EFFECT OF IMPELLER TYPE AND NUMBER AND LIQUID LEVEL ON TURBULENT BLEND TIME

Transcription

1 EFFECT OF IMPELLER TYPE AND NUMBER AND LIQUID LEVEL ON TURBULENT BLEND TIME Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Master of Science in Chemical Engineering By Jing Li Dayton, OH May 2017

2 EFFECT OF IMPELLER TYPE AND NUMBER AND LIQUID LEVEL ON TURBULENT BLEND TIME Name: Li, Jing APPROVED BY: Kevin J. Myers, D.Sc., P.E. Advisory Committee Chairman Research Advisor & Professor Chemical & Materials Engineering Eric E. Janz, P.E. Research Advisor Global Research and NPD Director Mixing Technologies National Oilwell Varco, L.P. Robert J. Wilkens, Ph.D., P.E. Committee Member Professor Chemical & Materials Engineering Robert J. Strong Committee Member Research Engineer National Oilwell Varco, L.P. Robert J. Wilkens, Ph.D., P.E. Associate Dean for Research and Innovation Professor School of Engineering Eddy M. Rojas, Ph.D., M.A., P.E. Dean, School of Engineering ii

3 Copyright by Jing Li All rights reserved 2017 iii

4 ABSTRACT EFFECT OF IMPELLER TYPE AND NUMBER AND LIQUID LEVEL ON TURBULENT BLEND TIME Name: Li, Jing University of Dayton Advisors: Kevin J. Myers Eric E. Janz Impellers are the core element of a mixing system. The size and the number of impellers affect the performance of a mixing system. There have been literature studies reporting a correlation among the power number, the blend time and the impeller size of a single impeller mixing system using one general equation. This current research tested numerous axial-flow and radial-flow impellers. This study found that the widely accepted FMP Parameter may not be as accurate as often stated, especially for multiple impeller system or higher liquid level. The impeller type may affect the value of FMP Parameter. Also the correlation between dimensionless blend time and impeller size may need to be developed individually for each impeller type. The FMP correlation indicates that for a fixed blend time and impeller diameter, the impeller power requirement should be the same for all impellers, regardless of type. This research found that this FMP correlation iv

5 predicts the mixing time reasonably well for most of the impeller types. As for the sawtooth impeller, it has larger experimental power requirement than the prediction. Based on the result above, FMP correlation has its limitation when predicting single impeller blend times. Further, double and triple impeller systems have been studied. Two methods of correlating the data are used for this multiple impeller blending study: (i) A modified FMP correlation among impeller system power number, the liquid level, and the blend time. (ii) Blend time correlation among impeller type, impeller number and liquid level separately for each impeller style based on Fasano and Penney approach (1991). The modified FMP correlation method offers a reasonable way that the blend time of all types of impeller can be predicted via the same correlation while taking liquid level into consideration. The second method that predicts the blend time according to impeller type has a smaller deviation between experimental data and correlation than first method. Key Words: Blend time; Power consumption; Multiple impeller system; Modified FMP correlation v

6 ACKNOWLEDGEMENTS I would like to thank Dr. Kevin Myers for his help during these three years. He encouraged me to go further not only on my thesis but with my academic courses. He taught me to focus on details and always summarize the material on hand. I learned how to think about problems and how to analyze problems based on the data I have obtained. Every effort he makes with me makes me closer to being a chemical engineer. I also thank NOV Mixing Technologies for letting me complete my thesis with their impellers and lab equipment in the last two years. The experience and knowledge I have learned in the laboratory are my treasure. I would also like to thank University of Dayton Graduate School who offered me the chance to study in the United States and the opportunity to study chemical engineering. Thanks to UD s international student scholarship and service center. Their international peer orientation leader program helped me with my leadership and make a lot of new friends. I also want to thank Dr. Myers wife, Shiow-Meei, for her kind assistance in reviewing this thesis and helping with my writing. Finally, I want to thank my parents who offered me a chance to study abroad and give me the chance to open my eyes and to be a chemical engineer. vi

7 TABLE OF CONTENTS ABSTRACT... iv ACKNOWLEDGEMENTS... vi LIST OF FIGURES...viii LIST OF TABLES... x NOMENCLATURE...xv CHAPTER 1 INTRODUCTION...1 CHAPTER 2 EXPERIMENTAL SETUP AND PROCEDURE Experimental Equipment and Materials Experimental Procedure Blend Time Measurement Power Number Measurement...16 CHAPTER 3 RESULTS AND DISCUSSION Single-impeller Systems at Z / T = Multiple-impeller Systems...30 CHAPTER 4 CONCLUSION BIBLIOGRAPHY APPENDIX A Single Impeller Experimental Blend Time Data...55 Down-Pumping System and Radial-Flow Systems...55 Up-Pumping Systems Changing Liquid Level Systems...67 APPENDIX B Single Impeller Experimental Power Number Data Changing Liquid Level Systems...75 APPENDIX C Two Impeller Experimental Blend Time Data...78 APPENDIX D Two Impeller Experimental Power Number Data APPENDIX E Three Impeller System Experimental Blend Time Data APPENDIX F Three Impeller System Experimental Power Number Data vii

8 LIST OF FIGURES Figure 1-1 Figure 2-1 Relation between impeller power number and its pumping number...6 Radial-flow impellers Figure 2-2 Axial-flow impellers Figure 2-3 Figure 2-4 Figure 3-1 Figure 3-2 Figure 3-3 Turbulent blend time measurement Multiple impeller system Effect of impeller type on FMP parameters of six inch single impellers...19 Effect of impeller type on FMP parameters of other size single impellers...21 Effect of D/T (impeller diameter to tank diameter) on FMP parameter of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers Figure 3-4 Figure 3-5 Relation between dimensionless blend time (Ntb) and (D/T) Comparison of all six-inch single-impeller normalized power requirement with fixed blend time Figure 3-6 Effect of D/T on normalized power requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time...27 Figure 3-7 Comparison of all six-inch single-impeller normalized torque requirements with fixed blend time Figure 3-8 Effect of D/T on normalized torque requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time...29 Figure 3-9 Comparison of FMP Parameter of multiple impeller systems at three different liquid levels...33 Figure 3-10 Relationship between FMP Parameter of multiple impeller systems and liquid level...33 viii

9 Figure 3-11 Figure 3-12 Comparison of predicted and experimental dimensionless blend times Comparison of multiple-impeller normalized power requirement with fixed blend time at Z/T = Figure 3-13 Comparison of multiple-impeller normalized power requirement with fixed blend time at Z/T = Figure 3-14 Comparison of multiple-impeller normalized power requirement with fixed blend time at Z/T = Figure 3-15 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z/T = Figure 3-16 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z/T = Figure 3-17 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z/T = Figure 3-18 HE-3 impeller relation between dimensionless blend time and liquid level with different impeller numbers Figure 3-19 HE-3 blend time correlation liquid level exponent (β) relation to the number of impellers Figure 3-20 Figure 3-21 Figure 3-22 HE-3 blend time correlation to number of impellers HE-3 parity plot...42 P-4 impeller relation between dimensionless blend time and liquid level with different impeller numbers...43 Figure 3-23 Figure 3-24 Figure 3-25 P-4 blend time correlation to number of impellers P-4 parity plot S-4 impeller relation between dimensionless blend time and liquid level with different impeller numbers Figure 3-26 Figure 3-27 S-4 parity plot Comparison of Magelli et al. correlation and the data of this study...49 ix

10 LIST OF TABLES Table 1-1 Table 1-2 Table 3-1 Table 3-2 Table 3-3 Table 3-4 Table 3-5 Fasano and Penney s a and b values...4 Selected axial flow impeller pumping number and power number data.5 Six-inch single impeller turbulent blending data (Z/T = 1, C/T= 1/3)...19 Other size single impeller turbulent blending data (Z/T = 1, C/T= 1/3)..21 Comparison of current and Fasano and Penney D/T exponent values...24 Comparison of all single impeller speed, torque, and power requirement data...26 Average blend time and associated parameters for multiple impeller systems (D/T = 0.34, C i /T = (i/ (n+1)) (Z/T)) Table 3-6 Comparison of all multiple impeller modified FMP Parameter, predicted blend time, and power and torque requirement data Table 3-7 Analysis of normalized power and torque requirements for equal blend time at three different liquid levels Table 3-8 Analysis of Magelli et al. correlation using the data of this study Table A inch HE-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...55 Table A-2 6 inch HE-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...56 Table A inch HE-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...56 Table A inch P-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...57 Table A-5 6 inch P-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...57 Table A inch P-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...58 Table A inch S-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...58 Table A-8 6 inch S-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...59 x

11 Table A inch S-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...59 Table A-10 6 inch S-6 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...60 Table A-11 6 inch D-6 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...60 Table A inch D-8 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...61 Table A-13 6 inch D-8 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...61 Table A inch CD-6 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...62 Table A-15 6 inch CD-6 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...62 Table A-16 5 inch ChemShear impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...63 Table A-17 6 inch ChemShear impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...63 Table A inch Maxflo W impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...64 Table A inch RL-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...64 Table A inch SC-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...65 Table A inch Sawtooth impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...65 Table A-22 6 inch P-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...66 Table A-23 6 inch HE-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 3)...66 Table A-24 6 inch S-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 2)...67 Table A-25 6 inch S-4 impeller experimental blend time data (Z / T = 1.5, C / T = 3 / 4)...67 Table A-26 6 inch S-4 impeller experimental blend time data (Z / T = 2, C / T = 1)...68 Table A-27 6 inch P-4 impeller experimental blend time data (Z / T = 1, C / T = 1 / 2)...68 Table A-28 6 inch P-4 impeller experimental blend time data (Z / T = 1.5, C / T = 3 / 4)...69 Table A-29 6 inch P-4 impeller experimental blend time data (Z / T = 2, C / T = 1)...69 Table A-30 6 inch HE-3 impeller experimental blend time data (Z / T = 1, C / T = 1 / 2)...70 Table A-31 6 inch HE-3 impeller experimental blend time data (Z / T = 1.5, C / T = 3 / 4)...70 Table A-32 6 inch HE-3 impeller experimental blend time data (Z / T = 2, C / T = 1)...71 Table B-1 HE-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...72 Table B-2 HE-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...72 Table B-3 HE-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...72 Table B-4 P-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...72 xi

12 Table B-5 P-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-6 P-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-7 S-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-8 S-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-9 S-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-10 Maxflo W impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...73 Table B-11 Sawtooth impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-12 D-6 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-13 D-8 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-14 CD-6 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-15 SC-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-16 RL-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...74 Table B-17 ChemShear impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...75 Table B-18 ChemShear impeller experimental power number data (Z / T = 1, C / T = 1 / 3)...75 Table B-19 S-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 2)...75 Table B-20 P-4 impeller experimental power number data (Z / T = 1, C / T = 1 / 2)...75 Table B-21 HE-3 impeller experimental power number data (Z / T = 1, C / T = 1 / 2)...75 Table B-22 S-4 impeller experimental power number data (Z / T = 1.5, C / T = 3 / 4)...76 Table B-23 P-4 impeller experimental power number data (Z / T = 1.5, C / T = 3 / 4)...76 Table B-24 HE-3 impeller experimental power number data (Z / T = 1.5, C / T = 3 / 4)...76 Table B-25 S-4 impeller experimental power number data (Z / T = 2, C / T = 1)...76 Table B-26 P-4 impeller experimental power number data (Z / T = 2, C / T = 1)...76 Table B-27 HE-3 impeller experimental power number data (Z / T = 2, C / T = 1)...77 Table C-1 Two 6 inch HE-3 impeller experimental blend time data (Z / T = 1)...78 Table C-2 Two 6 inch HE-3 impeller experimental blend time data (Z / T = 1.5)...79 Table C-3 Two 6 inch HE-3 impeller experimental blend time data (Z / T = 2)...79 Table C-4 Two 6 inch P-4 impeller experimental blend time data (Z / T = 1)...80 Table C-5 Two 6 inch P-4 impeller experimental blend time data (Z / T = 1.5)...80 xii

13 Table C-6 Two 6 inch P-4 impeller experimental blend time data (Z / T = 2)...81 Table C-7 Two 6 inch S-4 impeller experimental blend time data (Z / T = 1)...81 Table C-8 Two 6 inch S-4 impeller experimental blend time data (Z / T = 1.5)...82 Table C-9 Two 6 inch S-4 impeller experimental blend time data (Z / T = 2)...82 Table D-1 Two 6 inch HE-3 impeller experimental power number data (Z / T = 1)...83 Table D-2 Two 6 inch HE-3 impeller experimental power number data (Z / T = 1.5)...83 Table D-3 Two 6 inch HE-3 impeller experimental power number data (Z / T = 2.0)...83 Table D-4 Two 6 inch P-4 impeller experimental power number data (Z / T = 1)...84 Table D-5 Two 6 inch P-4 impeller experimental power number data (Z / T = 1.5)...84 Table D-6 Two 6 inch P-4 impeller experimental power number data (Z / T = 2)...84 Table D-7 Two 6 inch S-4 impeller experimental power number data (Z / T = 1)...84 Table D-8 Two 6 inch S-4 impeller experimental power number data (Z / T = 1.5)...84 Table D-9 Two 6 inch S-4 impeller experimental power number data (Z / T = 2)...85 Table E-1 Three 6 inch HE-3 impeller experimental blend time data (Z / T = 1)...86 Table E-2 Three 6 inch HE-3 impeller experimental blend time data (Z / T = 1.5)...87 Table E-3 Three 6 inch HE-3 impeller experimental blend time data (Z / T = 2)...87 Table E-4 Three 6 inch P-4 impeller experimental blend time data (Z / T = 1)...88 Table E-5 Three 6 inch P-4 impeller experimental blend time data (Z / T = 1.5 )...88 Table E-6 Three 6 inch P-4 impeller experimental blend time data (Z / T = 2)...89 Table E-7 Three 6 inch S-4 impeller experimental blend time data (Z / T = 1)...89 Table E-8 Three 6 inch S-4 impeller experimental blend time data (Z / T = 1.5)...90 Table E-9 Three 6 inch S-4 impeller experimental blend time data (Z / T = 2)...90 Table F-1 Three 6 inch HE-3 impeller experimental power number data (Z / T = 1)...91 Table F-2 Three 6 inch HE-3 impeller experimental power number data (Z / T = 1.5)...91 Table F-3 Three 6 inch HE-3 impeller experimental power number data (Z / T = 2)...91 Table F-4 Three 6 inch P-4 impeller experimental power number data (Z / T = 1)...92 Table F-5 Three 6 inch P-4impeller experimental power number data (Z / T = 1.5)...92 Table F-6 Three 6 inch P-4 impeller experimental power number data (Z / T = 2)...92 xiii

14 Table F-7 Three 6 inch S-4 impeller experimental power number data (Z / T = 1)...92 Table F-8 Three 6 inch S-4 impeller experimental power number data (Z / T = 1.5)...92 Table F-9 Three 6 inch S-4 impeller experimental power number data (Z / T = 2)...93 xiv

15 NOMENCLATURE a,b Impeller-dependent constants reported by Fasano and Penny (Equation 1-7) C Impeller off-bottom clearance, measured from the lowest point of the impeller to the tank bottom C 1 FMP Parameter constant (Equation 3-4) D i k M n N Nt b Np Np1 N ps NQ1 P t b tu T Impeller diameter Impeller number in multiple impeller system Turbulent mixing rate constant reported by Fasano and Penny Agitator torque Number of impellers Rotation speed Dimensionless blend time Impeller power number (dimensionless) Single impeller power number (dimensionless) Impeller power number for the system (dimensionless) Single impeller pumping number (dimensionless) Power requirement Blend time Time required to reach a given uniformity Tank diameter U Uniformity (%) Z Liquid level α Multiple impeller correlation constant (Equation 3-9) xv

16 β Multiple impeller correlation tank to liquid level (Z/T) exponent (Equation 3-9) ρ Density of blending solution xvi

17 CHAPTER 1 INTRODUCTION Blending is a common mixing operation used in chemical processing. Impellers are the core element of a mixing system. The size and the number of impellers will affect the performance of a mixing system. For a tall vessel, multiple impellers are typically used. The time taken to reach a degree of homogeneity is called blend time (tb). Blend time is a method used to measure the impeller blending efficiency. Estimation of blend time is important for agitator design. There are many studies reporting the relationship between the blend time and the impeller and vessel characteristics for single impeller systems; however, few works report a thorough study on multiple impeller systems. The product of blend time and rotational speed (Ntb) is dimensionless. Grenville and Nienow (2004) reported a general correlation for the dimensionless blend time (Ntb). For their experiments the impeller to tank diameter ratio (D/T) varied from 1/3 to 1/2 and the impeller clearance to tank diameter ratio (C/T) was 1/3. The experiments were performed with near square batch geometry (the liquid level to tank diameter ratio Z/T 1). The power number (Np) is a dimensionless number included in the correlation. The resulting correlation for 95% uniformity was reported as follows with standard deviation of 10% in 1

18 the right-hand side constant. FMP Parameter = Np 1/3 N t95 (D / T) 2 = 5.20 (1-1) Where Np = power number for each impeller, N = rotational speed, t95 = blend time, D = impeller diameter, T = tank diameter The following equation gives the definition of the power number for an impeller (Wei et al. 1991). Np = P / (ρ N 3 D 5 ) (1-2) Where P = power requirement = 2πNM, M = torque requirement, ρ = density of agitated liquid When these two equations are combined, it becomes P N 3 tb 3 (D / T) 6 / (ρ N 3 D 5 ) = constant (1-3) Since the tank diameter (T) and the density (ρ) may be considered constant, the equation becomes N 3 tb 3 P D 6 / (N 3 D 5 ) = constant (1-4) Simplifying the equation above yields tb 3 P D = constant (1-5) When the blend time is fixed, this further simplifies as follows. P D -1 (1-6) This derivation shows that the power requirement is inversely proportional to the impeller diameter for a blending system with constant tank diameter, constant fluid density, and fixed blend time; the larger the impeller, the lower the power consumption. This correlation also shows that for fixed D / T and power input per mass, turbulent blend time is independent of impeller type. 2

19 Fasano and Penney (1991) reported the following equation. k = a N (D / T) b (Z / T) -0.5 (1-7) Where k = turbulent mixing rate constant, N = rotational speed, a and b = impeller-dependent constants, Z = liquid level, T = tank diameter In this study, single impellers such as pitched blade, straight blade, disk turbine, and marine propeller were tested with the impeller Reynolds number greater than 5,000 with the impeller to tank diameter ratio (D/T) ranging from 0.15 to The time to reach a given uniformity (tu) is related to the mixing rate constant as follows according to Khang and Levenspiel (1976) and reported by Fasano and Penney (1991). tu = - ln (1-U)/ k (1-8) Where U = uniformity Combining Equations 1-7 and 1-8 a N (D / T) b (Z / T) tu = - ln (1 - U) (1-9) Rearranging the equation yields N tu = - ln (1 - U) (Z / T) 0.5 / (a (D / T) b ) (1-10) With Z / T = 1, Equation 1-10 is simplified as below. NtU = - ln (1 - U) (D / T) - b / a (1-11) According to Equation 1-7, single impeller turbulent mixing rate constant is affected by two impeller - related constants (a and b). Equation 1-11 shows that dimensionless blend time (NtU) is affected by impeller size (D / T) and type (a and b). Table 1-1 contains the a and b values reported by Fasano and Penney (1991). 3

20 Table 1-1 Fasano and Penney s a and b values Impeller a b D S P HE The result obtained above disagrees with FMP correlation which indicates that the dimensionless blend time can be predicted by a single relation regardless of the impeller type. In order to better understand other factors like the liquid level or impeller location on the blend time, more work is needed for the blend time correlation. On industrial scale, tall vessels are often used which require the use of multiple impellers. The number of impellers used to achieve the blending affects the cost and efficiency of a project. However, blending with multiple impellers in tall vessels has seldom been studied. There is not a widely accepted correlation which shows the effect of impeller type, diameter, number, and the liquid level on turbulent blend time. Cooke et al. (1988) found Nt90Np 1/3 (Z / D) = 3.3 (COV = 12%) (1-12) Where t90 = time required for all tracer concentrations to reach±10% of the equilibrium value, Np = power number for the impeller system Equation 1-12 shows the relation between dimensionless blend time, liquid level, impeller system power number and size. However, the effect of number of impellers and liquid level were not studied independently. They apparently only studied single impeller system at Z / T = 1 and three impellers system at Z / T = 3. Limited experiments may lead to unreliable blend time prediction. More work may be needed to determine the reliability of this equation. 4

21 Magelli et al. (2013) reported a blend time correlation for multiple axial flow impeller system with the hypothesis that blending is complete after a certain number of liquid circulations as shown below. tb (V / (NQ1 N D 3 ) (1-13) Where tb = blend time, V = vessel volume, NQ1 = single impeller pumping number, N = rotational speed, D = impeller diameter Magelli et al. used pumping number here and assumed that impeller spacing is large enough that NQ1 of single impellers apply to each impeller of multiple impeller systems. Power number is more often used than pumping number in blend time correlations. Post (2013: presented impeller pumping number and power number information and Table 1-2 shows this data. Table 1-2 Selected axial flow impeller pumping number and power number data Type N p1 N Q1 P Lightnin A HE-3 D/T = HE-3 D/T = HE-3 D/T = HE-3 D/T = Lightnin A Lightnin A Lightnin A Lightnin A

22 Figure 1-1 Relation between impeller power number and its pumping number (Data from Table 1-2) According to Figure 1-1, NQ1 is related to Np1 in the following manner. NQ1 = 0.77 Np1 1 / 3 (1-14) Where Np1 = single impeller power number Substituting Equation 1-14 into Equation 1-13 yields tb (V / (NP1 1/3 N D 3 ) (1-15) Equation 1-15 can be written as follows after substitution for volume (V = π T 2 Z / 4) and rearrangement. Ntb (Z / T) (D / T) -3 NP1-1 / 3 (1-16) According to Equation 1-16, the D / T dependence is stronger than FMP correlation and that reported by Fasano and Penney (1991). As shown in Equation 1-16, the Magelli et al. approach uses single impeller power number and lacks impeller number dependence, making this correlation unreasonable. It is reasonable to modify Magelli et al.(2013) s Equation 1-13 to add number of impellers (n) to denominator to get total pumping rate as below. Ntb (V / (n Np1 1 / 3 N D 3 ) (1-17) 6

23 Ntb (T 2 Z / (n Np1 1 / 3 N D 3 ) (1-18) Ntb (Z / T) (D / T) - 3 Np1-1 / 3 n -1 (1-19) Where n = number of impellers of the system, NP1 = power number for single impeller The correlation obtained by Magelli et al. is difficult to compare to other similar works, especially for this research, since the correlation obtained in this research measured power number for the impeller system, Np, not the single impeller power number Np1. Assuming that the impeller system power number is equal to the number of impellers multiplied by the single impeller power number. Np = n Np1 (1-20) Where Np = power number for multiple impeller system, Np1 = power number for single impeller the correlation of Equation 1-19 then can be rewritten as Ntb (Z / T) (D / T) -3 NP -1 / 3 n -2 /3 (1-21) In Equation 1-21 the power number is adjusted to impeller system power number. Equation 1-21 shows that the dimensionless blend time is dependent on impeller size and power number, liquid level and number of impellers. It is more reasonable than Equation 1-16 that does not include impeller number dependence. The Magelli et al. approach of Equation 1-13 is only for axial flow impellers, but Magelli et al. also developed a radial-flow impeller correlation that will not be considered here. For a single impeller system, Grenville and Nienow s FMP parameter approach has been widely accepted and applied to most impellers. The general idea with FMP correlation is that impeller type is accounted by impeller power number. Fasano and Penny (1991) correlation shows that the impeller type does have effect on single impeller 7

24 blend time. The present study includes experiments, blend time and power number data, for different types of single impeller systems with the liquid level to tank diameter ratio equal to one (Z / T =1). The experimental data are presented as (i) Effect of impeller type on FMP parameter, (ii) Effect of D / T (impeller diameter to tank diameter) on FMP Parameter of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers, and (iii) Relation between dimensionless blend time (Ntb) and (D / T). Additionally, all single-impeller normalized power and torque requirement with fixed blend time are compared. The comparison helps to show the efficiency of different impeller systems and may help with system selection. The effect of D / T on normalized power and torque requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time are presented. Due to the lack of general correlation for estimating the multiple impeller system blend time, a correlation taking the impeller type, size, number and liquid level into consideration is needed. Industrially common impellers HE-3, P-4 and S-4 are studied in this work with liquid levels of Z / T = 1.0, 1.5, 2.0 with multiple impeller systems (number of impellers, n = 1, 2, 3). FMP Parameter of multiple impeller systems at three different liquid levels (1 Z 2) are compared. Modified FMP Parameter correlation for multiple impeller systems and different liquid level is found. Multiple-impeller normalized power and torque requirements with fixed blend time at different liquid level are compared. HE-3, P-4 and S-4 impeller relations between dimensionless blend time and liquid level with different impeller numbers are worked out separately. 8

25 CHAPTER 2 EXPERIMENTAL SETUP AND PROCEDURE 2.1 Experimental Equipment and Materials Flat bottom clear acrylic tank with four flat-plate baffles was used as a blending vessel. Tank diameter, T, was equal to 0.445m (17.5 in) and its height was equal to 0.660m (36 in). The width of the four flat-plate baffles to tank diameter ratio was 3/35. Calibrated reaction strain gauge torque sensor was used to measure the torque requirement of each impeller system. A zero velocity magnetic rotational speed sensor was used to measure and control the shaft speed. Thirteen types of impellers with various diameters, supplied by NOV Mixing Technologies (Dayton, OH), were studied to investigate the effect of impeller type and diameter on turbulent blend time with single impeller system. Later three impeller types (HE-3, P-4 and S-4) were studied with multiple impeller system. All the impeller types are shown in Figure 2-1 and Figure 2-2. All the radial-flow impellers studied in this work are shown in Figure 2-1. The S-4 impeller is a commonly used inexpensive impeller with four flat blades. The S-6 is a six flat 9

26 blade impeller. The CS-6 (ChemShear-6) is a narrow-blade turbine with tapered blades. The D-6 impeller (also known as the Rushton turbine) is a flat-blade disc turbine with six straight blades. It is the traditional impeller for dispersion of immiscible fluids. The D-8 impeller is a flat-blade disc turbine with eight straight blades. The CD-6 impeller (also known as the Smith turbine) is a concave-blade disc turbine. Its direction of rotation is important (clockwise as viewed in Figure 2-1). It is optimal for gas-liquid dispersion. The CS-5 (ChemShear-5) is a narrow-blade turbine with short trapezoid blades at the outer edge of a disc. Sawtooth is a disc turbine with twenty angled teeth (ten up and ten down). CS-5, CS-6 and Sawtooth impeller are high-shear impellers used in high speed operations that do not produce as much flow as other impellers. Figure 2-1 Radial-flow impellers 10

27 The axial-flow impellers are generally used for blending, solids suspension, and heat transfer applications. All of these impellers can be used in up-pumping or down-pumping mode. Impellers studied in this work are shown in Figure 2-2. The HE-3 is a narrow-blade, high-efficiency impeller. It is usually used for low-viscosity blending and solid suspension. P-4 impeller is a pitched-blade turbine with four blades at forty-five-degree angle. P-4 impeller produces mainly axial-flow but with some radial flow. It is usually used in miscible fluid blending and solids suspension. HE-3 and P-4 impellers are the most commonly used impellers for blending. The Maxflo W is a wide-blade, high-efficiency impeller used for solids suspension, liquid-solid-gas and boiling or near boiling applications and is good at mass transfer. RL-3 is a wide pitched blade rag shedding impeller usually used as down-pumping system in wastewater treatment. SC-3 is a narrow curved blade impeller. It is engineered for deep tank applications. Figure 2-2 Axial-flow impellers (shown in down-pumping mode when rotated clockwise) For blend time measurements, phenolphthalein indicator (1% solution from 11

28 Riedel-deHaen) was used as reaction detector. Aqueous solution of Sodium Hydroxide (NaOH, 5.0 N) and Hydrochloric Acid (HCl, 5.0 N) (both from GFS Chemicals Inc.) were used as reaction system. Digital contact tachometer was from Extech instruments, stop watch was from Sport Line and micrometer for dimension measurements was from Mitutoyo Corporation. 2.2 Experimental Procedure Blend Time Measurement Phenolphthalein (C20H14O4) is a weak organic binary acid which is sensitive to the solution s ph that can be used as an acid-base indicator. Phenolphthalein molecules in acidic aqueous solution (ph < 8.5) are colorless. Phenolphthalein in the base solution (ph > 9) is in ionic state and can show a color from light pink to red. Tap water was used in the blending tank. The general experiment is shown in Figure 2-3. When phenolphthalein is added into the water, it changes water to light pink. As base is added to the water, the phenolphthalein changes from light pink to dark pink. Before each experiment, base is added to adjust the clear water to light pink as the starting point. In order to reduce errors, a small beaker was set up as the baseline, to make sure every time the experiment started at the same light pink color. Then 10ml of base was added to the light pink water. After mixing, as shown in Figure 2-3 (a), the water is dark pink and blend time experiment is ready to start. Acid (twice stoichiometric amount of acid was used for these experiments) is added quickly and close to the shaft above the top of the liquid level into the dark pink solution while starting the stop watch. Figure 2-3 (b) is 12

29 shortly after addition, when some clearing can be seen. The dark pink turns lighter as shown in Figure 2-3 (c) as time goes on. Finally, the tank water turns to clear as in Figure 2-3 (d) and the stop watch is stopped as the last pink disappears. The time taken from the addition of the acid to the last light pink disappearing in the tank is recorded as one experimental turbulent blend time for a particular impeller system. After one experiment, base is added to adjust the clear water to light pink baseline for next test. Since the blend time is found by visual determination, all the experiments were repeated ten times. Blend time data used in this report is the average of the ten individual measurements. The speed used in the experiment was adjusted to provide blend time around 20 to 25 seconds for each impeller system to reduce the error caused by the experiment method. 13

30 (a) (b) (c) (d) Figure 2-3 Turbulent blend time measurement (a) Base was added to make the water dark pink and the test is ready to start. (b) Twice stoichiometric amount of acid was added to start the blend time experiment. (c) Dark pink turns lighter as blending occurs. (d) Record blend time as all water turns clear (last pink disappears). For single impeller system, the turbulent blend time measuring experiment is started 14

31 by fixing a chosen type and size impeller (six inch S-4 impeller is shown in Figure 2-3) on the shaft and installing the shaft on the tank centerline. The liquid level was 0.44m (Z / T =1) with 20 ml phenolphthalein solution. The impeller clearance from the tank bottom was 0.15 m (C / T = 0.33). Ten ml of the base solution was added into the water after achieving the light pink baseline color and starting impeller rotation. The experiment was performed after waiting for about two minutes to make sure the solution is well mixed. The stop watch was started to record the blend time as 20ml of the acid was added into the system. The blend time is recorded as one experimental data point. Ten individual experiments were repeated to reduce the error. The multiple S-4 impeller system is shown in Figure 2-4. For multiple impellers, the experiment was started by fixing some chosen number of impellers on the shaft (three six inch S-4 impellers shown in Figure 2-4). The shaft was installed on the tank centerline and all impellers are spaced uniformly in the axial direction. The lowest impeller clearance from the tank bottom was changed according to different liquid level (Ci / T = i / (n + 1); n = number of impellers; for n = 3, C1 / T = 0.25, C2 / T = 0.50, C3 / T = 0.75 as in Figure 2-4). The blend time measurement of the multiple impeller system was similar to single impeller system, with speed adjusted to keep the blend time between 20 and 25 seconds. Use the same amount of acid and base as single impeller system. Again, the turbulent blend time is an average of ten individual measurements. 15

32 Figure 2-4 Multiple impeller system Power Number Measurement The impeller system was assembled and connected with calibrated reaction strain gauge torque sensor and zero velocity magnetic rotational speed sensor with the same tank used for blend time measurement experiment. The impeller locations and spacing are the same as blending experiment. The rotational speed is adjusted to provide torques from 10 to 20 in lbf to reduce measurement errors while avoiding air entrainment. The torque (M) and the rotation speed (N) were read from the calibrated stain gauge torque sensor. Record the speed and torque shown on the sensor after the numbers become steady around a value. Then increase the speed to change the reading of the speed and torque. Repeat the procedures to obtain more data points (usually five). The power requirement is calculated from the measured torque using Equation 2-1 shown below. Power number is 16

33 calculated after knowing the power requirement for each experiment with Equation 2-2 shown below. Power number data used in this report are the average of five individual measurements. P = 2πNM (2-1) Np = P / (ρ N 3 D 5 ) (2-2) 17

34 CHAPTER 3 RESULTS AND DISCUSSION 3.1 Single-impeller Systems at Z / T =1 The single-impeller blend time data for impellers with diameters very close to six inches (D / T 1/3) with the impeller off-bottom clearance equal to one-third of the tank diameter (C / T = 1/3) is compiled in Table 3-1. Recall the power number of each impeller is the average of five individual power number measurements at different speeds. All blend time data for a given impeller were taken at a fixed rotational speed and the tabulated blend time for each impeller is the average of ten individual blend time measurements. The speed used for each impeller was selected to provide a blend time between 20 and 25 seconds. The variation in blend time for each impeller is characterized by the coefficient of variation, COV. To make a comparison of different types of impellers, the dimensionless blend times (Ntb) and FMP Parameters (FMP Parameter = Np 1/3 N tb (D / T) 2 ) are included in Table 3-1. The single-impeller FMP Parameters are also plotted in Figure

35 Table 3-1 Six-inch single impeller turbulent blending data (Z / T = 1, C / T = 1 / 3) Impeller D / T Np N (rpm) N (rps) Ave tb (s) COV tb N tb FMP Parameter HE % HE-3(UP) % RL % SC % Maxflo W % P % P-4(UP) % ChemShear % S % S % CD % D % D % Figure 3-1 Effect of impeller type on FMP parameters of six inch single impellers The average FMP parameter of all the impellers with diameter close to six inches (D / T 1 / 3) is 4.02 and the COV is 17%. In their review, Grenville and Nienow (2004) reported an FMP Parameter of 5.20 and a COV of 10% (FMP Parameter Ratio = 4.02 / 19

36 5.20 = 0.77, COV Ratio = 17% / 10% = 1.7). Comparing the FMP Parameters of this study indicates that the difference in FMP Parameter can be as large as a factor of 1.66 (from D-8: 3.05 to ChemShear 6: 5.06). The average FMP Parameter of radial flow impellers is 9% higher than that of axial flow impellers (radial flow: 4.18 and axial flow: 3.82). The up-pumping and down-pumping FMP Parameters of HE-3 and P-4 are also different. For HE-3, the up-pumping FMP Parameter is almost 25% higher than down-pumping. The P-4 up-pumping FMP Parameter is around 13% less than down-pumping. The current research found a lower FMP Parameter value but higher COV than Grenville and Nienow. This difference may be caused by more types of impellers being studied in this research. Differences in measurement method may also be partly responsible. The single-impeller blend time data for impellers of various diameters other than six inches is compiled in Table 3-2. As before, the rotational speed was adjusted to provide blend times between 20 and 25 seconds and the reported blend times are averages of ten individual measurements. The effect of impeller type on FMP Parameters (FMP Parameter = Np 1 / 3 N tb (D / T) 2 ) of diameters other than six inches is plotted in Figure

37 Table 3-2 Other size single impeller turbulent blending data (Z / T = 1, C / T = 1 / 3) Impeller D / T Np N (rpm) N (rps) Ave tb (s) COV tb N tb FMP Parameter HE-3: % HE-3: % P-4: % P-4: % S-4: % S-4: % ChemShear % CD % D % Sawtooth % Figure 3-2 Effect of impeller type on FMP parameters of other size single impellers According to Figure 3-2, the average FMP Parameter of the impellers of other sizes is 5.42 and the COV is 25%. Figure 3-2 shows obviously that sawtooth impeller has a much higher FMP Parameter value. When the sawtooth FMP value is eliminated, the average FMP Parameter of the remaining impellers is reduced to 5.06 with a COV of 15%. The variation is now similar to Table 3-1, but FMP Parameter is 25% higher. The average FMP Parameter of radial flow impellers is 32% higher than that of axial flow 21

38 impellers (radial flow: 5.19 and axial flow: 3.92). Considering the sawtooth impeller is designed for dispersion operations, it may not have sufficient bulk flow to blend effectively. According to the behavior of sawtooth, the impeller type can affect the FMP Parameter value, contrary to common belief. To further investigate the FMP Parameter relation, the effect of D / T (impeller diameter to tank diameter ratio) on FMP Parameter of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers is shown in Figure 3-3. Figure 3-3 Effect of D / T (impeller diameter to tank diameter) on FMP Parameter of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers Figure 3-3 shows that for down-pumping axial flow P-4 and HE-3 impellers, six inch impellers have the smallest FMP Parameters. For radial flow S-4 impellers, the FMP Parameter decreases as the impeller diameter increases. Figure 3-3 shows that impeller size relative to the tank diameter does affect the FMP Parameter. Compiling the results of these experiments, current experimental results do not quite agree with widely accepted FMP Parameter correlation reported by Grenville (1992). The 22

39 FMP correlation which said all impellers exhibit same D / T dependence (Ntb (D / T) -2 ), cannot predict all current impeller type blending. The impeller type may also affect the value of FMP Parameter. The correlation between dimensionless blend time and size may need to be developed individually for each impeller type. Figure 3-4 shows the relation between dimensionless blend time (Ntb) and impeller diameter to tank diameter ratio (D / T). Figure 3-4 Relation between dimensionless blend time (Ntb) and (D / T) The correlating equations between dimensionless blend time (Ntb) and D / T in Figure 3-4 are shown below. S-4: Ntb = 1.91(D / T) (R² = 1.00) (3-1) P-4: Ntb = 4.14(D / T) (R² = 1.00) (3-2) HE-3: Ntb = 9.70 (D / T) (R² = 0.94) (3-3) According to Table 3-3, the D / T exponent for each impeller found in this study is almost equal to Fasano and Penney reported value. Recall Fasano and Penney s (1991) parameter b is impeller type dependent constant (k = a N (D / T) b (Z / T) - 0.5, with tb k -1 ). 23

40 Table 3-3 Comparison of current and Fasano and Penney D / T exponent values Type Current Exponent Fasano and Penney Exponent S P HE So based on the data presented above, the Fasano and Penney method, which separated the dimensionless blend time prediction equation according to the impeller type, is more consistent with the current study than the FMP method that uses a general impeller independent equation. Implications of the FMP blend time correlation will now be considered as Equation 1-6. (P D -1 ) Thus, the power required is independent of impeller type for a given blend time (with fixed density of the solution ρ, tank diameter T, and impeller diameter D). For fixed density and blend time, the power requirement only depends on impeller size and scale. Table 3-4 shows the comparison of all single impeller blending power requirements with fixed blend time. Rotation speed is obtained from each impeller s measured dimensionless blend time (Ntb) and then normalized by six inch single HE-3 impeller rotation speed. Power is determined using each impeller s measured power number (P = ρ Np N 3 D 5 ) and then normalized by six inch single HE-3 impeller power requirement. Torque is determined using each impeller s power requirement (M = P / 2 π N) and then normalized by six inch single HE-3 impeller torque requirement. Figure

41 shows the comparison of all six-inch single-impeller normalized power requirements with fixed blend time. Figure 3-6 shows the effect of impeller diameter to tank diameter ratio (D / T) on normalized power requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time. Note that all impeller speed, torque, and power requirements are normalized by six inch HE-3 impeller. 25

42 Table 3-4 Comparison of all single impeller speed, torque, and power requirement data Impeller Np D / T N tb FMP Parameter Normalized N* Normalized P** Normalized M*** S-4: S-4: S-4: P-4: P-4: P-4: HE-3: HE-3: HE-3: S D-6: D D-8: CD CD-6: ChemShear: ChemShear: Maxflo W RL SC Sawtooth HE-3(UP) P-4(UP) *Normalized N = (Ntb) / (Ntb) (HE-3: 6) **Normalized P = P / P (HE-3: 6) ***Normalized M = M / M (HE-3: 6) 26

43 Figure 3-5 Comparison of all six-inch single-impeller normalized power requirements with fixed blend time Figure 3-6 Effect of D / T on normalized power requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time Figure 3-5 shows that for six-inch diameter single impellers at fixed blend time, the power requirement varies with impeller type. The normalized power requirement variation is from 0.87 to 4.05 with a COV of 47%. According to the FMP blend time correlation, the power requirement at fixed blend time and impeller diameter should be independent of impeller type. The result of this study found that the power requirement is affected by the impeller type. 27

44 As seen in Equation 3-7, Grenville and Nienow (2004) reported that the power required by each impeller should be inversely proportional to impeller size (P D -1 ). Figure 3-6 shows a general trend that for S-4 and P-4 impellers, the larger the impeller, the less power it will consume. This result shows the effect of impeller diameter to tank diameter ratio (D / T) on power required is similar to the FMP correlation. For HE-3 the six-inch impeller has the lowest power requirement, inconsistent with the FMP correlation. Comparison of all six-inch single-impeller normalized torque (M = P / 2πN) requirements with fixed blend time is compiled in Figure 3-7. Effect of D / T on normalized torque requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time is compiled in Figure 3-8. Note that torque requirement is normalized by HE-3 six-inch single impeller. Figure 3-7 Comparison of all six-inch single-impeller normalized torque requirements with fixed blend time 28

45 Figure 3-8 Effect of D / T on normalized torque requirement of the radial-flow S-4 and down-pumping HE-3 and P-4 impellers with fixed blend time Figure 3-7 shows that for all six-inch diameter single impellers at fixed blend time the torque requirement varies with impeller type. The torque requirement variation is from 1 to 5.47 with the COV of 45%. Comparing the power and the torque results, they have similar variation range with a similar COV. Figure 3-8 shows a general trend that for S-4, P-4 and HE-3, the larger the impeller, the more torque it will require. Compared with P-4 and HE-3 impeller, the S-4 impeller torque required is generally higher and fairly constant. For P-4 and HE-3 two smaller impellers, the torque is relatively constant, increasing significantly for the largest impeller. To summarize, current experimental results show that the FMP Parameter has a larger variation than previously reported. The impeller power was not the same for all impellers at fixed blend time and impeller diameter, and D / T dependence is not the same for all impellers. The impeller type and size do affect the FMP Parameter. The current impeller type dependent b (impeller to tank diameter ratio exponent) is close to previously reported values of Fasano and Penney (1991) 29

46 3.2 Multiple-impeller Systems All blending data for six inch radial flow S-4 and down-pumping axial flow P-4 and HE-3 impellers with one, two, and three impellers is compiled in Table 3-5. All the impellers are spaced uniformly in the system (Ci = i Z / (n+1), where n is the number of impellers). The power number of each impeller is the average of five individual power number measurements at different speeds. All blend time data for a given impeller were taken at a fixed rotational speed and the tabulated blend time for each impeller is the average of ten individual blend time measurements. The speed used for each impeller system was selected to provide a blend time between 20 and 25 seconds. The variation in blend time for each impeller is characterized by the coefficient of variation, COV (COV = Standard Deviation / Mean). 30

47 Table 3-5 Average blend time and associated parameters for multiple impeller systems (D / T = 0.34, Ci / T = (i / (n+1)) (Z / T)) Type FMP n Z / T N p N N Avg. t b COV t b Nt b Parameter (rpm) (rps) (s) (%) % % % % S % % % % % % % % % P % % % % % % % % % HE % % % % %

48 Table 3-6 Comparison of all multiple impeller modified FMP Parameter, predicted blend time, and power and torque requirement data Modified Experimental Predicted Normalized Normalized n Z / T Np FMP Type Ntb Ntb* P** M*** Parameter S-4 P-4 HE *Predicted Nt b: Using the modified FMP Parameter correlation to predict dimensionless blend time (Nt b): Ntb = 3.21 Np -1 / 3 (D / T) -2 (Z / T) 1.4 **Normalized P = P / P (HE-3: n =1 at Z / T = 1) ***Normalized M = M / M (HE-3: n =1 at Z / T = 1) Figure 3-9 shows the comparison of FMP Parameter data at three different liquid levels, with this figure and Figure 3-10 indicating that the FMP Parameter, 32

49 Np 1 / 3 Ntb (D / T) 2, is proportional to (Z / T) 1.4. Figure 3-9 Comparison of FMP Parameter of multiple impeller systems at three different liquid levels Figure 3-10 Relationship between FMP Parameter of multiple impeller systems and liquid level The FMP Parameter correlation is modified to the following for multiple impeller systems (n = 1, 2, or 3) in taller vessels (1 Z / T 2). Np 1 / 3 Ntb (D / T) 2 (Z / T) -1.4 = 3.21 (COV = 18%) (3-4) 33

50 Table 3-6 contains the modified FMP Parameter for each system studied. The comparison of predicted dimensionless blend time obtained from modified FMP correlation and experimental data is shown in Table 3-6 and Figure The average and maximum differences between the predicted and experimental blend times are 14.4% and 38.8%, respectively. Figure 3-11 Comparison of predicted and experimental dimensionless blend times The impeller blending power requirements for multiple impeller systems is shown in Table 3-6. All power requirements were normalized by the one HE-3 impeller system at Z / T = 1 power requirement. Comparison of multiple impeller system power requirements at three different liquid levels with fixed blend time and impeller diameter are shown in Figures 3-12, 3-13, and

51 Figure 3-12 Comparison of multiple-impeller normalized power requirement with fixed blend time at Z / T = 1 Figure 3-13 Comparison of multiple-impeller normalized power requirement with fixed blend time at Z / T = 1.5 Figure 3-14 Comparison of multiple-impeller normalized power requirement with fixed blend time at Z / T = 2 35

52 Figure 3-12, Figure 3-13, and Figure 3-14 show that the power requirement varies significantly with impeller number, type and liquid level. At each liquid level multiple impeller systems usually have lower power requirements than single impeller systems. There is a trend that the more impellers in a system, the less power the impeller system required, except for S-4 impeller in the tallest vessel (at Z / T = 2). For S-4 impeller at Z / T = 2, single impeller system has lowest power requirement, while the two impeller system requires the most power. At tallest liquid level (Z / T = 2), down-pumping axial-flow three P-4 impeller system has the lowest power requirement. The higher the liquid level is, the more power is required to maintain constant blend time. The result of this study found that the power requirement for multiple impeller systems is affected by the impeller type and number of impellers and liquid level. Comparison of all multiple-impeller normalized torque (M = P / 2πN) requirements at three different liquid levels with fixed blend time are compiled in Figure 3-15, 3-16, and

53 Figure 3-15 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z / T = 1 Figure 3-16 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z / T = 1.5 Figure 3-17 Comparison of multiple-impeller normalized torque requirement with fixed blend time at Z / T = 2 37