AP10_1.vp 1 Introduction Large tall vessels with a draught tube (shown in Fig. 1) are used for mixing suspensions, especially when high homoge- neity is desirable. A short shaft and a small ground area are advantages of this configuration. 2 Modifications to a draught tube for particle suspension The 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 for initiating particle suspension np is significantly greater than the 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/ 5 Acta Polytechnica Vol. 50 No. 1/2010 Mixing Suspensions in Tall Vessels with a Draught Tube J. Brož, F. Rieger 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. Keywords: mixing equipment, draught tube, suspension. 45° h d 1 vessel 2 draught tube 3 impeller 4 baffles Pitched six-blade turbine CVS 69 1020 h/d 0.2� 3 1 2 4 d t H L H 2 H T D DT l 4 5 ° Fig. 1: Mixing vessel with a draught tube n k = 1269.8 c v 0.1026 n p = 2346.8 c v 0.2066 n k = 4532.8 c v 0.3166 n p = 4627.1 c v 0.3101 100 1000 10000 0.01 0.1 1 cv dp = 0.15 mm d = 0.15 mmp d = 1.28 mmp d = 1.28 mmp n n k p , m in [ ] � 1 Fig. 2: Comparison of impeller speed nk,p for particle diameters dp � 1.28; 0.15 mm draught tube shown in Fig. 3 has been proposed as a utility model [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 velocity in the gap causes particle suspension – Fig. 4b. Then the draught tube can gradually be lowered as the particles are sus- pended and the bed of settled particles decreases. 3 Experimental We need to know the power consumption and the critical agitator speed in order to design mixing equipment. Measurements were carried out on the model mixing equipment shown in Fig. 5, with the dimensions presented in Table 1. Water suspensions of five fractions of glass balotine with mean diameters from 0.15 to 1.28 mm with volumetric content of particles cv in the range from 0.025 to 0.45 were 6 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 50 No. 1/2010 1 3 2 4 5 a) operating position b) upper position Fig. 3: Vessel with telescopic draught tube a) b) Fig. 4: Draught tube above the sediment layer used in the measurements. The power consumption was measured by a tensometric pick-up with a GMV amplifier made by Lorenz Messtechnik at the agitator speed necessary to initiate np and maintain nk particle suspension. The critical speed of the agitator was determined visually and measured photoelectrically. 4 Experimental results The results of the power consumption measurements were processed to the form of power number Po dependence on volumetric content cv for various particle diameters shown in Fig. 6. This figure shows that the power number is independent of particle content and size. The power number at the speed necessary to initiate particle suspension Pop does not differ significantly from the power number at the speed necessary to keep a particle in suspension Pok, and its mean value is Po � �163 0 07. . . Measurements of the critical agitator speed necessary to keep a particle in suspension nk have been presented in [2]. The results were processed in the form of a dimensionless equation Fr p � � � � � � �� � A d D a (1) from which the critical agitator speed can be calculated. The coefficients in a and A depend on particle content and can be determined from the following relations a c� � �0 47 2 26. . v (2) A c� �40 07 17 62. exp ( . )v (3) List of symbols cv mean volumetric concentration of particles d agitator diameter dp particle diameter © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 7 Acta Polytechnica Vol. 50 No. 1/2010 D [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 54 Table 1 45° 1 2 4 5 3 direction of flow d t H L H 2 H T D DM l DT D1 Fig. 5: Vessel with telescopic draught tube 0.1 1 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.15 0.25 0.47 0.65 1.28 Pok = 1.73 P o k cv 0.1 1 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.15 0.25 0.47 0.65 1.28 Pop = 1.54 P o p cv a) b) Fig. 6: Power number Po dependence on the mean particle volumetric content cv: a) Pok � �173 0 08. . , b) Pop � �1 54 011. . D vessel diameter Fr� modified Froude number, Fr�= n d g k 2 � �� n agitator speed P power Po power number, Po P n d� �s 1 3 5 � density of liquid �s density of suspension �� solid-liquid density difference Acknowledgement This 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 Brož Prof. Ing. František Rieger, DrSc. phone: .+420 224 352 548 e-mail: frantisek.rieger@fs.cvut.cz Department of Process Engineering Czech Technical University in Prague Faculty of Mechanical Engineering Technická 4 166 07 Prague 6, Czech Republic 8 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 50 No. 1/2010