A tall vessel with a telescopic draught tube is proposed for mixing suspensions. The paper presents the relations for calculating the agitator power consumption and the speed necessary to keep a particle in suspension.

Brož, J.

Rieger, F.

Acta Polytechnica

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

1 IntroductionLarge tall vessels with a draught tube (shown in Fig. 1) areused for mixing suspensions, especially when high homoge-neity is desirable. A short shaft and a small ground area areadvantages of this configuration.2 Modifications to a draught tube forparticle suspensionThe main disadvantage of this arrangement is that parti-cle suspension is difficult after mixing has been interrupted.As shown in Fig. 2, in the case of small particles the speed forinitiating particle suspension np is significantly greater thanthe speed necessary to keep a particle in suspension nk.Operation at high speed requires high power consump-tion. To overcome this difficulty, the telescopic withdrawable©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 5Acta Polytechnica Vol. 50  No. 1/2010Mixing Suspensions in Tall Vessels witha Draught TubeJ. Brož, F. RiegerA tall vessel with a telescopic draught tube is proposed for mixing suspensions. The paper presents the relations for calculating the agitatorpower consumption and the speed necessary to keep a particle in suspension.Keywords: mixing equipment, draught tube, suspension.45°hd1 vessel2 draught tube3 impeller4 bafflesPitched six-blade turbineCVS 69 1020 h/d 0.23124dtH LH2HTDDTl45°Fig. 1: Mixing vessel with a draught tubenk = 1269.8 c v0.1026np = 2346.8 c v0.2066nk = 4532.8 c v0.3166np = 4627.1 c v0.31011001000100000.01 0.1 1cvdp = 0.15 mmd = 0.15 mmpd = 1.28 mmpd = 1.28 mmpnnkp,min[]1Fig. 2: Comparison of impeller speed nk,p for particle diametersdp  1.28; 0.15 mmdraught tube shown in Fig. 3 has been proposed as a utilitymodel [1].For settled particle suspension, the draught tube is with-drawn to the upper position with a small gap between the sed-iment and the draught tube – Fig. 4a. The high liquid velocityin the gap causes particle suspension – Fig. 4b. Then thedraught tube can gradually be lowered as the particles are sus-pended and the bed of settled particles decreases.3 ExperimentalWe need to know the power consumption and the criticalagitator speed in order to design mixing equipment.Measurements were carried out on the model mixingequipment shown in Fig. 5, with the dimensions presented inTable 1. Water suspensions of five fractions of glass balotinewith mean diameters from 0.15 to 1.28 mm with volumetriccontent of particles cv in the range from 0.025 to 0.45 were6 ©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/Acta Polytechnica Vol. 50  No. 1/201013245a) operating position b) upper positionFig. 3: Vessel with telescopic draught tubea) b)Fig. 4: Draught tube above the sediment layerused in the measurements. The power consumption wasmeasured by a tensometric pick-up with a GMV amplifiermade by Lorenz Messtechnik at the agitator speed necessaryto initiate np andmaintain nk particle suspension. The criticalspeed of the agitator was determined visually and measuredphotoelectrically.4 Experimental resultsThe results of the power consumptionmeasurements wereprocessed to the form of power number Po dependence onvolumetric content cv for various particle diameters shown inFig. 6.This figure shows that the power number is independentof particle content and size. The power number at the speednecessary to initiate particle suspension Pop does not differsignificantly from the power number at the speed necessaryto keep a particle in suspension Pok, and its mean value isPo 163 007. . .Measurements of the critical agitator speed necessary tokeep a particle in suspension nk have been presented in [2].The results were processed in the form of a dimensionlessequationFr p 	AdDa(1)from which the critical agitator speed can be calculated. Thecoefficients in a and A depend on particle content and can bedetermined from the following relationsa c  0 47 226. . v (2)A c 4007 17 62. exp( . )v (3)List of symbolscv mean volumetric concentration of particlesd agitator diameterdp particle diameter©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 7Acta Polytechnica Vol. 50  No. 1/2010D[mm]DT[mm]D1[mm]DM[mm]d[mm]H[mm]HT[mm]H2[mm]t[mm]L[mm]l[mm]300 72 120 81 65 600 14 444 8 540 54Table 145°1 2 4 53directionof flowdtHLH2HTDDMlDTD1Fig. 5: Vessel with telescopic draught tube0.11100 0.1 0.2 0.3 0.4 0.5 0.60.150.250.470.651.28Pok = 1.73Pokcv0.11100 0.1 0.2 0.3 0.4 0.5 0.60.150.250.470.651.28Pop = 1.54Popcva) b)Fig. 6: Power number Po dependence on the mean particle volumetric content cv: a) Pok  173 008. . , b) Pop  154 011. .D vessel diameterFr modified Froude number, Fr=n dgk2 n agitator speedP powerPo power number, Po P n d   s1 3 5 density of liquids density of suspension solid-liquid density differenceAcknowledgementThis work was supported by research project of the Minis-try of Education of the Czech Republic MSM6840770035.References[1] Utility model proposal PUV 2009-20921.[2] Brož, J., Rieger, F.: Czasopismo Techniczne. Vol. 105(M/2008), No. 6, p. 29–36.Jiří BrožProf. Ing. František Rieger, DrSc.phone: .+420 224 352 548e-mail: frantisek.rieger@fs.cvut.czDepartment of Process EngineeringCzech Technical University in PragueFaculty of Mechanical EngineeringTechnická 4166 07 Prague 6, Czech Republic8 ©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/Acta Polytechnica Vol. 50  No. 1/2010

Mixing Suspensions in Tall Vessels with a Draught Tube

A tall vessel with a telescopic draught tube is proposed for mixing suspensions. The paper presents the relations for calculating the agitator power consumption and the speed necessary to keep a particle in suspension

J. Brož

F. Rieger

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1 IntroductionLarge tall vessels with a draught tube (shown in Fig. 1) areused for mixing suspensions, especially when high homoge-neity is desirable. A short shaft and a small ground area areadvantages of this configuration.2 Modifications to a draught tube forparticle suspensionThe main disadvantage of this arrangement is that parti-cle suspension is difficult after mixing has been interrupted.As shown in Fig. 2, in the case of small particles the speed forinitiating particle suspension np is significantly greater thanthe speed necessary to keep a particle in suspension nk.Operation at high speed requires high power consump-tion. To overcome this difficulty, the telescopic withdrawable©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 5Acta Polytechnica Vol. 50  No. 1/2010Mixing Suspensions in Tall Vessels witha Draught TubeJ. Brož, F. RiegerA tall vessel with a telescopic draught tube is proposed for mixing suspensions. The paper presents the relations for calculating the agitatorpower consumption and the speed necessary to keep a particle in suspension.Keywords: mixing equipment, draught tube, suspension.45°hd1 vessel2 draught tube3 impeller4 bafflesPitched six-blade turbineCVS 69 1020 h/d 0.23124dtH LH2HTDDTl45°Fig. 1: Mixing vessel with a draught tubenk= 1269.8 cv0.1026np= 2346.8 cv0.2066nk= 4532.8 cv0.3166np= 4627.1 cv0.31011001000100000.01 0.1 1cvdp = 0.15 mmd = 0.15 mmpd = 1.28 mmpd = 1.28 mmpnnkp,min[]1Fig. 2: Comparison of impeller speed nk,p for particle diametersdp  1.28; 0.15 mmdraught tube shown in Fig. 3 has been proposed as a utilitymodel [1].For settled particle suspension, the draught tube is with-drawn to the upper position with a small gap between the sed-iment and the draught tube – Fig. 4a. The high liquid velocityin the gap causes particle suspension – Fig. 4b. Then thedraught tube can gradually be lowered as the particles are sus-pended and the bed of settled particles decreases.3 ExperimentalWe need to know the power consumption and the criticalagitator speed in order to design mixing equipment.Measurements were carried out on the model mixingequipment shown in Fig. 5, with the dimensions presented inTable 1. Water suspensions of five fractions of glass balotinewith mean diameters from 0.15 to 1.28 mm with volumetriccontent of particles cv in the range from 0.025 to 0.45 were6 ©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/Acta Polytechnica Vol. 50  No. 1/201013245a) operating position b) upper positionFig. 3: Vessel with telescopic draught tubea) b)Fig. 4: Draught tube above the sediment layerused in the measurements. The power consumption wasmeasured by a tensometric pick-up with a GMV amplifiermade by Lorenz Messtechnik at the agitator speed necessaryto initiate np and maintain nk particle suspension. The criticalspeed of the agitator was determined visually and measuredphotoelectrically.4 Experimental resultsThe results of the power consumption measurements wereprocessed to the form of power number Po dependence onvolumetric content cv for various particle diameters shown inFig. 6.This figure shows that the power number is independentof particle content and size. The power number at the speednecessary to initiate particle suspension Pop does not differsignificantly from the power number at the speed necessaryto keep a particle in suspension Pok, and its mean value isPo  163 007. . .Measurements of the critical agitator speed necessary tokeep a particle in suspension nk have been presented in [2].The results were processed in the form of a dimensionlessequationFr p 	AdDa(1)from which the critical agitator speed can be calculated. Thecoefficients in a and A depend on particle content and can bedetermined from the following relationsa c  0 47 226. . v (2)A c 4007 17 62. exp( . )v (3)List of symbolscv mean volumetric concentration of particlesd agitator diameterdp particle diameter©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 7Acta Polytechnica Vol. 50  No. 1/2010D[mm]DT[mm]D1[mm]DM[mm]d[mm]H[mm]HT[mm]H2[mm]t[mm]L[mm]l[mm]300 72 120 81 65 600 14 444 8 540 54Table 145°1 2 4 53directionof flowdtHLH2HTDDMlDTD1Fig. 5: Vessel with telescopic draught tube0.11100 0.1 0.2 0.3 0.4 0.5 0.60.150.250.470.651.28Pok = 1.73Pokcv0.11100 0.1 0.2 0.3 0.4 0.5 0.60.150.250.470.651.28Pop = 1.54Popcva) b)Fig. 6: Power number Po dependence on the mean particle volumetric content cv: a) Pok  173 008. . , b) Pop  154 011. .D vessel diameterFr modified Froude number, Fr=n dgk2 n agitator speedP powerPo power number, Po P n d   s1 3 5 density of liquids density of suspension solid-liquid density differenceAcknowledgementThis work was supported by research project of the Minis-try of Education of the Czech Republic MSM6840770035.References[1] Utility model proposal PUV 2009-20921.[2] Brož, J., Rieger, F.: Czasopismo Techniczne. Vol. 105(M/2008), No. 6, p. 29–36.Jiří BrožProf. Ing. František Rieger, DrSc.phone: .+420 224 352 548e-mail: frantisek.rieger@fs.cvut.czDepartment of Process EngineeringCzech Technical University in PragueFaculty of Mechanical EngineeringTechnická 4166 07 Prague 6, Czech Republic8 ©  Czech Technical University Publishing House http://ctn.cvut.cz/ap/Acta Polytechnica Vol. 50  No. 1/2010

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Mixing Suspensions in Tall Vessels with a Draught Tube

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