ap-6-10.dvi Acta Polytechnica Vol. 50 No. 6/2010 Pitched Blade Turbine Efficiency at Particle Suspension D. Ceres, T. Jirout, F. Rieger Abstract Mixing suspensions is a very important hydraulic operation. The pitched six-blade turbine is a widely-used axial-flow impeller. This paper deals with effect relative impeller size and particle content on the efficiency of a pitched six-blade turbine at particle suspension. Two pitched six-blade turbines were used in model measurements of just suspension impeller speed. The ratios of the vessel to agitator diameter D/d were 3 and 4.5. The measurements were carried out in a dish-bottomed vessel 300 mm in diameter. The just suspension impeller speeds weremeasured using an electrochemical method, andwere checked visually. A 2.5 % NaCl water solution was used as the liquid phase, and glass particles with four equivalent diameters between 0.18 and 0.89 mm and volumetric concentration from 2.5 % to 40 % were used as the solid phase. The criterion values πs = P o √ F r′3(d/D)7 were calculated from the particle suspension and power consumption measurements. The dependencies of πs on particle content cv show that larger agitators are more efficient for higher particle content. Keywords: Pitched blade turbine, particle suspension, agitator efficiency. 1 Introduction Mixing suspensions is a very important hydraulic op- eration. Suspensions are frequently mixed when dis- persions are prepared or homogenised, and in mass transfer operations between solid particles and a liq- uid, often accompanied by a chemical or biochemical reaction. It is estimated that about 60 % of mixing involves heterogeneous particulate solid phase-liquid systems. Fig. 1 Numerous papers on particle suspension in agi- tatedvesselshavebeenpublished. Reviewshavebeen published by Rieger and Ditl [1] and more recently by Kasat and Pandit [2]. These authors show that axial-flow pattern impellers are generally considered themost suitable agitators in suchcases. Thepitched six-blade turbine shown in Fig. 1 is the one of most widely-used axial-flow impellers. The present paper deals with the effect of relative impeller size and par- ticle content on the efficiency of a pitched six-blade turbine atparticle suspension. This problemwasalso the topic of our earlier papers [3, 4], in which atten- tion was focused on relative impeller size, and mea- surements were carried out for two particle contents only. 2 Theoretical background Inorder todesignmixingapparatuses, it is important to know the reference state of just off-bottom parti- cle suspension, which is often defined as the state at which no particle remains in contact with the vessel bottom for longer than a certain time. The impeller speed corresponding to this state is referred to as the critical (just-suspended) impeller speed nc. On the basis of inspection analysis of the equa- tion of continuity, the Navier-Stokes equation and the equation expressing the balance of forces affect- ing the suspended particle, Rieger and Ditl [1] pro- posed the following relationship linking the modified Froude number F r′, the dimensionless particle diam- eter dp/D and the mean volumetric concentration of the solid phase cv 13 Acta Polytechnica Vol. 50 No. 6/2010 F r′ = n2c dρ gΔρ = f ( dp D , cv ) . (1) This relation holds for geometrically similar mixing equipment and a turbulent regime. The results of critical (just-suspended) impeller speed measurements for the given solid phase con- centration cv can be correlated in the power form F r′ = C ( dp D )γ (2) The values of coefficients C and γ depend on par- ticle volumetric concentration cv. A mathematical description of these dependencies was proposed by Rieger [5, 6] in the form C = Aexp(Bcv) (3) and γ = α + βcv. (4) The dimensionless criterion πs = P o √ F r′3(d/D)7 (5) was proposed in [7] for comparing the agitator power consumption necessary for suspension of solid parti- cles. 3 Experimental Two pitched six-blade turbines with pitch blade an- gle 45◦ and blade width 0.2 · d were used in model measurements of just suspension impeller speed. The ratios of the vessel to the agitator diameter D/d were 3 and 4.5. The measurements were carried out in a dish-bottomed vessel 300 mm in diameter. The height of the impellers above the vessel bottom was 0.5d. The impellers were operated to pump the liq- uid down toward bottom of the vessel. The vessels were equipped with four radial baffles b = 0.1 · D in width. The height of the liquid levelwas equal to the vessel diameter H = D. The just suspension impeller speeds were mea- sured by an electrochemical method described e.g. in [8], and were checked visually. A 2.5 % NaCl wa- ter solution was used as the liquid, and glass parti- cles with four equivalent diameters between 0.18 and 0.89mmand volumetric concentration from2.5% to 40 % were used as the solid phase. 4 Results The dependences of coefficient C and exponent γ on theparticle volumetric concentration cv for both D/d ratio values were presented in [9]. The plot of expo- nent γ on the particle volumetric concentration cv shown in Fig. 2 shows that it rises linearly with in- creasing cv. The dependence of coefficient C on par- ticle concentration cv, see Fig. 3, shows that the de- pendences can be approximated in semi-logarithmic coordinates by straight lines. This is in agreement with Eqs. (3) and (4). Fig. 2 Fig. 3 The values of criterion πs were calculated from the results of particle suspension measurements (Eqs. (2–4)) and from the results of power consump- tion measurements presented in [7, 10, 11]. The results are presented in Figs. 4 and 5. Fig. 4 for smaller particles shows that at low particle content the smaller agitator needs less power for particle sus- pension, while the converse is true for higher particle content. Fig. 5 shows that for larger particles with low particle content, the two agitators need practi- cally the same power for particle suspension. For higher particle content, the larger agitator is again more advantageous. Fig. 4 14 Acta Polytechnica Vol. 50 No. 6/2010 Fig. 5 We can conclude that larger agitators are more efficient for higher particle content. This is in agree- ment with the conclusions presented earlier [3, 4]. 5 Symbols A, B constants in Eq. (3) cv volumetric concentration of particles C coefficient in Eq. (2) d agitator diameter dp particle diameter D vessel diameter F r′ modifiedFroude number defined byEq. (1) g gravity acceleration n agitator speed nc critical agitator speed P o power number, P o = P ρn3d5 α, β constants in Eq. (4) γ exponent in Eq. (2) πs dimensionless criterion defined by Eq. (5) ρ liquid density Δρ solid-liquid density difference Acknowledgement This project was crried out with financial support fromtheMinistry of Industry andTradeof theCzech Republic (project number FR-TI1/005). References [1] Rieger, F., Ditl, P.: Chem. Eng. Sci., 49, 2219, 1994. [2] Kasat, G. R., Pandit, A. B.: Can. J. Chem. Eng., 83, 618, 2005. [3] Rieger, F., Ditl, P.: Zeszyty Naukowe Politech- niky Lódzkiej. Inžyniera Chemiczna i Proce- sowa. Lódž, Politechnika Lódzka, 1997, 181. ISSN 0137-2602. [4] Rieger, F., Ditl, P.: The 4th International Symposium on Mixing in Industrial Processes. Toulouse, PROGEP-ISMIP 4, 458, 2001. [5] Rieger, F.: Chem. Eng. J., 79, 171, 2000. [6] Rieger, F.: Chem. Eng. Proces., 41, 381, 2002. [7] Rieger, F.: Proceedings of VI. Polish Seminar on Mixing, Krakow 1993, 79. [8] Jirout, T., Moravec, J., Rieger, F., Sinevič, V., Špidla, M., Soboĺık, V., Tihon, J.: Inż. Chem. Proc. (Chemical and Process Engineering). 26, No. 3, 485, 2005. [9] Ceres, D., Moravec, J., Jirout, T., Rieger, F.: Inż. Ap. Chem. 49, nr. 1, 25, 2010. [10] Medek, J.: Proceedings of Czech Conference on Mixing, Brno, 1982, 127. [11] Ceres, D., Moravec, J., Jirout, T., Rieger, F.: Proceedings of CHISA 2009. Ing. Dorin Ceres Doc. Ing. Tomáš Jirout, Ph.D. Prof. Ing. Frantǐsek Rieger, DrSc. Phone: +420 224 352 548 E-mail: frantisek.rieger@fs.cvut.cz Czech Technical University in Prague Faculty of Mechanical Engineering Department of Process Engineering Technická 4, 166 07 Prague 6, Czech Republic 15