Impeller Power Draw Across the Full Reynolds Number

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IMPELLER POWER DRAW

ACROSS THE FULL REYNOLDS NUMBER SPECTRUM

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

Zheng Ma

Dayton, OH

August, 2014

IMPELLER POWER DRAW

ACROSS THE FULL REYNOLDS NUMBER SPECTRUM

Name: Ma, Zheng

APPROVED BY:

______Kevin J. Myers, D.Sc., P.E. Eric E. Janz, P.E. Advisory Committee Chairman Research Advisor Research Advisor & Professor Chemineer Research & Chemical & Materials Engineering Development Manager NOV-Process & Flow Technologies

______Robert J. Wilkens, Ph.D., P.E. Committee Member & Professor Chemical & Materials Engineering

______John G. Weber, Ph.D. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean Dean, School of Engineering School of Engineering

ABSTRACT

IMPELLER POWER DRAW

ACROSS THE FULL REYNOLDS NUMBER SPECTRUM

Name: Ma, Zheng University of Dayton

Research Advisors: Dr. Kevin J. Myers Eric E. Janz

The objective of this work is to gain information that could be used to design full scale mixing systems, and also could develop a design guide that can provide a reliable prediction of the power draw of different types of impellers. To achieve this goal, the power number behavior，including three operation regimes, the limits of the operation regimes, and the effect of baffling on power number，was compared across the full

Reynolds number spectrum for Newtonian fluids in a laboratory-scale agitator. Six industrially significant impellers were tested, including three radial flow impellers: D-6,

CD-6, and S-4, and also three axial flow impellers: P-4, SC-3, and HE-3.

Results in laminar regime indicate that baffling has no effect on power number in this operation regime. There is an inversely proportional relationship between power number and Reynolds number. The upper limit for this operation regime should be lower than 10, the limit commonly noted in the literature. The product of power number and

iii

Reynolds number in this particular regime is approximately proportional to the number of blades for these six impellers; however, other shape factors that were not included in this study also contribute to it.

In turbulent operation, baffling has a significant effect on power number: the power number for most impellers remains relatively constant in the baffled configuration while that for unbaffled configuration decreases with increasing Reynolds number. The impeller blade number is not the dominant factor that affects power number in this regime. Two hydrofoil impellers, SC-3 and HE-3, exhibit much lower power numbers when compared with the other impellers. Additionally, the impellers with higher power numbers in baffled tank tend to have lower ratios between unbaffled power number and average baffled power number when comparing at same Reynolds number.

No difference between two configurations, baffled and unbaffled, exists at low

Reynolds number end of transitional regime, and the difference starts at intermediate

Reynolds number and increases with an increase of Reynolds number. In the baffled configuration, four out of six impellers exhibit a minimum power number. In the unbaffled configuration, power numbers drop with increasing Reynolds number throughout the entire transitional regime for all impellers. The ratio of unbaffled to turbulent average power number for the six impellers retains a consistent order through the entire Reynolds number range with two high efficiency impellers having the highest ratio, then pitched blade impeller, and three radial flow impellers having the lowest ratios.

ACKNOWLEDGEMENTS

I would like to thank Dr. Kevin Myers for all the help he has given throughout the past three years. Without his encouragement and guidance I would have never made it this far. Dr. Myers gave me a great opportunity to pick up chemical engineering from basics three years ago. He accepted me to work on this research so I can complete the degree with a written thesis and get prepared for future study. I will be thankful to him for his support and benefactions forever. I also want to thank Eric Janz who offered me this opportunity to be part of the team and gave me the access to carry out this experiment in the Chemineer laboratory. I want to express my thankfulness to Prof.

Robert Wilkens for being my committee member and providing constructive feedback on my thesis. I would also like to thank Erin Duff, Robert Strong, and Michael Adams for their support on both the laboratory measurements and my daily life.

I want to acknowledge everyone else who has offered support: my family for their continuous love; my boyfriend, Zhengchao, as he has tried his best to take care of me and been supportive all the way through; Jin, my best friend here in UD, for all the suggestions and her willingness to share my joys and sorrows; Jie and his wife, Jing, who encouraged me when I had a tough time. I would have failed my study here in UD without those people.

TABLE OF CONTENTS

ABSTRACT ...... iii

ACKNOWLEDGEMENTS ...... v

LIST OF FIGURES ...... vii

LIST OF TABLES ...... ix

NOMENCLATURE ...... xi

CHAPTER 1 INTRODUCTION ...... 1

1.1 Background ...... 1

1.2 Power Number and Reynolds Number...... 2

1.3 Rheology ...... 4

1.4 System Geometry ...... 5

1.5 Objective ...... 6

CHAPTER 2 EXPERIMENTAL SETUP AND PROCEDURE ...... 7

2.1 Experimental Setup ...... 7

2.2 Viscosity Measurement ...... 9

2.3 Procedure ...... 10

CHAPTER 3 RESULTS AND DISCUSSION ...... 12

CHAPTER 4 CONCLUSIONS AND RECOMMENDATIONS ...... 42

BIBLIOGRAPHY ...... 46

APPENDIX: RAW AND REDUCED EXPERIMENTAL DATA ...... 47

LIST OF FIGURES

Figure 1-1: Haake viscometer data for corn syrup at different temperatures (μ [=] Pa s) .. 5

Figure 2-1: Experimental apparatus ...... 8

Figure 2-2: Readout of torque and speed from agitator ...... 9

Figure 2-3: Assembled agitator shaft and impeller ...... 9

Figure 3-1: D-6 low Reynolds number data ...... 13

Figure 3-2: CD-6 low Reynolds number data ...... 13

Figure 3-3: S-4 low Reynolds number data ...... 14

Figure 3-4: P-4 low Reynolds number data ...... 14

Figure 3-5: SC-3 low Reynolds number data ...... 15

Figure 3-6: HE-3 low Reynolds number data ...... 15

Figure 3-7: Comparison of baffled low Reynolds number data ...... 18

Figure 3-8: D-6 high Reynolds number data ...... 19

Figure 3-9: CD-6 high Reynolds number data ...... 19

Figure 3-10: S-4 high Reynolds number data ...... 20

Figure 3-11: P-4 high Reynolds number data ...... 20

Figure 3-12: SC-3 high Reynolds number data ...... 21

Figure 3-13: HE-3 high Reynolds number data ...... 21

Figure 3-14: Comparison of baffled high Reynolds number data ...... 25

Figure 3-15: Comparison of unbaffled high Reynolds number data ...... 26

vii

Figure 3-16: D-6 transitional Reynolds number data ...... 27

Figure 3-17: CD-6 transitional Reynolds number data ...... 27

Figure 3-18: S-4 transitional Reynolds number data ...... 28

Figure 3-19: P-4 transitional Reynolds number data ...... 28

Figure 3-20: SC-3 transitional Reynolds number data ...... 29

Figure 3-21: HE-3 transitional Reynolds number data ...... 29

Figure 3-22: Ratio of unbaffled to baffled power numbers in transitional and turbulent operation ...... 34

Figure 3-23: Ratio of unbaffled to turbulent average power numbers in transitional and turbulent operation ...... 34

Figure 3-24: Ratio of baffled to turbulent average power numbers in transitional and turbulent operation ...... 35

Figure 3-25: Comparison of all baffled power number data ...... 38

Figure 3-26: Comparison of all unbaffled power number data ...... 38

Figure 3-27: Baffled and unbaffled data of D-6 for all Reynolds numbers ...... 39

Figure 3-28: Baffled and unbaffled data of CD-6 for all Reynolds numbers ...... 39

Figure 3-29: Baffled and unbaffled data of S-4 for all Reynolds numbers ...... 40

Figure 3-30: Baffled and unbaffled data of P-4 for all Reynolds numbers ...... 40

Figure 3-31: Baffled and unbaffled data of SC-3 for all Reynolds numbers ...... 41

Figure 3-32: Baffled and unbaffled data of HE-3 for all Reynolds numbers ...... 41

viii

LIST OF TABLES

Table 2-1: Impellers ...... 8

Table 3-1: Comparison of baffled and unbaffled Newtonian fluid KL values ...... 17

Table 3-2: Highest Reynolds number for laminar operation ...... 17

Table 3-3: Comparison of baffled Newtonian fluid turbulent power numbers ...... 23

Table 3-4: Unbaffled to baffled power number ratios in turbulent operation ...... 23

Table 3-5: Lowest Reynolds number for turbulent power number in baffled configuration ...... 24

Table 3-6: Power number comparison ...... 25

Table 3-7: Reynolds number range with baffled NP lower than average baffled turbulent Np ...... 31

Table 3-8: Unbaffled to baffled power number ratios in transitional operation ...... 33

Table 3-9:Unbaffled power number to turbulent average power number ratios in transitional operation ...... 36

Table 3-10: Baffled power number to turbulent average power number ratios in transitional operation ...... 37

Appendix 1: Raw and reduced data from impeller power draw experiments for baffled

D-6…………………………………………………...... …………………47

Appendix 2: Raw and reduced data from impeller power draw experiments for unbaffled D-6 ...... 49

Appendix 3: Raw and reduced data from impeller power draw experiments for baffled

CD-6 ...... 51

Appendix 4: Raw and reduced data from impeller power draw experiments for unbaffled CD-6 ...... 53

Appendix 5: Raw and reduced data from impeller power draw experiments for baffled

S-4 ...... 55

Appendix 6: Raw and reduced data from impeller power draw experiments for unbaffled S-4 ...... 57

Appendix 7: Raw and reduced data from impeller power draw experiments for baffled

P-4 ...... 59

Appendix 8: Raw and reduced data from impeller power draw experiments for unbaffled P-4 ...... 61

Appendix 9: Raw and reduced data from impeller power draw experiments for baffled

SC-3 ...... 63

Appendix 10: Raw and reduced data from impeller power draw experiments for unbaffled SC-3 ...... 65

Appendix 11: Raw and reduced data from impeller power draw experiments for baffled

HE-3 ...... 67

Appendix 12: Raw and reduced data from impeller power draw experiments for unbaffled HE-3 ...... 69

NOMENCLATURE

A Impeller area which the fluid is pumped through (m2)

D Impeller diameter (m)

H Velocity head (Pa)

KL Constant that equals to the product of power number and Reynolds number in laminar regime (-)

L Characteristic length (m)

M Torque (N∙m)

N Agitator rotational speed (rpm)

NP Power number (-)

NRe Reynolds number (-)

P Power draw (W)

Q Impeller pumping rate (m3/s)

T Tank diameter (m)

υ Fluid velocity (m/s)

W Impeller blade width (m)

Z Liquid level (m)

γ Shear rate (1/s)

μ Fluid viscosity (Pa∙s)

ρ Fluid density (kg/m3)

τ Shear stress (Pa)

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

Agitation is the introduced motion of a material in a circulatory pattern inside a container. This operation tends to reduce gradients in composition and properties.

During agitation, kinetic energy is transferred from a rotating impeller to the surrounding fluid. Mechanical agitators are widely used in the chemical processing and related industries as they speed interphase mass transfer and chemical reactions. Additionally, the suspension of solids in liquids, the dispersion of liquids and gases, and the agitation of dry solid powders are commonly encountered applications of agitation. Agitators are a necessity in the processing industries due to their various applications.

Agitators must be designed from both mechanical and process viewpoints.

Mechanical design, such as the design of motor, gear reducer, seal, shaft, impellers and tank, is essential for successful operation, and is usually determined by the component manufacturer. However, process environment, such as fluid properties, desired process results, and agitator’s power consumption, directly impact the mechanical design. Power number, one of the most important parameters in mixing research and practice (Calabrese et al., 2014), is used to predict the power requirement of a given agitation system and is the main focus of this study.

In order to design full-scale mixing systems and develop a design guide that can be used to reliably predict the different types of impellers’ power draw, this study focused on the relationship between power number and Reynolds number for Newtonian fluids in a laboratory-scale agitator across the spectrum of Reynolds number for six industrially significant impellers.

1.2 POWER NUMBER AND REYNOLDS NUMBER

As mentioned, power number can be used to predict power consumption and is a key consideration in both the mechanical and process design of an agitation system. The power applied to the agitation system impeller produces velocity head, H, and pumping capacity, Q, with the impeller power draw being the product of these two quantities

(Hemrajani et al., 2004):

( 1.1 )

The velocity head that provides the kinetic energy is dependent on the product of the fluid density and the square of its velocity:

( 1.2 )

The fluid velocity near the impeller is directly proportional to the impeller tip (πND) and thus:

( 1.3 )

The pumping capacity Q is the product of the fluid velocity and area through which the fluid is pumped:

( )( ) ( 1.4 )

Then Equation 1.1 can be rewritten as:

( ) ( ) ( 1.5 )

The preceding result leads to the most commonly seen dimensionless form for the power number, NP (Rushton et al., 1950):

( 1.6 )

The power number is a function of impeller type, Reynolds number, and geometric parameters such as the impeller diameter to tank diameter ratio, D/T (Bates et al., 1966). It can be seen from this equation that if the power number for a given system is known, the power consumption, P, can be predicted from the fluid density, ρ, impeller diameter, D, and rotational speed, N.

The Reynolds number is the ratio of inertial forces to viscous forces (McCabe et al., 2005). It is defined as:

( 1.7 )

L represents a characteristic length, represents velocity, and μ represents the fluid viscosity. For agitation, impeller diameter, D, is employed as characteristic length, and the velocity is proportional to the impeller tip speed and can be replaced by the product of impeller rotational speed and the impeller diameter:

( ) ( 1.8 )

The Reynolds number can be used to classify the impeller operation regimes (McCabe et al., 2005). In the laminar regime, the power number is inversely proportional to

-1 Reynolds number (NP  NRe ); in the turbulent regime, the power number is constant in

3 fully baffled tanks; and the transitional regime occurs at Reynolds numbers between the laminar and turbulent regimes with the power number gradually changing from laminar

(inversely dependent on Reynolds number) to fully developed turbulent behavior

(Reynolds number independent). The laminar regime is generally taken to occur when the Reynolds number is smaller than ten, and viscosity dominates in this regime. At high

4 Reynolds number of turbulent operation (i.e., NRe > 10 ), viscosity has little effect and the process is mainly controlled by inertial forces. In transitional regime, both viscous and inertial forces affect the process.

1.3 RHEOLOGY

Fluids can be classified as Newtonian and non-Newtonian depending upon the relationship between shear stress and shear rate (Strong and Myers, 2013). For

Newtonian fluids, the shear stress, τ, is proportional to the local shear rate, γ, at every point:

( 1.9 )

The constant of proportionality, μ, is known as Newtonian viscosity. It depends only on the material and its temperature and pressure. Figure 1-1 presents the shear stress - shear rate data taken using a Haake concentric cylinder viscometer for corn syrup at different temperatures. It can be seen that the slope of shear stress-shear rate (the viscosity, μ) is constant at each temperature, but it decreases with increasing temperature. Both water and aqueous corn syrup solutions used in this study are Newtonian fluids.

2000 T=20.5C τ = 154 γ 1800 τ = 118 γ 1600 T=22.5C

1400 T=24.5C

τ = 89.8 γ 1200 T=26.5C τ = 67.5 γ 1000 T=28.5C τ = 51.5 γ

800 Shear Shear (Pa)Stress 600 T=30.5C τ = 39.7 γ

400 T=32.5C τ = 31.7 γ 200 T=34.5C τ = 25.3 γ 0 0 10 20 30 40 50 Shear Rate (1/s) Figure 1-1: Haake viscometer data for corn syrup at different temperatures (μ [=] Pa s)

1.4 SYSTEM GEOMETRY

Besides Reynolds number, system geometry, such as impeller geometry, impeller clearance from the tank bottom, the ratio of impeller diameter to tank diameter, D/T, and the baffles, etc., also has significant effect on power number. In this work, power draw of different types of impellers has been studied since impeller geometry has been considered as one major factor that influences power number.

According to the flow pattern produced by the impeller, impellers can be classified as radial-flow, axial-flow, and mixed flow (Oldshue, 1983). Radial-flow impellers, such as the D-6, CD-6, and S-4, generate discharge fluid flow perpendicular to the impeller axis of rotation; when using axial-flow impellers, such as SC-3 and HE-3, in turbulent operation, the fluid flows parallel to the impeller’s axis of rotation; for mixed flow impeller, such as P-4, both radial and axial flow will be produced. Impellers can be

5 further classified by the application. Propellers, pitched-blade turbines, and high- efficiency impellers are normally used for low- to moderate-viscosity liquids, while helical impellers and anchor agitators are employed for high viscosity liquids. For the six impellers used in this study, SC-3 and HE-3 are high-efficiency impellers, and the other four impellers, D-6, CD-6, P-4 and S-4, are turbines.

1.5 OBJECTIVE

The objective of this work is to gain information that could be used to design full scale mixing systems, and also could develop a design guide that can provide a reliable prediction of the power draw of different types of impellers. To achieve this goal, extensive power number data was taken in Newtonian fluids on six industrially significant impellers from Reynolds numbers less than 0.1 to greater than 100,000.

Power number behaviors of these impellers, including laminar operation, turbulent operation, transitional operation, the Reynolds number limits of the operating regimes, and the effect of baffling on power number were compared.

CHAPTER 2

EXPERIMENTAL SETUP AND PROCEDURE

2.1 EXPERIMENTAL SETUP

All experiments were performed in a flat-bottomed clear acrylic cylindrical tank of 23.5 inches diameter. To broaden the understanding of the effects of impeller type on power draw, ten different impellers that were supplied by Chemineer, Inc. (Dayton, OH) were studied, although the data for only six impellers are reported in this thesis, with the data of the other four impellers being proprietary. Table 2-1 shows the images of the impellers and lists the impeller diameter to tank diameter ratios (D/T). The off-bottom clearance for the impellers was set to 7.8 inches (C/T=1/3), while the liquid level to tank diameter ratio was set equal to unity (Z/T=1).

A laboratory-scale mixer, shown Figure 2-1, was used in this study. A Baldor

(Fort Smith, AR) three phase electric motor (VM3558T) that was used as a power source to provide shaft and impeller rotation was connected to a 4-speed gearshift transmission, with gear ratios of 1:1, 1.33:1, 2:1 and 4:1. A zero velocity magnetic pickup was used as transducer to measure the rotational speed, N. A 500 in∙lbf (56.5 N∙m) strain gauge was used to measure shaft torque, M. Both the speed signal and torque signal were sent to a

Honeywell (Columbus, OH) conditioner indicator (Model 7541) with a digital readout.

This conditioner indicator is shown in Figure 2-2. Accurate determination of the power

7 draw, P, can be obtained by knowing the torque and speed of an agitator since .

Assembled agitator shaft with impeller is shown in Figure 2-3. The shaft has a 0.75 inch diameter at the drive that reduced to a 0.50 inch diameter about midway along the shaft.

Impellers were mounted to the bottom end of the shaft with setscrews as shown in the same figure.

Table 2-1: Impellers Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Diameter 7.99 8.78 9.54 9.50 9.50 9.51 (inch) D/T 0.340 0.374 0.406 0.404 0.404 0.405

Figure 2-1: Experimental apparatus 8

Figure 2-2: Readout of torque and speed from agitator

Figure 2-3: Assembled agitator shaft and impeller

2.2 VISCOSITY MEASUREMENT

The viscosity data of Figure 1-1 was taken using a concentric cylinder Haake viscometer designed to provide viscosity as a function of shear rate. This viscometer was not used during power number testing because insertion of a sample in the viscometer cup would change the sample temperature and thus its viscosity. Viscosity measurements were performed by Brookfield DV-E Viscometer, Gardco® Standard Ford Viscosity Cups

9 and Cannon-Fenske Routine (Capillary) Viscometer from Cannon Instrument Company® depending on the viscosity range. Brookfield DV-E Viscometer was employed when viscosity was higher than 200 cp. This type of viscometer measures fluid dynamic viscosity at given rotational speeds. After immersing a sensing element (spindle) in a fluid, the viscous drag of the test fluid against the spindle is measured with a rotary transducer that provides a torque signal. The range of measurement is affected by the spindle’s rotational speed, size and shape, and the container in which the spindle is rotating. For Newtonian fluids, viscosity appears in units of centipoise (cp) on the viscometer’s display directly. Standard Ford Viscosity Cups were used to achieve better accuracy when viscosity was between 50 and 200 cp. This viscometer is a simple gravity device. By timing the flow of known volume of liquid passing through an orifice located at the bottom of the Ford Cup, kinematic viscosity in mm2/s (cSt) can be determined by referring to the corresponding conversion table. The dynamic viscosity can then be found by multiplying the kinematic viscosity by the density of fluid in gram per milliliter (g/ml) that is defined as its weight per unit volume. When viscosity was lower than 50 cp,

Cannon-Fenske Routine Viscometer was used. Similar to Standard Ford Viscosity Cups,

Cannon-Fenske Routine Viscometer measures kinematic viscosity instead of dynamic viscosity using the time required for gravity flow of a fixed volume of fluid through a capillary.

2.3 PROCEDURE

The experimental procedure began with agitating the Newtonian fluid to reach a spatially uniform status. After that, the density of the Newtonian fluid was measured by weighting a 100 ml volumetric flask sample that was taken from the tank. Temperature

10 and viscosity were recorded. In order to produce Reynolds number and power number for the chosen impeller, readings of torque at various impeller rotational speeds were required. Temperature and viscosity measurements were performed again after the power number data collection process. The viscosity at each torque data point was estimated by using the viscosities measured before and after data collection and linearly interpolating based on torque. When at high viscosity (μ > 300 cp), the agitation process tended to take a longer time than for agitation at lower viscosity. Temperature changed significantly due to conversion of mechanical energy to thermal energy. That led to a significant viscosity change as shown in Figure 1-1. At low viscosity (μ < 50 cp), agitation in unbaffled tank led to the formation of a large surface vortex when the

Reynolds number is high (greater than about to 104). Data acquisition was stopped before the vortex reached the impeller, and gaps in the data at higher Reynolds number appeared due to the fact that data could be obtained at only a few speeds at each fluid viscosity.

CHAPTER 3

RESULTS AND DISCUSSION

A key parameter in agitator design, power number strongly depends on both

Reynolds number and the impeller geometry. In advance of a study of impeller power draw in non-Newtonian fluids, extensive data was taken in Newtonian fluids with both baffled and unbaffled configurations. This section compares the power number behaviors of these different impellers, including three operation regimes (laminar, transitional, and turbulent), the Reynolds number limits of the operation regimes, and the effect of baffling on power number.

Figures 3-1 through 3-6 present the measured power numbers as functions of

Reynolds number in the laminar regime (D-6 in Figure 3-1, CD-6 in Figure 3-2, S-4 in

Figure 3-3, P-4 in Figure 3-4, SC-3 in Figure 3-5, and HE-3 in Figure 3-6). As can been clearly seen, the data for all six impellers in both baffled and unbaffled configurations agree with each other, indicating that the baffling has no effect on power number at low

Reynolds number. Another point these impellers have in common is that the slopes of the power number – Reynolds number relations on logarithmic coordinates are all equal to -1, indicating that the power number in this regime is inversely proportional to

-1 Reynolds number (NP  NRe , with data correlations included on each figure).

1,000

-1 N = 60.7 N ) P Re P 100

10 Power Number Power Number (N

D-6 Baffled D-6 Unbaffled 1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-1: D-6 low Reynolds number data

1,000

-1

NP = 61.9 NRe )

P 100

10 Power Number Power Number (N

CD-6 Baffled CD-6 Unbaffled 1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-2: CD-6 low Reynolds number data

1,000

-1 ) N = 45.5 N P 100 P Re

Power Number Power Number (N 10

S-4 Baffled S-4 Unbaffled 1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-3: S-4 low Reynolds number data

1,000

-1 ) N = 43.2 N P 100 P Re

Power Number (N 10

P-4 Baffled P-4 Unbaffled 1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-4: P-4 low Reynolds number data

1,000

N = 26.0 N -1

100 P Re

) P

10 Power Number Power Number (N 1

SC-3 Baffled SC-3 Unbaffled 0.1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-5: SC-3 low Reynolds number data

1,000

-1 NP = 27.0 NRe

100

) P

10 Power Number Power Number (N 1

HE-3 Baffled HE-3 Unbaffled 0.1 0.01 0.1 1 10 100

Reynolds Number (NRe)

Figure 3-6: HE-3 low Reynolds number data

Due to the inversely proportional relationship, the product of power number and

Reynolds number in laminar regime is a constant as shown in Equation 3.1 below.

( 3.1 )

This constant KL also equals the impeller power number at a Reynolds number of one.

Table 3-1 presents the values of KL for different types of impeller. As can be seen, the

KL values of baffled and unbaffled configurations differ by no more than two percent for all six impellers, reinforcing the conclusion that the baffles have no effect on impeller power draw in laminar operation. Besides this, the small KL COV (coefficient of variation, which equals the ratio of the standard deviation to the arithmetic average) shows the low point to point variation in the data. Because of the lack of baffling effect, it is reasonable to take a weighted average of the baffled and unbaffled KL values for each impeller (weighted by the number of data points taken with each configuration.).

D-6 and P-4 values agree with literature KL values while the HE-3 is considerably lower.

Table 3-2 lists the laminar operation range for different impellers based on the experimental results. The highest Reynolds number with less than ten percent difference between the experimental power number value and that found from the data correlation

(Np= KL/NRe, with the baffled-unbaffled weighted average KL being used) is treated as the highest laminar operation Reynolds number data point for each impeller. It is widely accepted that laminar operation takes place when Reynolds number is less than 10. From the results from this work, the upper limit for laminar operation should be lower than 10, as four out of six impellers have their highest laminar operation Reynolds number smaller than 10.

Table 3-1: Comparison of baffled and unbaffled Newtonian fluid KL values Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

K L 61.0 61.7 45.4 43.1 25.7 26.9 Average Baffled K L 2.6% 2.7% 2.5% 1.2% 3.3% 2.5% COV** K L 60.4 62.1 45.5 43.2 26.2 27.4 Average Unbaffled K L 2.7% 2.2% 2.1% 1.3% 3.1% 2.4% COV** Weighted K L 60.7 61.9 45.5 43.2 26.0 27.2 Average

* Literature KL 65 N/A N/A 44.5 N/A 43

* Literature KL values are from McCabe et al. [4]. ** COV = Coefficient of Variation = Standard Deviation/Arithmetic Average

Table 3-2: Highest Reynolds number for laminar operation Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

* Highest NRe 8.6 7.6 10.0 8.0 7.2 10.3

* The highest NRe with less than 10% difference between the experimental value and that found from the data correlation, Np= KL/NRe

According to Table 3-1, KL values seem to be affected only by the impeller’s blade number, with the impellers that have the same number of blades having similar KL values and impellers with more blades having higher KL values with the KL values being roughly proportional to the number of blades. This phenomenon is illustrated graphically in Figure 3-7, as CD-6 and D-6, S-4 and P-4, and SC-3 and HE-3 data almost coincide.

However, this conclusion is not applicable to all impellers. Other shape factors such as the ratio between the width of impeller blades and the impeller diameter (W/D) (Smith,

1985) also contribute to the value of KL. One wide-blade impeller that was tested has a

KL value close to 100 with only three blades. This impeller’s data is not included here due to confidentiality. Figure 3-7 presents only baffled data for these six impellers’ power number-Reynolds number laminar results since baffling doesn’t affect the data in

17 this regime. It should also be noticed that all data sets in this regime are parallel, which reinforces what was said in the previous discussion that these impellers have same exponent of -1 in their laminar regime power number-Reynolds number relations.

1,000

100

) p

D-6 CD-6 10

Power Number Power Number (N S-4 P-4 SC-3 HE-3 1 0.01 0.1 1 10 Reynolds Number (NRe) Figure 3-7: Comparison of baffled low Reynolds number data

Figures 3-8 through 3-13 present the measured power numbers as functions of

Reynolds number in the turbulent regime (D-6 in Figure 3-8, CD-6 in Figure 3-9, S-4 in

Figure 3-10, P-4 in Figure 3-11, SC-3 in Figure 3-12, and HE-3 in Figure 3-13. Due to their lower baffled turbulent power numbers, the SC-3 and HE-3 data plots use a different y axis range than the other four impellers). The average baffled power number and power-law correlations for the unbaffled power numbers are included as well. Baffling has significant effect on power number in this regime for all six impellers: power number stays relatively constant in the baffled tank while in the tank with no baffles installed, the power number drops with increasing Reynolds number.

NP = 5.41

) P

-0.198 NP = 8.35 NRe

Power Number Power Number (N R² = 0.98 D-6 Baffled

D-6 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-8: D-6 high Reynolds number data

NP = 2.79

) P

-0.184 NP = 5.55 NRe

Power Number Power Number (N R² = 0.99

CD-6 Baffled CD-6 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-9: CD-6 high Reynolds number data

NP = 3.10

) P

-0.162 NP = 4.14 NRe Power Number Power Number (N R² = 0.97

S-4 Baffled S-4 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-10: S-4 high Reynolds number data

) P NP = 1.15

1 Power Number Power Number (N -0.144 NP = 2.42 NRe R² = 0.98 P-4 Baffled P-4 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-11: P-4 high Reynolds number data

NP = 0.503

) P

Power Number Power Number (N -0.144 NP = 1.13 NRe R² = 0.98 SC-3 Baffled SC-3 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-12: SC-3 high Reynolds number data

) P

NP = 0.309 Power Number Power Number (N -0.120 NP = 0.695 NRe HE-3 Baffled R² = 0.94 HE-3 Unbaffled 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-13: HE-3 high Reynolds number data

Table 3-3 shows power number values for the six impellers in baffled tank when the Reynolds number is larger than 104. In this range, SC-3 and HE-3 power numbers are more than an order of magnitude lower than that of the D-6 (recall from Table 3-1 that these power numbers vary by only a factor of two in the laminar regime). Their low turbulent power numbers make the SC-3 and HE-3 impellers the popular choice when mixing low or moderate viscosity liquids. CD-6 and S-4 have similar power numbers which indicates the number of impeller blades is no longer the dominant factor that affects power number in this regime. Comparison of the P-4 and S-4 power numbers illustrates the impact that blade angle has on turbulent power number in baffled tanks. It is normally considered that the turbulent power number in a baffled tank should remain constant. According to the results in this work, the power numbers for D-6 and S-4 still increase with increasing Reynolds number. The ranges in the power numbers of these impellers is more than ten percent of the average values and they both have a relatively large coefficient of variation when compared with the other impellers. When available, the average values of the baffled impeller power numbers obtained during this work agree with the literature values with less than 10% difference. For D-6, using 6.3 as its turbulent power number as reported by Rushton et al. (1950) is considered to be high; with 5.5 being more acceptable according to Bates et al. (1966).

In Table 3-4, power number ratio between unbaffled power number correlation equation and baffled power number average has been used to examine the difference between these two configurations. For all impellers, unbaffled power number continually decreases with increasing Reynolds number. Besides this, the impellers with higher power numbers in baffled tank tend to have lower power number ratios when comparing

22 at same Reynolds number. HE-3, the only impeller with power number ratio larger than

0.5 in the entire turbulent regime, has the lowest baffled power number.

Table 3-3: Comparison of baffled Newtonian fluid turbulent power numbers Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Lowest NP 5.03 2.75 2.86 1.10 0.484 0.300 Highest 5.70 2.84 3.28 1.18 0.521 0.321 NP N P 5.41 2.79 3.10 1.15 0.503 0.309 Average Range 12.4% 3.2% 13.5% 7.0% 7.4% 6.8% /Average

NP COV 4.3% 1.0% 4.8% 2.0% 2.4% 2.1%

[1] [3] Literature 4.8-5.5 [4] [4] 1.1 [4] * [7] 2.9 3.1 [4] N/A 0.28 NP 6.3 1.27 * Literature NP values are from McCabe et al. [4], Rushton et al. [7], Bates et al. [1], and Deng [3]

Table 3-4: Unbaffled to baffled power number ratios in turbulent operation Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

-0.198 -0.184 -0.162 -0.144 -0.144 -0.120 Unbaffled NP 8.35 NRe 5.55 NRe 4.14 NRe 2.42 NRe 1.13 NRe 0.696 NRe

Average Baffled NP 5.41 2.79 3.10 1.15 0.503 0.309

NP Ratio -0.198 -0.184 -0.162 -0.144 -0.144 -0.120 1.54 NRe 1.99 NRe 1.34 NRe 2.10 NRe 2.26 NRe 2.25 NRe (Unbaffled NP /Baffled NP)

NRe NP Ratio

10,000 0.25 0.37 0.30 0.56 0.60 0.75

20,000 0.22 0.32 0.27 0.50 0.54 0.69

50,000 0.18 0.28 0.23 0.44 0.48 0.61

100,000 0.16 0.24 0.21 0.40 0.43 0.57

200,000 0.14 0.21 0.19 0.36 0.39 0.52

Table 3-5: Lowest Reynolds number for turbulent power number in baffled configuration Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Average Np 5.41 2.79 3.10 1.15 0.503 0.309 Lowest N in the Re 10,500 176 4160 2800 5790 1040 ±10% NP range

Corresponding Np 5.03 3.04 2.79 1.04 0.454 0.336

Table 3-5 shows the lowest Reynolds number for which power number remains within 10% of the average turbulent power number in the baffled configuration. This lowest Reynolds number for D-6 is higher than 10,000, the point that is generally accepted as starting point for turbulent regime. For CD-6, the impeller with the lowest power number coefficient of variation in Table 3-3, the lowest Reynolds number where the power number is within 10% of its turbulent value is 176. This is considerably less than 10,000, indicating that the baffled power number of the CD-6 is relatively constant throughout much of the transitional regime. Except for CD-6 and HE-3, the power numbers for the other four impellers are all lower than their average turbulent power numbers, indicating that their power numbers exhibit a minimum in transitional operation.

Turbulent operation results for the six impellers are compared both quantitatively

(Table 3-6) and qualitatively (Figure 3-14 and 3-15 for baffled and unbaffled configurations, respectively). In Table 3-6, the two configurations’ power numbers in laminar and turbulent operation are normalized by the HE-3’s corresponding power number to obtain the relative values. The relative unbaffled turbulent power number is calculated by averaging the ratio of each impeller and the HE-3’s correlation power numbers at five Reynolds numbers (10,000, 20,000, 50,000, 100,000, and 200,000). In the laminar regime, D-6 has a power number that is twice that of the HE-3. In the turbulent regime, the power numbers vary by a factor of 18 for these two impellers in

24 baffled operation. As has been discussed relative to Table 3-4, the turbulent power number decreases significantly in the unbaffled configuration for D-6, but it is still four times higher than that of the SC-3 and over five times higher than that of the HE-3.

Table 3-6: Power number comparison Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Average Laminar KL 60.7 61.9 45.5 43.2 26.2 27.4

Relative Laminar KL 2.2 2.3 1.7 1.6 0.96 1 Average Baffled 5.41 2.79 3.10 1.15 0.503 0.309 Turbulent Np Relative Baffled * 18 9.0 10 3.7 1.6 1 Turbulent Np Relative Unbaffled * 5.2 4.0 3.8 2.7 1.3 1 Turbulent Np * All relative power number values are normalized with respect to the HE-3

) P

1 D-6 CD-6

S-4 Power Number Power Number (N P-4 SC-3 HE-3 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-14: Comparison of baffled high Reynolds number data

) P

1 D-6 CD-6

S-4 Power Number Power Number (N P-4 SC-3 HE-3 0.1 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-15: Comparison of unbaffled high Reynolds number data

Figures 3-16 through 3-21 present the measured power numbers as functions of

Reynolds number in the transitional regime (D-6 in Figure 3-16, CD-6 in Figure 3-17,

S-4 in Figure 3-18, P-4 in Figure 3-19, SC-3 in Figure 3-20, and HE-3 in Figure 3-21).

For reference, the baffled turbulent power number for each impeller is included in the corresponding figure. Additionally, these figures include power law correlations for unbaffled data at higher Reynolds numbers, with the Reynolds number range for each curve noted below the corresponding power law equation. In the transitional regime, baffling has no effect on the power number at low Reynolds number, as was observed in the laminar regime. With increasing Reynolds number there is an increasing difference between the unbaffled and baffled power numbers of all impellers, with the D-6 having the biggest power number difference between the two configurations and the HE-3 having the least difference. Besides this, D-6, S-4, P-4, and SC-3 impellers, as was

26 suggested when discussing baffled turbulent operation, exhibit a minimum power number in baffled transitional operation. The CD-6, one of two impellers that have no minimum power number in baffled transitional operation, has a power number higher than the average turbulent power number by an average of 4% and a maximum of 8% for

Reynolds numbers between 490 and 2500.

) P NP = 5.41

-0.241 NP = 12.2 NRe

Power Number Power Number (N R² = 0.99 D-6 Baffled NRe = 210 - 10,200 D-6 Unbaffled 1 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-16: D-6 transitional Reynolds number data

) P

NP = 2.79

1 -0.253 NP = 10.3 NRe R² = 1.00

NRe = 20 - 10,500 Power Number Power Number (N CD-6 Baffled CD-6 Unbaffled 0.1 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-17: CD-6 transitional Reynolds number data

) P

NP = 3.1 1 -0.234 NP = 7.85 NRe R² = 1.00

NRe = 200 - 10,500 Power Number Power Number (N

S-4 Baffled S-4 Unbaffled 0.1 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-18: S-4 transitional Reynolds number data

) P

1 NP = 1.15

-0.193 NP = 3.77 NRe Power Number Power Number (N R² = 0.99 NRe = 190 - 10,900 P-4 Baffled P-4 Unbaffled 0.1 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-19: P-4 transitional Reynolds number data

) P 1

NP = 0.503 -0.155 NP = 1.23 NRe

0.1 R² = 0.99 Power Number Power Number (N NRe = 960 - 8100

SC-3 Baffled SC-3 Unbaffled 0.01 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-20: SC-3 transitional Reynolds number data

) P 1

-0.143 NP = 0.309 NP = 0.85 NRe

0.1 R² = 0.96 Power Number Power Number (N NRe = 970 - 9700

HE-3 Baffled HE-3 Unbaffled 0.01 1 10 100 1,000 10,000 100,000

Reynolds Number (NRe)

Figure 3-21: HE-3 transitional Reynolds number data

Table 3-7 presents the Reynolds number range for each impeller for which the baffled power number is lower than the average baffled turbulent power number. This is not applicable for CD-6 and HE-3 as their power numbers do not have a minimum in the transitional regime. For the other four impellers, the lower Reynolds number value is the lowest Reynolds number for which the measured power number is less than the turbulent average value, while the upper Reynolds number is that for which the measured power number is more than ten percent less than the turbulent average value (as in Table 3-5).

Also, the lower Reynolds number value can be either from baffled or unbaffled configuration since baffling makes no difference in the results at low Reynolds number, but the upper Reynolds number limit is from baffled configuration only. For D-6 and S-4, two impellers that have relatively high coefficients of variation in their average baffled turbulent power numbers according to Table 3-3, this Reynolds number range extends through more than two orders of magnitude. For the P-4, which has the lowest coefficient of variation in the average baffled turbulent power number among these four impellers, the Reynolds number range is less than one order of magnitude.

Table 3-7 also presents the minimum transitional power number with its corresponding Reynolds number for each impeller in the baffled configuration. Again, this is not applicable for CD-6 and HE-3 as has been stated previously. For the other four impellers, D-6 and S-4 have the minimum power number at relatively low Reynolds number of approximately 200, while the P-4 and SC-3 have their minimum power numbers at higher Reynolds number near 2000. The power number ratios between the minimum power number and the average turbulent power number for S-4, P-4 and SC-3

30 are close to each other, ranging between eighty and ninety percent, while the ratio for the

D-6 is significantly lower than the rest with a value of 0.66.

Table 3-7: Reynolds number range with baffled NP lower than average baffled turbulent Np Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Average baffled 5.41 2.79 3.10 1.15 0.503 0.309 turbulent Np

NRe range 18.7 - 10,500 N/A 35.7 - 4160 773 - 2800 504 – 5790 N/A

Minimum Np 3.56 N/A 2.47 1.02 0.422 N/A

Corresponding 200 N/A 200 2200 2000 N/A NRe

NP Ratio (Minimum N / P 0.66 N/A 0.80 0.89 0.83 N/A Average turbulent NP)

Figure 3-22 is plotted based on the result from Table 3-8 that presents the power number ratios between baffled and unbaffled configurations in both transitional and turbulent operation (Table 3-8 contains transitional data while the turbulent data was previously presented in Table 3-4. Interpolation with approximately four adjacent data points was used to generate the value at each particular Reynolds numbers in the table.).

The ratio for laminar operation is not included as baffling has no effect in this regime and the ratio will be equal to one for all impellers. In the transitional regime, the ratios of unbaffled to baffled power numbers for all impellers stay above 0.9 until the Reynolds number reaches 200. When the Reynolds number is higher than 200, the ratios for three radial flow impellers, D-6, CD-6 and S-4, drop significantly to lower than 0.75 and then stay similar through the entire Reynolds number range. As Reynolds number hits 2000, the ratio for P-4 is lower than 0.9 as well and leaves only the two hydrofoil impellers above the 0.9 line. The unbaffled power number is about half of the baffled power

31 number at this Reynolds number for the three radial flow impellers. For Reynolds number higher than 5,000, SC-3 and P-4 are similar with the SC-3 being a bit higher.

HE-3 is the only impeller that the unbaffled to baffled power number ratio remains above

0.5 in the entire Reynolds number range.

Figures 3-23 and 3-24 are generated from data in Tables 3-9 and 3-10, respectively (again, data interpolation was used to generate these values at particular

Reynolds numbers). Figure 3-23 and Table 3-9 show the ratios between unbaffled power numbers and turbulent average power numbers in transitional and turbulent operation (the turbulent data in Figure 3-23 was previously presented in Table 3-4), while Figure 3-24 and Table 3-10 show the ratios between baffled power numbers and turbulent average power numbers in the same Reynolds number range. In Figure 3-23, the ratios for the six impellers retain the same order through the entire Reynolds number range with HE-3 having the highest unbaffled to turbulent average baffled power number ratio and the D-6 having the lowest ratio. When Reynolds number equals ten, the ratio for HE-3 is 8.96, which is more than six times larger than the 1.35 ratio of the D-6. As expected, the ratios of all impellers continually decrease with increasing Reynolds number. The baffled to baffled turbulent average power number ratios in Figure 3-24 exhibit a similar trend as that in Figure 3-23 for Reynolds numbers lower than 100. After that, the ratios start to converge to one. It should be noticed that the ratios in Figure 3-24 for CD-6 and HE-3 stay above one in transitional operation, as there is no minimum power number point for these two impellers in the baffled configuration. Laminar operation ratios are not included for Figures 3-23 and 3-24 as this would compress the power number axis since the ratios increase rapidly with decreasing Reynolds number. The ratios for laminar

32 operation at Reynolds number less than ten can be found by using the fact that the power numbers are inversely proportional to Reynolds number in this regime.

Table 3-8: Unbaffled to baffled power number ratios in transitional operation Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Unbaffled NP 7.29 7.32 5.02 4.65 2.97 2.77

10 Baffled NP 7.13 7.26 4.89 4.78 2.95 2.87 Ratio 1.02 1.01 1.03 0.97 1.00 0.97

Unbaffled NP 5.17 4.84 3.71 3.09 1.84 1.79

20 Baffled NP 5.32 4.95 3.70 3.22 1.85 1.80 Ratio 0.97 0.98 1.00 0.96 0.99 0.99

Unbaffled NP 4.03 3.84 2.82 2.01 1.12 1.05

50 Baffled NP 4.07 3.83 2.89 2.10 1.11 1.08 Ratio 0.99 1.00 0.97 0.96 1.00 0.97

Unbaffled NP 3.59 3.22 2.50 1.59 0.822 0.756

100 Baffled NP 3.73 3.32 2.64 1.63 0.832 0.738 Ratio 0.96 0.97 0.95 0.98 0.99 1.02

Unbaffled NP 3.29 2.70 2.27 1.36 0.624 0.541

200 Baffled NP 3.58 2.95 2.51 1.38 0.665 0.553 Ratio 0.92 0.92 0.90 0.99 0.93 0.98 NRe Unbaffled NP 2.72 2.14 1.83 1.14 0.504 0.401

500 Baffled NP 3.86 2.90 2.69 1.21 0.507 0.409 Ratio 0.70 0.74 0.68 0.94 0.98 0.98

Unbaffled NP 2.30 1.80 1.56 0.99 0.420 0.318

1,000 Baffled NP 4.21 2.93 2.74 1.09 0.451 0.340 Ratio 0.55 0.61 0.57 0.91 0.93 0.94

Unbaffled NP 1.95 1.51 1.33 0.87 0.377 0.288

2,000 Baffled NP 4.67 2.98 2.72 1.05 0.412 0.317 Ratio 0.42 0.51 0.49 0.83 0.92 0.91

Unbaffled NP 1.56 1.20 1.07 0.73 0.327 0.253

5,000 Baffled NP 4.72 2.83 2.82 1.07 0.447 0.305 Ratio 0.33 0.42 0.38 0.68 0.73 0.83

Unbaffled NP 1.32 1.00 0.91 0.64 0.294 0.229

10,000 Baffled NP 4.97 2.80 2.83 1.12 0.494 0.310 Ratio 0.27 0.36 0.32 0.57 0.60 0.74 The highlighted values are the highest Reynolds number for which the ratio is greater than ninety percent.

1.2

1.0

Ratio = 0.9 0.8

0.6 D-6 Ratio = 0.5 0.4 CD-6 S-4 P-4 0.2

Power Number Power Number Ratio (Unbaffled/Baffled) SC-3 HE-3 0.0 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-22: Ratio of unbaffled to baffled power numbers in transitional and turbulent operation

1 D-6 CD-6 S-4 P-4 SC-3

Power Number Ratio (Unbaffled/Turbulent Average) (Unbaffled/Turbulent Number RatioPower HE-3 0.1 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-23: Ratio of unbaffled to turbulent average power numbers in transitional and turbulent operation

1 D-6 CD-6 S-4 P-4 SC-3

Power Number Ratio (Baffled/Turbulent Average) HE-3 0.1 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-24: Ratio of baffled to turbulent average power numbers in transitional and turbulent operation

Table 3-9: Unbaffled power number to turbulent average power number ratios in transitional operation Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Average baffled turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

Np 7.29 7.32 5.02 4.65 2.97 2.77 10 Ratio 1.35 2.62 1.62 4.04 5.90 8.96

Np 5.17 4.84 3.71 3.09 1.84 1.79 20 Ratio 0.96 1.73 1.20 2.69 3.66 5.79

Np 4.03 3.84 2.82 2.01 1.12 1.05 50 Ratio 0.74 1.38 0.91 1.75 2.23 3.40

Np 3.59 3.22 2.50 1.59 0.822 0.756 100 Ratio 0.66 1.15 0.81 1.38 1.63 2.45

Np 3.29 2.70 2.27 1.36 0.624 0.541 200 Ratio 0.61 0.97 0.73 1.18 1.24 1.75 NRe Np 2.72 2.14 1.83 1.14 0.504 0.401 500 Ratio 0.50 0.77 0.59 0.99 1.00 1.30

Np 2.30 1.80 1.56 0.99 0.420 0.318 1,000 Ratio 0.43 0.65 0.50 0.86 0.83 1.03

Np 1.95 1.51 1.33 0.87 0.377 0.288 2,000 Ratio 0.36 0.54 0.43 0.76 0.75 0.93

Np 1.56 1.20 1.07 0.73 0.327 0.253 5,000 Ratio 0.29 0.43 0.35 0.63 0.65 0.82

Np 1.32 1.00 0.91 0.64 0.294 0.229 10,000 Ratio 0.24 0.36 0.29 0.56 0.58 0.74

Table 3-10: Baffled power number to turbulent average power number ratios in transitional operation Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Average baffled turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

Np 7.13 7.26 4.89 4.78 2.95 2.87 10 Ratio 1.32 2.60 1.58 4.16 5.86 9.29

Np 5.32 4.95 3.70 3.22 1.85 1.80 20 Ratio 0.98 1.77 1.19 2.80 3.68 5.83

Np 4.07 3.83 2.89 2.10 1.11 1.08 50 Ratio 0.75 1.37 0.93 1.83 2.21 3.50

Np 3.73 3.32 2.64 1.63 0.832 0.738 100 Ratio 0.69 1.19 0.85 1.42 1.65 2.39

Np 3.58 2.95 2.51 1.38 0.665 0.553 200 Ratio 0.66 1.06 0.81 1.20 1.32 1.80

Np 3.86 2.90 2.69 1.24 0.507 0.409 500 Ratio 0.70 1.04 0.87 1.08 1.01 1.32

Np 4.21 2.93 2.74 1.09 0.451 0.340 1,000 Ratio 0.78 1.05 0.88 0.95 0.90 1.10 NRe Np 4.67 2.98 2.72 1.05 0.412 0.317 2,000 Ratio 0.86 1.07 0.88 0.91 0.82 1.03

Np 4.72 2.83 2.82 1.07 0.447 0.305 5,000 Ratio 0.87 1.01 0.91 0.93 0.89 0.99

Np 4.97 2.80 2.83 1.12 0.494 0.310 10,000 Ratio 0.92 1.00 0.91 0.97 0.98 1.00

Np 5.22 2.81 2.97 1.13 0.496 0.307 20,000 Ratio 0.96 1.01 0.96 0.98 0.99 0.99

Np 5.42 2.80 3.10 1.14 0.503 0.309 50,000 Ratio 1.00 1.00 1.00 1.00 1.00 1.00

Np 5.58 2.80 3.19 1.16 0.508 0.311 100,000 Ratio 1.03 1 1.03 1 1.01 1.01

Np 5.74 2.79 3.30 1.17 0.514 0.312 200,000 Ratio 1.06 1 1.06 1.01 1.02 1.01

To conclude the power number data presentation, Figure 3-25 combines the baffled data for all six impellers through the entire Reynolds number range, and Figure

3-26 compares the impellers’ unbaffled data. Figures 3-27 through 3-32 present the baffled and unbaffled data of each impeller for all Reynolds numbers.

1,000

100

) P

10 D-6 CD-6 S-4 1 Power Number Power Number (N P-4 SC-3 HE-3 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-25: Comparison of all baffled power number data

1,000

100

) P

10 D-6 CD-6 S-4 1 Power Number Power Number (N P-4 SC-3 HE-3 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-26: Comparison of all unbaffled power number data

1,000

100

) P

Power Number Power Number (N 1 D-6 Baffled

D-6 Unbaffled 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-27: Baffled and unbaffled data of D-6 for all Reynolds numbers

1,000

100

) P

Power Number Power Number (N 1 CD-6 Baffled

CD-6 Unbaffled 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-28: Baffled and unbaffled data of CD-6 for all Reynolds numbers

1,000

100

) P

Power Number Power Number (N 1 S-4 Baffled

S-4 Unbaffled 0.1 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-29: Baffled and unbaffled data of S-4 for all Reynolds numbers

1,000

100

) P

10 Power Number Power Number (N 1 P-4 Baffled

P-4 Unbaffled 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-30: Baffled and unbaffled data of P-4 for all Reynolds numbers

1,000

100

) P

Power Number Power Number (N 1 SC-3 Baffled

SC-3 Unbaffled 0.10 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-31: Baffled and unbaffled data of SC-3 for all Reynolds numbers

1,000

100

) P

Power Number Power Number (N 1 HE-3 Baffled

HE-3 Unbaffled 0.10 0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Reynolds Number (NRe)

Figure 3-32: Baffled and unbaffled data of HE-3 for all Reynolds numbers

CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS

This work aimed to acquire design information for Newtonian fluid mixing, focusing on measuring the power numbers of six different impellers across the full

Reynolds number spectrum. Power number behaviors of these six impellers were compared in three operation regimes – laminar, turbulent, and transitional.

In laminar operation, baffling has no effect on power number for all six impellers.

The slope of the power number – Reynolds number relations on logarithmic coordinates are all equal to -1, indicating an inversely proportional relationship between power number and Reynolds number. It is widely accepted that laminar operation takes place when Reynolds number is less than 10; however, four of the six impellers in this work have their highest laminar operation Reynolds number smaller than 10, suggesting that the upper limit for laminar operation should be lower than 10. The constant KL, the product of power number and Reynolds number in this particular regime, is approximately proportional to the number of blades based on the results from these six impellers. However, this is not applicable for all the impellers. Other shape factors such as the ratio between the width of impeller blades and the impeller diameter also contribute to the parameter KL.

In turbulent operation, baffling has a significant effect on power number for all six impellers with the power number continually decreasing with increasing Reynolds

42 number for unbaffled configuration while the power number in a baffled configuration remains relatively constant for most impellers; however, the power number for D-6 and

S-4 still increase with increasing Reynolds number, with their power numbers increasing by more than ten percent as the Reynolds number increases from 10,000 to 200,000. In turbulent operation, the number of impeller blades is not the dominant factor that affects power number. In the baffled configuration, two hydrofoil impellers exhibit much lower power numbers when compared with the other impellers: the baffled power number range of the six impellers was only a factor of two in the laminar regime and increased to 18 in the turbulent regime. In the unbaffled configuration, power number decreases with increasing Reynolds numbers with power-law exponents between -0.20 and -0.12

n depending on impeller (NP = K NRe , -0.20 < n < -0.12). Additionally, the impellers with higher power numbers in baffled tank tend to have lower ratios between unbaffled power number and average baffled power number when comparing at same Reynolds number.

At the low Reynolds number end of transitional regime, the power numbers show no difference between baffled and unbaffled configurations for all impellers. The differences between the two configurations start at intermediate Reynolds numbers and increase with an increase of Reynolds number. In the baffled configuration, four of six impellers exhibit a minimum power number, with the D-6 and S-4 having the minimum at Reynolds number of approximately 200 and the P-4 and SC-3 having their minima at

Reynolds number near 2000. Three of these impellers have ratios between the minimum power number and the average turbulent power number that are close to each other, in the range between eighty and ninety percent, while D-6 has a considerably lower ratio of

0.66. The range of Reynolds numbers for which the baffled transitional power number is

43 less than the baffled turbulent value extends through more than two orders of magnitude for D-6 and S-4, around one order of magnitude for SC-3, and less than one order of magnitude for P-4. The CD-6, one of two impellers that have no minimum power number in baffled transitional operation, has a power number higher than the average turbulent power number by an average of 4% and a maximum of 8% for Reynolds numbers in the range of 490 and 2500. For HE-3, there is little difference between the baffled power number and the average turbulent power number in the high Reynolds number end of transitional regime (NRe > 1,000). In the unbaffled configuration, power numbers drop with increasing Reynolds number throughout the entire transitional regime for all impellers. The range of the exponent of power law correlations in unbaffled data

n is between -0.25 and -0.14 (NP = K NRe , -0.25 < n < -0.14). The HE-3 has an unbaffled to baffled power number ratio above 0.5 over the entire Reynolds number range, while the ratios for the other five impellers are lower than 0.4 for high Reynolds number. For the power number ratios between unbaffled and turbulent average power numbers, the same order occurred throughout both transitional and turbulent operation, with this order being the reverse of the order of the baffled turbulent power number (D-6 < S-4 < CD-6 <

P-4 < SC-3 < HE-3).

Extensive power number data has been taken for six industrially significant impellers; power number behavior and significant trends have been identified and compared; however, the data has a degree of uncertainty due to inherent uncertainty and temporal variance in the system and the method of mentally averaging the visually displayed torque data. An automated data acquisition system that can determine the uncertainty of each data point statistically would help to improve this. Additional

44 uncertainty could be caused by the way viscosity was measured since the viscosity for each torque data point was not measured. Finding a way to physically measure the viscosity for every torque data point would help to achieve better accuracy.

Other variables such as different tank geometry (dish bottom, non-standard baffling, etc.), impeller off-bottom clearance and impeller to tank diameter ratio and system scale could be investigated in the future to learn about the effects these system parameters might have on power draw. Additionally, non-Newtonian fluids power draw measurements on these six impellers could be performed with the data of this work providing a basis for comparison.

BIBLIOGRAPHY

1. Bates, R. L., P. L. Fondy, and J. G. Fenic. (1966). “Impeller characteristics and power”, Chapter 3 in Mixing: Theory and Practice. V. W. Uhl and J. B. Gray (Eds.). New York, Academic Press Inc. 2. Calabrese, R. V., S. M. Kresta, and M. Liu. (2014). "Recognizing the 21 Most Influential Contributions To Mixing Research." Chemical Engineering Progress. January: 20-29. 3. Deng, J. (May 2014). Mechanical Mixing of High Concentration Biomass Slurry. Thesis, Chemical and Materials Engineering. University of Dayton. Dayton, Ohio. Master of Science in Chemical Engineering. 4. McCabe, W. L., J. C. Smith, and P. Harriott. (2005). “Agitation and Mixing of Liquids”, Chapter 9 in Unit Operations of Chemical Engineering. New York, McGraw-Hill. 5. Oldshue, J. Y. (1983). Fluid Mixing Technology. New York: McGraw-Hill. 6. Hemrajani, R. R., and G. B. Tatterson. (2004). “Mechanically Stirred Vessels”, Chapter 6 in Handbook of Industrial Mixing - Science and Practice. Paul, E. L., V. A. Atiemo-Obeng, and S. M. Kresta (Eds.). Hoboken, John Wiley & Sons, Inc. 7. Rushton, J. H., E. W. Costich, and H. J. Everett. (1950). "Power characteristics of mixing impellers." Chemical Engineering Progress 46: 395-404, and 467-479. 8. Strong, R. J., and K. J. Myers (November, 2013). "Introductory Rheology". 9. Smith, J. M. (1985). “Dispersion of Gases in Liquids: The Hydrodynamics of Gas Dispersion in Low Viscosity Liquids”, Chapter 5 in Mixing of Liquids by Mechanical Agitation. J. J. Ulbrecht and G. K. Patterson (Eds.). New York, Gordon and Breach Science Publishers.

APPENDIX: RAW AND REDUCED EXPERIMENTAL DATA Appendix 1: Raw and reduced data from impeller power draw experiments for baffled D-6 Impeller: D-6 Configuration: Baffled Diameter: 7.99'' D/T: 0.34 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 8 11.75 1.48 122886 909 0.066 23 35.15 1.48 122861 329 0.19 32.5 49.45 1.48 122845 232 0.27 44 66.525 1.48 122827 170 0.37 56 84.55 1.48 122807 133 0.47 68 103.2 1.48 122787 110 0.57 81 122.375 1.48 122767 92.3 0.67 94 140.25 1.48 122747 78.6 0.78 116 171 1.48 122714 62.9 0.97 74 50 1.42 57659 47.7 1.25 97.5 65.4 1.42 57279 35.9 1.65 115 76.9 1.42 57789 30.4 1.94 144.5 96.9 1.42 57867 24.2 2.43 177 119.6 1.42 57968 19.9 2.98 207 139 1.42 58054 16.9 3.48 74.5 7.675 1.40 8294 7.33 8.63 107 13.15 1.40 8292 6.09 12.4 188 33.125 1.40 8281 4.97 21.8 244 52.325 1.40 8271 4.66 28.4 281 67.075 1.40 8263 4.50 32.7 315 81.85 1.40 8255 4.37 36.7 355 100.9 1.40 8245 4.24 41.4 391 119.8 1.40 8235 4.15 45.6 390 119.1 1.40 8236 4.15 45.5 416 133.75 1.40 8228 4.10 48.6 415 132.9 1.40 8228 4.09 48.5 463 162.4 1.40 8213 4.01 54.2 462 161.6 1.40 8213 4.01 54.1 461 160.9 1.40 8214 4.01 53.9 460 160.5 1.40 8214 4.02 53.8 315.5 73 1.37 4123 4.07 59.5 112 8.775 1.37 1503 3.79 70.1 132.5 12.25 1.37 1501 3.78 83.0 173 20.625 1.37 1497 3.73 109 217 31.8 1.37 1492 3.66 137 250 41.675 1.37 1487 3.61 158 282.5 52.75 1.37 1482 3.58 179 313 64.475 1.37 1476 3.56 199 342 76.875 1.37 1470 3.56 219 372 91.925 1.37 1463 3.60 239 395 104.25 1.37 1457 3.62 255 417 116.3 1.37 1452 3.62 270 442 132.75 1.37 1444 3.68 288 466.5 149 1.37 1436 3.71 306 199 26.7 1.32 386 3.79 468 224.5 35.2 1.32 384 3.93 529

Appendix 1: Raw and reduced data from impeller power draw experiments for baffled D-6 (continued) Impeller: D-6 Configuration: Baffled Diameter: 7.99'' D/T: 0.34 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 224.5 35.2 1.32 383 3.89 596 252 44 1.32 381 4.01 671 282 56.7 1.32 379 4.13 722 302 67 1.32 378 4.11 755 315 72.5 1.32 377 4.16 798 127.5 11.5 1.29 135 4.07 835 157 18 1.29 135 4.20 1028 202 30.65 1.29 135 4.32 1322 229 40.5 1.29 135 4.44 1499 254 50.3 1.29 135 4.48 1663 288.5 65.5 1.29 135 4.53 1888 312.5 78 1.29 135 4.59 2046 127 12.05 1.25 50.6 4.43 2154 181 25.55 1.25 50.6 4.63 3070 217.5 37.5 1.25 50.6 4.71 3689 255 52 1.25 50.6 4.75 4325 289.5 67.6 1.25 50.6 4.79 4910 315 80.5 1.25 50.6 4.82 5342 149.5 17.6 1.22 19.8 4.81 6298 200 31.75 1.22 19.8 4.85 8426 250 51.5 1.22 19.8 5.03 10532 300 74.35 1.22 19.8 5.04 12639 114 10.4 1.13 5.08 5.24 17447 149.5 18 1.13 5.08 5.27 22879 200 33.1 1.13 5.08 5.42 30608 250 51.6 1.13 5.08 5.40 38260 300 74.2 1.13 5.08 5.40 45912 118 10.2 1.00 1.09 5.45 74167 159 19.05 1.00 1.09 5.61 99937 210 33.75 1.00 1.09 5.70 131993 262 52.45 1.00 1.09 5.69 164677 304 70.25 1.00 1.09 5.66 191075

Appendix 2: Raw and reduced data from impeller power draw experiments for unbaffled D-6 Impeller: D-6 Configuration: Unbaffled Diameter: 7.99'' D/T: 0.34 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 8 11.75 1.48 122886 909 0.066 10.5 7.3 1.42 58284 346 0.18 19.5 13.5 1.42 58246 185 0.33 32 21.925 1.42 58195 112 0.54 50 34.9 1.42 58115 72.9 0.84 73.5 51.75 1.42 58012 50.1 1.24 97 67.7 1.42 57915 37.6 1.63 122 83.9 1.42 57815 29.5 2.06 159.5 109 1.42 57662 22.4 2.70 185 126 1.42 57558 19.2 3.13 216 142 1.42 57460 15.9 3.66 54 8.45 1.40 13753 15.4 3.77 70 11 1.40 13744 11.9 4.90 104 18 1.40 13720 8.82 7.29 182 38.4 1.40 13650 6.14 12.8 232 56.275 1.40 13589 5.54 16.4 264 69.275 1.40 13544 5.27 18.7 303 87.2 1.40 13482 5.03 21.6 337 104.1 1.40 13424 4.86 24.1 378 126.4 1.40 13348 4.69 27.2 104 9.2 1.37 3495 4.61 28.0 128 13.025 1.37 3485 4.31 34.5 165.5 20.675 1.37 3464 4.09 44.9 224 36.05 1.37 3422 3.89 61.6 276 53.15 1.37 3376 3.78 76.9 111 8.225 1.37 1252 3.62 83.4 140.5 12.85 1.37 1250 3.53 106 170.5 18.8 1.37 1248 3.50 128 196 24.625 1.37 1246 3.47 148 221 30.85 1.37 1244 3.42 167 239.5 35.75 1.37 1242 3.38 181 258 40.9 1.37 1240 3.33 196 279.5 46.65 1.37 1238 3.23 212 307 55.075 1.37 1235 3.16 234 162.5 14.75 1.34 589 3.09 254 205 22.975 1.34 586 3.02 322 232.5 29.05 1.34 584 2.97 367 264.5 37.1 1.34 581 2.93 419 152 11.8 1.32 321 2.88 428 181 15.9 1.32 322 2.73 509 222 23.45 1.32 323 2.68 623 250.5 29.25 1.32 323 2.62 701 274 34.5 1.32 324 2.59 766 192 16 1.31 223 2.45 776 238 23.4 1.31 223 2.34 962 273.5 29.4 1.31 223 2.22 1106 202 15.65 1.29 153 2.21 1169 227 19 1.29 153 2.12 1314 255.5 23.85 1.29 153 2.10 1479 287 29.65 1.29 153 2.07 1661 188 11.95 1.28 93.8 1.96 1766 213 15 1.28 93.8 1.91 2001 235.5 18.05 1.28 93.8 1.88 2213 265 22.3 1.28 93.8 1.84 2490

Appendix 2: Raw and reduced data from impeller power draw experiments for unbaffled D-6 (continued) Impeller: D-6 Configuration: Unbaffled Diameter: 7.99'' D/T: 0.34 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 284.5 25.4 1.28 93.8 1.81 2673 181.5 9.35 1.25 53.2 1.68 2928 210 12.2 1.25 53.2 1.64 3388 235 15.25 1.25 53.2 1.64 3791 261 18.45 1.25 53.2 1.61 4210 281 21.25 1.25 53.2 1.60 4533 199 9.05 1.22 19.8 1.40 8384 220 10.9 1.22 19.8 1.38 9268 242 13.05 1.22 19.8 1.36 10195 265 15.55 1.22 19.8 1.35 11164 283 17.55 1.22 19.8 1.34 11922 233 8.5 1.14 5.00 1.02 36472 244 9.2 1.14 5.00 1.01 38193 256 10.05 1.14 5.00 1.00 40072 265 7.65 1.00 1.09 0.81 166562

Appendix 3: Raw and reduced data from impeller power draw experiments for baffled CD-6 Impeller: CD-6 Configuration: Baffled Diameter: 8.78'' D/T: 0.374 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 11.625 1.48 108357 738 0.079 19.5 34.075 1.4 107735 279 0.22 13 10.425 1.42 51786 201 0.30 23.5 19.4 1.42 51483 115 0.54 41.5 33.95 1.42 50993 64.3 0.96 60.5 48.775 1.42 50493 43.5 1.41 94 74.475 1.42 49626 27.5 2.23 113.5 89.55 1.42 49118 22.7 2.72 141.5 110 1.42 48429 17.9 3.44 181 140 1.42 47417 13.9 4.49 57 11.05 1.40 11525 11.2 5.74 56 8 1.40 8518 8.44 7.63 69.5 10.85 1.40 8514 7.43 9.47 139 29.95 1.40 8487 5.13 19.0 77 8.1 1.37 3754 4.62 23.3 111 15.325 1.37 3753 4.20 33.6 147.5 25.225 1.37 3751 3.92 44.7 212 48 1.37 3746 3.61 64.3 256 67.65 1.37 3742 3.49 77.7 255 66.95 1.37 3742 3.48 77.4 291 85.45 1.37 3739 3.41 88.4 290 84.9 1.37 3739 3.41 88.1 327 105.15 1.37 3735 3.32 99.4 326 104.5 1.37 3735 3.32 99.1 349 118.3 1.37 3732 3.28 106 347 117 1.37 3732 3.28 106 369 130.45 1.37 3730 3.24 112 368 129.85 1.37 3730 3.24 112 389 143.25 1.37 3727 3.20 119 388 142.65 1.37 3727 3.20 118 417 162.3 1.37 3723 3.15 127 414 160.2 1.37 3724 3.16 126 428 169.85 1.37 3722 3.13 131 427 169.2 1.37 3722 3.14 130 426 168.2 1.37 3722 3.13 130 88 8.2 1.37 1499 3.11 149 119.5 14.375 1.37 1498 3.04 176 157 23.675 1.37 1497 2.97 203 196 35.35 1.37 1496 2.87 228 231 47.95 1.37 1495 2.84 245 267 62.575 1.37 1493 2.80 264 299 75.8 1.37 1491 2.78 280 321.5 86.9 1.37 1490 2.75 303 346 99.3 1.37 1489 2.75 302 367 110.85 1.37 1487 2.77 318 396 127.6 1.37 1486 2.78 332 395 127.15 1.37 1486 2.83 344 126 12.85 1.32 373 2.84 369 167 22.6 1.32 373 2.84 490 202.5 34.8 1.32 372 2.98 595 238.5 48.3 1.32 372 2.98 702 265 60.2 1.32 371 3.01 781 286.5 70.25 1.32 371 3.00 845 108 9.35 1.29 134 2.88 864

Appendix 3: Raw and reduced data from impeller power draw experiments for baffled CD-6 (continued) Impeller: CD-6 Configuration: Baffled Diameter: 8.78'' D/T: 0.374 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 116.5 10.95 1.29 133.5 2.90 933 148 17.95 1.29 133.5 2.94 1185 189 29.9 1.29 133.5 3.01 1513 221 40.9 1.29 133.5 3.01 1769 252 53.3 1.29 133.5 3.02 2017 110.5 9.7 1.25 52.4 2.94 2185 127.5 12.85 1.25 52.4 2.93 2521 169.5 22.4 1.25 52.4 2.89 3352 208 33.5 1.25 52.4 2.87 4113 233.5 41.8 1.25 52.4 2.84 4618 274 57.6 1.25 52.4 2.84 5419 116.5 9.95 1.22 19.8 2.79 5926 150 16.5 1.22 19.8 2.79 7631 200.5 29.5 1.22 19.8 2.80 10200 250 45.75 1.22 19.8 2.79 12718 300 65.6 1.22 19.8 2.78 15261 121 9.95 1.14 5.05 2.77 22595 170 20.1 1.14 5.05 2.83 31744 221 33.9 1.14 5.05 2.83 41268 272 51.5 1.14 5.05 2.84 50791 135 10.8 1.09 1.00 2.75 102461 185 20.45 1.09 1.00 2.78 140410 236 33.4 1.09 1.00 2.79 179118 286.5 49 1.09 1.00 2.77 217446

Appendix 4: Raw and reduced data from impeller power draw experiments for unbaffled CD-6 Impeller: CD-6 Configuration: Unbaffled Diameter: 8.78'' D/T: 0.374 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 11.625 1.48 108357 738 0.079 19.5 34.075 1.48 107735 279 0.22 13.5 10.5 1.42 48250 188 0.33 23 18.1 1.42 48206 112 0.56 36.5 28.6 1.42 48145 70.0 0.89 48 37.65 1.42 48092 53.3 1.17 61 47.825 1.42 48033 41.9 1.49 75 58.7 1.42 47970 34.0 1.84 90 69.85 1.42 47906 28.1 2.21 112 86.85 1.42 47807 22.6 2.76 34.5 6.275 1.40 11523 17.4 3.47 57 11.05 1.40 11525 11.2 5.74 86 18 1.40 11529 8.05 8.66 143 36.15 1.40 11538 5.85 14.4 186 54.25 1.40 11546 5.19 18.7 73 7.825 1.37 3725 4.96 22.3 92 10.675 1.37 3719 4.26 28.1 130 19.475 1.37 3700 3.89 39.9 171.5 31.675 1.37 3674 3.64 53.0 214 46.75 1.37 3641 3.45 66.8 252 62.6 1.37 3607 3.33 79.3 283 76.7 1.37 3577 3.24 89.9 327 98.9 1.37 3529 3.13 105 358 115.9 1.37 3492 3.06 116 389 134.55 1.37 3452 3.01 128 154 20.35 1.37 1270 2.90 138 184.5 28.4 1.37 1269 2.82 165 209 35.3 1.37 1267 2.73 187 229 41.45 1.37 1266 2.67 205 251 48.475 1.37 1265 2.60 225 267 53.5 1.37 1264 2.54 240 155.5 17.425 1.34 590 2.49 293 179.5 22.75 1.34 590 2.44 339 194.5 26.1 1.34 590 2.38 367 214 30.75 1.34 590 2.32 403 234.5 36.25 1.34 591 2.27 442 253 41.35 1.34 591 2.23 476 174 17.85 1.32 314 2.08 604 216 26 1.32 312 1.96 754 235 30.575 1.32 311 1.95 823 251 34.75 1.32 310 1.94 882 136 9.15 1.29 134 1.78 1087 171.5 13.5 1.29 134 1.65 1371 205 18.6 1.29 134 1.59 1639 234.5 23.8 1.29 134 1.55 1874 248 26.15 1.29 134 1.53 1982 211 17.55 1.28 93.0 1.42 2413 238.5 21.8 1.28 93.0 1.38 2728 252 24.15 1.28 93.0 1.37 2882 173 10.1 1.25 53.0 1.25 3383 193 12.5 1.25 53.0 1.24 3774 214 15.05 1.25 53.0 1.22 4184 237 18 1.25 53.0 1.19 4634 263 22 1.25 53.0 1.18 5142 185 9.15 1.22 19.8 1.02 9411

Appendix 4: Raw and reduced data from impeller power draw experiments for unbaffled CD-6 (continued) Impeller: CD-6 Configuration: Unbaffled Diameter: 8.78'' D/T: 0.374 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 207 11.25 1.22 19.8 1.00 10530 227 13.45 1.22 19.8 0.99 11548 249 16.05 1.22 19.8 0.99 12667 263 17.9 1.22 19.8 0.99 13379 230 9.75 1.14 5.00 0.75 43473 240 10.6 1.14 5.00 0.75 45363 260 8.75 1.00 1.09 0.60 197333

Appendix 5: Raw and reduced data from impeller power draw experiments for baffled S-4 Impeller: S-4 Configuration: Baffled Diameter: 9.54'' D/T: 0.406 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 13.2 1.48 122714 559 0.082 22.5 41.375 1.48 122485 170 0.27 12.5 9.75 1.42 53230 134 0.33 26.5 20.95 1.42 52832 64 0.70 40 31.5 1.42 52458 42.4 1.06 52.5 41.5 1.42 52103 32.4 1.40 74 57.75 1.42 51526 22.7 2.00 95.5 73.6 1.42 50963 17.4 2.60 97 73.35 1.42 49722 16.8 2.71 115.5 86.675 1.42 49224 14.0 3.26 135 100.75 1.42 48698 11.9 3.85 164 120.2 1.42 47971 9.62 4.75 196 142 1.42 47156 7.96 5.78 51.5 7.35 1.40 9823 6.05 7.18 71.5 11.35 1.40 9782 4.85 10.0 134 29.8 1.40 9590 3.62 19.1 182 50.25 1.40 9378 3.31 26.6 227 73.85 1.40 9133 3.13 34.1 262 94.8 1.40 8916 3.02 40.3 297 118.3 1.40 8673 2.93 46.9 296 117.8 1.40 8678 2.94 46.7 295 116.8 1.40 8688 2.93 46.5 293 115.2 1.40 8705 2.93 46.1 320 134.8 1.40 8501 2.87 51.6 318 133.2 1.40 8518 2.88 51.2 192 45.925 1.37 3973 2.78 64.8 239 69.05 1.37 3969 2.70 80.7 267 85.1 1.37 3966 2.66 90.3 300 106.05 1.37 3962 2.63 102 332 128.2 1.37 3958 2.60 112 331 127.8 1.37 3958 2.60 112 367 155 1.37 3954 2.57 124 366 154.3 1.37 3954 2.57 124 385 169.85 1.37 3951 2.56 131 384 168.85 1.37 3951 2.56 130 168.5 32.175 1.37 1549 2.53 146 191.5 41.025 1.37 1544 2.50 166 228 57.5 1.37 1536 2.47 199 249 69.6 1.37 1529 2.51 218 270.5 83.425 1.37 1522 2.54 238 280.5 90.3 1.37 1518 2.56 248 297 102.475 1.37 1512 2.59 263 312.5 114.05 1.37 1506 2.61 278 329.5 126.65 1.37 1499 2.60 295 119 16.1 1.33 496 2.61 313 148 25.9 1.33 496 2.71 389 176 36.8 1.33 496 2.72 463 94.5 10.15 1.31 230 2.65 528 115 15.25 1.31 230 2.69 643 143 23.8 1.31 229 2.71 802 178 37.6 1.31 228 2.77 1003 199 46.75 1.31 227 2.75 1125 225 59.8 1.31 226 2.75 1277 249 73.4 1.31 225 2.76 1420 266 84 1.31 224 2.77 1522

Appendix 5: Raw and reduced data from impeller power draw experiments for baffled S-4 (continued) Impeller: S-4 Configuration: Baffled Diameter: 9.54'' D/T: 0.406 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 133 19.975 1.28 96.0 2.69 1740 174 35.2 1.28 96.0 2.77 2276 200 46.35 1.28 96.0 2.76 2616 233.5 63.4 1.28 96.0 2.77 3054 128 18.5 1.25 48.6 2.76 3220 165.5 31.25 1.25 48.6 2.79 4163 200 46.25 1.25 48.6 2.83 5031 235 64.5 1.25 48.6 2.86 5912 260 79 1.25 48.6 2.86 6541 123.5 16.9 1.22 19.8 2.79 7417 149.5 24.75 1.22 19.8 2.79 8979 190 41 1.22 19.8 2.86 11411 231 61.5 1.22 19.8 2.90 13874 97 10.2 1.13 5.13 2.92 20981 135 20.3 1.13 5.13 3.00 29201 167.5 32.2 1.13 5.13 3.10 36231 200 47 1.13 5.13 3.17 43261 238 67.3 1.13 5.13 3.21 51480 103 11 1.00 1.09 3.18 92294 150 23.5 1.00 1.09 3.20 134408 200 42.25 1.00 1.09 3.24 179211 252 68 1.00 1.09 3.28 225806

Appendix 6: Raw and reduced data from impeller power draw experiments for unbaffled S-4 Impeller: S-4 Configuration: Unbaffled Diameter: 9.54'' D/T: 0.406 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 13.2 1.48 122714 559 0.082 22.5 41.375 1.48 122485 170 0.27 12.5 9.75 1.42 53230 134 0.33 26.5 20.95 1.42 52832 64.2 0.70 40 31.5 1.42 52458 42.4 1.06 52.5 41.5 1.42 52103 32.4 1.40 74 57.75 1.42 51526 22.7 2.00 95.5 73.6 1.42 50963 17.4 2.60 121 92.6 1.42 50288 13.6 3.34 150 114 1.42 49528 10.9 4.21 182.5 136 1.42 48747 8.79 5.20 203.5 150 1.42 48250 7.80 5.86 53 8.55 1.40 10518 6.65 6.90 62 10.5 1.40 10527 5.97 8.07 108 22.8 1.40 10584 4.27 14.0 159 41.95 1.40 10674 3.62 20.4 199 61.25 1.40 10764 3.38 25.3 233.5 80.55 1.40 10854 3.23 29.5 262 97.85 1.40 10935 3.11 32.8 287 114.5 1.40 11012 3.04 35.7 286 113.6 1.40 11008 3.03 35.6 322 139.6 1.40 11129 2.94 39.6 321 138.675 1.40 11125 2.94 39.5 125.5 20.375 1.37 3806 2.89 44.2 170.5 35.5 1.37 3798 2.73 60.2 213 53.325 1.37 3788 2.62 75.4 241 66.725 1.37 3781 2.56 85.5 270 82.35 1.37 3772 2.52 96.0 304 102.6 1.37 3761 2.48 108 339 124.7 1.37 3748 2.42 121 367 145.35 1.37 3737 2.41 132 366 144.6 1.37 3737 2.41 131 394 166.8 1.37 3725 2.40 142 149.5 23.4 1.37 1293 2.34 155 168 29.425 1.37 1289 2.33 175 194.5 38.675 1.37 1284 2.28 203 214 45.025 1.37 1281 2.19 224 231 52.75 1.37 1276 2.21 243 252 61.175 1.37 1272 2.15 266 259 64.35 1.37 1270 2.14 273 136 16.4 1.34 532 2.02 336 165 22.95 1.34 533 1.92 407 190 29.475 1.34 533 1.86 468 205 33.775 1.34 534 1.83 504 223.5 39.25 1.34 535 1.79 549 149 16.5 1.32 313 1.73 613 178 22.7 1.32 312 1.67 734 210.5 30.8 1.32 311 1.62 872 234 37.35 1.32 310 1.59 972 116 8.68 1.29 134 1.53 1095 139 11.85 1.29 134 1.45 1312 164.5 16.05 1.29 134 1.41 1552 189 20.55 1.29 134 1.36 1783 208.5 24.6 1.29 134 1.34 1967 223 27.85 1.29 134 1.33 2104

Appendix 6: Raw and reduced data from impeller power draw experiments for unbaffled S-4 (continued) Impeller: S-4 Configuration: Unbaffled Diameter: 9.54'' D/T: 0.406 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 177 16.55 1.28 97.5 1.26 2280 208 22.3 1.28 97.5 1.23 2679 231 27.3 1.28 97.5 1.22 2975 163 12.1 1.26 52.3 1.11 3843 187 15.8 1.26 52.3 1.10 4409 202 18 1.26 52.3 1.07 4763 225 21.9 1.26 52.3 1.05 5305 154 8.95 1.22 19.8 0.95 9249 174 11.2 1.22 19.8 0.93 10450 194 13.8 1.22 19.8 0.92 11651 217 17.1 1.22 19.8 0.91 13033 154 8.95 1.00 1.09 0.71 41060 174 11.2 1.00 1.09 0.71 43068 194 13.8 1.00 1.09 0.71 46416 207 8.475 1.00 1.09 0.61 185483

Appendix 7: Raw and reduced data from impeller power draw experiments for baffled P-4 Impeller: P-4 Configuration: Baffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 6.5 11.05 1.48 121371 552 0.077 18 30.475 1.48 120843 198 0.21 26.5 44.9 1.48 120450 135 0.32 39 66.825 1.48 119854 92.7 0.47 47.5 80.9 1.48 119471 75.6 0.57 60 101.2 1.48 118919 59.3 0.72 79.5 130.25 1.48 118129 43.5 0.97 43.5 34.925 1.42 56532 40.6 1.06 54 43.3 1.42 56175 32.7 1.32 73 57.5 1.42 55571 23.7 1.81 100 78.4 1.42 54681 17.2 2.52 121 92.85 1.42 54066 13.9 3.08 151.5 115 1.42 53123 11.0 3.93 183 138.2 1.42 52136 9.07 4.84 56 10.1 1.40 12451 7.18 6.11 104 21.55 1.40 12310 4.44 11.5 150 35.45 1.40 12138 3.51 16.8 177 45 1.40 12020 3.20 20.0 207 56.825 1.40 11874 2.96 23.7 231 67 1.40 11749 2.80 26.7 259 79.375 1.40 11596 2.64 30.3 281.5 89.55 1.40 11470 2.52 33.3 311 104.1 1.40 11290 2.40 37.4 352 124.6 1.40 11037 2.24 43.3 387 144 1.40 10798 2.14 48.7 386 143 1.40 10810 2.14 48.5 187.5 29.9 1.37 4210 1.94 59.2 239.5 44.625 1.37 4193 1.77 76.0 297 63.975 1.37 4169 1.65 94.7 355 86.375 1.37 4142 1.56 114 400 106.175 1.37 4118 1.51 129 438 124.5 1.37 4096 1.48 142 468 139.9 1.37 4077 1.46 153 467 139.1 1.37 4078 1.45 152 492 152.6 1.37 4062 1.44 161 491 151.8 1.37 4063 1.44 161 516 165.9 1.37 4046 1.42 170 515 165.15 1.37 4047 1.42 169 527 171.5 1.37 4039 1.41 173 213 28.375 1.37 1594 1.43 178 250 37.575 1.37 1590 1.37 209 270.5 43.325 1.37 1587 1.35 227 306.5 55.225 1.37 1581 1.34 258 337.5 65.4 1.37 1576 1.31 285 374.5 79.4 1.37 1569 1.29 317 412.5 94.9 1.37 1561 1.27 351 149.5 11.85 1.34 506 1.23 385 190 18.85 1.34 505 1.22 490 251 31.975 1.34 503 1.18 650 297.5 43.45 1.34 501 1.14 773 326 50.5 1.34 500 1.11 849 169 13.25 1.31 234 1.10 922 222 22.15 1.31 233 1.07 1213 276.5 34.2 1.31 232 1.06 1514 318.5 45.25 1.31 232 1.06 1749

Appendix 7: Raw and reduced data from impeller power draw experiments for baffled P-4 (continued) Impeller: P-4 Configuration: Baffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 355.5 56.65 1.31 231 1.07 1956 166 11.6 1.28 96.0 1.02 2153 216 19.85 1.28 96.0 1.04 2802 270 31.3 1.28 96.0 1.04 3502 320 44.35 1.28 96.0 1.05 4151 354 54.65 1.28 96.0 1.06 4592 400 70.85 1.28 96.0 1.08 5188 244 25.55 1.25 48.9 1.07 6054 293.5 37.3 1.25 48.9 1.08 7282 340.5 50.85 1.25 48.9 1.10 8448 393.5 69.2 1.25 48.9 1.12 9763 419.5 79 1.25 48.9 1.12 10408 185 14.6 1.22 19.8 1.10 11018 238 24.55 1.22 19.8 1.11 14174 288 36.05 1.22 19.8 1.12 17152 344.5 52.4 1.22 19.8 1.13 20517 404 72.9 1.22 19.8 1.15 24061 160 10.8 1.14 4.96 1.16 35585 220 20.45 1.14 4.96 1.16 48929 281 33.5 1.14 4.96 1.17 62496 340 49 1.14 4.96 1.16 75617 401.5 68.1 1.14 4.96 1.16 89295 175 11.2 1.00 1.09 1.15 155497 224.5 18.55 1.00 1.09 1.15 199481 275 28 1.00 1.09 1.16 244353 330 40.5 1.00 1.09 1.16 293223 375 53 1.00 1.09 1.18 333208

Appendix 8: Raw and reduced data from impeller power draw experiments for unbaffled P-4 Impeller: P-4 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 6.5 11.05 1.48 121371 552 0.077 18 30.475 1.48 120843 198 0.21 26.5 44.9 1.48 120450 135 0.32 39 66.825 1.48 119854 92.7 0.47 47.5 80.9 1.48 119471 75.6 0.57 60 101.2 1.48 118919 59.3 0.72 79.5 130.25 1.48 118129 43.5 0.97 38.5 22.1 1.42 40003 32.8 1.33 56 32.475 1.42 39988 22.8 1.93 74 43.3 1.42 39973 17.4 2.55 92 53.2 1.42 39958 13.8 3.17 103.5 59.55 1.42 39949 12.2 3.57 118 68.15 1.42 39936 10.8 4.07 130 74.225 1.42 39927 9.66 4.49 148.5 84.2 1.42 39913 8.40 5.13 168 95.5 1.42 39896 7.44 5.80 190 107.7 1.42 39879 6.56 6.57 218 124.7 1.42 39854 5.77 7.54 230 130 1.42 39846 5.40 7.96 87.5 14.3 1.40 10170 4.17 11.7 78.5 12.275 1.40 10171 4.44 10.5 141 27.8 1.40 10164 3.12 18.8 194 45 1.40 10157 2.67 26.0 242 63.55 1.40 10148 2.42 32.4 276 77.55 1.40 10142 2.27 37.0 318 96.3 1.40 10134 2.12 42.6 373 123.3 1.40 10122 1.98 50.1 372 122.675 1.40 10123 1.98 49.9 428 152.85 1.40 10109 1.86 57.5 427 152.2 1.40 10110 1.86 57.4 426 151.15 1.40 10110 1.86 57.3 172 24.875 1.37 3763 1.92 60.8 210 34.25 1.37 3755 1.77 74.4 255 47.125 1.37 3744 1.65 90.6 299 61.2 1.37 3733 1.56 107 334 74 1.37 3722 1.51 119 366 86.2 1.37 3712 1.47 131 136 11.825 1.37 1307 1.46 138 186 20.6 1.37 1305 1.36 189 211 26.05 1.37 1304 1.33 215 230 30.475 1.37 1303 1.31 235 252 36.575 1.37 1302 1.31 257 267.5 40.4 1.37 1301 1.29 273 148 12.075 1.36 683 1.27 285 187.5 18.65 1.36 692 1.22 357 223 25.65 1.36 702 1.19 419 247 30.25 1.36 708 1.14 460 176 14.6 1.32 425 1.11 531 201 18.5 1.32 424 1.08 607 230 24.1 1.32 424 1.08 695 238 25.8 1.32 424 1.08 719 181 14.5 1.32 314 1.05 737 212 19.475 1.32 314 1.03 862 226 21.8 1.32 314 1.01 918 177 13.2 1.31 223 1.00 1012

Appendix 8: Raw and reduced data from impeller power draw experiments for unbaffled P-4 (continued) Impeller: P-4 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 197 16.4 1.31 223 1.01 1126 216 18.8 1.31 96.8 0.82 2445 170 9.6 1.28 96.8 0.81 2574 180 11.1 1.28 96.8 0.81 2703 190 12.1 1.28 49.4 0.74 4109 200 13.3 1.28 49.4 0.74 4951 210 14.7 1.28 49.4 0.72 5694 166 8.2 1.26 49.4 0.70 6288 200 12 1.26 49.4 0.71 6758 230 15.3 1.26 19.8 0.64 10839 254 18.2 1.26 19.8 0.63 12090 273 21.5 1.26 19.8 0.62 13400 182 8.2 1.22 19.8 0.62 14353 203 10.15 1.22 5.00 0.51 44478 225 12.15 1.22 5.00 0.50 47798 241 14.05 1.22 5.00 0.50 51117 201 7.45 1.14 1.09 0.43 205256

Appendix 9: Raw and reduced data from impeller power draw experiments for baffled SC-3 Impeller: SC-3 Configuration: Baffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 11.5 10.45 1.48 114300 163 0.15 27 26.7 1.48 113171 75.7 0.35 40 40.05 1.48 112244 51.7 0.52 57 56.75 1.48 111084 36.1 0.74 69 68.6 1.48 110260 29.8 0.91 84.5 82 1.48 109330 23.7 1.12 48 19.475 1.42 49035 18.6 1.35 69.5 28.2 1.42 48716 12.8 1.97 91 36.775 1.42 48403 9.76 2.59 108 43.325 1.42 48163 8.17 3.09 125.5 50.4 1.42 47905 7.04 3.61 159 64 1.42 47408 5.57 4.62 180.5 71 1.42 47152 4.79 5.28 207 82 1.42 46750 4.21 6.10 73 7.125 1.40 10140 2.98 9.78 98.5 10.425 1.40 10138 2.40 13.2 136 16 1.40 10135 1.93 18.2 189 25.45 1.40 10129 1.59 25.4 254 39.25 1.40 10120 1.36 34.1 303 50.85 1.40 10113 1.24 40.7 348 62.675 1.40 10105 1.15 46.8 390 74.3 1.40 10098 1.09 52.5 181.5 14.625 1.37 4023 1.01 60.0 52.5 24.725 1.37 3995 0.88 84.0 349 41.825 1.37 3947 0.78 118 426 58.075 1.37 3901 0.73 145 503 76.825 1.37 3849 0.69 174 552 89.675 1.37 3813 0.67 193 582.5 98.275 1.37 3789 0.66 204 596.5 101.975 1.37 3778 0.65 210 627 110.95 1.37 3753 0.64 222 626 110.6 1.37 3754 0.64 222 267.5 19.375 1.37 1438 0.62 247 319 26.6 1.37 1439 0.60 295 372 35.2 1.37 1441 0.58 343 418 41.175 1.37 1442 0.54 386 468 50.3 1.37 1443 0.52 431 520 60.4 1.37 1445 0.51 478 231 11.7 1.34 607 0.51 495 313.5 20.05 1.34 608 0.47 672 382 28.7 1.34 609 0.46 818 455 40 1.34 609 0.45 972 498.5 47.8 1.34 610 0.45 1064 459 39.5 1.32 313 0.45 1872 217 8.2 1.29 133 0.42 2044 238 9.95 1.29 133 0.43 2240 252 11.25 1.29 133 0.43 2371 290 15.1 1.29 133 0.43 2724 355 22.65 1.29 134 0.44 3324 400 28.95 1.29 134 0.44 3735 462 38.95 1.29 135 0.44 4295 501 46.7 1.29 135 0.45 4643 229 9.25 1.25 53.0 0.44 5242 253 11.4 1.25 53.0 0.45 5791 308 17.2 1.25 53.0 0.46 7050

Appendix 9: Raw and reduced data from impeller power draw experiments for baffled SC-3 (continued) Impeller: SC-3 Configuration: Baffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 369.5 25.4 1.25 53.0 0.47 8458 415.5 33.6 1.25 53.0 0.50 9511 466 42.25 1.25 53.0 0.50 10667 522 53.35 1.25 53.0 0.50 11949 236 10.5 1.22 19.8 0.48 14055 287 15.6 1.22 19.8 0.49 17093 338 21.7 1.22 19.8 0.49 20130 382 28 1.22 19.8 0.49 22751 446 38.65 1.22 19.8 0.50 26562 251 11.7 1.13 5.06 0.51 54540 301 16.9 1.13 5.06 0.51 65404 381.5 27 1.13 5.06 0.51 82896 451.5 38 1.13 5.06 0.51 98107 267 11.45 1.00 1.09 0.50 237244 321 16.85 1.00 1.09 0.51 285226 389.5 25.25 1.00 1.09 0.52 346092 506.5 42.7 1.00 1.09 0.52 450053

Appendix 10: Raw and reduced data from impeller power draw experiments for unbaffled SC-3 Impeller: SC-3 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 11.5 10.45 1.48 114300 163 0.15 27 26.7 1.48 113171 75.7 0.35 40 40.05 1.48 112244 51.7 0.52 57 56.75 1.48 111084 36.1 0.74 69 68.6 1.48 110260 29.8 0.91 84.5 82 1.48 109330 23.7 1.12 53.5 25.25 1.42 55237 19.4 1.33 71 33.725 1.42 55033 14.7 1.78 90 42.875 1.42 54812 11.6 2.26 106.5 50.7 1.42 54623 9.83 2.69 135.5 64 1.42 54303 7.66 3.44 168 78.3 1.42 53958 6.10 4.29 202.5 93 1.42 53604 4.99 5.21 241.5 108.5 1.42 53230 4.09 6.25 70 8.35 1.40 13178 3.80 7.22 97.5 12.525 1.40 13115 2.94 10.1 156 22.525 1.40 12964 2.06 16.4 246 42.15 1.40 12667 1.55 26.4 317 60.975 1.40 12383 1.35 34.8 378 78.525 1.40 12117 1.23 42.4 436 96.85 1.40 11840 1.14 50.0 154 10.9 1.37 3698 1.05 55.4 204 17 1.37 3690 0.93 73.5 256 24.3 1.37 3681 0.85 92.5 320 34.725 1.37 3668 0.77 116 393 48.35 1.37 3652 0.71 143 457 61.7 1.37 3635 0.67 167 458 61.8 1.37 3635 0.67 168 515 74.6 1.37 3619 0.64 189 514 74.2 1.37 3620 0.64 189 188 9.55 1.37 1261 0.62 198 223.5 13.1 1.37 1259 0.60 236 270.5 18.55 1.37 1257 0.58 286 299.5 22.1 1.37 1255 0.56 317 326 25.7 1.37 1253 0.55 346 345.5 28.45 1.37 1252 0.54 367 263 16.05 1.35 781 0.54 443 299.5 19.5 1.35 781 0.50 504 330 23.05 1.35 782 0.49 555 226 10.4 1.33 527 0.48 555 266 14 1.33 520 0.46 661 292 16.55 1.33 516 0.45 733 310.5 18.45 1.33 512 0.45 784 326 20 1.33 510 0.44 828 263 12.55 1.32 392 0.43 860 294.5 15.5 1.32 394 0.42 959 321 18.4 1.32 395 0.42 1040 330 19.2 1.32 396 0.42 1068 288 14.4 1.32 316 0.41 1165 305.5 16 1.32 318 0.41 1228 329 18.65 1.32 321 0.41 1309 271 12.4 1.31 264 0.40 1310 294 14.55 1.31 264 0.40 1421 319 16.75 1.31 264 0.39 1542 246 9.3 1.29 134 0.37 2302

Appendix 10: Raw and reduced data from impeller power draw experiments for unbaffled SC-3 (continued) Impeller: SC-3 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 275 11.35 1.29 134 0.36 2573 292 12.6 1.29 134 0.36 2732 305 13.75 1.29 134 0.36 2854 256 9.25 1.28 96.0 0.34 3321 291 11.95 1.28 96.0 0.34 3775 301.5 12.5 1.28 96.0 0.33 3911 318 14.2 1.28 96.0 0.34 4125 331 15.15 1.28 96.0 0.34 4293 263 8.7 1.25 52.6 0.31 6066 286.5 10.25 1.25 52.6 0.31 6608 304 11.6 1.25 52.6 0.31 7012 321 12.9 1.25 52.6 0.31 7404 350 15.2 1.25 52.6 0.31 8073 280 8.55 1.22 19.8 0.28 16676 302 9.85 1.22 19.8 0.28 17986 324 11.2 1.22 19.8 0.27 19296 340 12.3 1.22 19.8 0.27 20249 301 7.35 1.14 5.00 0.22 66607 312.5 7.75 1.14 5.00 0.22 69152 313 6 1.00 1.09 0.19 278118

Appendix 11: Raw and reduced data from impeller power draw experiments for baffled HE-3 Impeller: HE-3 Configuration: Baffled Diameter: 9.51'' D/T: 0.405 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 6.65 1.48 114500 285 0.088 19.5 20.15 1.48 114056 111 0.25 33 34.05 1.48 113598 65.6 0.42 44 45.4 1.48 113225 49.2 0.56 57 58.02 1.48 112809 37.5 0.73 72 73.375 1.48 112304 29.7 0.92 90 90 1.48 111757 23.3 1.16 50 20.825 1.42 46615 18.2 1.48 70 28.275 1.42 46546 12.6 2.08 92 37.275 1.42 46462 9.63 2.73 111 45.45 1.42 46385 8.07 3.30 141.5 58.625 1.42 46262 6.40 4.22 175 72 1.42 46137 5.14 5.24 204 84 1.42 46025 4.41 6.12 75 7.6 1.40 11018 3.00 9.27 95 10.325 1.40 10992 2.54 11.8 171 22.65 1.40 10875 1.72 21.4 261 40.975 1.40 10701 1.33 33.2 287 47 1.40 10644 1.27 36.7 332 58.025 1.40 10539 1.17 42.9 376 69.55 1.40 10429 1.09 49.1 427 83.2 1.40 10300 1.01 56.5 489 100 1.40 10140 0.93 65.7 259 23.175 1.37 3947 0.78 87.5 362 39 1.37 3943 0.67 123 440 53 1.37 3934 0.62 149 510 67.125 1.37 3926 0.59 173 572 80.725 1.37 3918 0.56 195 624.5 92.25 1.37 3910 0.54 213 685 106.7 1.37 3904 0.52 234 751 123.7 1.37 3896 0.50 258 329 22.775 1.37 1464 0.48 299 387 30.45 1.37 1455 0.46 354 423.5 35.45 1.37 1449 0.45 389 464 40.325 1.37 1443 0.42 428 511.5 48.1 1.37 1434 0.42 475 559 55.45 1.37 1425 0.40 523 610.5 64.125 1.37 1414 0.39 575 640 69.65 1.37 1407 0.39 606 663 73.875 1.37 1402 0.38 630 259 10.7 1.34 533 0.37 634 349.5 18.275 1.34 529 0.35 862 419 25.5 1.34 525 0.34 1041 483.5 33.55 1.34 521 0.33 1212 529 39.75 1.34 517 0.33 1335 568 45.575 1.34 514 0.33 1442 610.5 52.45 1.34 510 0.33 1561 653.5 59.95 1.34 506 0.33 1685 406.5 21.55 1.31 231 0.31 2250 493.4 31.85 1.31 230 0.31 2733 566.5 42 1.31 230 0.31 3139 639 54.2 1.31 230 0.31 3544 682 62.1 1.31 230 0.32 3784 370 17.2 1.28 97 0.30 4760 462.5 27.25 1.28 97 0.31 5950

Appendix 11: Raw and reduced data from impeller power draw experiments for baffled HE-3 (continued) Impeller: HE-3 Configuration: Baffled Diameter: 9.51'' D/T: 0.405 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 534.5 36.45 1.28 97 0.31 6876 602 46.5 1.28 97.0 0.31 7744 391 19 1.25 49.2 0.31 9668 463 26.8 1.25 49.2 0.31 11449 538 36.25 1.25 49.2 0.31 13303 614 47.3 1.25 49.2 0.31 15183 291.5 10 1.22 19.8 0.30 17397 387.5 17.9 1.22 19.8 0.30 23127 479 27.8 1.22 19.8 0.31 28588 546 36.05 1.22 19.8 0.31 32586 310 10.6 1.13 5.11 0.30 66920 380 15.9 1.13 5.11 0.30 82031 450.5 22.8 1.13 5.11 0.31 97250 518 29.4 1.13 5.11 0.30 111821 338 10.5 1.00 1.09 0.32 268362 414 15.5 1.00 1.09 0.32 328704 501 22.7 1.00 1.09 0.32 397780 577 30.4 1.00 1.09 0.32 458122

Appendix 12: Raw and reduced data from impeller power draw experiments for unbaffled HE-3 Impeller: HE-3 Configuration: Unbaffled Diameter: 9.51'' D/T: 0.405 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 7 6.65 1.48 114500 285 0.088 19.5 20.15 1.48 114056 111 0.25 33 34.05 1.48 113598 65.6 0.42 44 45.4 1.48 113225 49.2 0.56 57 58.02 1.48 112809 37.5 0.73 72 73.375 1.48 112304 29.7 0.92 90 90 1.48 111757 23.3 1.16 35.5 11.225 1.42 35511 19.5 1.38 50 16.1 1.42 35537 14.1 1.94 73 23.85 1.42 35579 9.79 2.83 93.5 29.95 1.42 35612 7.49 3.63 114.5 36.925 1.42 35649 6.16 4.44 136 44.75 1.42 35691 5.29 5.26 163 53.8 1.42 35740 4.43 6.30 186.5 61.725 1.42 35783 3.88 7.20 210.5 69.55 1.42 35825 3.43 8.12 234 76.875 1.42 35864 3.07 9.01 267 88 1.42 35924 2.70 10.3 103.5 12.15 1.40 11559 2.52 12.2 174 23.9 1.40 11434 1.75 20.7 248 39.025 1.40 11273 1.41 30.0 313 54.35 1.40 11110 1.23 38.4 117.5 7.325 1.37 4159 1.20 37.6 146 10.175 1.37 4152 1.08 46.9 198.5 16.125 1.37 4136 0.93 63.9 252 23.075 1.37 4118 0.82 81.5 307.5 30.925 1.37 4097 0.74 100 365 40.175 1.37 4073 0.68 119 422 50.15 1.37 4047 0.64 139 489 62.775 1.37 4014 0.60 162 539.5 72.95 1.37 3987 0.57 180 596 85.05 1.37 3955 0.54 201 194 8.775 1.37 1271 0.53 203 216.5 10.6 1.37 1269 0.51 227 265.5 15.05 1.37 1266 0.48 280 317 20.35 1.37 1261 0.46 335 362.5 25.35 1.37 1257 0.44 384 401.5 29.9 1.37 1253 0.42 427 245 10.875 1.36 728 0.42 444 293.5 14.775 1.36 732 0.39 529 345.5 19.725 1.36 737 0.38 618 247 9.8 1.33 507 0.37 632 270.5 11.55 1.33 506 0.37 693 335 16.45 1.33 506 0.34 859 354 18.2 1.33 505 0.34 909 376.5 20.2 1.33 505 0.33 967 319 14.1 1.32 395 0.33 1036 355 17.2 1.32 395 0.32 1154 375.5 19 1.32 395 0.32 1222 316.5 12.85 1.32 313 0.30 1294 340 14.6 1.32 313 0.30 1389 358 16.1 1.32 313 0.30 1462 325 13.125 1.31 264 0.29 1574 347.5 14.75 1.31 264 0.29 1683 359.5 15.8 1.31 264 0.29 1741

Appendix 12: Raw and reduced data from impeller power draw experiments for unbaffled HE-3 (continued) Impeller: HE-3 Configuration: Unbaffled Diameter: 9.51'' D/T: 0.405 N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-) 334 13.1 1.31 223 0.28 1913 350.5 14.45 1.31 223 0.28 2007 293 9.25 1.28 98.3 0.26 3721 315 10.5 1.28 98.3 0.26 4001 329 11.35 1.28 98.3 0.25 4179 343 12.5 1.28 98.3 0.26 4356 362 13.85 1.28 98.3 0.26 4598 381.5 15.25 1.28 98.3 0.25 4845 307 8.95 1.25 49.4 0.24 7550 325.5 10.1 1.25 49.4 0.24 8005 344 11.2 1.25 49.4 0.24 8460 371 13.2 1.25 49.4 0.24 9124 394 14.6 1.25 49.4 0.23 9690 313 8.1 1.22 19.8 0.21 18680 334.5 9.2 1.22 19.8 0.21 19964 359.5 10.7 1.22 19.8 0.21 21456 373 11.55 1.22 19.8 0.21 22261 332 6.9 1.14 5.00 0.17 73621 347 7.5 1.14 5.00 0.17 76948 344 5.6 1.00 1.09 0.17 273126