# Effect of Viscosity on Pump Performance

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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 issmallerthanwouldbepr

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