869Chapter 13Influence of the Medium on PerformanceJ. F. Glich, Centrifugal Pumps,DOI 10.1007/978-3-642-40114-5_13, Springer-Verlag Berlin Heidelberg 2014Highviscosities(lowReynoldsnumbers)impairthepumpperformance.Liquids with up to = 3000 mm2/s (3000 cSt) can be pumped with centrifugal pumps, but efficiencies drop to very low levels which make the operation highly uneconomic. Large amounts of free gas entrained in the liquid seriously deteriorate performance and restrict the range where pumping is possible at all. Centrifugal pumps can han-dlelargeamountsofsolidmattereventhoughtheefficiencysuffersbecausethe flow paths of the solids deviate from those of the liquid due to differences in density. Empiricalmethodsareusedtoestimatethedropinperformanceinapplications which involve the fluids mentioned above.13.1Pumping Highly Viscous Fluids13.1.1 Effect of Viscosity on Losses and Performance CharacteristicsWhenacentrifugalpumpisusedfortransportingafluidwithaviscositymuch higherthancoldwater,additionallossesimpairtheperformance.Therefore,the pump characteristics determined for water must not be applied without correction to pumping highly viscous fluids as encountered for example in the oil and process industry.At a sufficiently high viscosity the flow regime becomes laminar. Depending on the size and the speed of the pump, the transition from turbulent to laminar flow occursatabout = 10 4m2/s.For < 10 5m2/stheviscosityinfluenceissmall; therefore, the methods of efficiency scaling explained in Sect. 3.10 may be applied in this range.Howtheperformancedataandpumpcharacteristicsarechangedfromservice with water (subscript w) to operation with a viscous fluid (subscript v) is calculated byempiricalmethods.Tothisend,Eq.(13.1)definescorrectionfactorsforflow rate, head and efficiency (similar to Sect. 3.10.3):870 13Influence of the Medium on PerformancefQQfHHfQvwHvwvw= = =(13.1)Priortodiscussingtheempiricalmethodsindetail,letusexaminesomegeneral principles concerning the physical phenomena involved and the magnitude of the losses to be expected. Consider the impact of high viscosities on the power balance of a pump and the secondary losses according to Sects. 3.5 and 3.6:1.The mechanical losses are independent of the properties of the medium delive-red; for pumping a viscous fluid they are the same as for pumping water.2.LeakagelossesthroughtheannularsealsdiminishwithdecreasingReynolds number or growing viscosity. However, this drop is less important than would be expected from calculating with the viscosity prevalent at the temperature in thesuctionnozzle: AsdiscussedinSect.3.6.2highshearstressesaregenera-ted in the narrow gaps of annular seals. Per surface unit the mechanical energy Pd/A = o wisdissipatedintoheat(oisthewallshearstress).Consequently, extremeshearstressesinanannularsealinevitablyresultinheatingupofthe medium flowing through the gap. The more so, because the flow through the gap is small and the thermal transport properties of oil are not as good as those of water.1 Since the viscosity of oil decreases strongly with rising temperature, the viscosity in the seal drops to values lower than at the temperature in the suction nozzle. Therefore,itmaybeassumedthattheleakagelossesslightlydiminish with increasing viscosity, but that their overall impact on the efficiency is small when changing from operation with water to a viscous fluid. Changes in volume-tric efficiency may thus be conservatively neglected.3.Disk friction losses grow with decreasing Reynolds number or increasing visco-sity. Their influence on the efficiency is very important, as will be shown later on, especially with low specific speeds.4.Thehydrauliclossesininlet,impellerandvoluteordiffuseraccordingto Sect. 3.8 are made up by friction losses which depend on the Reynolds number and by losses due to turbulent dissipation which are virtually independent of the Reynolds number.5.As mentioned above, the flow regime of highly viscous fluids tends to be lami-nar.Thatiswhytheroughnessoftheimpellersidewallsandofthehydraulic channels is of little importance for operation with highly viscous fluids.Disk friction losses and friction losses in the hydraulic channels are the controlling factorsinviscouspumping. TheycanbeestimatedinaccordancewithSect.3as follows:Disk friction losses:The impact of disk friction can be determined from Table 3.6, calculating the friction factor kRR from Eq. (T3.6.3)2. The ratio PRR/Pu of the disk fric-tion losses PRR to the useful power Pu of an impeller is derived from Eq. (T3.5.13). 1 The term oil in the following text is meant to include all highly viscous fluids.2 This equation covers the whole range from laminar to fully turbulent flow.871 13.1Pumping Highly Viscous Fluids Figure 13.1 shows this ratio as a function of the viscosity with the specific speed as a parameter.The following data have been assumed for this calculation: head coefficient opt according to Eq. (3.26), n = 1450 rpm, d2 = 350 mm and sax/r2 = 0.035. The character of the curves in Fig. 13.1 depends little on these assumptions. If the viscosity in-creases from 106 to 3 10 3 m2/s, the ratio of the disk friction to the useful power grows by a factor of 35. At a specific speed of nq = 7, disk friction losses are about 18-timeslargerthantheusefulpower.Evenatnq = 45,thediskfrictionisalmost as high as the useful power if the viscosity reaches 3 10 3 m2/s. The power con-sumption of the pump increases over the whole flow rate range by the difference in disk friction losses PRR = (PRR,vPRR,w). The power curve thus shifts upward nearly parallel to the curve for water.Disregarding any other influences, let us now consider how disk friction losses alone affect the efficiency when the pump operation is changed from water to oil. The efficiency of a single-stage pump can be defined according to Table 3.5 (with PRec = Ps3 = Per = 0) by the approximate expression: +mvol h1 PPRRu(13.2)Assuming vol h = 0.86, the calculation with the values for PRR/Pu from Fig. 13.1 yieldstheefficiencycorrectionfactorsshowninFig.13.2.Thesefactorsinclude solelytheeffectofthehigherdiskfrictionresultingfromgrowingviscosity(the mechanical efficiency cancels if the factor f is formed).From these considerations as well as from Fig. 13.2, it is evident that the increase in power consumption and the drop in efficiency of a pump in viscous service de-pend strongly on the specific speedand this alone due to the effect of disk friction.Hydraulic losses:The influence of the viscosity on the hydraulic losses is discus-sed with reference to Sect. 3.10.3, where these losses are considered as the sum of Reynolds-dependent friction losses ZR and mixing losses ZM which do not depend 0.010.101.0010.00100.001.E-06 1.E-05 1.E-04 1.E-03 1.E-02PRR/PuKinematic viscosity [m2/s]nq = 45nq = 20nq = 7Fig. 13.1Influence of the viscosity on the disk friction losses PRR/Pu; calculated with n = 1450 rpm, d2 = 350 mm and sax/r2 = 0.035872 13Influence of the Medium on Performanceon the viscosity. Consequently, the theoretical head for operation with water and a highly viscous fluid can be expressed as (see also Table 3.8):H H Z Z H Z Zth w R, w M, w v R, v M, v= + + = + + (13.3)InEq.(13.3)itisassumedthattheviscosityhasnoinfluenceontheslipfactor, hence none on the theoretical head either. According to tests in [1] on a pump with nq = 30, this assumption seems to be justifiable even at = 1200 10 6 m2/s (at least as a first approximation).Since the mixing losses are considered to be independent of the Reynolds num-ber, ZM, v = ZM, w in Eq. (13.3) cancels. Hence it is possible to relate Hv to Hw in terms of the multiplier fH defined in Eq. (13.1):fHH1ZHZZ1 1ZHcc1HvwRwwRvRwRwwf vf w= = = , ,,, ,,(13.4)Equations (13.3) and (13.4) apply at any specific flow rate Qx, i.e. for a given theo-retical head. However, at the reduced flow Qv the theoretical head is higher than at Qw as demonstrated by Fig. 13.3. This implies that the hydraulic efficiency is lower than fH if the slip is not affected by the viscosity, Eq. (13.4a). In contrast, if the slip factor diminishes (v < w), the factors fh and fH come closer together.HwQHvHth,vHQvQwHth,wFig. 13.3Derivation of hydraulic efficiency factor0.00.20.40.60.81.01.E-06 1.E-05 1.E-04 1.E-03 1.E-02fRRKinematic viscosity [m2/s]nq= 7nq= 20nq= 45Fig.13.2Influenceofthediskfrictionlossesontheefficiency;calculatedwith,n = 1450rpm, d2 = 350 mm and sax/r2 = 0.035873 13.1Pumping Highly Viscous Fluids fHHHHfHHftanhhvhwvwthwthvHthwthvHw2La 22 = = =,,,,,,,BBv2La 22BQtanf ,(13.4a)IftheratioofthefrictionlossestotheheadinoperationwithwaterZR,w/Hwis known, the head loss in pumping viscous fluids can be estimated from Eq. (13.4). Head correction factors have been calculated in this way for the above example. The result is shown in Fig. 13.4 where the ratio of the friction losses to the head ZR,w/Hw was used as a parameter.With reference to Sect. 3.10.3, the efficiency correction factor given by Eq. (13.5) can be derived from Eqs. (13.2 and 13.4):f fPPPPkf khRRuwvol hwRRuwRRvQ RRWvol =++11,,,hw ,(13.5)The efficiency correction factor given by Fig. 13.5 was derived for fQ fH by means of Eq. (13.5). Figure 13.5 shows once more the great impact of the specific speed. Moreover, the efficiency impairments calculated from this theoretical treatment of losses are similar to those resulting from the tests in Fig. 13.9 below.Thermal effects:The efficiency correction factor includes the effects of disk fric-tion,hydrauliclossesandvolumetriclosses. Theratioofthediskfrictioncoeffi-cients in viscous pumping to those in water is calculated from Eq. (T3.10.9) which includes the factor ftherm accounting for the viscosity decrease in the impeller side-wall gaps. This drop is caused by high shear stresses which raise the temperature in the boundary layers due to dissipation, as has been explained above when discus-singthevolumetriclosses,[2].Consequently,thewallfrictionathighviscosities issmallerthanwouldbepredictedbycalculatingwiththenominaltemperature 0.60.81.01.E-06 1.E-05 1.E-04 1.E-03 1.E-02fH13.40.050.025ZRw/Hw = 0.075Kinematic viscosity [m2/s]Fig.13.4Influenceoftheviscosityonthehydrauliclosses;calculatedwith,n = 1450rpm, d2 = 350 mm874 13Influence of the Medium on Performanceprevailing in the suction nozzle. From tests reported in [2], it may be concluded that at viscosities above about 400 10 6 m2/s the fluid is heated appreciably due to the dissipationcausedbyshearstresses.Basedonthesetestsandananalysisofdata from tests with pumps operating with highly viscous fluids, an empirical factor ftherm has been derived in [3] that allows estimating how much the disk friction is reduced because of thermal effects:f exp 2 10 with =10 m/therm5Ref1 34Ref2 j(,\,( .6ss (13.6)Temperaturemeasurementswithinasingle-stageprocesspumpconfirmthatthe fluid temperature significantly increases in the impeller side rooms and the annular seals. Typical results are shown in Fig. 13.6 which gives the suction temperature Ts, the temperature T2a in the impeller side room (ISR) at the diameter d2 and the tem-peratures near the inlet (Tsp,1) and at the outlet (Tsp,2) of the annular seal. In addition, the viscosities at these local temperatures are given.Two tests are shown in Fig. 13.6: (1) with a viscosity at suction of 450 mm2/s the oil is heated in the impeller sidewall clearance (ISR) locally by up to 15 C and the local viscosity drops from 450 to 240 mm2/s. In the annular seal the oil is heated byanother2 C;(2)withaviscosityatsuctionof205mm2/stheoilisheatedin the impeller sidewall clearance by 7 C and the local viscosity drops from 205 to 150 mm2/s. In the annular seal the oil is heated by 1 C.The temperature rise from the suction to the discharge nozzle was 5.6 C in the testwithaviscosityof450mm2/sand3.3 Cinthetest2with205mm2/s.The temperatureriseintheimpellerisonlyabout20 %ofthesevaluesbecausethe hydraulic losses in the impeller are much smaller than in the volute (as discussed in detail below). The main flow temperature rise at the impeller outlet is thus about 1.1 C at 450 mm2/s and 0.7 C at 205 mm2/s. Overall it is recognized that there are large temperature gradients between the main flow and the ISR and within the ISR. 0.00.20.40.60.81.01.E-06 1.E-05 1.E-04 1.E-03 1.E-02fKinematic viscosity [m2/s]13.5 nq= 12.5 (0.06) nq= 22 (0.045)nq= 30 (0.035)Fig.13.5Influenceoftheviscosityontheefficiency;calculatedwithoptfromEq.(3.26), n = 1450 rpm, d2 = 400 mm and sax/r2 = 0.035. The figures in parentheses represent the fraction of friction losses in water ZR, w/Hw875 13.1Pumping Highly Viscous Fluids Such gradients, which depend on the flow conditions (geometry), make a theoreti-cal analysis of the disk friction losses very difficult because the local temperatures and viscosities cannot be described by analytical methods.The heating of the fluid within the pump increases with the shear stress, hence with the impeller tip speed and the viscosity. This is confirmed by the sample test shown in Fig. 13.7 which shows the temperature rise in the ISR due to disk friction asafunctionofthetipspeedu2andtheviscosity.Consequently,thefactorftherm defined by Eq. (13.6) should include the impeller tip speed. But other features of the pump (for example the impeller side wall clearance and gap A) have an influ-ence too.05101520253010 20 30 40 50 60 70 80Tsp,1-Ts[C]u2[m/s]450 cSt, A = 0.3 mm350 cSt, A = 0.3 mm200 cSt, A = 0.3 mm620 cSt450 cSt350 cSt200 cSt350 cSt, A = 0.6 mm450 cSt, A = 0.6 mmFig. 13.7Sample test: temperature rise in impeller sidewall clearance; the data are specific to the particular test set up and the test fluid T2a = 33 C = 290 mm2/sTs = 23 C = 450 mm2/sTsp,2 = 40 C = 220 mm2/sTsp,1 = 38 C = 240 mm2/sT2a = 48 CTs = 42 C = 205 mm2/sTsp,2 = 50 C = 146 mm2/sTsp,1 = 49 C = 150 mm2/s = 160 mm2/sFig.13.6Temperaturesinanoilpumpnq = 7,n = 3000rpm,q* = 1:leftcolumn:Ts = 23 Cand = 450 mm2/s; right column: Ts = 42 C and = 205 mm2/s, Agap/r2 = 0.04876 13Influence of the Medium on PerformanceFrom Figs. 13.6 and 13.7 it becomes clear that the disk friction losses are over-predicted if calculated with the viscosity at the inlet to the pump. As a consequence, itisnotpossibletodeterminethehydraulicefficiencyfromthelossanalysisand from Eq. (T3.5.8) as done in tests with water if the actual temperatures and viscosi-ties in the ISR and annular seal cannot be predicted. Hence it is equally impossible to determine the slip factor from Eq. (T3.2.9).ForthetestspresentedinFig.13.7thethermaleffectscanbedescribedby Eq. (13.6a), where kRR(T) is the disk friction coefficient calculated from Eq. (T3.6.3) with the viscosity at the average temperature in the impeller sidewall clearance and kRR(Ts) is the friction coefficient calculated with the viscosity at suction.fk Tk T1 145 10AruthermRRRR s5gap21 54Re j(,\,(j(,\,(( )( )..ff2x4Ref4Refuexp 3 2 101 xp 2 2 10j(,\,( ..x e(13.6a)with uRef = 27.3 m/s and Ref = 10 6 m2/sThe correlation given by Eq. (13.6a) covers a range of Agap/r2 = 0.0019 to 0.04 (Agap is the radial clearance at gap A according to Table 0.2).ThefactorfthermfromEq.(13.6a)isspecifictothepumpandoiltestedsince thermal effects depend on several parameters:1.Heat removal via the leakages through the impeller sidewall gap, hence annular seal geometry.2.Animportanteffectistheexchangeoffluidbetweentheimpellersidewall clearances and the main flow. It is brought about by the pumping action of the shrouds(similartoafrictionpump)andbyexchangeofmomentumthrough gap A.3.Heatremovalfromthefluidowingtoconvectionandconductionthroughthe impeller shrouds and the casing.4.Dependencyoftheviscosityontemperature: = f(T).Thesteeperthecurve = f(T) the stronger will be the reduction of the losses in a given pump. In other words: a given pump with a given viscosity at the suction nozzle will have quite differentlossesandefficiencymultipliersifthefluidshavedifferentcurves = f(T). This can be the case with different oils, but the effect can be even stron-ger when pumping different fluids, e.g. oil versus molasses.5.Heattransportpropertiesofthepumpedfluid(thermalconductivity,specific heat, Prandtl number). Because of different transport properties, some substan-cese.g.oilandmolassesbehaveindifferentwayseventhoughtheymay have the same viscosity.Givenalloftheseinfluencesandthelackofprecisedata,Eq.(13.6a)hastobe considered as a rough approximation only. The strong impact of the heating of the fluidontheefficiencyevenatmoderateviscositiescontributestothescatter 877 13.1Pumping Highly Viscous Fluids anduncertaintiesofstatisticalviscositycorrectionfactorswhicharediscussedin Sect. 13.1.2.Characteristics:Figure13.8ashowshowthecharacteristicsarechangedwhen highly viscous fluids are pumped as compared with water transport. If the charac-teristics for viscous fluids are referred to the data at the best efficiency point (BEP) withwaterpumping,themultipliersaccordingtoEq.(13.1)canbereaddirectly from this plot. Suppose that curve 1 in Fig. 13.6a shows the characteristics measu-red with water that correspond to the a hydraulic efficiency of h,w = 0.9. Imagine that the same pump operates with appreciably higher hydraulic losses, such as could be caused by excessive surface roughness, throttling or indeed by a higher viscosity. As a consequence, the Q-H-curve may degrade down to curve 2. Higher hydraulic lossescausethebestefficiencypointtoshifttolowerflowrates.Accordingto Sect. 4.2 it might be expected (as a first approximation) that the BEP moves along line 3 which represents the volute/diffuser characteristics.Figure 13.9 shows test results from [1] performed on a single-stage volute pump nq = 30whichconfirmthisassumptionquitewell(asdemonstratedbythevolute characteristic and its intersection with the curve for 1200 mm2/s).Likewise,testswithviscositiesupto3000mm2/sonthreesingle-stagevolute pumps of nq = 12, 22 and 45 yielded best efficiency points that were close to the val-ues resulting from the volute characteristics, [4]. If such is the case, it follows that fH = fQ applies. With low Reynolds numbers (high viscosities, low speeds, small im-peller diameters) the efficiency curves become very flat, see for example Fig. 13.10. It becomes than difficult to define the BEP. The volute characteristic drawn to the water BEP provides the best guess in this case.Theoretically, the formulae given in Table 4.1 for calculating the best efficiency flow do not allow a prediction of the BEP in viscous fluids from the collector char-acteristic, because the hydraulic efficiency cancels in the equations. Empirically, an Hw w , optHH 1.0 Hv 2 1 1 3 w , optQQ 1.0 fH fQ a2 v wQ P1 2 bFig. 13.8Change of performance curves when pumping highly viscous fluids..878 13Influence of the Medium on Performanceestimation of the BEP flow rate is possible by drawing a straight line, representing thevolute/diffusercharacteristic,fromtheorigintotheBEPwithwaterandthen calculating the head for pumping viscous fluids from Eq. (13.7):H = Hfv w H(13.7)With viscous fluids the power consumption shifts upwards, roughly parallel to the curve for pumping water, as shown in Fig. 13.8b. At flow rates near Q = 0 the power increase is lower because the fluid is heated in the pump. The power increase caused by viscous fluids is almost entirely due to greater disk friction losses on the impeller shrouds and annular seals, because the theoretical head Hth (and consequently Pth) remain essentially constant.The effect of viscosity on the individual losses and the efficiency as well as on the BEP can be estimated by means of the formulae from Sects. 3.6, 3.8, 3.10.3 and 4.2 as discussed above. This procedure allows the specific design parameters of any Fig. 13.9Characteristics of a single-stage volute pump measured with different viscosities, nq = 30, [1]879 13.1Pumping Highly Viscous Fluids pumptobetakenintoaccount.Conversely,onlyempiricalmethods(orpossibly CFD) can be relied upon for investigating the drop in viscosity caused by the local heating of the boundary layers.Dimensionlessperformancecurvesmeasuredonasingle-stagevolutepump nq = 7withviscositiesof450and200mm2/sareplottedinFig.13.10.Figurea shows the pressure coefficients () and the static pressure rise created by the im-peller in terms of p() determined as per Sect. 4.1.3. Interestingly, the static pres-sure rise p() crosses the curve () at a flow rate Qco which drops with increasing viscosity. At flow rates higher than this cross-over, the static head at the impeller outlet exceeds the total head in the discharge nozzle. Accordingly, energy is dissi-pated in the volute above the cross-over flow rate. Only below the cross-over flow rateQco,voluteordiffuserareabletofulfilltheirfunctionofpressurerecovery. Additional tests with higher viscosity and lower speed showed that the cross-over flow rate drops also when decreasing the speed at a given viscosity. Consequently, the Reynolds-number is the controlling factor.The shift of the cross-over flow rate to lower flows when decreasing the Reyn-olds number can be explained by the boundary layer blockage in the volute and dif-fuser (discharge nozzle). The smaller the hydraulic channels (the lower the specific speed),thehigheristherelativeboundarylayerblockage. Asaconsequenceof the reduced flow deceleration (c3q/c2) the onset of stall and recirculation is shifted tolowerflowrates.Forthisreason,pumpsinviscousoperationworksmoothly without undue vibrations at flows with low ratios of Q/Qopt,water where water pumps would be affected strongly by flow recirculation. The steep drop of the head coef-ficientinFig.13.10aatthelargestflowratemeasuredisduetocavitationinthe volute throat area.In Fig. 13.10 the BEPs are found at flows close to the cross-over of the curves p()with().Fromthisobservationitcanbeconcludedthatboundarylayer blockage is also a main responsible for the shift of the BEP to lower flows when the viscosity is increased. This because higher disk friction and lower leakage flows would tend to shift the BEP rather to higher flow rates.In order to increase the capacity of a given machine for pumping high-viscosity fluids, an opening of the volute (or diffuser) throat area would therefore be worth considering.As discussed above, it is not possible to determine the hydraulic efficiency from the loss analysis as per Eq. (T3.5.8). Therefore, the slip factor has been assumed to be equal to that derived from the tests with water. Using this slip factor, the theo-retical head can be calculated from Eqs. (T3.2.7) and (T3.3.1). The hydraulic effi-ciency then follows from h = H/Hth. The hydraulic losses in impeller and volute can subsequently be derived as per Sect. 4.1.3. The losses derived that way are plotted in Fig. 13.10b. These results suggest: (1) There are virtually no shock losses in the impeller. This observation may be explained by the hypothesis that the fluid motion isabletoadapttothebladeswhichactintheupstreamdirectionduetothehigh viscosity. (2) The losses in the volute and the diffusing discharge nozzle make up about 80 % of the hydraulic losses (as expected at low specific speeds); (3) character and magnitude of the impeller losses are quite similar to the water test data shown 880 13Influence of the Medium on Performance0.40.50.60.70.80.91.01.11.21.30.000 0.005 0.010 0.015 0.020 0.0252psi-waterpsi-p waterpsi 200 cStpsi-p 200 cStPsi 450 cStpsi-p 450 cSt0.00.10.20.30.40.50.005 0.010 0.015 0.020 0.0252water200 cSt450 cSt0.000.050.100.150.000 0.005 0.010 0.015 0.020 0.0252water 200 cSt 450 cSt0.00.10.20.30.40.50.60.70.80.91.00.000 0.005 0.010 0.015 0.020 0.0252zeta-Le, waterzeta-Le, 200 cStzeta-La 200, cStzeta-Le, 450 cStzeta-La 450, cSt bacdQcoFig. 13.10Pressure coefficient, static pressure rise in impeller (a), efficiency (b), power coeffi-cient (c), and impeller and volute losses (d); n = 3000 rpm; nq = 7881 13.1Pumping Highly Viscous Fluids in Fig. 4.7; (4) in contrast, the dependence of the volute losses on the flow rate is completely different from Fig. 4.8 in that there is scarcely a minimum in the func-tion Le = f(). With a viscosity of 200 cSt the casing losses depend little on the flow rate, but with increasing viscosity the losses rise steadily from shut-off.As mentioned above the power curves are shifted up by a constant amount due totheincreaseddiskfrictionlosseswhentheviscosityisincreasedexceptnear shutoff where the viscosity drops because the oil is heated due to the large power dissipation at small or no through-flow. The test in Fig. 13.10c well confirms this observation.13.1.2 Estimation of Viscous Performance from the Characteristics Measured with WaterThe discussion in Sect. 13.1.1 demonstrates (as could be expected a priori) that the hydraulic losses and the efficiency of a pump operating with viscous fluids depend ontheReynoldsnumberandthespecificspeed.Thelatterreflects,asafirstap-proximation, the geometry of the hydraulic channels and the distribution of losses. In addition, the flow rate ratio q* may be expected to have an influence. Therefore, the correction factors defined by Eq. (13.1) are in general terms described by the expression:f f n q f nQHd qx q= = ( , , *) ( , , , , *, ) Re2For estimating the performance with highly viscous fluids from test data measured with water, two methods are available: A) Loss analysis; B) Various empirical pro-cedures.13.1.2.1Loss AnalysisIfsufficientgeometricaldataofthepumptobeinvestigatedareavailable,aloss analysis as described in Sect. 3.10.3 and Table 3.10 promises to yield the most ac-curate results. Nevertheless, it is always advisable to compare the results with em-pirical methods since the local variations of viscosity resulting from thermal effects are difficult to capture.The test data reported in [1, 58] have been compared to the predictions of the loss analysis method. This comparison has been discussed in detail in [9 and 3]. The results are given in Figs. 13.11 and 13.12 which show the correction factors for ef-ficiency and head as measured and as predicted from the loss analysis. In order to determine the influences of Reynolds number, pump type (single- or double-entry) and specific speed, these correction factors are plotted against a modified Reynolds number which is defined by Eq. (13.8):Re = Re fmod s1 5q0 75. .(13.8)882 13Influence of the Medium on PerformanceThe test data plotted in Figs. 13.11 and 13.12 cover the following range: 250 < Re-mod 20, for example, according to [4] the procedure [N.4] risks to greatly over-predictpowerconsumptionwithviscousfluids,whereasthepowerpredictedfor nq < 15 risks to be too low. The tests shown in Fig. 13.9 with a pump nq = 30 give anexample forthisdiscrepancy: the efficiency measured at 1200 10 6 m2/scor-responds to a factor f =0.49, whereas method [N.4] predicts f = 0.2.Applyingeitherofthestatisticalmethodstovariouspumptypesharborslarge uncertainties because pump design, hydraulic layout and surface finish have an ef-fect on the magnitude of the various losses. In view of these uncertainties, an exact descriptionoftheproceduresreportedin[N.4]and[B.5]hasnotbeenattempted when deriving the equations in Table 13.1(1). The formulae in Table 13.2(1) agree well with the general characteristics of both of these methods, but they do not al-ways yield identical values as can be read from the graphs.Table 13.2 (1) Estimation of pump characteristics when pumping viscous fluids according to [N.4] and [B.5] SI-units; Q [m3/s]; H [m] Eq. Procedure[N.4][B.5] Parameter 125 . 0 25 . 0HI) H g ( Q480B=qHI25 . 0) s (n15B ) H g (n Q100 B ==13.2.1 Correction factor for flow rate 5 . 5HI) B (log 11 . 0Qe f=4) B (log 165 . 0B 013 . 0qQen15f=13.2.2 Correction factor for flow rate ratio ) 1 * q )( 1 B ( 014 . 0 1 fHI * q =13.2.3 Correction factor for head * q Q Hf ) f 75 . 0 25 . 0 ( f + =13.2.4 Correction factor for efficiency 5 . 0 B 04 . 0HIe 05 . 0= 59 . 0B 083 . 0 = qn B f = 13.2.5 With expeller vanes thought valid for all configurations nq < 25:nq = 0.005 (25- nq) nq > 30:nq = 0.005 (nq - 30) Without expeller vanes 08 . 1HI) 5 . 0 B (e f = f,o = 0.4 + 0.6 f 13.2.6 Power vv v vvH Q gP=13.2.7 887 13.1Pumping Highly Viscous Fluids Themethoddescribedin[N.11]isempiricaltoo.Ityieldsvaluesquitesimi-lartothoseresultingfromthecalculationaccordingtoEqs.(T13.1.1to13.1.4). Table 13.2(2) gives a representation which is equivalent to [N.11].All of the empirical procedures for predicting pump characteristics as reported in[N.4],[N.11]and[B.5]arebasedontestswithrelativelysmall,single-stage, single-entry process pumps with Reynolds numbers of approximately 4 106 when operating with water. Therefore, the empirical methods can be expected to produce reasonably accurate predictions for this type of pump only. For large pumps with Reynolds numbers well above 107 in water service, these methods are not accurate enough. For such pumps the absolute Reynolds number (and not just the viscosity) has to be taken into consideration. The performance estimation of a large pump for oil transport starting from this data base of relatively small model pumps is likely to be too conservative and a loss analysis is recommended instead.13.1.3Influence of Viscosity on the Suction CapacityThe procedures in [N.4] and [B.5] give no information about cavitation behavior. Due to additional losses at the inlet of the pump, a certain increase of the required Table 13.2 (2) Estimation of pump characteristics when pumping viscous fluids according to [N.11]SI-units; Q [m3/s]; H [m] Simplified representation; for information only; always refer to newest edition of respective standard! Eq. Parameter 25 . 0qf Re , q125 . 0 25 . 0nn) H g ( Q480B= nq,Ref = 2013.2.8 Correction factor for flow rate 15 . 3) B (log 165 . 0Qe f=13.2.9 Correction factor for head at BEP Q BEP , Hf f =13.2.10 Correction factor for head at q* 1 75 . 0BEP , H H*) q )( f 1 ( 1 *) q ( f =BEPQQ* q = 13.2.11 Correction factor for efficiency = B fwith69 . 0B 0547 . 0 = 13.2.12 Power at coupling vv v vvH Q gP=13.2.13 Correction factor for NPSH3 nss,Ref = 200 33 . 1ssf Re , ssBEP , H1 NPSHnn1f1A 1 f + =13.2.14 End suction pumps: A1 = 0.1; pumps with radial inlet: A1 = 0.5 Apply fNPSH at constant flow. 888 13Influence of the Medium on PerformanceNPSH3 should be expected. Hence a safety margin is recommended. The inlet loss-esaccordingtoSect.6.3.2are:Hv,E = E c1m2/(2g).Assumingthattheselosses increase with the ratio of the friction coefficients cf,v/cf,w, the correction factor for NPSH can be calculated from:f =1 +ccc2 g NPSHNPSH Ef vf w1m23,,(13.12)The friction coefficients cf,v and cf,w are calculated from Table 3.10. According to Sect. 6.3.2 the loss coefficient of the inlet follows from E = c1. For pumps with an axial inlet E = 0.1 to 0.15 can be expected, for between-bearing pumps (radial inlet casings) E = 0.25 to 0.5.The NPSH3 for water pumping has to be multiplied by the factor fNPSH so that at least part of the additional losses occurring in a viscous fluid is taken into account. This correction is applied at constant flow rates (i.e. without shifting the flow by the factor fQ).Test results on the suction behavior with highly viscous fluids are not available. Due to thermodynamic effects, a slight reduction of the NPSH required is expected for various substances in comparison with water, see Sect. 6.4.1. Thermodynamic effects can thus compensate for the impact of higher viscosities on the NPSH3 to some extent.13.1.4Start-up of Pumps in Viscous ServiceWhenoperatingmultistagepumpswithhigh-viscosityfluids,theheatingofthe medium from stage to stage may be appreciable at low flow rates. The temperature rise in each stage Tst can be derived from Eq. (11.9). With the power and efficiency of the stage represented by Pst and st we get:T =1Pc Q =11gHcst ststp ststp( ) (13.12a)A stage-by-stage calculation can be done using the temperature and viscosity at ev-ery stage inlet as calculated from Eq. (13.12.a). Also the axial thrust balance device receives fluid heated by the previous stages. These effects increase as the flow rate isreduced.Thelowerthespecificspeed,thehigheristhetemperaturerisefrom stage to stage.Duringstart-upatlowflow,heatingeffectsbecomemostpronounced.When pumping a viscous fluid in a closed system (e.g. a pump for transformer oil cool-ing),thesystemcanbewarmedupduringstart-upbyoperatingthepumpatlow flow (in the case of a variable speed drive also at reduced speed). Thus it is pos-sible to start the pump without needing to especially size the motor power for cold start-up. Likewise, processes can be started by recycling fluid over a minimum flow 889 13.1Pumping Highly Viscous Fluids bypass if temperatures of the product are higher during normal operation than under start-up conditions (an example are oil wells).13.1.5 Viscous Pumping Applications-Recommendations and Comments1.According to the available test data, pumps with specific speeds in the range of nq = 20 to about 40 will give the best efficiencies when pumping viscous fluids.2.Withagivenheadandspeed,highheadcoefficientsyieldsmallerimpeller diameters, and consequently lower disk friction losses and better efficiencies. Thatiswhyhighheadcoefficientsshouldpreferablybechosenforpumping highly viscous fluids. Since the Q-H-curve becomes very steep when viscous fluids are pumped, impellers with higher than normal pressure coefficients can be used without the risk of an unstable Q-H-curve (some tests are presented in [6]). However, for water pumping such impellers would not be acceptable.3.Asthediskfrictionismuchhigherwhenpumpingfluidsmoreviscousthan water, expeller vanes do not seem to be a good choice with regard to efficiency. Rather,theobvioussolutionforbalancingtheaxialthrustarebalanceholes combinedwithanannularsealontherearshroud,becausetheannularseal losses become less important with increasing viscosity. Disk friction losses will be reduced by the heating of the fluid in the impeller sidewall gaps due to dis-sipation because the local viscosity decreases at higher temperatures.4.In turbulent flow the disk friction losses depend very little on the width of the impeller sidewall gap, in laminar flow these losses grow in inverse proportion to the axial clearance between the casing and the impeller, Eq. (T3.6.3). The-refore narrow impeller sidewall gaps should be avoided when pumping highly viscous fluids. The width of the impeller sidewall gap is also an important fac-torofuncertaintyinperformanceprediction,sinceitdoesnotenterintothe calculation as per [N.11] and [B.5]. This is especially true at low specific speeds where the viscous power increase is goverend by extremely high disk friction losses. It is thus to be expected that two otherwise identical pumps with diffe-rent axial clearances of the impeller sidewall gaps attain different efficiencies when pumping high-viscosity fluids. The high losses are to some extent offset by thermal effects resulting from dissipation in the narrow sidewall gaps.5.Predictionsofthepumpcharacteristicsbasedonthecorrectionfactorsgiven in[N.11]and[B.5]mustbeconsideredasrelativelyroughapproximations, because the dependence of the losses on the Reynolds number can vary appre-ciably in different pumps. The absolute values of efficiency and Reynolds num-ber, the pump design, as well as the quality of execution, all have an impact on viscous performance predictions.6.Two otherwise identical pumps with different surface roughness have different efficienciesinturbulentflow,butequalefficienciesinlaminarflow.Conse-890 13Influence of the Medium on Performancequently,differentfactorsfHundfshouldbeusedforestimatingtheperfor-mance in viscous pumping from data measured with water. This effect can only be accounted for by a detailed loss analysis based on known surface roughness.7.Duetothehighlosseswhenpumpinghighlyviscousfluidsthethermome-tricmethodcanbeeasilyappliedinaplanttodeterminetheefficiencyfrom Eq.(11.9)asdescribedinSect.11.6. Thetemperaturesmentionedincontext with Fig. 13.6 are an example.8.Thesuctionpipeshouldbeasshortaspossible;hencethepumpshouldtake suction immediately from the tank. If the suction pipe has some length, its dia-meter should be one nominal size large than the suction nozzle of the pump.9. Pumping viscous fluids requires more motor power. The starting torque and the start-up current are higher as well. Therefore, it has to be checked whether the pump shaft, coupling and driver are suitable for these conditions.10.Given the uncertainties of the calculation methods and the possible variations ofthephysicalpropertiesofthefluidstobepumped,adequatemarginsare necessary when selecting the pump and the motor.11.Viscous fluids risk disturbing the adequate functioning of auxiliary equipment (such as shaft seals, barrier fluid injection or cooling circuits, etc.). Therefore care should be taken when specifying these systems.12.The calculation methods discussed apply to Newtonian fluids; the behavior of Non-Newtonian fluids can be different, as discussed in Sect. 13.5.13.2Pumping of Gas-Liquid MixturesGas-liquid mixtures are encountered in the process industry as well as in the pro-duction and transport of oil, which often is accompanied by natural gas. An impor-tant application of high economical significance is the transport of oil-gas-mixtures coming out of oil wells. By means of two-phase pumps the pressure at the well-head can be decreased, thus boosting oil production. However, handling mixtures with highfractionsofgasbycentrifugalpumpsisadifficulttasksincegasandliquid tendtoseparatebecauseoftheirlargedensitydifferences.Pumpingcanthenbe-come very inefficient or even impossible. As discussed in detail below, this phase separation is caused by body forces and buoyancy which is due to pressure gradi-ents perpendicular to the main flow direction.13.2.1Two-phase Flow Patterns in Straight Pipe FlowPrior to the discussion of the complex flow phenomena in pump impellers and col-lectors, it is appropriate to review the different flow patterns in a horizontal pipe or channel. All the more so, since this type of flow is relevant for the inlet to a two-phase pump and can have an impact on performance.