can be drawn. This integration was performed for the biggerimpeller and the comparison between numerical and experimentalresults is shown in Figs. 1517.

For all the flow rates tested, the agreement between model andexperimental results is acceptable, both in value and angle. As canbe observed in these three figures, the numerical model repro-duces very precisely the pressure fluctuations at the blade-passingfrequency, independent of the operating condition.

Therefore, when only the pressure fluctuations are considered,the numerical and experimental results describe almost the sameforce both in amplitude and phase. The effect of the axial spanvariations and the lack of uniform velocity around the volute are,thus, important when the unsteady forces are examined. This is

opposite to the case of the steady forces.Of course, when comparing the numerical results for the un-steady forces, the total force and the pressure force which doesnot account for the momentum exchange show relevant differ-ences. A comparison of these forces is plotted in Fig. 18. At thelow flow rate shown and as a general rule for the rates studied, themomentum components of the fluctuation force produce a signifi-cant increase of the envelope of the force and a slight turning ofthis envelope. In general, the effect of the other dynamic forcecomponents apart from the pressure one contributes to the un-steady radial forces damping their effects. In other words, theshape of the force envelope becomes more circular, thus decreas-ing the unbalanced force on the shaft.

Fig. 12 Vector diagram of unsteady radial pressure force fromexperiments. A blade-passing period for D2 =190 mm.

Fig. 13 Vector diagram of unsteady radial pressure force fromexperiments. A blade passing period for D2 =200 mm.

Fig. 14 Vector diagram of unsteady radial force numericallycalculated during a blade passing period for D2 =200 mm


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Conclusions

The static and dynamic effects of the flow in a vaneless volutecentrifugal pump with two different impellers were studied. Theaverage pressure and pressure fluctuations in the shroud side ofthe volute have been used to obtain the resulting forces averageand at blade-passing frequency both experimentally and numeri-cally.

The experimental and numerical approaches used in the studyhave produced enough data to structure the study in two items,namely the static and unsteady effects of the flow passing throughthe pump mainly pressure and radial forces . The unsteady or

dynamic effects are more important at the blade-passing fre-quency and so this predominant frequency has been analyzed.

In spite of the difference in the average pressure at differentaxial planes, good agreement for the average force angle has beenfound. The experimental and numerical results are almost thesame in the angle of the force, but differ in value for high flowrates.

However, a similar situation cannot be assumed for the blade-passing frequency. This could suggest that the general trend found

Fig. 15 Comparison of the vector diagram of unsteady radialforce due to the pressure fluctuations during a blade-passingperiod for D

2=200 mm. Q=0.6QN.

Fig. 16 Comparison of the vector diagram of unsteady radialforce due to the pressure fluctuations during a blade-passingperiod for D2 =200 mm. Q=QN.

Fig. 17 Comparison of the vector diagram of unsteady radialforce due to the pressure fluctuations during a blade-passing

period for D2 =200 mm. Q=1.5QN.

Fig. 18 Comparison of the vector diagram of unsteady radialforce due to the pressure fluctuations and total force during ablade-passing period for D2 =200 mm. Q=0.5QN.


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experimentally, considering only the pressure at the shroud side, isnot a good estimate of the force at that particular frequency. Inparticular, the integration procedure for the unsteady forces can beused to filter the radial unsteady forces at the blade-passing fre-quency. The results, numerically obtained for the two impellers,have shown a lack of axial uniformity, which could be the originof the differences observed. When the effect of the unsteady pres-sure pattern is isolated, the results of the numerical model and theexperiments agree for all flow rates.

The difference in the radial gaps, from 15.8% to 10% of theimpeller radius, does not produce a strong effect on the pressure

fluctuations at any frequency and, in particular, at the blade-passing frequency. Nevertheless, an increase of 10% in the un-steady forces has been found for the bigger impeller. This couldsuggest that decreasing the impeller diameter in further stepswould give rise to even higher forces. These dynamic effectsshould be considered together with the static force results, whichindicated larger forces for the highest flow rates in the case of thesmaller impeller.

Acknowledgment

The authors gratefully acknowledge the financial support fromthe Ministerio de Ciencia y Tecnologia Spain under Project Nos.MCT-01-DPI-2598, DPI2002-04266-C02-02, and DPI2003-09712.

Nomenclatureb2 impeller discharge width, m

D2 impeller discharge diameter, m

F radial force due the unsteady pressure patternsin the absolute coordinate system, N

Fx, Fy unsteady force components horizontal andvertical in the absolute coordinate system, N.Nondimensionalized with the product1

2bD2U2

2

fR ,fBP rotating frequency, blade-passing frequency, Hz

k turbulent kinetic energy, m2/ s2

P ,pA pressure, pressure amplitude at the blade-passing frequency, Pa. Nondimensionalized

with the product1

2U2

2

P0

total pressure at inlet, PaQ , QN flow rate, flow rate at nominal point, m

3/ s

R radial position, m

U2 peripheral velocity at impeller outlet, m/s

X, Y main coordinates, m

Z number of blades

z axial position, m

turbulent dissipation, m 2/ s3

density of the fluid water , Kg/m3

angular position around impeller from the vo-lute tongue location in the rotating direction,deg

rotating speed, rad/s

s QN1/2

/ gHN3/4, specific speed

References

1 Brennen, C. E., 1994, Hydrodynamics of Pumps, Oxford University Press andCETI Inc., Norwich, Vermont, USA.

2 Chu, S., Dong, R., and Katz, J., 1995, Relationship Between Unsteady Flow,Pressure Fluctuations, and Noise in a Centrifugal Pump-Part B: Effects of

Blade-Tongue Interactions, ASME J. Fluids Eng., 117, pp. 3035. 3 Parrondo, J. L., Gonzlez, J., and Fernndez, J., 2002, The Effect of the

Operating Point on the Pressure Fluctuations at the Blade Passage Frequencyin the Volute of a Centrifugal Pump, ASME J. Fluids Eng., 124, pp. 784

790. 4 Dong, R., Chu, S., and Katz, J., 1997, Effect of Modification to Tongue and

Impeller Geometry on Unsteady Flow, Pressure Fluctuations, and Noise in a

Centrifugal Pump, ASME J. Turbomach., 119, pp. 506515. 5 Morgenroth, M., and Weaver, D. S., 1998, Sound Generation by a Centrifugal

Pump at Blade Passing Frequency, ASME J. Turbomach., 120, pp. 736743.

6 Neumann, B., 1991, The Interaction Between Geometry and Performance of aCentrifugal Pump, MEP, London.

7 Gonzlez, J., 2000, Modelizacin Numrica del Flujo no Estacionario enBombas Centrfugas. Efectos Dinmicos de la Interaccin entre Rodete y Vo-

luta, Ph.D. thesis in Spanish , Universidad de Oviedo, Spain.

8 Parrondo, J. L., Gonzlez, J., Prez, J., and Fernndez, J., 2002, A Compari-son Between the Fbp Pressure Fluctuation Data in the Volute of a Centrifugal

Pump and the Predictions From a Simple Acoustic Model, Proc. XXIst IAHR

Symposium on Hydraulic Machinery and Systems, EPFL, Lausanne, Switzer-land.

9 Gonzlez, J., Fernndez, J., Blanco, E., and Santolaria, C., 2002, NumericalSimulation of the Dynamic Effects due to Impeller-Volute Interaction in a

Centrifugal Pump, ASME J. Fluids Eng., 124, pp. 348355. 10 Blanco, E., Fernndez, J., Gonzlez, J., and Santolaria, C, 2000, Numerical

Flow Simulation in a Centrifugal Pump With Impeller-Volute Interaction,ASME-FEDSM-200-11297.

11 Freitas, C. J., 1993, Journal of Fluids Engineering Editorial Policy Statementon the Control of Numerical Accuracy, ASME J. Fluids Eng., 115, pp. 339

340. 12 Karassik, I. G., Krutzsch, W. C., Fraser, W. H., and Messina, J. P., 1985, Pump

Handbook, 2nd ed., McGraw-Hill, New York. 13 Kaupert, K. A., and Staubli, T., 1999, The Unsteady Pressure Field in a High

Specific Speed Centrifugal Pump ImpellerPart I: Influence of the Volute,

ASME J. Fluids Eng., 121, pp. 621626.

14 Gonzlez, J., Santolaria, C., Parrondo, J., Blanco, E., and Fernndez, J., 2003,Unsteady Radial Forces on the Impeller of a Centrifugal Pump With RadialGap Variation, ASME-FEDSM-2003-45400.

15 Tsukamoto, H., Uno, M., Hamafuku, N., and Okamura, T., 1995, PressureFluctuation Downstream of a Diffuser Pump Impeller, FED Am. Soc. Mech.Eng. , 216, pp. 133138.


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