REFERENCE

NBS

PUBLICATIONS

NBSIR 85-3030

NAT'L INST. OF STAND & TECH

AlllDb D31fiEl

THE DEVELOPMENT OF A

PERFORMANCE TEST PROCEDURE AND

MEASUREMENTTECHNIQUE IN A BATCH

MIXING SYSTEM

Douglas M. Ginley

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

July 1985

-QC

100

.056

85-3030

I 1985

Research Information Center

iNalioual Bureau of Standards

Gaithersburg, Maryland 20899

NBSIR 85-3030

THE DEVELOPMENT OF A

PERFORMANCE TEST PROCEDURE AND

MEASUREMENTTECHNIQUE IN A BATCH

MIXING SYSTEM

Douglas M. Ginley

Chemical Engineering Science Division Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

July 1985

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

ABSTRACT 1

INTRODUCTION 1

BACKGROUND 3

APPARATUS 5

Physical Equipment 6

Data Collection 6

Measurement Equipment 7

Materials 9

CALIBRATION AND ACCURACY 10

Probe Location 10

Probe Calibration 12

Reproducibility and Accuracy 16

PROCEDURE 19

PROBE RESPONSE 23

Signal Noise and Probe Response Time 24

Probe Location 25

Flow Patterns 26

Impeller Types 27

C/T Values 27

RPM 27

Concentration 28

MIXTIME ANALYSIS 28

Determination of Mixtime 29

Probe Location 29

Flow Patterns 31

Impel 1 er Types 31

C/T Values 32

RPM 32

Concentration 33

TORQUE MEASUREMENTS 33

FUTURE WORK 36

Experimentation 37

Data Analysis 38

SUMMARY 39

CONCLUSIONS 45

RECOMMENDATIONS 45

ACKNOWLEDGMENT 46

REFERENCES 46

TABLES 49

FIGURES 59

APPENDICES 94

FIGURES

Page

FIGURE 1

- Mixing Vessel Specifications 61

FIGURE 2 - Impellers 62

FIGURE 3 - Laboratory Experimental Design 63

FIGURE 4 - Probe Locations 64

FIGURE 5 - Conductivity Probes 65

FIGURE 6 - NBS Probe Circuit 66

6a - 18 Pin Connector Probe Circuits 67

FIGURE 7 - Torque Measurement 68

FIGURE 8 - Injection Point 69

FIGURE 9 - Tracer Addition System 70

FIGURE 10 - Signal Amplitude versus Meter Reading 71

FIGURE 11 - Reading Probe 4 versus Meter Reading 72

FIGURE 12 - Reading Probe 1 versus Meter Reading (Calibration

Temperatures) 73

FIGURE 13 - Default List for Geometric Parameters 74

FIGURE 14 - Experimental Run Fact Sheet and Graphical Representation. . 75

FIGURE 15 - (Example Data) (FILE #AVG50P12) 76

15a (1 of 4) - Example Data Probe #3 77

15b (2 of 4) - Example Data Probe #4 78

15c (3 of 4) - Example Data Probe #5 79

15d (4 of 4) - Example Data Probe #6 80

FIGURE 16 - Example Data for Comparison (FILE #AVG50P13) 81

FIGURE 17 - Back-Mixing Data (FILE #AVG50P62) 82

FIGURE 18 - Comparison of Impeller Types 83

FIGURE 19 - Comparison of C/T Values 84

FIGURE 20 - Comparison of Rotation Rates 85

FIGURE 21 - Mixtime Determination 86

FIGURE 22 - Concentration versus Mixtime 87

FIGURE 23 - Power versus C/T 88

V
FIGURES

(conti nued)

Page

FIGURE 24 - Power Comparison: Power versus RPM 89

FIGURE 25 - Power Comparison: Flat Blade Turbine 90

FIGURE 26 - Power Comparison: Pitch (45 deg) Blade Turbine 90a

FIGURE 27 - Power Comparison: Pitch vs. Flat Blade Turbine 91

FIGURE 28 - Re versus Np 92

FIGURE 29 - Mixtime Analysis Technique 93

vi
TABLES

Page

TABLE 1

- EXPERIMENTAL DESIGN 50

TABLE 2 - PROBE AND INJECTION LOCATION COORDINATES 51

TABLE 3 - SIGNAL AMPLITUDE EQUATIONS 52

TABLE 4 - CALIBRATION DESIGN 53

TABLE 5 - PROBE RESPONSE EQUATIONS 54

TABLE 6 - TEMPERATURE CONVERSION FACTORS 56

TABLE 7 - CONCENTRATION ACCURACY STATISTICS 57

TABLE 8 - CORRELATION COEFFICIENTS 58

TABLE A - PROBE #6 MIXTIMES 31

vii
APPENDICES

Page

Appendix I NBS Workshop on Mixer Performance Standards 95

Appendix II

Moderate Scale Facility Design 102

Appendix III

Computer Program for Laboratory Scale Batch Mixing Experiments . .108

Appendix IV

Immiscible Liquid Dispersion Experiment 109

Apppendix V

Flow Visualization Experimentation Ill

Appendix VI

Mixtime Data 113

Appendix VII

Torque Comparison Power Data 116

Appendix VIII

Fluid Mixing Statistics 119

Appendix IX

Experimental Test Procedure 126

Appendix X

Experimental Data 128
NOMENCLATURE

Bpr = probe response intercept

Bsa = signal amplitude intercept

C = height of the impeller from the bottom of the tank

C/T = ratio of impeller height to tank diameter

CSSD = cumulative successive squared difference

CV = weight of liquid in the calibration loop

Ct = concentration at time t

D = diameter of the impeller

D/T = ratio of impeller diameter to tank diameter

Den = salt solution density

Df = degrees of freedom

Hp = horsepower

Ki = change in intercept/°C change in temperature

Ks = change in slope/°C change in temperature

MR = meter reading

Mpr = probe response slope

Msa = signal amplitude slope

N = impeller rotation speed (when in conjunction with Np)

N = the number of salt additions to be made between changes of the tank fluid

Np = power number (dimensionless)

P = power

PR = probe response

PRt = theoretical probe response at a given concentration, voltage (SA) and

experimental temperature (T)

S = the amount of NaCl in grams per run

S(t) = CSSD

SA = signal amplitude

ix
T = diameter of the tank

T = temperature of the experiment

Tbase = base calibration temperature (24 °C)

V = weight of liquid in the mixing vessel

W = the weight percent of NaCl in the mixing vessel after N additions

Z = height of liquid

Z/T = ratio of liquid height to tank diameter

b = intercept for point concentration calculation

d = depth of an impeller blade

g = gravitational constant

m = slope for point concentration calculation

p = liquid density

ssd = sum of standard deviation squared

w = width of an impeller blade

X
The Development of a Performance Test Procedure

and Measurement Technique in a Batch Mixing System

Douglas Ginley

National Bureau of Standards

Boulder, Colorado 80303

A performance test procedure and measurement technique for a batch mixing system is described using conductivity probes. The

design of the automated experimental apparatus is described, and

experimental procedures are given. Data collected from the experiments are explained, and a mixtime analysis of the data is performed.

Conductivity probe response curves provide a good representation of

the system dynamics. Mixtime analysis allows for probe response

comparisons to evaluate system geometry and probe location.

Key words: batch mixing; calibration techniques; conductivity

probes; experimental apparatus; mixtime analysis; torque

measurements

INTRODUCTION

Mixing is one of the most important and one of the most frequently performed operations that occurs in industrial processes for material conversion.

Surprisingly, it is also one of the least clearly understood processes. The

diversity of mixing systems and the variety of techniques used for analysis of

the mixing process make communication and cooperative efforts between

interested parties difficult. Much work needs to be done to establish

standards for performance and analysis in the mixing field.

The purpose of this project is to develop performance test procedures and

measurement techniques for batch mixing systems. The performance tests are to

be designed such that they will enhance understanding of the mixing process,

aid in facility design, and be useful for in-plant trouble-shooting of batch

mixing systems.

Work for this project was carried out in three basic areas. First, an investigation of the literature was made to determine the scope of work to be

done, the mixing system to be used, the components to be mixed, and the type

of measurements to be made. Second, based upon knowledge gained from the

literature, an experimental apparatus was designed and built. Third,

experiments were designed, performed, and analyzed in such a manner as to

fulfill the goal of developing a performance test procedure and measurement

technique.

Due to the complexity of mixing systems, and the large number and variety

of parameters, limitations had to be set regarding the scope of work to be

1
done. A single standard geometry was specified for the laboratory scale equipment, and research was carried out in only the simplest mixing system (i.e.,

liquid blending). Because of limited resources, the experimental work was limited to the laboratory scale. The variables that were allowed to change were the impeller type (pitch and flat blade turbines), impeller speed (50,

150, and 300 rpm) , impeller height from the tank bottom (C/T = 0.13, 0.33 and

0.50), and the concentration of NaCl in the system (<0.10 wt percent). The

data collected were analyzed to determine the viability of using the

measurement technique as a means for evaluating the mixing process. The data were not compared to other work in the field, as this project was not designed

or intended to be a comprehensive research analysis and comparison effort.

The following conclusions were formulated based upon the work done:

1) A performance test using conductivity probes was developed which can be

used to enhance understanding of the mixing process, aid in facility

design, and be useful for in-plant trouble-shooting for a batch mixing

system.

2) A standard geometry has been determined for use in laboratory testing.

3) Conductivity probes are flexible, accurate, reliable, and give reproducible results.

4) Probe response curves are a viable means of observing the dynamics of the

mixing process in a qualitative manner.

5) Mixtime analysis provides useful insights into the mixing process, and

can be used to enhance understanding of the mixing process, aid in facility design, and be useful for in-plant trouble-shooting of batch mixing

processes.

6) The torque-arm/weigh-scale technique used for these experiments to mea- sure torque provides accurate, reliable, and reproducible information

needed for power calculations.

The following recommendations were formulated based upon the work done:

1) The work done in this project is incomplete, and further testing is

necessary for a better understanding of the mixing process.

2) Further work should be done using an expanded parameter list and a broader range of testing for each parameter.

3) A moderate size facility (approximately 0.379-0.757 m^ (100-200 gallons))

is needed for comparison testing of work done in the laboratory scale

equipment. All experiments run on the laboratory scale should in turn be run on the moderate scale equipment.

2
4) Work should be expanded to include other mixing systems. The system which

should be worked on after miscible liquids is most likely a sol id- liquid

system,

5) The information collected should be more rigorously analyzed, removing

qualitative analysis as much as possible from the tabulated results.

BACKGROUND

Mixing, as one of the key chemical processes in most industrial chemical

plants, has been studied seriously for the last 35 to 40 years. Many advances

have been made in the understanding of mixing and the mechanisms which

surround it. Much work has already been carried out by the likes of Rushton,

Oldshue, Brodkey, Gray and Uhl, Nagata, and many others. In just the last

decade, approximately 100 papers have been published annually concerning the

field of mixing. All of the work was meant to help define mixing patterns,

methods for enhancing mixing operations, and methods for improving mixing

efficiencies. However, much is still unknown, and there are many areas of

disagreement yet to be resolved. One major problem is the lack of

standardization in experimental procedures, design criteria, and design

correlations. Standardization in these areas would allow the various

individuals in the mixing field to communicate more effectively with one another.

The subject of mixing covers many different areas such as pipe mixing,

continuous stirred tank mixing, and batch mixing. This paper will investigate

only the area of batch mixing. In studying batch mixing, one must select the

system, materials in the system, and measurement technique(s) to be used.

In 1981, Hilby stated that because of the number of possible variables in

the mixing system, the simplest system possible should be used as a basis for

initial studies (Hilby, 1981). To this end, a large number of studies deal

with blending of miscible liquids. This is as opposed to immiscible liquids,

gas-liquid, or solid-liquid systems. If blending of miscible liquids is

selected as the system to be studied, then it only remains to determine the

materials and measurement technique most suitable for the given operating con- ditions.

Measurement techniques and materials used are related to one another as Kappel (1979) described in his survey of appropriate techniques for measuring

changes in a batch mixing system (Kappel, 1979). He concluded that a tracertype measurement would be most effective and convey the most information in a blending-type operation. To this end, photographic tracers, and/or color

3
detectable tracers were considered best. However, as is often the case in the

mixing field, disagreement about tracers is quite apparent. Many feel that

the use of electrolytic tracers and conductivity probes is a better system to use (Neal, Bankoff, 1963). This is because of the relative degree of sensitivity, and the increased flexibility which conductivity probes provide over other types of tracers. The difficulty with conductivity probes revolves

around the construction and operation of the probe circuitry which is needed

to obtain meaningful responses. It was felt that our research could be best

carried out by the use of conductivity probes, which are more flexible and more likely to be used in the field than other similar tracer techniques.

The idea for and use of conductivity probes as a measurement technique is

not new. In 1935, Jones and Bollinger evaluated the notion of using resistance

as a way to measure ion concentration (Jones, Bollinger, 1935). They proved

that the use of electrodes to measure concentration changes was possible (an

NaCl solution was used). Later, in 1956 Prausnitz and Wilhelm developed a usable probe using platinized electrodes in a small tank (Prausnitz, Wilhelm,

1956). The design of the probe, which measured an entire tank's concentration, was substantially improved in 1960 by Cairns and Prausnitz (Cairns,

Prausnitz, 1960). Late in 1960, Lamb et al . measured concentration gradients

with their version of a platinized conductivity probe (Lamb, Manning, Wilhelm,

1960). Keeler and Gibson in 1963 and 1964 further improved the probe such

that volumes as small as 5 x lOE-10 m^ could be measured inside of a tank

(Gibson, 1963) (Keeler, 1964). Torres! and Ranz (1969) realized that resolution of the conductivity probe could most properly be enhanced through the

design of the circuitry connected to it as opposed to further work on the

probe itself (Torres!, Ranz, 1969). They improved the probe response by the

use of a filtered ac bridge circuit. In 1975, Khang and Fitzgerald further

improved the circuit to the point where there was a linear response to concentration, high and low noise were reduced, and errors caused by cross-talk were

removed (Khang, Fitzgerald, 1975). This allowed accurate use of more than one probe at a time. Sheppard and Doddington (1977) improved accuracy even more

by adding calibration routines for concentration and temperature to the use of

conductivity probes (Sheppard, Doddington, 1977).

In our studies, it was important to determine the system, materials, and

measurement techniques most appropriate for fulfilling our objective of

creating standard performance tests and measurement techniques for batch

mixing systems. Because mixing systems vary so greatly, it was clearly

4
understood that one technique would not suffice for all systems. Thus, keeping

in mind that several techniques would eventually be required, the simplest

system was investigated first. That system being blending of low viscosity

miscible liquids. The materials chosen were an NaCl solution and deionized

water at room temperature. The use of these materials allows for the use of

conductivity probes, which are more flexible than most tracer systems, and

also are capable of operating in a field situation, such that tests can be

performed on-site. Thus, the system, materials to be used, and measurement

technique for our experimentation were established based upon previous work

done in the fields of mixing and conductivity probe construction.

APPARATUS

The apparatus for the mixing experiments was designed with consideration

being given to six specific criteria: safety, automation, reliability, reproducibility, ease of operation, and the ability for the equipment to be used

later by industry in a plant environment. Careful consideration was given to

creating an efficient unit that would satisfy the criteria and produce results

which would fulfill the requirements of the project's stated objective. To

insure that work done would be usable by industry, a workshop was held in

October 1983 to discuss the research to be attempted and the equipment to be

used (see Appendix I).

Members of the workshop represented the manufacturers of mixing equipment,

the users of mixing equipment, and academic researchers in the mixing field.

This group of experts was called in to help in evaluating the direction of the

project's research, and the equipment that should be used to perform the

research. It was decided that a standard geometry of some kind should be used

such that the largest number of interested parties could correlate the NBS

data with their own results in the most direct manner. Thus, the members of

the workshop made recommendations for the tank size, baffles, impellers, rotation rates, and horsepower, as well as making suggestions which specified

geometric configurations for the mixing equipment. It was left to the re- searcher to decide which recommendations and suggestions should be put into

effect and which should not.

The actual experimental apparatus consists of four major parts. The

first is the physical equipment such as the tank, baffles, impeller, and

motor. The second is the data collection system which consists of a computer

and its accompanying software. The third is the measurement devices for

5
concentration, tracer addition, and torque. Finally, there are the materials

used in the experiments.

Physical Equipment:

The physical equipment was meant to be two specific sizes, such that

scale-up information could be obtained. There was to be an approximately

0.30 m (1.0 foot) diameter tank with accompanying attachments, and there was

to be an identically equipped 0.91 m (3 foot) diameter facility (see Appendix

II). Due to limited resources, the research was restricted to work using the

0.30 m (actually 0.25 m (9.75 in)) diameter facility only.

In the 0.25 m diameter facility, the Z/T ratio was held at 1.0. This was

a fairly standard value from the literature inside the specified range between

0.8 and 1.5 for Z/T. The C/T ratio was shifted in the range between 0.00 and

0.50 in three steps (0.13, 0.33, and 0.50). The D/T ratio was to be

maintained between 0.25 and 0.50, and was actually maintained at 0.41 for all

impellers used. A standard geometric configuration was decided upon using

four full length baffles with minimal bottom and side clearance, spaced 90 deg

apart. Initial studies used a flat bottomed, clear tank (see fig. 1). There were two impellers used, one a flat, six-blade turbine with a w/d = 1/6, and

the second a 45 degree pitch, six-blade turbine with a w/d = 1/5 (see fig. 2).

The use of four-bladed impellers was preferable as it is more common to have

four-bladed impellers in industry, but because of the small scale and easy

availability of the six-blade turbines (commercially available equipment), it was felt that they would be adequate for initial studies. Only single

impeller tests were run on a vertical shaft centrally located. A 186 watt

(1/4 hp) variable speed motor was used to insure that up to 2.95 kW/m^ (15

hp/1000 gal) was available. The combination of all of the aforementioned

attributes was deemed to present the best representation of a standard batch

mixing geometry (see fig. 1).

Data Collection:

The second part of the experimental apparatus is the data collection system. It consists of two parts, the computer hardware and the computer software. The hardware in this case is a high-speed, scientific computer with a 32-bit internal structure and an accompanying multi programmer unit (see

fig. 3). The computer, with the multi programmer, is designed to send and

receive signals to or from external devices (up to approximately

6
30000/^). In this way, the computer can control the experimental run, reducing

the chance for error, as well as collecting data from the' experiment. The

multi programmer consists of five A/D cards, five 4k memory cards, a timing

card, and a relay card. The computer, by the use of software, controls the

functions and operation of these cards.

The software is truly the heart of the experiment. It is designed such

that once the experiment is started, no manual changes need or in fact can be

made. The computer program not only controls the experiment, but also controls

the timing of the experiment and collects the data. The program is also capable of converting the data into concentrations, and provides a graphical representation of the just completed experiment (see Appendix III for program

listing). More information concerning the user input to the program during

the experiment will be given in the experimental procedure.

Measurement Equipment:

The third part of the experimental apparatus is the measurement equipment.

The measurement equipment consists of the conductivity probes, the probe circuits, a torque measuring device, and an rpm meter. The conductivity probes measure the changes in ion concentration that occur within the system. To gain

insight into the workings in the batch mixer, it was necessary to position

probes in several locations throughout the tank. Four probes were used.

Probe locations were determined based upon general knowledge of flow patterns

obtained from the literature. Thus, the probes were positioned in an area of

good mixing in the tank, and an area of poor mixing on the surface of the

mixing fluid, in front of a baffle and behind a baffle (see fig. 4).

The original experiments were performed with homemade probes (described

by Khang and Fitzgerald, 1975) which measured essentially a point volume.

These probes proved unreliable, and experimental results were not reproducible. Initial testing of commercial probes indicated they would be much

more reliable with more reproducible results. For this reason, commercial

probes were used in the experiment. Many types are available, and the one selected was picked based upon its similarity to the homemade probes, its ease

of acquisition, and its cost. It must be pointed out that any one of many

various commercial probes will work adequately. The probe selected uses two

small platinized plate electrodes approximately 2 mm apart, with a measurement

volume of about 8 x lOE-6 m^ (see fig. 5). This volume was felt to be small

enough to be considered a point volume when compared to the volume (10.830 m^)

7
of the mixing vessel (less than 0.0001 percent of the mixing vessel volume).

The probes were equipped with glass jackets to help reduce extraneous noise.

At least in intent, these probes followed the ideals of probe design as suggested by Khang and Fitzgerald (1975), and subsequently were felt to be

adequate. They proved reliable, and are readily available to all members of

the mixing community.

As was discussed earlier, the resolution of a conductivity probe is significantly increased by the design of its accompanying circuit. This is also

the case with the setup used in these experiments. The circuit was designed

such that it has a wide range of sensitivity, responds proportionally to

changes in concentration, eliminates high and low end noise, and reduces cross- talk to the point where more than one probe can be accurately used simultaneously (modification of Khang and Fitzgerald (1975) design by D. M. Ginley

and Nolan Frederick 1984). The use of an oscillator amplifier, several

filters and operational amplifiers make this possible (see fig. 6). Because

each probe needs its own circuit, four pc-boards were built, each with its own

set of external adjusting knobs. The pc-boards were also connected to a common voltmeter so that calibrations and comparisons between probes could be

performed reproducibly.

The other parts of the measurement equipment, are the rpm and torque devices. These two devices combine to allow one to calculate the power used for

the experiment. The rpm meter is a belt-driven tachometer that is read

manually, and used to set the rpm for a given experiment. Torque measurement

may be obtained in several different ways. A strain gauge may be placed on the impeller shaft, or the motor may be mounted on a "frictionless" bearing

with torque being measured by use of a weigh scale and torque arm, or a plate

and strain gauge apparatus may be placed beneath the tank and torque measured

by the plate's movement relative to a fixed reference point. All of these

methods have their advantages and disadvantages which will be discussed in more detail in a following section. Because of design difficulties, and the

need for flexibility, as well as availability of equipment, a "frictionless"

bearing was positioned under the motor and gear box, and changes in torque were measured by a weigh scale using a weight connected to a torque arm attached to the gear box (see fig. 7). Although not as sophisticated as some other methods, this torque measuring method proved both reliable and reproducible.

8
Materials;

The final part of the experimental apparatus is the materials used in the

system, and the transport equipment necessary for tracer injection. Although

many materials are available, considerations for safety and disposal dictated

that simple materials be used. The simplest electrolytic blending system that

meets the criteria of safety and easy disposal is most probably a tracer of

NaCl solution, and deionized water. In using these materials a 9.62 wt.

percent solution of NaCl was added in approximately 0.0107E-3 m^ amounts to

the mixing vessel at the beginning of each run. One pulse only was added for

each experimental run. Acetic acid was also tested and found acceptable, but

less desirable for use because of problems with the safety and disposal

requirements. Use of the probes was also attempted in a two-phase system of

immiscible liquids (dichloromethane and deionized water). The probes read

both phases at the same time, and as such averaged the concentrations in the

separate phases. This made it very difficult to discern what was taking place

in the experiment. Because of handling, safety and disposal problems it was

felt that further investigation into this behavior of the probes, at this

time, was unwarranted (see Appendix IV).

Injection of the tracer into the system is a very important part of the

experiment, and if not done properly could negatively affect the results of

the experiment. To this end, careful consideration was given to how to inject

the tracer, where to inject the tracer and how much of the tracer was to be

injected. The amount of tracer injected needed to be small in respect to the

volume of the tank (< 0.10 vol. percent). This insures that the injection has

the least effect on the mixing flow patterns, and the relative integrity of

the system is unchanged. The injection point needed to be a point that could

be standardized for all experimental configurations, and insure that the tracer

entered the mixing flow pattern as quickly and with the least disturbance possible. Thus, the injection point was selected to be 0.1875 x D above the impeller, and 0.375 x D away from the impeller shaft center (see Figure 8).

Other injection points are of course possible, but a study of injection points

was felt to be beyond the scope of the current experimental work.

The only remaining question is how to inject a standard amount of tracer

reproducibly in a substantially short amount of time (< 0.75 s). This was accomplished by the use of a tracer addition system (design help from S. J. Khang). This system consisted of two separate loops with a common calibrated

tracer loop of 0.0107E-3 m^ (0.0897 vol. percent of total tank liquid). The

9
first loop was designed to flush and fill the calibrated tracer loop with the

tracer. The second loop ran continually, taking a small amount of liquid out

of the tank, and then putting it back in at the injection point (approximately

1.07E-5 m^/s (0.17 gpm)). The suction point was located in an area of good

mixing 180 deg away from the injection point (see fig. 8). At the appropriate

time, the tracer was flushed from the calibrated tracer loop, and into the tank

at the injection point. The time for complete injection, out of the addition

system and into the tank was 0.6 seconds. To insure reproducibility, the

addition system was computer controlled, and rigorously tested before use in

the experiments. The system only failed once in 588 experimental runs. The

design of this system is such, that by replacing one calibrated loop for

another, differing amounts of tracer could be added. The system will also

work with a variety of tracers and at a variety of injection points with only

minor modifications (see fig. 9).

CALIBRATION AND ACCURACY

Developing appropriate equipment is not enough to insure a successful

experiment. It is also important to organize the experiment in such a manner

that the most and best information possible is obtained (see table 1). For

the experiments that will be performed, it is therefore essential that the

location of the probes in the mixing vessel be carefully thought out. Probe

location should be such that the four probes being used in the vessel give the

most coherent picture of what is actually happening in the mixing vessel. In

addition, the probes must be properly calibrated and the reproducibility and

accuracy of their responses verified.

Probe Location:

Once the system geometry is established, it is important to decide where

the probes should be located in the mixing vessel such that the largest amount

of information is obtained for an experiment. This can only be done if the

flow patterns and mixing vessel geometry are carefully considered. Another

point of importance is the physical positioning of the probes. It is essential to establish a technique for reproducibly positioning the probes, such

that placement of the probes can be repeated.

Theoretically, placement of the probes should be performed in such a way

as to most clearly show what is occurring in the mixing vessel. Because the

probes are measuring a very small volume in respect to the total system

10
volume, probes should be placed at points in the mixing vessel which represent

where the mixing will be best, and points where the mixing will be the

poorest. These positions in the vessel will be related to the vessel geometry

and the flow pattern established (Voncken, Rotte, Houten, 1965). Best and

worst locations will vary with changes to the mixing system parameters, and

thus probes should be positioned so as to best note changes in the system.

Absolute positioning in the best and worst locations is not realistically

achievable due to these locations' variability, and approximations of these

positions must be used.

Two types of flow patterns are observable while performing flow

visualization studies (see Appendix V). These are axial and radial flow.

Although it was not possible to create perfect axial or radial flow when

performing the studies, the general flow pattern could be established in such

a way that it approximated what was desired. Flow patterns were established

by using different impellers (flat and pitch (45 deg) blade turbines) at

specific C/T values. Flow reversal could be found for a given impeller by

varying the C/T value until the flow pattern changed from axial to radial or radial to axial flow. Thus, using a flat blade turbine at a C/T of 0.13

created axial flow, while changing the C/T to 0.33 reversed the flow pattern to

a radial one. In the case of the pitch (45 deg) blade turbine, a C/T of 0.33

developed axial flow and a C/T of 0.50 developed radial flow. It is important

to consider the possible flow patterns carefully when placing the probes.

In locating the probes for our experiments, the vessel geometry, location

of the intake and outlet of the tracer addition system, and the assumption

that both axial and radial flow were possible, had to be taken into account.

These criteria, coupled with the physical limitations of the probes, led to

placement of the four probes in the following manner:

1) Probe #3 was placed in front of the baffle which was 290 deg away (in the

direction of impeller rotation) from the tracer addition point. It was located close to the wall of the vessel, and 0.28 times the vessel

diameter from the bottom. This location was meant to represent an area

of good mixing near a baffle which was as far away from the tracer

addition point as possible. Closer positioning of the probe to the

tracer addition point (i.e., a radial location to the tracer addition

point of > 290 deg) would allow the probe to see back-mixing at the time

of addition. The back-mixing information would distort information

regarding the overall mixing in the vessel.

11
2) Probe #4 was positioned behind the baffle where probe #3 was located, at

the same distance from the vessel wall, and the same height from the ves- sel's bottom. Positioning the probe at this location was meant to represent an area of moderate to poor mixing. It was also meant to show the

effect that baffles have on mixing.

3) Probe #5 was located approximately 175 deg away from the tracer addition

point. It was also located away from all baffles, positioned near the

vessel wall, and approximately 0.28 times the vessel diameter away from

the bottom. This location was meant to represent an area of good mixing,

away from the effects of baffles and positioned such that circulation

information (when compared to probe #3) could be obtained.

4) Probe #6 was positioned directly above probe #5, near the vessel wall and

essentially on the surface. This location represents an area of poor

mixing in the vessel. The probe was positioned such that it could be

directly compared with probe #5 (an area of good mixing), and such that

it would indicate the extreme in regards to the difficulty of mixing in

the vessel

Probe location was determined by the use of a three coordinate

measurement system. In this system, each probe was located by its radial

location (angle) about the vessel, its distance from the vessel center and its

height from the vessel's bottom (see fig. 4). Special measuring tools were constructed to insure accurate placement and replacement of the probes and the

tracer addition system's inlet and outlet. The baffles were used as reference

points for the radial measurements with the baffles being placed at 90 deg

intervals starting at 0 or 360 degrees. The angle increased in the direction

of impeller rotation. This system for probe location was quick, simple, and

reproducible, and proved accurately repeatable when attempted by a number of

different individuals (±6.4E-3 m in any direction) (see table 2).

Probe Calibration:

Calibration of the conductivity probes is the next logical step once the

geometry of the mixing system has been established. Calibration of the conductivity probes is a relatively simple, although time consuming, process in which

probe responses are recorded as the dependent variable against the independent

variables of NaCl concentration, pc-board meter reading, and temperature.

12
The first step in the calibration process is to develop an equation which

will relate the pc-board meter reading to the actual voltage of the circuit's

output sine wave. This voltage may be observed as the amplitude of the sine wave generated by the oscillator-amplifier part of the circuit. By setting

the pc-board meter to read specific values, and using a voltmeter to record

amplitude values, a table of data may be generated. A statistical analysis

using F-factors can then be used to determine linearity (see fig. 10), and

an equation for each pc-board generated. These equations are independent of

the probes and should remain constant so long as the circuit components do not

change significantly. The equation will have the following form:

general form: SA = (Msa MR) + Bsa [1]

where: SA = signal amplitude, Msa = signal amplitude slope, MR = meter

reading, and Bsa = signal amplitude intercept (see table 3).

The next step in the calibration process is to zero the probes in deionized water. The actual zero point was specified as +3.5 volts. This was

done so that the maximum possible range of response was used for each probe.

Meter readings for all pc-boards were set at a value of 50.00. This was thought to be a good average value for the sensitivity range in which the

probes would operate. Use of the computer allowed for highly accurate adjustment for probe zeroing (±0.02 volts).

After the probes were zeroed, standard salt solutions 4.0E-4 m^ (400 cc) were prepared at three different temperatures. Salt solutions were made with

0.00, 0.02, 0.04, 0.06, 0.08, and 0.10 weight percent NaCl in them. The

temperature of these solutions was then regulated to a specific value for the

calibration run. The temperatures used were 19, 24, and 29 degrees Celsius.

This range of temperatures was felt to cover all possible ambient conditions

which might occur in the laboratory environment.

With the salt solutions prepared, all probes being calibrated were placed

in one of the thoroughly mixed solutions at the specified temperature. Probe

responses were recorded by the computer with the pc-board meter readings being

set manually to sequentially different values. An average of 1000 actual

points was used to represent the probe response. Meter values were varied

from 10 to 160 in steps of 5. The subsequent data obtained could then be

analyzed for linearity, and equations generated (see table 4).

Six probes were put through the calibration routine at the six different

concentrations and three temperatures. Probes #1 and #2 were homemade probes

13
which proved less sensitive and less reliable than the commercial probes (#3,

#4, #5, and #6). For this reason, the homemade probes were not used in further

experimentation, and only the tested and calibrated commercial probes were

used. Recalibration of the probes after six weeks of intensive experimentation showed no degradation with less than a 1 percent change in the probe response

for probes #3, #4, #5, and #6.

The configuration of probes and pc-boards was also an important consideration. The probe response could vary depending upon the pc-board it was attached to. It had to be determined if a probe would respond with a cleaner, more accurate and more sensitive signal if it were attached to a specific pcboard. Calibration tests were thus run with all the possible configurations

of pc-board and probe. The configuration which was selected as the best possible for probe responses, for the commercial probes used, is as follows:

With the configuration selected and the data collected, the linear equations

for the probe responses could be formulated. Using probe #3 as an example,

the following equation was formulated for a 0.04 weight percent solution at 24

deg C.

where: PR = probe response, Mpr = probe response slope, MR = meter reading

and Bpr = probe response intercept (see table 5).

Because there is a limited range of responses for a given sensitivity,

not all values for probe responses were used in formulating the equations.

Only those responses which had meaning (i.e.

,

were not outside the range +3.5

to - 10.24 volts) were used. Thus, in the above case, only nine actual res- ponses were used to formulate the equation. This indicates that the maximum

useful sensitivity for these conditions corresponds to a maximum meter reading

of 50 (10 + 5 • 8) (initial reading + change in reading degrees of freedom).

This also shows the only portion of the responses which fit a linear model

(see fig. 11).

Probe Configuration:

pc-board # probe #

1

2

3

4

3

4

5

6

probe response = -0.273 meter reading + 3.84

degrees of freedom = 8

general form: PR = (Mpr • MR) + Bpr [ 2 ]

14
Determination of temperature conversion factors was done graphically (see

fig. 12). Two conversion factors were obtained (see table 6):

1) Ks = change in slope/°C change in temperature.

2) Ki = change in intercept/°C change in temperature.

These values are necessary if accurate conversion to concentration information

is to be obtained from the raw data. Use of temperature conversion factors is

done in the following manner: adding temperature conversion factors to equation [2]

PR = Mpr[Ks(T - Tbase)] • MR + Bpr[Ki(T - Tbase)] [3]

where: T = temperature of the experiment (°C), Tbase = base calibration

temperature (24 °C).

With the calibration information obtained as described, and the equations

which were subsequently generated, the concentration can be calculated. This

is done by using the following technique:

1) A final concentration for a set of experimental runs for the mixing

vessel is determined.

2) By a step-wise analysis the meter reading value for the most sensitive

pc-board/probe set is determined.

3) The meter reading value determined is converted to voltage based upon the

signal amplitude equation [1].

4) Meter reading values for the other probes are backcalculated from the

voltage found in step 3 (SA) by use of modified equation [1].

MR = (SA - Bsa)/Msa [4]

5) All pc-boards are set to the appropriate meter reading values, and the

experiment is run.

6) For conversion to concentration, theoretical probe responses are calculated based upon the voltage (SA) and the temperature at which the ex- periment was run (T). This is done for all calibration concentrations

(i.e., 0.00, 0.02, 0.04, 0.06, 0.08, and 0.10 weight percent).

For any single concentration and any one probe:

Substituting equation [4] into equation [3]:

PRt = Mpr[Ks(T - Tbase)] • [(SA - Bsa)/Msa] + Bpr[Ki(T - Tbase)] [5]

where: PRt = theoretical probe response at a given concentration,

voltage (SA) and experimental temperature (T).

15
7) Once all of the theoretical probe responses for each probe at the six

concentrations are calculated, a step-wise analysis is used for conversion

of each data point. Each point is fit into the appropriate range between

theoretical probe responses and corresponding calibration concentrations,

and converted to concentration values. For instance: A point probe res- ponse falls into the range between theoretical probe responses 3 and 4.

If this is the case, then the following occurs:

m = (calib. cone. 4 - calib. cone. 3)/(theo. probe response 4

- theo. probe response 3)

b = calib. cone. 4 - m theo. probe response 4

and

point concentration = (m point probe response) + b

For ease of analysis, the starting concentrations for all probes are nor- malized to a single value. This constitutes a maximum change in the

starting concentration curves for any probe of less than 2 percent.

In summary, probe calibration is a time consuming operation that, if done

correctly, need not be repeated often. After six weeks of extensive use, no significant change in response of the probes (#3, #4, #5, and #6) was observed. The probe calibration process consists of three distinct parts.

These parts are the calibration of the meter reading values for each pc-board,

the calibration of the probes for the various concentrations, and the

establishment of temperature correction factors for the probes. It is also

necessary for experimentation purposes to select and maintain a standard

configuration of probe to pc-board. In addition, selection must be made such

that operating conditions of final concentration in the mixing vessel and

experimental temperature of the mixing fluid are such that they will insure

that the calibration conversion equations are usable. In this manner, results

are given as concentration. Concentration results are easily comparable to

other similar work, and readily understood by members of the mixing community.

Reproducibility And Accuracy

In order to have a successful experiment, the measurement devices should

be accurate, reliable, and results should be reproducible. In the case of the

conductivity probes, this is doubly important because the measurement technique

is not only desired for the specific experiment, but also as a standard method

for measuring mixer performance. To this end, the probes' accuracy.

16
reliability, and ability to reproduce information were severely tested.

Reliability is the ability of a system to perform repeatedly without failure. Prevention of failure is an important aspect to consider in any system

that will possibly have an industrial application. The probe system is com- prised of three essential components. They are the probe, the probe circuit

board, and the wiring connecting them. A failure of any part constitutes a failure of the probe to provide adequate information. Reliability was based

upon the 588 experiments run under laboratory conditions throughout the course

of the investigation. The rate of failure for probes #3, #4, #5, and #6 are

as follows:

Probe #3 5 failures 0.85%

Probe #4 8 failures 1.36%

Probe #5 17 failures 2.89%

Probe #6 3 failures 0.51%

Total 33 failures 5.61%

In any experimental setup there are inevitably going to be failures. The

above rates are very low, and well within the realm of acceptability for

experimental design (Mendenhall, Scheaffer, 1973). Failures of the probes were generally due to faulty connections between the probe and its

accompanying pc-board. No failures were due to the actual probe failing, and

only one failure was caused by a circuit malfunction (op-amp burned out).

Accuracy, in experimentation, is the ability to obtain expected or known

values. In the blending experiments the known values are the final

concentrations of NaCl. These values can be readily calculated by knowing the

weight of liquid in the mixing vessel and the amount of NaCl added for each

run. The general formula for this calculation is as follows:

(S-N/(V + S-N)) 100 = W

where: S = the amount of NaCl/run (1.029 g), N = the number of salt additions, V = weight of the liquid in the mixing vessel and the recirculation

loop (10830 g) and W = the weight percent NaCl in the mixing vessel after N

additions (see table 7) [there is a maximum 0.7 percent error in the

calculations due to volume consideration in the addition loop].

In all, 49 runs were made at each of 7 different concentrations. All

probes were used in each run. A correlation matrix shows that only the intended concentration is of consequence when observing end-of-run, probe res- ponse concentrations. The variables rpm, impeller type and C/T do not affect

final concentrations in the mixing vessel. Variation in response from probe

to probe was less than 5 percent, such that all probe responses could be compared to

17
the expected final concentration by averaging the probe responses first, and

then comparing them (see table 7). The percent errors between the observed

concentrations and expected concentrations were less than 2 percent except for the case of the first NaCl addition. This error was 3.8 percent, and is attributable to

impurities in the addition system at the start of the experiment (see table

7). These low percentage values indicate a higher than average degree of

accuracy in the experimental method and the measurement devices.

Reproducibility is the ability to obtain a given result if the experiment

is repeated using identical conditions. Reproducibility was tested for the

conductivity probes by observing the final concentrations for each run. As in

the accuracy tests, 49 runs at each of the 7 concentrations were used to

evaluate the probes' response reproducibility. Ranges of responses varied

less than 4.5 percent from the calculated sample mean, except for the case of

the first NaCl addition where possible impurities in the addition system

broadened the range to 11.9 percent. All probe responses fell within a 95

percent confidence interval generated about the sample mean. The combination

of a small variation in the range of response and the consistent appearance of

probe responses inside of a 95 percent confidence interval are good

indications of a reproducible system (Plane, 1977).

As is the case with all experiments, it is important to mention sources

of error in the experiments. In the mixing experiments, error sources can be

found in the establishment of the liquid level in the mixing vessel, the

makeup of the NaCl solutions, the addition of the NaCl solutions, the setting

of the impeller rpm, the reading of the voltage output from the probes, and

any roundoff errors generated by the computers' manipulation of the data. An

additional source of error is in the probe calibration curves, the temperature

readings, and the assumptions used concerning calculations when evaluating

probe responses. Obviously, human involvement in the placing of probes,

filling of the mixing vessel, makeup of the NaCl solutions, and establishment

of appropriate rpm values are all error sources. However, it is important to

note, that whenever possible, automation was used to reduce error, and the

statistical analysis substantiates the success of this practice.

In summary, the use of automation significantly reduced error sources to

the point where the experiments proved to be very reproducible with highly

improved accuracy. A sound, well-thought-out experimental design, using

tested hardware

18
and solid state electronics, provided probe responses which were highly reliable. Some error sources exist, but these have been kept to a minimum, and

results show them not to have a significant effect on the information obtained.

PROCEDURE

The procedure for the experimental runs consists of three parts. They

are the preparation of the salt solution, the preparation of the equipment,

and the actual running of the experiment. Much of an experimental run is

controlled by the computer, but operator responses to computer prompts are also necessary. The following paragraphs will describe the three parts of the

procedure.

The salt solution is prepared by first determining the final desired con- centration in the mixing vessel. For our experiments this value was 0.06

weight percent. This value was determined to be optimum for probe responses

throughout a set of experimental runs. The final concentration in the mixing

vessel should not exceed 0.10 weight percent because calibration data was not

taken beyond this level. The next step is to decide the desired number of

salt additions for the experiment (7 salt additions were used, one addition/run). Now, the weight of salt and the weight of water in each

injection must be determined. This is done by solving two equations in two

unknowns. The equations are as follows:

(1) (S • 7)/(V + (S • 7)) = 0.0006

(2) S + W = CV Den

where:

S = weight of salt in the calibration volume in grams,

W = weight of water in the calibration volume in grams,

V = weight of water in the mixing vessel in grams,

CV = Calibration volume in cm3, (10.7 cm3) (0.0107E-3 m^).

Den = salt solution density, and

7 is the number of additions to be made.

Once values for S and W have been determined, a salt solution should be

made with 20 times the volume of that which you plan to add to the mixing vessel. This is because there is waste when flushing and refilling the calibration loop.

19
The preparation of the equipment consists of the following steps:

(see fig. 9 for addition system information)

1) Turn the probe circuits on. They must be on for at least one (1) hour

prior to the running of an experiment in order to reach an equilibrium

state.

2) Turn on the oscilloscope, multiprogrammer, salt addition system and weigh

scale at least ten (10) minutes prior to the running of an experiment.

3) Zero the weigh scale.

4) Open the air valves for the salt addition system.

5) Make sure that the inlet to the salt-side of the addition system is immersed in the prepared salt solution. The outlet should be positioned

over an empty beaker.

6) Fill the mixing tank to the indicated level such that the appropriate Z/T

ratio is established (usually Z/T = 1.0).

7) Prepare the salt addition system. Put the computer/manual switch into

the 'manual' position. Turn the salt side pump (#1) on with the calibration loop closed. After 15 seconds, operate the four-way valve (#1) and

open the calibration loop. Run in this position for 15 seconds, and then

close valve #1, isolating the calibration loop with salt solution in it.

Continue to run for 15 seconds more before turning off the salt side pump

(#1). Return the switch to the 'computer' position.

8) Load the computer with the experimental program. This completes preparation for the experiment.

To run the experiment, the following are done:

1) Run the experimental program. It will ask you to answer certain questions, and perform certain tasks.

2) After prompt: Input the time and date.

3) After prompt: Input which mixing vessel is being used.

4) After prompt: Input the number of times salt solution will be added before changing the mixing vessel liquid. This values should correspond

with that used to make the salt solution (i.e., 7).

5) After prompt: Input the experimental run's name. The nomenclature for

this is a letter (R-Z), followed by the date (month then day), followed

by the salt addition number, [example: first salt addition on May 12 =

R5121] You enter only the first letter and date, the computer inputs the

salt addition number.

20
6) After prompt: Input the temperature of the liquid in the mixing vessel

(degrees C).

7) After prompt: Input the incremental amount of salt (S) in grams to be

added in each run (1.029 g).

8) At this point, the computer will ask you to 'zero' all probes to a value

of +3.5 volts with the probe meter set at 50.00 for all probes. The

probes should be in deionized water appropriately positioned in the

mixing vessel. The value of +3.5 is selected to give the probe resistivity the maximum possible range for response (+3.5 to -10.24 volts). The

meter reading of 50.00 is an average value which approximates the possible

values which might be used for an experiment. The meter reading is directly proportional to the amplitude of the circuit carrier wave for the

probe signals. Fifty is also the value at which the probes were calibrated, and is therefore an essential zeroing point if the conversion

routines are to be used.

9) After the completion of step 8, the computer will calculate what meter

values should be used for all probes to insure maximum sensitivity for

the experiment. These meter values are based upon the final mixing

vessel concentration. Each probe must be adjusted to have the

appropriate meter value. This meter value is different for each probe

because each probe is slightly different, as is each probe circuit.

10) After prompt: Input any desired changes to the default values given for

the geometric parameters (see fig. 13).

11) After prompt: Input the number of data points desired (1000 points were

taken in our experiments), and the run time in seconds. The run time must

be based upon the rpm value chosen for the experiment (i.e., slower rpm

values need longer run times {50 rpm - 200 s, 150 rpm - 75 s, 300 rpm -

30 s}).

12) After prompt: Input the rotation speed (rpm).

13) All the preliminary information has now been entered, and the experimental

run is ready to begin. The computer will tell you it is ready to take

the 'tare torque' measurement, and ask that the mixer be turned on at zero rpm. This measurement is used to establish a base point from which

the power requirement for mixing can be calculated.

21
14) When the 'tare torque' measurement is complete (approximately 10 s), the

computer will ask you to set the mixer to the experimental rpm value

which you previously specified. It will then ask you to perform several

visual checks on the equipment to insure that everything is in order to

proceed. Once you verify that the experiment is indeed ready to run, the

computer will start the experimental run. 15) The computer runs the experiment in the following manner:

a) The addition system is activated, and all valves are placed in their

start positions. The salt-side pump in the addition system is

started, and the salt solution flushes and then is trapped in the

calibrated loop. The salt-side pump is then turned off.

b) The mixing vessel pump is turned on and allowed to run for 10 seconds

until its effect on the flow patterns in the mixing vessel, if any,

have reached equilibrium.

c) The data collection system (i.e., multiprogrammer) is activated, and

data collection is started based upon the number of points desired

and the total run time for the experiment.

d) Standard conditions data is collected for 1/10 of the total run

time. After which time the calibration loop, with the salt solution

in it, is flushed into the mixing vessel with fluid from the mixing

vessel

e) At the end of the total run time, data collection stops and the

addition system is deactivated with all valves being placed in the

appropriate positions, and all pumps being turned off.

16) After the experiment is completed, the data is first converted to all

positive numbers (for ease of calculations), and then displayed for

visual inspection. Display consists of a summary of information

regarding the experimental setup, and a graphical representation of the

experimental run (see fig. 14).

17) If there are no problems found with the visual inspection, then the

computer will store the resistivity, or raw data, on a floppy disk. The

information thus stored may be retrieved at a later date for conversion

to concentration data and subsequent analysis.

22
18) The computer now allows for conversion to concentration data. This

conversion is based upon calibration data for each probe and takes into

account the amplitude of the circuit's carrier wave, the expected final

salt concentration, and the temperature in the mixing vessel at the time

of the run. It will also allow you to store the concentration data if

you desire.

19) At this point, one complete run has been made. The computer will return

to the start of the program and automatically set values for another salt

addition. No rezeroing of the probes should be necessary. The

experiment will be run as many times as you specified salt additions,

each time following the steps (6-18 excluding steps 8 and 9) as described

above.

20) After all runs have been made, the mixing vessel should be emptied and

refilled with deionized water such that all probes are completely covered.

The addition system should also be flushed of all salt solution and

filled with deionized water. These precautions are designed to minimize

contamination, minimize equipment failure, and promote the highest degree

of reproducibility and reliability in the experiments.

PROBE RESPONSE

The objective of these experiments was to select a measurement technique

and then prove its viability as a means of observing the mixing process. To

this end, conductivity probes were selected for use in simple blending experiments. The conductivity probes were tested for reliability, reproducibility,

and accuracy and found satisfactory. Observation of the probe responses can

tell much about the mixing process and how such variables as probe noise,

probe location, flow pattern, impeller type, C/T, rpm, and concentration

relate to the mixing process.

The data displayed in the graphs (see Appendix X) is an average probe

response obtained from seven identical experimental runs. The time of injection precedes the first noticeable change in probe #5 by approximately 5 seconds. Responses are initially normalized to a specific starting concentration, and then left alone to show each individual probe's response. Each

probe response curve consists of 1000 individual data points, each individually averaged. All probe responses for a given experiment were taken simultaneously so that, should it be desired, a point by point comparison of probe

responses is possible. Total experimental run times were predetermined and

23
kept constant for each of the seven experiments. Seven experiments were run

to insure that the average value would be within the 95 percent confidence interval

of the true average. The actual needed number of experiments is less than seven based upon a desired standard deviation of the mean of 0.0001 weight percent, and an expected standard deviation of approximately 0.0015 weight

percent. The actual standard deviation proved to be less than expected and,

as such, the experimental design of seven identical experiments was more than

adequate.

Signal Noise and Probe Response Time:

It has been shown that probe responses when related to final concentrations in the mixing vessel following an experimental run, are accurate, reliable, and reproducible. It now remains to examine the ability of the probe to

model the dynamic system of the mixing vessel during an experiment. To this

end, it is important to first investigate the signal noise and the probe res- ponse time.

Probe response time is the measure of how quickly the probe system records

a change in concentration. A simple experiment which plunges the probe into a stagnant salt solution and triggers a timer was used to determine a response

time. This time must be of a sufficiently short order that changes caused by

the dynamics of the mixing system are observed. Although extensive tests were

not made to determine probe response time, experimentation shows that the

probe response time is approximately 0.0005 seconds or less. This is the time

between when an event occurred and when the probe showed the event occurring.

For the experiments run, the fastest responses needed were 0.03 seconds.

Experiments run to test diffusion rates for the probes showed times in excess

of two hours. Therefore, it was felt that the probe response time was sufficiently fast enough to show the events or dynamics occurring within the

mixing vessel. This is easily observable in the data which was taken for the

experiments (see Appendix X).

Noise in the system can come from several sources. It can come from the

experimental apparatus itself, the probe circuits, or the data collection

setup. It is important to determine the effect that noise has on the

experiment and the data taken if any. Observable noise was recorded both

before and after the experiment. The noise level was found to be less than 5

percent of the signal in approximately 97 percent of the cases. This is

sufficiently low, such that experimental data taken is not significantly

24
affected by noise (Mendenhall, Scheaffer, 1973). Several trends were noticeable in the noise with regards to the independent variables used in the experiments. Noise was reduced with increased rotation rates. Signal noise was increased slightly with increased concentrations. The pitch blade turbine

experiments had higher noise levels on the average than did the flat blade

turbine experiments. And in the case of the flat blade turbine, increasing

the C/T reduced the experimental noise level (see Appendix X for an example of

noise data).

In summary, the probe response time is easily fast enough for system dynamics to be observed. The overall noise level is sufficiently low, such that

it does not affect the experimental results taken. Signal noise is affected

by experimental parameters, especially impeller type, concentration and rpm.

Further work is needed to verify these results, but time and resources were

not available. The observed noise in the experiment is such that it tends to

average out to zero. That is, there is as much noise on the positive side of

the response curve as there is on the negative side. This can readily be

observed in the accuracy of the probe responses when relating final concen- trations to expected results.

Probe Location:

The location of the probes is such that if the probes' response truly

models the dynamics of the experiment, then differences between probe

responses should be observable throughout the experimental runs. This is

indeed the case, as can readily be seen in fig. 15. Although the probe

response curves begin at the same concentration, and end at the same concentration, the path taken between these concentrations varies according to

the probe location (see fig. 15a (1-4)). Thus, probe #5 sees the injection

first, when it is most concentrated, and the resulting peak observed is the

highest. Probes #3 and #4 are close together and thus have similar curves. However, a noticeable lag is seen in probe #4 because it is behind the baffle

that probe #3 is in front of. Probe #6 shows only a slow rise to the final

concentration because it is the surface probe and mixing at that point is

relatively poor. In summary, the probe location affects the probe response as

a function of time, but not the final concentration. Probe location is a very

important consideration in the experimental design.

25
Flow Patterns

A closer examination of the probe response curves gives information about

the flow patterns in the mixing vessel. For example, the response curve for

probe #5 shows two distinct peaks approximately 16 seconds apart (see fig.

15)

. This 16 seconds is a measure of the circulation rate of fluid at the

vessel wall. A comparison of probes #3 and #4 shows the effect of a baffle in

the flow pattern. Probe #4 lags probe #3 responses because of the presence of

the baffle. A comparison of probes #5 and #6 shows areas of theoretically

good mixing and theoretically poor mixing respectively.

A comparison of response curves for different sets of parameters for the

mixing system can point out the effects of flow patterns on mixing (see figs.

15 and 16). In these cases, only the C/T value was changed. Notice that under

the conditions of the experiment which the second graph represents (see fig,

16)

, the probe response for probe #6 is quite different from the probe response

in fig. 15. The difference is an indication that much better mixing is

occurring at the surface of the fluid in the second case. The effect of the

baffle (comparison of probes #3 and #4) is not so clear for these two examples.

The lag is clearly defined in fig. 15, but not in fig. 16. The response of

probe #5, its initial peak, is less sharply defined in fig. 16, indicating

that the flow pattern at that point in the mixing vessel is not as well defined or is more turbulent than it was in the first case (fig. 15).

Special events can on occasion be observed in the data presented, as is

the case for a pitch blade impeller rotating at 50 rpm with a C/T of 0.33 (see

fig. 17). In this case, a small peak can be seen in probe #4's response at

approximately 10 seconds into the run. This peak shows back-mixing which oc- curred at the time of injection. Back-mixing is a momentary flow in the

opposite direction of the impeller rotation. Back-mixing was originally

detected by visual observation during the experiment. On the whole, however,

it must be noted that these probes were never intended for observing micromixing, and as such are inefficient in doing so. The intent of the experiments was to show that the probes could pick up basic trends in mixing and

discern flow reversal (i.e., a change in flow pattern from axial to radial

flow).

In summary, by observing the individual probe response curves and com- paring them to each other, it is entirely possible to gain an insight into the

mixing process, (use of multiple probes is a drawback for industrial

applications.) Effects of baffles, areas of good and poor mixing, and

circulation rates may all be observed. Although the probes are not meant to

26
measure micro-mixing, such disturbances as back-mixing at the time of injection

may be spotted. In addition, the comparison of separate experiments can demonstrate the effects of different flow patterns on the probe responses, and

thus the mixing process.

Impel ler Types:

Comparisons of the data for different experimental runs may also be used

to observe differences caused by the use of various impeller types. Only two

impeller types were used in the experiments; one being a flat blade turbine,

and the other being a pitch (45 deg) blade turbine. Under identical conditions of rpm, C/T and concentration, all probes showed observable differences

when different impellers were used (see fig. 18). The flat blade turbine

showed poorer mixing of the surface of the mixing fluid (probe #6) than did

the pitch blade turbine. The flat blade turbine also showed a more pronounced

baffle effect (comparison of probes #3 and #4), and sharper peaks for probes

#3, #4, and #5. Peak maximum values and circulation rates are essentially the

same for both the flat and pitch blade turbines. From these observations it can be concluded that when the impeller type is allowed to change, and all

other conditions of the mixing experiment are being held constant, an observable difference is seen in the probe responses.

C/T Values:

Not unlike the impeller type, changes in C/T can also be observed by

looking at the probe response curves (see fig. 19). The most apparent difference is probe #6, which shows the effect of changing the C/T on surface

mixing. Probe #5 shows a false peak, and less clearly defined peaks and valleys in the case where the C/T value is low (0.13). The higher C/T value

(0.33) shows a much better delineation between probes #3 and #4, whose com- parison can be related to the effect of the baffle between them. Therefore,

it is valid to say that C/T variations do affect the appearance of the probe

response curves.

RPM:

Changing the rotation rate of the impeller changes the probe response

curves in two different ways (see fig. 20). First, the length of time in

which the mixing experiment runs varies inversely with the rpm. That is, as the rpm increases the length of time needed for the mixing experiment to occur

27
decreases. The second observable change is in the probe response curves themselves. Changes in probe #6 (the surface probe) are most apparent, with mixing

improving as the rpm increases, until at 300 rpm, the response curve for probe

#6 looks fairly much like those of probes #3, #4, and #5. The probe response

for probe #5 becomes less sharply defined with a decreasing maximum first peak

value as the rpm increases. This indicates a quicker dispersion of the tracer

into the mixing system at higher rpm values. Probes #3 and #4 also show a reduction in maximum first peak values as the rpm increases. They also show

an increased separation of peaks as the rpm increases, indicating that baffles

have an increased effect at higher rpm values.

In summary, changing the rotation rate through three distinct levels

(i.e., 50, 150, and 300 rpm) produces noticeable changes in the probe response

curves for all probes with differences in response being greatest for probe

#6, but changes being quite observable for probes #3, #4, and #5. Increases

in the rotation rate also decrease the time needed to run a mixing experiment

and have some affect on the flow pattern.

Concentration:

Another variable which must be considered regarding its effect on probe

responses is the average concentration during an experimental run. As has

been previously discussed, the concentration in the mixing vessel at the time

of an experimental run affects the calibration of the probes and subsequent

conversion of raw data into concentration data. It also affects the noise

level in the experiment. The only other observable effect of concentration

levels in the mixing vessel on probe responses is a quantitative change in the

magnitude of the response. That is, as the average concentration in the mixing

vessel increases, the probe responses increase proportionally.

MIXTIME ANALYSIS

It has been shown through our experimentation that the dynamics of the

mixing system are observable through investigation of probe responses. The

information obtained is of a qualitative nature, and is meant only to point

out what the probes can and cannot 'see' in the mixing system. A quantitative

analysis of the data is useful for demonstrating what information can be

gained through the use of the measurement technique and/or the experimental

apparatus. A quantitative analysis can be performed using mixtime as a dependent variable, and considering some of the independent variables that

affect the mixtime such as the probe location, flow pattern, impeller type,

C/T, rpm, power, and concentration (see^^able 8).
Determination of Mixtime:

Determination of the mixtime as the dependent variable is a very important part of the analysis of the data. There are many techniques used to

determine mixtime, and unfortunately most of these are highly qualitative in

nature. An effort was made to make the mixtime estimates as accurately and

reproducibly as possible. A qualitative, graphical technique was used in this

study to determine mixtimes because work on a strictly quantitative technique

is beyond the scope of the work for this project. Possible quantitative

techniques are discussed in a later section of this report.

The graphical technique which was used selected a mixtime within a range

of approximately 10 seconds. This range was found by looking at the probe

response curves for each probe and estimating visually what the mixtime was likely to be. The mixtime is the point in time at which the response curve

ceases to change with respect to concentration. After the range was determined, this area of the graph was expanded, and the final estimate of the

mixtime was obtained by visual observation (see fig. 21). Use of this

graphical technique provided mixtimes which were consistent with one another

to within ±5 percent in 92 percent of all the experimental cases. This

consistency only held for probes #3, #4, and #5, with probe #6 being an exception. Probe #6 mixtime variations were not solely a function of the

technique used but, rather, a function of the experiments themselves (i.e., in some experiments, mixing was never completed for probe #6). Overall, it was possible to reproduce mixtimes to within ±10 percent for all of the

experiments run (see Appendix VI).

In summary, the mixtime was determined graphically by visual observation

for each probe. The values obtained were consistent to within ±5 percent in

most cases, excluding probe #6. Probe #6 mixtime determinations varied con- siderably due to the experiments and not the technique for determination.

Mixtime determination was reproducible for all probes to within ±10 percent

for all experimental runs. A strictly controlled technique of qualitative

mixtime determination provides adequate information, and allows for further

analysis of the effect of various independent variables on the mixtime.

Probe Location:

As has been previously noted through observation of the probe response

curves, probe location is an important factor in the information received for

an experiment. It is quite apparent that discernable mixing equilibrium is

not completed at all locations in the tank simultaneously but varies with

location in the vessel. 29
Because of this, probe location can be seen to have a strong effect on mixtime. Much can be learned concerning the flow patterns and areas of both

good and poor mixing by a comparison of the mixtimes for various probes.

A comparison of mixtimes for probes #3 and #4 shows the effect of a baffle

by measuring the mixtimes (time to uniformity) for a location in front of and

behind a baffle respectively. Mixtimes for probe #4 (behind the baffle) lagged

those of probe #3 by approximately 5 percent in 89 percent of the applicable

cases. Cases which were not applicable were those where C/T = 0.13 and the

flat blade turbine was used. This combination of C/T and impeller type produced a condition of extreme axial flow, which was observed in the flow

visualization experiments. (Appendix V explains flow visualization.) Under

extreme conditions of axial flow, probe #4 did not lag probe #3 significantly.

Baffle effects were apparently removed, at the level from the tank bottom of

probes #3 and #4, for rotation rates in the range of 50 to 300 rpm when

extreme axial flow conditions existed.

A comparison of probe #5 and probe #3 mixtimes shows probe #5 lagging

probe #3 in 67 percent of all cases. In cases where the flow pattern was

axial, 67 percent of the time probe #5 did not lag probe #3 irrespective of

impeller type used or rotation rate. From this information it can be con- cluded that turbulence caused by a baffle promote better local mixing in the area in front of the baffle. The effectiveness of the baffle is reduced under

axial flow conditions, and circulation rates become less important than flow

patterns when extreme axial flow is present.

Examination of probe #6 mixtimes is very useful in gaining insight about

the mixing process. A comparison of probe #6 mixtimes to mixtimes for probes

#3, #4, and #5 shows probe #6 mixtimes lagging all other probe mixtimes significantly in 75 percent of all cases, and 100 percent of the cases where radial

flow was not involved. It can be concluded, based upon mixtimes, that under

most conditions of rpm, impeller type and C/T, surface mixing is not as good

as the mixing at probe locations elsewhere in the mixing vessel.

In summary, probe location has a strong effect on the measured mixtime.

The effectiveness of a baffle can be determined by comparison of mixtimes for

probes in front of and behind a baffle. Baffle effects are minimized under

conditions of extreme axial flow. Circulation rates become less important

than flow patterns when determining mixtimes under conditions of extreme axial

flow. Surface mixing is generally poorer than mixing elsewhere in the tank,

with the exception of extreme radial flow in which surface mixtimes compare

well with mixtimes at other locations in the mixing vessel.

30
Flow Patterns:

Further investigation of probe #6 mixtimes can provide insight and information concerning flow patterns in the mixing system. Flow reversal can be

inferred for some cases based upon probe #6 responses. This is because both

radial and axial flow conditions may be observed by using the surface probe.

With only the C/T varying to create conditions of either axial or radial flow,

and all else being held constant, mixtimes changed thusly:

TABLE A

PROBE #6 MIXTIMES IN SECONDS

impel ler fl at pitch

flow axial radial axial radial

C/T 0.13 0.33 0.33 0.50

rpm mixtimes

50 172 174 122 82

150 42 44 54 30

300 21.6 20.3 16.4 15.5

Flow visualization experiments were used to determine impeller positions in

which either radial or axial flow conditions existed. For the pitch (45 deg)

blade turbine, axial flow was observed at a C/T of 0.33, and radial flow was observed at a C/T of 0.50. For the flat blade turbine, C/T values of 0.13 and

0.33 created conditions of axial and radial flow respectively. Insufficient

energy was put into the flat blade turbine system until the 300 rpm level for

a significant difference in mixtimes between axial and radial flow to be observed at the probe #6 location. Radial and axial flow differences were

easily observable from probe #6 mixtimes for the pitch blade turbine at all

rpm values tested (see table A).

Impeller Types:

Useful information was also gained concerning the effectiveness of one type of impeller over another. A comparison of probe #6 mixtimes with all

system parameters except impeller type held constant was made (see table A).

31
The C/T value was kept at 0.33 and the flat and pitch blade turbine experimental runs were observed. The flat blade turbine at a C/T of 0.33 produces a radial flow pattern, and has shorter mixtimes at probe #6 than does the pitch

blade turbine when the rotation rate is 150 rpm. When the rotation rate is 50

rpm, mixtimes are shorter for the flat blade turbine for probes #3, #4, and

#5, but longer for probe #6 (see Appendix VI). At the 300 rpm rate, the difference between the flat and pitch blade turbines is slight, with the pitch

blade mixtime being slightly less. This is possibly due to the fact that with

a C/T of 0.33 and the pitch blade turbine, the flow pattern is axial not radial.

In summary, with a C/T of 0.33 and rotation rates of 50 and 150 rpm, the

flat blade turbine produces shorter mixtimes than does the pitch blade turbine

for all probes with the exception of probe #6 at 50 rpm. At the higher rate

of 300 rpm, the difference in mixtimes is less well-defined with the axial

flow pattern of the pitch blade impeller giving a slightly shorter mixtime for

probe #6. It is important to note that power levels differ depending upon

which impeller is used.

C/T Values:

As has been previously stated and observed, with all else held constant,

a change in the C/T can produce a change in the flow pattern. Probe #6 is

most strongly affected by impeller location changes because of its position on the surface of the mixing fluid. Probes #3, #4, and #5 are affected to a much

lesser extent due to their close proximity to the impeller regardless of the

C/T value chosen, provided this C/T value is between 0 and 0.50. A change in

C/T may be used to change the flow pattern from radial to axial or axial to

radial. The other technique for changing the flow pattern is to use a different type of impeller.

RPM:

Mixtime as a dependent variable is most strongly affected by the rotation

rate of the impeller. The rotation rate is directly related to the energy

input into the system. If the energy to the system is increased with all else

held constant, it is reasonable to assume that up to a point, the mixtimes in

the vessel will be correspondingly shortened. This indeed can be seen in the

mixtimes for all probes, but especially for probe #6 (see table A). Probe #6,

as the probe on the surface, is in the position where the mixing is poorest

(considering all probe locations used) and, as such, changes at this location

are more dramatic and thus more easily observable than elsewhere. It can also

32
be seen that, at low rpm values, the rotation rates effect on mixtime is

strongly influenced by the type of impeller used.

Concentration:

The last variable for consideration in its effect on mixtimes is the average concentration in the mixing vessel during an experimental run. Analysis

of mixtimes as a function of concentration show that there is no significant

dependence on concentration in determining mixtimes (see fig. 22). Concentrations affect the probe response curves in the manner previously stated, but in no way affect the mixtimes. This is a wholly reasonable conclusion as no reaction is occurring within the vessel, and physical parameters of the system

should indeed have the greatest influence on mixtimes.

It must be understood that not all possible parameters were investigated

for their effect on mixtime. Also, those parameters tested were only evaluated

under a very small set of specific conditions. The intent was to show that

probe response curves could be analyzed for mixtimes, and these mixtimes could

in turn be analyzed to determine the effect of various independent variables

on mixtime. From this analysis, conclusions could be drawn regarding the

mixing process. The methodology used for experimentation and the technique

used for analysis did positively show that information gained in this fashion

is appropriate for enhanced engineering design, trouble shooting, and general

understanding of the mixing process.

TORQUE MEASUREMENTS

In mixing experiments it is important to measure the torque or, more

accurately, the power input into the system. Measuring the power input is

important for two reasons. First, any design of batch mixing equipment must

take into account the operational costs of running the equipment. Trying to

develop the most efficient design that fully performs the desired work demands

knowledge of the energy requirements for the system. Second, the use of power,

or of the power number , to develop correlations has become one of the few

standards about which members of the mixing community can communicate. Thus,

*5<C torque measurements, as a measure of power , are taken so that the

^ 3 5

Power number: Np = P • g/(p • N • D ) where: Np = power number, P = power, g = gravity constant, p = liquid density, N = impeller rotation

speed, D = impeller diameter (Oldshue, 1983).

Torque to power: Hp = [(torque (in-lbs)) • (rpm)]/63000

where: Flp = horsepower (Chemineer-Kenics, 1981)

33
ability to create practical, energy-efficient designs is possible, and

information gained through experimentation may be properly communicated to

interested parties in the mixing community.

Power measurement in a batch mixing system is done in essentially five

different ways. First, a wattmeter may be used to measure the current and

voltage (power being derived form this information) for the mixing motor. The

problem with this technique is that readings at low levels are difficult, and

system losses such as the bearings and gearbox are not accounted for. The

advantage of a wattmeter is that it is portable and may readily be used at an on-site facility.

A second method for determining the power is done by using a weigh scale

(micro-balance) and a torque arm. In this method, a weight is hung from a torque arm on the motor, with the motor mounted and balanced on a "frictionless" bearing. Variations in the weight, as accurately read by the electronic

weigh scale are easily interpreted as torque values. These values are then

converted into power by knowing the rpm value for the motor (see fig. 7). The

advantage of this system is that small torque values are easily obtained, the

accuracy is high (within 7.77 percent for the flat blade turbine, and 5.25

percent for the pitch (45 deg) blade turbine), gearbox losses are accounted

for, and the equipment for taking the measurements is simple and relatively

trouble free. The disadvantage is that the setup is impractical for field

use, and sensitivity is limited by the ability to choose the correct hanging

weight.

Another technique for measuring torque is the use of a hollow torque ring.

In this case, the motor is mounted to a hollow ring which in turn is mounted

on a rigid structure. The impeller shaft runs through the center of the ring,

and torque is calculated by using a strain gauge to measure the torsional

deformation in the ring. This technique gives accurate responses (approximately ±5 percent as stated by manufacturers), and is usable on fairly large

size units. However, the range for any torque ring is small, so that careful

sizing is necessary if realistic results are to be obtained. Use of a torque

ring in the field would be difficult but not impossible.

A fourth technique for measuring power is the use of strain guages mounted

on the impeller shaft. Both torsional and vertical deformation of the shaft

are measured, with torque values being calculated from this information. This

34
is a generally accepted technique for measuring torque. This method does remove errors caused by bearing and gearbox losses. The difficulty with shaft

mounted strain guages is that the reading must be taken off a rotating object,

the range for any one strain gauge is small, and calibration is difficult.

The final method used to measure torque is one in which the mixing vessel

or the mixer drive is mounted on a flat plate. The plate is in turn mounted

on a specially built cylinder attached to a rigid structure. Strain guages measure the torsional deformation of the cylinder as the top plate rotates

relative to the rigid structure. Torque values are then calculated from this

information. This technique gives very accurate information (within 5.98

percent of the expected value for the flat blade turbine, and 5.29 percent for

the pitch (45 deg) blade turbine) under a limited set of conditions. The

values obtained approximate more closely the actual energy put into mixing

than most other systems for torque measurement (i.e., taking into account

bearing and gearbox losses). However, a particular plate device will only

work for limited weights and tank sizes, and the absolute largest size is

still small on an industrial scale. The setup would also be difficult to use

in the field as most mixing vessels are secured to fixed structures, and most

vessels are not specially balanced about the center of the vessel.

Because the work being performed was of a laboratory nature, it was felt

that accuracy of reading, ease of operation, and reliability of the equipment

were of prime importance. For this reason, two methods for measuring the

torque were used. First, the weigh scale approach was used because of its

reliability (only 6 failures in 588 uses) and ease of use. Second, a torque

plate was installed because of its ability to obtain accurate information.

Calibration of the torque plate is easy, and the torque plate and the weigh

scale method may both be used at the same time. Thus comparison of techniques

is possible. The most realistic method for measuring torque in the field is

probably the wattmeter. However, testing of wattmeters on laboratory scale

equipment is inappropriate. It was planned to test wattmeters on the larger

scale 0.379-0.757 m^ (100-200 gallon) facility when it was built.

Testing of the two types of torque measurement devices was performed with

both flat and pitch (45 deg) blade turbines at different C/T values (0.13-0.50)

and three different rotation rates (50, 150, and 300 rpm) (see Appendix VII).

The change in power at different C/T values was minimal (< 2.5 percent) for

both the torque plate and the weigh scale techniques (see fig. 23). An initial

35
comparison of the theoretical (given by manufacturer), torque plate and weigh

scale horsepowers versus rpm showed that the weigh scale values were off by a factor of ten (see fig. 24). Examination of the calculations used to determine

the horsepower from the weigh scale readings showed that the calculations had

been set up for a 2000 gram hanging weight, when in fact a 200 gram hanging

weight had actually been used. A replot of the horsepower versus rpm for the

theoretical, torque plate and weigh scale values, after correcting the weigh

scale horsepower, shows that the torque plate and weigh scale readings are within 4 percent of each other, and both are approximately 17 percent lower

than the theoretical values (see fig. 25 and fig. 26). This 17 percent

difference corresponds to the approximate expected loss in the bearings and

gearbox. An additional plot of the power versus rpm shows that at any given

rpm, the flat blade turbine requires more power input than does the pitch (45

deg) blade turbine (see fig. 27 and fig. 28). Experimental data proved to be

highly linear, so only the linear plots through the data points are shown.

In summary, two different methods were investigated to determine the

torque in a given experiment. One method used a torque arm attached to the

mixing motor, with a hanging weight attached to the torque arm and positioned

on a weigh scale. The other method used a torque plate centered beneath the

mixing vessel, with information being obtained from strain guages. Both techniques proved accurate and reproducible over the range of rpm values (50-300

rpm), C/T values (0.13-0.5) and impeller types (flat and pitch (45 deg) blade

turbines) used in the experiments. Variation between methods of torque

measurement were less than 4 percent. Variation between these values and

those theoretical values provided by the manufacturer were on the order of 17

percent. This latter difference being attributable to bearing and gearbox

losses.

FUTURE WORK

As is the case with most research work, there is always more to be done.

Mixing research is no exception. Although the experiments run were very useful and provided a great deal of information, they only scratched the surface

of the mixing field. Mixing is an extremely complicated subject with a great

deal of diversity. To properly study even a small aspect of mixing demands

that a significant commitment be made both in terms of time and money. The

approach for the work done here was different from similar work done elsewhere

because the desired result was a methodology and analysis technique, instead

of a 36
correlation or body of data. This work is useful and should be continued with

emphasis being put on improving the existing experiments,- doing further

experimentation, and developing better analysis techniques.

Experimentation:

The experimental apparatus for the set of experiments run was designed

for flexibility, reliability, and reproducibility. Experiments showed that

the equipment met all these criteria. Further work needs to be done in the

calibration of the addition loop, the torque measurement technique, and the

makeup of NaCl solutions. Most of the work that needs to be done is in

carrying out additional experiments and data analysis.

The experiments that have been run are useful but not complete. Further

experiments need to be run for all process variables. Different types of impellers with different numbers of blades should be tested. A greater spectrum

of rotation rates should also be investigated. Impeller positions should be

changed at smaller intervals to gain greater insight into flow pattern generation. Probe locations should be varied to prove whether or not the selected

probe locations truly give the best representation of the mixing system. The

tracer injection point should also be changed to note its effect on the

response curves. Alternate concentrations should be tried to determine if the

probes respond well outside of the tested range.

Additional experiments should be run at different viscosities, using different materials for mixing with the same basic parameter set. Experimentation

should also be performed in different sized vessels to determine the difficulties in data collection and analysis caused by changes of scale. After a sufficient amount of information has been obtained for miscible liquid blending,

immiscible liquid mixing should be investigated. Other mixing systems of

liquid-liquid, liquid-solid, and gas-liquid should also be investigated. Further work will definitely include the use of probes other than conductivity

probes, and may include systems where chemical reactions and changes in

viscosity and temperature occur.

It is of course important to remember that the mixing field is very large,

and a research program must be carefully planned and organized if useful information is to be obtained, and the project may be accomplished in a reasonable

amount of time.

A reasonable step forward for this project would be to build a moderate

size 0.379-0.757 m^ (100-200 gallon) facility, perform the identical

37
experiments in the larger facility that have been performed in the laboratory

scale facility, and expand the experiments in the laboratory scale equipment

to include a wider variation of the parameters of probe location, impeller

type, C/T and rpm. Additional variables that should be looked at are Z/T,

D/T, baffles, and viscosities. A new set of experiments should be designed

for the sol id- liquid mixing system. All experiments run on the laboratory

scale should later be run on the moderate size facility, with some testing

being done at plant sites with the large scale equipment that exists there.

Data Analysis:

The data generated in the mixing experiments is typical of data generated

in many different kinds of experiments. The data is in the general form of a decaying sine wave but displays extensive non-linear type behavior. The analysis of this type of data is difficult at best. For truly useful information

to be obtained from the mixing experiments, it will be necessary to devise a much more quantitative method for analysis than the visual observation of

graphical data. Throughout the course of experimentation, many different

techniques have been tried to analyze the data. Most of these techniques were designed specifically to calculate a mixtime. Straight observation of the

data in a graphical format is one such method. Fitting the peak points of the curves to a decaying exponential and then calculating the rate of decay is

another. Looking for deviation from the final concentration value is another

alternative, and is possible in several different ways. An integration to

determine the rate of change of the area under the curve is also a possibility. In all, many methods were attempted, and the simple graphical

technique proved most reproducible, even though it is more qualitative than

the others. Strange perturbations in the data as well as the necessity to

make qualifying assumptions, detract from the other techniques tried. More

work is needed in developing a quantitative system of analysis for this type

of data. To this end, some work has been started.

One possible technique for analyzing the data is to use a strictly statistical analysis technique. In this technique, one would, as before, obtain a set of average probe response curves in the form of time versus concentration

for each probe. Each individual probe response curve would then be looked at on a point by point basis. A sum of the standard deviation squared (SSD)

would be calculated for the curve and then normalized to a value of one (1),

such that at each point in time along the curve a fraction of the total SSD

38
would be represented. The resultant point for point statistical information

can then be plotted against time (see fig. 29). Observation of the slope of

the curve generated, as well as perturbations in the curve, should give much

insight into the mixing system. Mixtimes would be calculated by starting at

the end of the experiment and backtracking the slope value until it varied

significantly for a statistically significant number of points. The use of

this technique sounds simple, but there are assumptions to be made regarding

the noise in the experiment, the effect that concentration has during the

experiment, what constitutes significance, etc. It is, nevertheless, an interesting analysis technique which bares further scrutiny (see Appendix

VIII).

In summary, the experiments investigated to this point demonstrate a viable approach for determining measurement techniques for mixing processes.

However, further work is necessary for a better understanding of the mixing

process and development of future measurement techniques. This work should

involve the use of an expanded parameter list with a broader range of testing

for each parameter. Scale-up facilities are needed as is testing of different

mixing systems (i.e., solid-liquid, etc.). Finally, analysis of the data collected must be improved if the measurement technique is to provide truly useful information.

SUMMARY

Work for this project was carried out in three basic areas. First, an investigation of the literature was made to determine the scope of work to be

done, the mixing system to be used, the components to be mixed, and the type

of measurements to be made. Second, based upon knowledge gained from the

investigation of the literature, an experimental apparatus was built, keeping

in mind the criteria of safety, automation, reliability, reproducibility, ease

of operation, and the ability of the equipment to be used later by industry in

a plant environment. Third, experiments were designed, performed, and

analyzed in such a manner as to fulfill the goals of the project and present

meaningful information to the mixing community.

The objective of the project was to develop performance test procedures

and measurement techniques for batch mixing systems. The performance tests were to be designed such that they would enhance understanding of the mixing

process, aid in facility design, and be useful for in-plant trouble-shooting

of batch mixing systems. Due to the complex nature and variety of the mixing

39
process, and the limitations imposed upon the project by time, money, and man- power constraints, it was necessary to carefully select which type of mixing

system was to be investigated, what parameters would be considered, what equipment would be used, and what analysis of the data would be performed.

The performance test which was established through the investigation of

the literature, and the help of a panel of experts (see Appendix I) is as follows:

1) Mixing system - miscible liquid blending with no reactions carried out at

ambient condition.

2) Mixing components = deionized water as the mixing fluid and an approximately 10 wt percent NaCl solution as the tracer.

3) Parameters = impeller type, C/T, RPM, concentration, probe location, and

power (torque).

4) Measurement technique = measurement of ion concentration by the use of

conductivity probes, measurement of power by the use of a tachometer and

torque arm/weigh scale combined apparatus (see Appendix IX).

The second part of the project was the design of the apparatus. The apparatus consists of three parts: the physical equipment, the data collection system, and the measurement equipment.

1) Geometric configuration (to be considered as a standard for laboratory

testing) is as follows:

Tank diameter (T) = 0.25 m (9.75 in) (range = 0.23-0.38 m (9-15 in))

Z/T =1.0 (range = 0.8 to 1.5)

C/T = 0.13, 0.33, 0.50 (range = 0 to 0.50)

Baffles = four baffles, 90 deg spacing, minimal bottom and

side clearance

Tank bottom = flat

Impellers = flat blade turbine with four blades w/d = 1/6,

pitch (45 deg) blade turbine with four blades

w/d = 1/5 {note: six bladed turbines were used

in the experiments}

Shaft = vertical shaft centrally located

Power = motor to establish 2.95 kW/m^ (15 hp/1000 gal)

2) Data collection system:

Hardware = high-speed, scientific computer with 32-bit internal

structure and an accompanying multi programmer with 5

A/D, 5 memory (4k), 1 timing and 1 relay cards

40
Software = interactive program for controlling the experiment,

collecting and manipulating data

3) Measurement equipment:

Probe type = conductivity (commercially available)

Probe circuit = for linearity, sensitivity, noise reduction and

the elimination of crosstalk (see fig. 6)

Probe number = four

Probe locations: (see table 2)

Probe #3 = in front of baffle

Probe #4 = behind baffle (same baffle as probe #3)

Probe #5 = area of good mixing (away from baffles)

Probe #6 = on surface above probe #5

RPM = tachometer attached by belt to impeller shaft

Torque = hanging weight on electronic weigh scale, tension from

torque arm on mixing motor

Injection = automated addition of tracer from 0.0107E-3 m^ (10,7 cc)

calibrated loop, injection located in area of good

mixing (see fig. 8)

The third portion of this project was the design, running, and analysis

of the actual experiments. A matrix type design of experiments was developed

such that the most information could be gained given the constraints of time,

money, and manpower (see table 1). Running of the experiments consisted of

first calibrating the probes, and then performing the experiments as specified

in the matrix design. Analysis consisted of first determining the accuracy,

reliability, and reproducibility of the probes, then analyzing the probe

response curves and finally performing a mixtime comparison analysis with the

independent variables in the system. Work was also done on alternate torque

measurement techniques.

Calibration and accuracy for the probes entail the positioning of the

probes, calibration of the probes for both temperature and concentration, and

a verification of the accuracy, reliability, and reproducibility of the

probes. It is not possible to position the probes in absolute locations of

best and worst mixing as these locations change dependent upon the system

parameters. Probes were positioned in locations where it was felt the most

information could be gained. Thusly, a probe was placed in front of a baffle

and behind the same one. A probe was placed in an area where good mixing

should generally occur, and in an area of poor mixing (see fig. 4 and

41
table 2). Probe locations were carefully determined using a three dimensional

coordinate system.

Probe calibration is a time consuming operation that, if done correctly,

need not be repeated often. After six weeks of extensive use, all probe res- ponses were within 1 percent of their previous values. The probe calibration

process consists of three distinct parts. They are: 1) Calibration of meter

reading values for each pc-board (i.e., the oscillator-amplifier sine wave

amplitude). 2) Calibration of the probe responses at different concentrations

(up to 0.10 wt percent). 3) Establishment of temperature correction factors

for the probes in the range of ambient conditions (19 to 29°C). In addition

to these three parts, it is also necessary to maintain a standard probe to

pc-board configuration, and run experiments in the range where conversion to

concentration values is possible (i.e., ranges of concentration and temperature).

In order to have a successful experiment, the conductivity probes should

be accurate, reliable and reproducible. In all, probes failed in only 5.61

percent of the runs, with probe #5 failing the most often (51.5 percent of all

failures). A probe failure is considered a failure of the probe, pc-board or connecting wiring. In all, 97 percent of the failures were due to failures in

the connecting wiring. Accuracy of results was high, with nearly all observed

concentrations falling within 2 percent of the expected values. Reproducibility was also high, with all experimental results falling within a 95 percent

confidence interval about the sample mean. Probe responses were examined for their ability to detect changes in the

mixing system. To this end, probe responses were observed and related to the

variables of probe noise, probe location, flow pattern, impeller type, C/T,

RPM, and concentration. The purpose of this phase of the analysis was to

qualitatively prove the viability of using conductivity probes as a means of

observing the mixing process.

A summary of findings for probe responses show that:

• probe response time is easily fast enough for system dynamics to be observed

• probe response noise is sufficiently low and of an averaging nature such

that it does not significantly affect information gained from the experiment

• probe response noise is affected by experimental parameters, especially

impeller type, concentration, and rpm

42
• probe location affects the probe response as a function of time, but not

the final concentration in the system

• comparison of individual probe response curves can show the effect of

baffles, indicate areas of good and poor mixing, show circulation rates

and indicate back-mixing occurrences

• probe responses are not an effective measure of micro-mixing

• comparisons of separate experiments demonstrate the effects of different

flow patterns on the probe responses

variations caused by different impeller types can be observed in the probe

responses when comparing separate experiments

• changes in the C/T change the flow pattern, and as such change the probe

response, as observed through comparisons of separate experiments

• probe responses are strongly affected by changes in rpm, both in curve

shape and response as a function of time

• probe responses are not significantly affected by changes in the average

run concentration, other than the obvious change in magnitude

Once it was established that probe response curves did indeed model the

dynamics of the mixing system, it was important to determine a method for

analyzing the data other than in a qualitative manner. To this end, mixtimes

were determined as the dependent variable, and subsequently related to the

independent variables of probe location, flow pattern, impeller type, C/T,

RPM, power, and concentration.

A summary of findings related to the mixtime analysis are as follows:

• mixtime was determined graphically by visual observation for each probe

to within ±5 percent of the sample mean

• probe #6 mixtime determinations varied considerably due to the nature of

the experiments and the location of this probe

• mixtime determinations were reproducible to with ±10 percent

• graphical mixtime determination, as described, provides adequate

information for further analysis

• mixtime varies according to probe location and experimental conditions

• probe #4 lagged probe #3 mixtimes by 5 percent in 89 percent of the applicable cases (applicable cases did not have extremely axial flow)

• mixing generally takes longer behind a baffle than in front of it

• probe #5 mixtimes lags probe #3 mixtimes when axial flow was not

present, this is an indication that under the right conditions, mixing in

front of the baffle is better than in the free area between baffles

43
• in cases of extreme axial flow, baffle effects are minimized and probe #5

and probe #3 mixtimes are comparable

• probe #6 (surface) mixtimes lagged all other probe mixtimes in all cases where extreme radial flow did not exist

• probe #6 responses are more dramatic for system changes

• probe #6 mixtimes can be used to show flow pattern changes, indicating

whether a flow is predominately axial or radial

• flow pattern reversal was most easily observed in the probe #6 mixtimes

when a pitch blade turbine was used

• the flat blade turbine gives shorter mixtimes at 50 and 150 rpm for all

probes except probe #6 at 50 rpm than does the pitch blade turbine

(C/T = 0.33)

• the two impellers produce similar mixtimes when the rotation rate is 300

rpm (C/T = 0.33)

• C/T can be used to change the flow pattern from axial to radial or radial

to axial

• increasing rpm decreases mixtimes for all probes

• the average concentration of an experimental run does not affect the

mixtime

• power is directly related to rpm, and thus its effect on mixtime is the same

A final area of consideration is the measurement of the torque. Two different methods were investigated to determine the torque in a given

experiment. One method used a torque arm attached to the mixing motor, with a hanging weight attached to the torque arm and positioned on a weigh scale

(this method was used for the experiments). The other method used a torque

plate centered beneath the mixing vessel, with information being obtained from

strain guages. Both techniques provided accurate and reproducible results over the range of rpm values, C/T values, and impeller types used in the

experiments. Variation between methods was less than 4 percent, and

variations with the theoretical values as given by the manufacturer was on the

order of 17 percent. This latter difference is attributable to bearing and

gearbox losses.

44
CONCLUSIONS

1) A performance test using conductivity probes was developed which can be

used to enhance understanding of the mixing process, aid in facility design, and may be useful for in-plant trouble-shooting for a batch mixing

system.

2) A standard geometry has been determined for use in laboratory testing.

3) Conductivity probes are flexible, accurate, reliable, and give

reproducible results.

4) Probe response curves are a viable means of observing the dynamics of the

mixing process in a qualitative manner.

5) Mixtime analysis provides useful insights into the mixing process and can

be used to enhance understanding of the mixing process, aid in facility

design, and be useful for in-plant trouble-shooting of batch mixing

processes.

6) The torque-arm/weigh-scale technique used for these experiments to mea- sure torque provides accurate, reliable, and reproducible information

needed for power calculations.

RECOMMENDATIONS

1) The work done in this project is incomplete, and further testing is neces- sary for a better understanding of the mixing process.

2) Further work should be done using an expanded parameter list, and a broader range of testing for each parameter.

3) A moderate size facility 0.379-0.757 m^ (100-200 gallons) is needed for

comparison testing of work done in the laboratory scale equipment. All

experiments run on the laboratory scale should in turn be run on the

moderate scale equipment.

4) Work should be expanded to include other mixing systems. The system

which should be worked on after miscible liquids is most likely a sol id- liquid system.

5) The information collected should be more rigorously analyzed, removing

qualitative analysis as much as possible from the tabulated results.

45
ACKNOWLEDGMENT

The author gratefully acknowledges the support and assistance of the

following people: Dr. David Dickey of Chemineer, Inc., Dr. James Oldshue of

Mixing Equipment Company, Mr. Larry Lynch of Syntex Chemicals, Dr. S. J. Khang

of the University of Cincinnati, and NBS employees R. 0. Voth, J. Filla, D. Friday, D. Lindenberger, and S. Valverde.

REFERENCES

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the Study of Mixing Phenomena in Liquids": Electrochimica Acta, Vol . 28,

No. 5, pp. 619-626, Pergamon Press Ltd., Great Britain, 1983.

Brodkey, Robert, S. , Turbulence in Mixing Operations: Academic Press, Inc.,

New York, 1975.

Cairns, E. J. and Prausnitz, J. M. , "Longitudinal Mixing in Fluidization":

AIChE Journal, Vol. 6, No. 3, pp. 400-405, September 1960.

Cairns, E. J. and Prausnitz, J. M. , "Macroscopic Mixing in Fluidization":

AIChE Journal, Vol. 6, No. 4, pp. 554-560, December 1960.

Chemineer-Kenics, Experimental Agitator Laboratory Manual for Model ELB : Dayton, Ohio, 1981.

Clements, W. C. , Jr. and Schnelle, K. B. , Jr., "Electrical Conductivity in

Dynamic Testing": ISA Journal, pp. 63-68, July 1963.

Clements, William C. , Jr., "Electrical Conductivity Monitor": Instruments &

Control Systems, Vol. 41, pp. 97-98, November 1968.

Fietz, T. R. , "A Simple Mean Conductivity Meter": Journal of Science

Instruments, Vol. 42, pp. 163-164, 1965.

Gibson, C. H. and Schwartz, W. H. , Journal of Fluid Mechanics, Vol. 16, pp.

357-365, 1963.

Grimmer, D. P. , Jones, G. F. , and Tafoya, J. , (Fitzgerald, T. J.),

"Development of a Point-electrode Conductivity Sal i nometer with High

Spatial Resolution for Use in Very Saline Solutions": Rev. Sci.

Instrum., Vol. 54, No. 12, pp. 1744-1747, December 1983.

Hilby, J. W. , "Definition and Measurement of the Degree of Mixing in Liquid

Mixtures": International Chemical Engineering, Vol. 21, No. 2, pp.

197-204, Federal Republic of Germany, April 1981.

Holmes, D. B. , Voncken, R. M. , and Dekker, J. A., "Fluid Flow in

Turbine-stirred, Baffled Tanks": Chemical Engineering Science, Vol. 19,

pp. 201-208, Pergamon Press Ltd. , Oxford, England, 1964.

46
Jones, G. and Bollinger, D. M. , Journal of the American Chemical Society, Vol.

57, 280, 1935.

Kappel, M. , "Development and Application of a Method for Measuring the Mixture

Quality of Miscible Liquids. I. State of Research and Theoretical

Principles": International Chemical Engineering, Vol. 19, No. 2, pp.

196-215, Federal Republic of Germany, April, 1979.

Keeler, R. N. , Ph.D. thesis in chemical engineering, University of California,

Berkeley, 1964.

Keeler, R. N. , Peterson, E. E. , and Prausnitz, J. M. , AIChE Journal, Vol. 11,

221, 1965.

Khang, S. J. and Fitzgerald, T. J. , "A New Probe and Circuit for measuring

Electrolyte Conductivity": Ind. Eng. Chem. Fundam. , Vol. 14, No. 3, pp.

208-213, 1975.

Khang, S. J. and Levenspiel, 0., "The Mixing-Rate Number for Agitator-Stirred

Tanks": Chemical Engineering, October 11, 1976.

Khang, S. J. and Levenspiel, 0., "New Scale-Up and Design Method for Stirrer

Agitated Batch Mixing Vessels": Chemical Engineering Science, Vol. 31,

pp. 569-577, Pergamon Press Ltd. , Oxford, England, 1976.

Kramers, H. , Baars, G. M. , and Knoll, W. H. , "A Comparative Study on the Rate

of Mixing in Stirred Tanks": Chemical Engineering Science, Vol. 2, pp.

35-42, Pergamon Press Ltd., Oxford, England, 1953.

Lamb, D. E. , Manning, F. S. , and Wilhelm, R. H. , "Measurement of Concentration

Fluctuations with an Electrical Conductivity Probe": AIChE Journal, Vol.

6, No. 4, pp. 682-685, December 1960.

Levenspiel, 0., Chemical Reaction Engineering: John Wiley & Sons, Inc., New

York, 1972.

Mendenhall, W. and Scheaffer, R. L. , Mathematical Statistics with

Appl i cations : Duxbury Press, North Scituate, Massachusetts, 1973.

Murthy, S. N. B. (Edited by). Turbulent Mixing in Nonreactive and Reactive

Flows : Plenum Press, New York, 1975.

Nagata, S. , Mixing Principles and Applications: Kodansha, Ltd., Tokyo, Japan,

1975.

Neal, L. G. and Bankoff, S. G. , "A High Resolution Resistivity Probe for

Determination of Local Void Properties in Gas- Li quid Flow": AIChE

Journal, Vol. 9, No. 4, pp. 490-494, July 1963.

Oldshue, J. Y. , Fluid Mixing Technology: Chemical Engineering, McGraw-Hill

Publications Co., New YOrk, 1983.

Prausnitz, J. M. and Wilhelm, R. H. , "Turbulent Concentration Fluctuations

through Electrical Conductivity Measurements": The Review of Scientific

Instruments, Vol. 27, No. 11, pp. 941-943, November 1956.

47
Plane, D. R. and Opperman, E. B. , Statistics for Management Decisions : Business Publications, Inc., Dallas Texas, 1977,

Rosenthal, L. A., "Conductivity Measurement Method by Means of Multivibrator

Frequency Control": Ind. Eng. Chem. Fundam. , Vol. 16, No. 4, pp,

483-486, 1977.

Sheppard, D, M. and Doddington, FI. W. , "Laboratory Instrument for Measuring

Electrical Conductivity in Stratified NaCl Solutions": Rev. Sci,

Instrum., Vol. 48, No. 3, pp. 287-289, March 1977,

Sparks, R. E. and Hoelscher, H. E. , "Method for Measuring Time-Average

Concentration in a Turbulent Wake of Electrolyte": Rev. Sci. Instrum.,

Vol. 32, No. 4, pp. 417-420, April 1961.

Torres! , R. S. and Ranz, W. E. , "Improved Conductivity System for Measurement

of Turbulent Concentration Fluctuations": I&EC Fundamentals, Vol. 8, No.

4, pp, 810-816, November 1969.

Uhl, V. W, and Gray, J. B. , Mixing Theory and Practice Volume I : Academic

Press, New York, 1966.

Uhl, V. W. and Gray, J. B, , Mixing Theory and Practice Volume II : Academic

Press, New York, 1967.

Uram, E. M. and Goldschmidt, V. W. , Fluid Mechanics of Mixing : The American

Society of Mechanical Engineers, New York, 1973.

Voncken, R. M, , Rotte, J, W. , and Ten Houten, A. Th. , "Circulation Model for

Continuous-Flow Turbine-Stirred, Baffled Tanks": AIChE-International

Chemical Engineers Symposium Series No, 10, London, 1965.

48
TABLES

Page

TABLE 1 - EXPERIMENTAL DESIGN 50

TABLE 2 - PROBE AND INJECTION LOCATION COORDINATES 51

TABLE 3 - SIGNAL AMPLITUDE EQUATIONS 52

TABLE 4 - CALIBRATION DESIGN 53

TABLE 5 - PROBE RESPONSE EQUATIONS 54

TABLE 6 - TEMPERATURE CONVERSION FACTORS 56

TABLE 7 - CONCENTRATION ACCURACY STATISTICS 57

TABLE 8 - CORRELATION COEFFICIENTS 58

TABLE A - PROBE #6 MIXTIMES 31

49
EXPERIMENTAL DESIGN

TABLE 1

RPM IMPELLER C/T CONCENTRATION *

50 PITCH 0.33 TO 0.06 NTX (7 STEPS

50 PITCH 0.50 1 f

50 FLAT 0 . 1 3

1 f

50 FLAT 0.33 i«

150 PITCH 0.33 • 1

150 PITCH 0.50 • f

150 FLAT 0.13 1

150 FLAT 0.33 1

300 PITCH 0 . 33 1

300 PITCH 0.50 1

300 FLAT 0.13 1

300 FLAT 0.33 1 f

SEVEN CONCENTRATION S ARE AS FOLLONS (WT%) ; 0.00949,

0.01896, 0.02833, 0 .0378^, 0.0^725, 0.05664, 0.06601

(THESE ARE EXPECTED VALUES)

NOTE; AT EACH SET OF CONDITIONS SEVEN IDENTICAL EXPERIMENT

HERE RUN.

50

CO
PROBE AND INJECTION

LOCATION COORDINATES *

TABLE 2

ANGLE X Y

<DEG) in < in . > m ( in .

)

PROBE #3 195 0.121 <4.75) 0.057 (2.25)

PROBE 175 0.121 <4. 75) 0,057 (2.25)

PROBE #5 300 0.121 (4.75) 0.057 (2.25)

PROBE 300 0.083 (3.25) 0.216 (8.50)

INJEC. POINT 125 0.038 (1 .50) 0.076 (3.00)

RECIRC POINT 350 0.095 (3.75) 0,051 (2.00)

REFERENCE BAFFLE IS AT 0 DEG., ANGLE TAKEN FROM THIS

POINT AROUND THE CIRCUMFERENCE OF THE TANK. X=DISTANCE FROM

CENTER! OF TANK. Y=DISTANCE FROM BOTTOM OF TANK.

INJECTION POINT DEPENDS UPON IMPELLER LOCATION • RECIRCULATION POINT IS FIXED AND DOES NOT DEPEND UPON

IMPELLER LOCATION,

51
GENERAL FORM: SA =

PC-BOARD

SIGNAL AMPLITUDE

EQUATIONS

TABLE 3

<Msa * MR) + Bsa

Msa

0 . 00582

0 . 00563

0 .00541

0.00559

Bsa

-0.001 15

-0.03046

-0.00542

-0.01045

WHERE: SA=SIGNAL AMPLITUDE, Msa=SIGNAL AMPLITUDE SLOPE,

MR=METER READING, Bsa=SIGNAL AMPLITUDE INTERCEPT

52
TEMPERATURE

(DEGREE C)

CALIBRATION DESIGN ** TABLE 4

CONCENTRATION

(WT*/ NaCl)

METER READING

(PROBE CIRCUIT)

19 0.00 10-160 IN STEPS OF

19 0.02 f • 19 0.04 • t 19 0.06 M

19 0.08 ft 19 0.10 tl 24 0.00 M

24 0.02 • « 24 0.04 f 1 24 0.06 M

24 0.08 II 24 0,10 1

29 0.00 1

29 0.02 • 1 29 0.04 If 29 0.06 II 29 0.08 II 29 0.10 1

• METER READINGS = 10. 15, 20, 25, 30, 35, -^0. ^5. 50.

55, GO. 65, 70, 75. 80, 85, 90, 95, 100, 110, 120, 130, 140,

150, 160 ** CALIBRATION DESIGN IS FOR PROBES ^3, «'4, #5 AND ^6

WHEN THEY ARE CONNECTED TO PC-BOARDS 1, 2, 3 AND 4

RESPECTIVELY.

53
PROBE RESPONSE

EOUPTIONS

TPBLE 5

GENERAL FORM: PR = (Mpr * MR) + Bpr

TEMP. CONC. PROBE

<DEG. C) <WT7. NaCl) p Mpr Bpr

19 0.00 3 -.0047 3.619

19 0.02 3 -.1246 3.627

19 0.04 3 -.2492 3.692

19 0.06 3 -.3495 3.661

19 0.08 3 -.4833 3.808

19 0.10 3 -.5919 3.833

19 0.00 4 -.0039 3.594

19 0.02 4 -.1185 4.168

19 0.04 4 -.2247 4.512

19 0.06 4 -.3398 5.403

19 0.08 4 -.4604 6.035

19 0.10 4 -.5641 6.666

19 0.00 5 -.0042 3.607

19 0.02 5 -.1232 3.675

19 0.04 5 -.2376 3.558

19 0.06 5 -.3506 3.884

19 0.08 5 -.4723 3.894

19 0.10 5 -.4388 3.438

19 0.00 6 -.0042 3.607

19 0.02 6 -.1186 3.839

19 0.04 6 -.2294 3.925

19 0.06 6 -.3391 4.423

19 0.08 6 -.4627 4.748

19 0.10 6 -.5672 5.037

24 0.00 3 -.0063 3.815

24 0.02 3 -.1415 3.805

24 0.04 3 -.2732 3.839

24 0.06 3 -.4020 3.842

24 0.08 3 -.5331 3.932

24 0.10 o -.6631 3.989

24 0.00 3 -.0054 3.770

24 0.02 4 - . 1 346 4.417

24 0.04 4 -.2612 5.124

24 0.06 4 -.3858 5.813

24 0.08 4 -.5128 6.549

24 0.10 4 -.6418 7.299

24 0.00 5 -.0057 3.786

24 0.02 5 -.1403 3.881

24 0.04 5 -.2738 3.992

24 0.06 5 -.4012 4.090

24 0.08 5 -.5304 4.191

24 0.10 5 -.6486 4.303

24 0.00 6 -.0056 3.780

24 0.02 6 -.1368 4.097

24 0.04 6 -.2650 4.402

24 0.06 6 -.3923 4.734

24 0.08 6 -.5083 4.916

24 0.10 6 -.6417 5.387

Df

24

19

9

6

3

2

24

19

11

7

5

4

24

19

10

6

4

2

24

20

11

6

4

3

24

18

8

5

3

2

24

19

9

6

4

3

24

18

8

5

3

2

24

18

9

5

4

2

54
TABLE 5

(CONTINUED)

TEMP.

(DEG. C)

CONC.

(WT7. NaCl)

PROBE

it Mpr Bpr Df

29 0.00 3 -.0075 3.879 24

29 0.02 3 -.1553 3.879 16

29 0.0^ 3 -.3035 4.071 7

29 0.06 3 -.4532 4.149 4

29 0.08 3 -.5993 4.001 2

29 0.10 3 -.6970 3.589 2

29 0.00 4 -.0065 3.824 24

29 0.02 4 -.1506 4.571 18

29 0.04 4 -.2915 5.348 8

29 0.06 4 -.4362 6.213 5

29 0.08 4 -.5694 6.830 4

29 0.10 4 -.7164 7.752 3

29 0.00 5 -.0068 3.849 24

29 0.02 5 -.1559 3.991 16

29 0.04 5 -.3018 4.070 7

29 0.06 5 -.4496 4,257 4

29 0.08 5 -.5898 4.268 2

29 0.10 5 -.7312 4.404 2

29 0.00 6 -.0067 3.837 24

29 0.02 6 -.1528 4.203 17

29 0.04 6 -.291

4.533 8

29 0.06 6 -.4327 4.862 5

29 0.08 6 -.4359 4.917 3

29 0.10 6 -.7216 5.645 2

WHERE: PR=PROBE RESPONSE, Mpr=PROBE RESPONSE SLOPE,

MR=METER READING, Bpr=PROBE RESPONSE INTERCEPT

Df=DEGREES OF FREEDOM: AS THE DEGREES OF FREEDOM DECREASE

THE ERROR IN VALUES INCREASES

55
TEMPERATURE

CONVERSION FACTORS

TABLE 6

PROBE K s Ki

Oo 0,021

0.0096

4 0 .0185 0 . 0133

5 0.0237 0.0103

0 0.0238 0.0090

BASE TEMPERATURE (Tbase) IS 24 DEGREE C

Ks = CHANGE IN SLOPE/DEGREE C CHANGE IN TEMPERATURE

Ki = CHANGE IN INTERCEPT/DEGREE C CHANGE IN TEMPERATURE

56
CONCENTRATION ACCURACY

STATISTIC r*

ABLE 7

EXPECTED OBSERVED PROBE- TO-PROBE RANGE OF

CONC. CONC. ERROR VARIATION RESPONSE

(WTX NaCl) (WT7 NaCl) < 7.

)

CL) ( 7

)

0.009A9 0.00913 o r> o • o 4.4 11.9

0.01896 0.01873 1 o

1 « ^ 2.2 3.2

0.02833 0.02813 0.7 C. » ^ yj % L.

0 , 03784 0.03743 1 .

1 .6 3.4

0.04725 0.04665 1 .3 1 .8 4.2

0 . 05664 0.05583 1 .4 1 .0 3.4

0.06601 0.06478 1 .9 0.4 o . 5

57
CORRELATION COEFFICIENTS

TABLE 8

SUMMARY STATISTICS

ON DATA SET:

MIXTIMES AND CONCENTRATIONS <WT */>

(SUBFILES IGNORED)

CORRELATION MATRIX

MIXTIME #4 MIXTIME #5 MIXTIME #6 RPM IMPELLER CONC.

MIXTIME .9984560 .9902375 .7943061 -.8812963 .1343965 -.0624895

MIXTIME

MIXTIME #5

MIXTIME #6

RPM

IMPELLER

.9926423 .7874389

.8088981

-.8809342

-.8952735

-.8185558

.1410659

.1054441

-.2317648

.0138727

-.0675428

-.0789490

-.0425129

.0209695

-.0184337

MIXTIME #3

C/T

.0628910

MIXTIME #4 .0815206

MIXTIME #5 .0740451

MIXTIME #6 -.2265783

RPM .0188891

IMPELLER .7016182

CONC. -.0250995

58
FIGURES

Page

FIGURE 1 - Mixing Vessel Specifications 61

FIGURE 2 - Impellers 62

FIGURE 3 - Laboratory Experimental Design 63

FIGURE 4 - Probe Locations 64

FIGURE 5 - Conductivity Probes 65

FIGURE 6 - NBS Probe Circuit 66

6a - 18 Pin Connector Probe Circuits 67

FIGURE 7 - Torque Measurement 68

FIGURE 8 - Injection Point 69

FIGURE 9 - Tracer Addition System 70

FIGURE 10 - Signal Amplitude versus Meter Reading 71

FIGURE 11 - Reading Probe 4 versus Meter Reading 72

FIGURE 12 - Reading Probe 1 versus Meter Reading (Calibration

Temperatures) 73

FIGURE 13 - Default List for Geometric Parameters 74

FIGURE 14 - Experimental Run Fact Sheet and Graphical Representation. . 75

FIGURE 15 - (Example Data) (FILE #AVG50P12) 76

15a (1 of 4) - Example Data Probe #3 77

15b (2 of 4) - Example Data Probe #4 78

15c (3 of 4) - Example Data Probe #5 79

15d (4 of 4) - Example Data Probe #6 80

FIGURE 16 - Example Data for Comparison (FILE #AVG50P13) 81

FIGURE 17 - Back-Mixing Data (FILE #AVG50P62) 82

FIGURE 18 - Comparison of Impeller Types 83

FIGURE 19 - Comparison of C/T Values 84

FIGURE 20 - Comparison of Rotation Rates 85

FIGURE 21 - Mixtime Determination 86

FIGURE 22 - Concentration versus Mixtime 87

FIGURE 23 - Power versus C/T 88

59
FIGURES

(conti nued)

Page

FIGURE 24 - Power Comparison: Power versus RPM 89

FIGURE 25 - Power Comparison: Flat Blade Turbine 90

FIGURE 26 - Power Comparison: Pitch (45 deg) Blade Turbine 90a

FIGURE 27 - Power Comparison: Pitch vs. Flat Blade Turbine 91

FIGURE 28 - Re versus Np 92

FIGURE 29 - Mixtime Analysis Technique 93

60
FIGURE 1

Mixing Vessel Specifications

Specif icatioTis:

Glass Tank (1.89E-2 m"3><5 gallon)

0.29 m I.D. X 0.^4 m high (9.75 in I.D. X 17.5 in high)

C/T « 0 to 0.50 D/T - 0.4t Z/T - 1.0

Baffles = 4 baffles (0.083 X I.D. uidth)/90 degree spacing

minimal bottom and side spacing (<3.2E-3 m)

Impeller • flat blade turbine (6 blades) pitch (45 deg.)

blade turbine (6 blades)

Mixing Motor • variable speed <0-1100 rpm), 186 W (1/4 hp>

Tank bottom * flat

61
FIGURE 2

IHPELLERS

Pitch Blade Turbine

<4 in)

(A in)

62
Figure 3

Laboratory Experimental Design

Mixer

63
FIGURE 4

0)

0) +J

0)E

0)iinl

cn

•H

(U X

T)S

~o

oJ X o

(0

0) -4u

at z>

CC

64

Probe

#6
Homemade

Probe

Commercial

Probe

I

65

O.Ot**

tlalldMi

wh%

Jal

Khanf

antf

J.

Cyp<»vttfyllx!(

Eitf.

Cham.

Fafitfam.

VaL

14,

Na.

S,

1176.
FIGURE

e

NBS

Probe

Circuit

66
FIGURE 6fl 18 Pin Connector for Probe Circuits

67

•J to •n pco6« cIrcuH

d*s(gn«j by SJ Khar>g and

TJ Fltzow^ald (1976)
Figure 7

Torque Measurement

Mixeir Torque Arm,,,^^

RPM

Hanging

Weighto

a

a

3

CO

k.0) X

Torque Plate

Signal To

Multiprogrammer

1

To Computer

68
FIGURE 8

Injection Point

270®

69
FIGURE 9

Tracer Addition System

70
71
PC-BORRD

4

WEIGHT

Z

-

.0999124

RERDING

PROBE

4

VERSUS

METER

RERDING

Q © S s 63 8 8

Q s o Q eg Q Q 8 8 8

+ 4* 1 I + + + + + + + U U u u U u U U U U U

S s C9 Q (O OJ CD 8 CM

• • • • • • • • • • • (y GO GO OJ in ts. GO

1 1 1 1 i I 1 1 <SnOA AlIAIlSIS3a>

^ 380^d 9NiaU3d

72

0.0E+00

2.0E4-01

4.0E+01

6.0E+01

8.0E4-01

1.0E4-02
73
DEFAULT LIST FOR

GEOHETRIC PARAMETERS

FIGURE

.»*«**«* ASSIGNMENT SECTION FOR DEFAULT PARAMETERS.

Tp$=”PITCH”

Psz*4

Nblade*6

!TYPE OF IMPELLER

DIAMETER OF IMPELLER

NUMBER OF IMPELLER BLADES

Ic'3.250

Ag1»195

X1-4.75

! CLEARANCE IMPELLER TO TANK BOTTOM

•PROBE 3 ANGLE LOCATION (DEGREES)

tPROBE 3 RADIAL LOCATION (IN.)

(IN.)

Yl'2.25

Ag2=175

X2«4,75

PROBE 3 CLEARANCE FROM TANK BOTTOM

!PROBE A ANGLE LOCATION (DEG.)

PROBE A RADIAL LOCATION (IN.)

(IN.)

Y2=2.250

Ag3=300

X3«4.75

! PROBE A CLEARANCE FROM TANK BOTTOM

PROBE 5 ANGLE LOCATION (DEG.)

PROBE 5 RADIAL LOCATION (IN.)

(IN.)

Y3=2.250

Ag^=300

XA-3.2S

PROBE 5 CLEARANCE FROM TANK BOTTOM

fPROBE 6 ANGLE LOCATION (DEG.)

PROBE 8 RADIAL LOCATION (IN.)

(IN.)

Y4=8.5

Aqs=125

Xs'l .50

! PROBE 6 CLEARANCE FROM TANK BOTTOM

LIQUID INPUT ANGLE LOCATION (DEG.)

!LIOUID INPUT RADIAL LOCATION (IN.)

(IN.)

Ys=5.00

Bafw' . 75

?LIOUID INPUT VERTICAL LOCATION (IN

BAFFLE WIDTH (IN.)

.)

Bafc«2.625

Nbaf

Bspace=90

BAFFLE CLEARANCE FROM TANK BOTTOM

NUMBER OF BAFFLES

ANGLE LOCATION OF BAFFLES (DEG.)

(IN.)

74
EXPERIMENTAL RUN

FACT SHEET AND

GRAPHICAL REPRESENTATION

FIGURE 14

13:41:59 23 Aug 1984 50 RPM RUN #:S8231 NUMBER OF POINTS • TIME PER POINT - .2

TANK: VOL- 11.939 L DIAMETER- 24.765 CM IMPELLOR :PITCH< 4 IN)

SALT START- 0 GM, SALT FINISH- 1.029 GM

WATTS OF STIRRING ENERGY - .008284

RUN WUKBD? ! S823t

19,

18.

17,

w in

^ > 13

kJ

'' m

14 .

13.

12 .

eee

eee

B.BB 50.ee lee.ee

TIRE (BCCONOSl

ISB.BB eee.ee

100C

75
FIGURE

15

76
FIGURE

15fl

(1

OF

4)

77
FIGURE

15fl

<2

OF

4>

78
FIGURE

15A

<3

OF

4)

79
so

TIME

(SECONDS)
FIGURE

te

SG

G O CD (VJ G CD CD (\J G CM

CVJ G G G G G G

G G G G G G G G G G G G • • • « • • • • • • • • G G G G G G G G G G G G

I

GG

(VJ

G

• G

in

G

G

tnQ

z

o

o

LJ

If) U

GG• G

in

(^uoojod -^m) N0IlByiN3DN0D

81
FIGURE

17

32
FIGURE 18

COMPARISON OF IMPELLER TYPES

83
FIGURE 19

COMPARISON OF C/T VALUES

9

OmZ

PVETRBGE DRTR FILE i^YGS0F42

- se t 3.037 to 4.U6 a NoCI

TIME < SECONDS)

84
FIGURE 20

COMPARISON OF ROTATION RATES <RPM)

RVCRPGC Dfrm FILE • RS^BPIE

TZrC (8CC0NXB)

WVOCTGC DRTH riLX BVCiSBPIg

- 15* I • «a I.C3 1 NaCl

t

umzi

ea

ata

ais

ai4

aiz

aia

T TTTTTTnrr iimirrr TTDHIII iminii TTTmTTT miiiiii iiiiimT TTTTTrm

- -

j >DM

-

-

1 \

1 rCrn -

- u L-

- PROBE ; 1 - f

F»ROBI : 6 -

1

J

-

-

- rf — /. -

I mint 1 mmiij iiiiiiiii iiiiimi iuimii injinij imiiiii iUUiUl

a.ee la.aa ta. ae sa.ae 4a. ae sa.aa aa.aa ?a. TIME CKCOMXB)

4*II

X

s

fr/ERWC Dfrm FILE fr^C300Pl2

85
86
FIGURE

22

CONC.

VS.

MIXTIME

(EXRMPLE)

00-0

00

00*9

00*5

00*tr

00 *e

00*2

00* I

00*0

G Q Q Q G G G G G G G

Q Q Q G G G G G G G G

Q N O sn G Ui W cn G

cn CM fVI (U

(SQNODBS) 3WI1XIW

I 1 1 1 1 1

1 1 1 r

I I I I I I \ I I I

87

CONCENTRRTION

(GRRMS

OF

NaCl

)
POWER,

HP

0.001

0.002

0.003

0.004

0.005

±/0

88

Figure

23:

Power

versus

C/T

(P

=

torque

plate,

W

=

weigh

scale)
RPM

RPM

POWER. HP

POWER. W

POWER. HP

10'^ 10"^ 10'^ 10"^

POWER. W

Figure 24: Power comparison. Upper graph is the Pitch Blade Impeller

and the lower graph is the Flat Blade Impeller.

89
POWE

m CO

UJ

o

Q.

lAIdd

90

Figure

25:

Power

comparison

Flat

Blade

Impeller.
POWER.

HP

10"5

10

”'*

10"3

10

"

m cc

LU

o

QlAIdd

90a

Figure

26:

Power

comparison

Pitch

Blade

Impeller.

91

Figure

27:

Power

(Flat

versus

Pitch

Blade

Impeller).
FIGURE

28

Re

VS.

Np

COMPRRISON
MIXTIME

ANALYSIS

TECHNIQUE

93.
APPENDICES

Page

Appendix I NBS Workshop on Mixer Performance Standards 95

Appendix II Moderate Scale Facility Design 102

Appendix III

Computer Program for Laboratory Scale Batch Mixing Experiments . .108

Appendix IV

Immiscible Liquid Dispersion Experiment 109

Apppendix V

Flow Visualization Experimentation Ill

Appendix VI

Mixtime Data 113

Appendix VII

Torque Comparison Power Data 116

Appendix VIII

Fluid Mixing Statistics 119

Appendix IX

Experimental Test Procedure 126

Appendix X

Experimental Data 128

94
Appendix I

NBS Workshop on Mixer Performance

Standards

95
Workshop Summary

Goal ;

To develop standard test methods and measurement techniques for evaluating

the performance of Impeller-type mixing equipment*

Systems to be Studied In Order of Preference:

1) Blending (conductivity probes)

2) Liquid-Solid

3) Liquid-Liquid

4) Llquld-Gas

Experimental Equipment;

1) Existing laboratory scale equipment.

2) 3' diameter tank with standard type geometry (Z/T 1.0, C/T'^ J3, etc.)

3) Large scale (to be supplied by industry).

Recommendations;

1) Establish Steering Committee.

2) Keep experiments simple.

3) Publish Information on test methods and measurement techniques as Investigated; not performance standards.

96
LIST OF PARTICrPAHTS

Charles N. Carpenter

Engineering Superintendent

Monsanto Company, CS6F

800 M. Lindbergh Blvd.

St. Louis, MO 63166

(314) 694-6145

David S. Diclcey

Technical Director

Chemineer, Inc.

P.O. Box 1123

Dayton, OH 45401

(513) 229-7000

H. Kir)c Fowler

Technical Director

Cleveland Mixer

Executive Drive

Hudson, NH 03051

(603) 883-5520

Charles M. Garrison

Group Leader

Procter & Gamble

7162 Reading Road

Cincinnati, OH 45222

(513) 763-4760

Douglas Ginley

Chemical Eng. Science Div. 773.10

National Bureau of Standards

325 Broadway

Boulder, CO 80303

(303) 497-3521

Michael Hi za , Jr

.

Chemical Eng. Science Div. 773.10

National Bureau of Standards

325 Broadway

Boulder, CO 80303

(303) 497-3127

Gaithersburg, MD

(301 ) 921-3281

Jesse Hord, Director

Center for Cherocial Eng. 770

Na*. ' snal Bureau of Standards

325- Broadway

Boulder, CO 80303

(303) 497-5108

Soon-Jai Khang

Dept, of Chemical C Nuclear Eng.

Mail Location 171

University of Cincinnati

Cincinnati, OH 45221

(513) 475-5724

475-2761

Douglas £. Leng

Central Research-Chemical Processes

Dow Chemical Company

M. E. Pruitt Building

Midland, MI 48640

(517) 636-3387

James McMichael

FM 105

National Bureau of Standards

Washington, DC 20234

(301) 921-3681

Godfrey Martin

Senior Research Engineer

Shell Development Company

P. 0. Box 1380

Houston, TX 77002

(713) 493-7940

Neil A. Olein, Chief

Chemical Eng. Science Div. 773.10

National Bureau of St2mdards

325 Broadway

Boulder, CO 80303

(303) 497-3257

Jean-Claude Pharamond

Vice President Sales

Mixing Equipment Co., Inc.

135 Mt. Read Blvd.

Rochester, NY 14611

(716) 436-5550

David G. R. Short

E. I. duPont de Nemours & Co.

Louviers Bldg., Room 1253

Wilmington, DE 19898

(302) 366-6315

97
LIST OF PARTICIPANTS (cont.)

Subhas K. Sikdar

Chemical Eng. Science Div. 773.10

National Bureau of Standards

325 Broadway

Boulder, CO 80303

(303) 497-5232

Jaromir J. Olbrecht

Dept of Chemical Eng.

State University of New York

Furnas Hall

Buffalo, NY 14260

(716) 636-2909

Roland 0. Voth

Chemical Eng. Science Div. 773.10

National Bureau of Standards

325 Broadway

Boulder, CO 80303

(303) 497-3632

98
October 27, 1983

Co

•*' v-'\

\.W/ *Utti o* *

UNITED STATES DEPARTMENT DF COMMERCE

National Bureau of Standards

325 Breadway

Boulder, Colorado B0303

Reply to the attention of: 773.10

David S. Dickey

Technical Director

Chemlneer, Inc.

P. 0. Box 1123

Dayton, OH 45401

Dear Dave:

As a result of the recent workshop, I am transmitting herein the collective

views of the National Bureau of Standards-Boul der staff relative to the planned

stirred tank mixing orogram.

Goal I To develop performance test procedures and measurement

techniques for batch mixing systems.

Objective : The performance test should enhance understanding of

fundamentals of mixing processes by improvinq mixinq

measurement techniques, and enabling more intelligent

troubleshooting of ailing systems.

Performance

Test: Performance tests should be designed so as to be repeatable by different individuals in the field. Tests should

specify:

1) Definition of mixing system (i.e., liquid-liquid,

liquid-solid, etc.)

2) System geometry

3) Probe type, number and location

4) Procedure for data collection

5) Method(s) for data analysis (including the possibility

of experimentally verified modeling)

6) Components to be mixed

Physical System

at

WS-Boulder : Emphasis should be on inexpensive simple fixed geometries.

1) Two transparent tank sizes (1‘ and 3' diameters)*

2) 1/1 = .8 to 1.5

3) C/T = approximately 0 to .5
4) D/T » .25 to .5 (in three steps)

5) Four baffles, 90® spacing, minimal bottom and side clearance

6) Tank bottom to be flat or dished (possibility for one of each)

7) Impellers » one flat, one pitch (45®) four blades w/d * 1/5

for pitch and 1/6 for flat

8) Vertical shaft centrally located for single impeller (dual

impellers to be considered at a later date)

9) Motor to establish 15 HP/1000 gal (i.e., approximately 5 HP

motor for three foot diameter tank)

* Most tests to be performed on three foot diameter tanks, then one foot

diameter tanks with an occasional spot check on a one liter tank and very large

diameter tank. Large tests to be performed cooperatively with industry.

Mixing System at

NBS-Boul der:"

1) Initially single phase fluids will be used. Viscosity and

density will be varied such that the range of the Reynolds

number will be between 200 and 20000 at three fixed RPM

values.

2) Multiphase systems will be as simple as possible, including

macro mixing for solid-liquid, immiscible liquids, and then

aas-liquid systems. These experiments may be qualitative

(i.e., designed for general understanding).

3) The selection and use of probes in the above mentioned systems

will satisfy the goal and objective of the program.

‘’ossible Probes

to he

Investigated:

1) Conductivity

2) PH

3) Fiber Optics

4) Fluorescence

5) Viscosity

6) Temperature

7) Hot-wire anemometers

8) Redox reactions

Independent Variables

for .Data Analysis

and Seal inn:

1) Torque measurement

2) Viscosity

3) Density

4) RPf’ 5) Imneller geometry

6) Injection location

100
Immediate Suggested

Plan for MBS:

1) Continue work with conductivity probes keeping in mind the new

goal agreed upon at the workshop.

2) Develop a three foot diameter tank facility as quickly as possible for further testing.

3) Establish a Steering Committee for annual progress reviews.

4) Develop a communications system for relating information,

data, and problems to the Steering Committee.

If you have any questions or comments, please feel free to call me at

(303)497-3521.

Sincerely,

DOUGLAb lalNLtT

Chemical Engineering Science Division

Center for Chemical Engineering

101
Appendix II

Moderate Scale

Facility Design

102
MIXER SPECIFICATIONS

1) Tank sizes are 24" to 36" diameters

2) Mixer is to be mounted on an A-frame type structure

3) Mixer should be capable of being used with a reaction

torque ring

4) Shaft is to be a large diameter <1.5-2"), with

Jacobson drill-chuck on the end. Shaft should be

capable of having a strain guage mounted on it, and

RPM values read from it.

5) A smaller shaft (.5-1") for tank entry should be

designed. It should have an appropr iately sized

impeller hub designed for changable blades. A

number of different impellers is also acceptable.

6) Two types of impellers will be used, each with four

blades. A) Flat blade turbine (w/d=1/6) B) 45

Pitch blade turbine (w/d=1/5)

7) Motor and drive design criteria:

RPM range - approximately 50 to 1000

viscosity - 1 to 20000 cp

D/T - .25 to .5 (3 steps)

Z/T - .8 to 1.5 (1.0 for 36" tank)

Power - to at least 15 Hp/1000 gal

C/T - 0 to .5

motor - prefer AC (possibility of adjustable

frequency drive), but is not essential

103
TANK DESIGN

36" Plexiglass Tank

^4" high plexiglass to form 36" ID tank <1/2" wall

thickness)

3/4" thick bottom plate notched for 36" ID tank, to be

glued and screwed to plate, offcenter drain hole

3/4" thick top ring, notched for 36" ID tank, screwed

into place

all seams to be reinforced

104
MIXER SPECIFICATIONS

1> Tank sizes are 18" to 2A” dianeters

2) Mixer is to be nounted on an A-frame type struLcture

3) Mixer should be capable of being used with a reaction

torque ring

4) Shaft is to be a large diameter <1.5-2"), with

Jacobson drill-chuck on the end. Shaft should be

capable of having a strain guage mounted on it, and

RPM values read from it.

5) A smaller shaft <.5-1") for tank entry should be

designed. It should have an appropriately sized

impeller hub designed for changable blades. A

number of different impellers is also acceptable.

6) Two types of impellers will be used, each with four

blades. A) Flat blade turbine <w/d=1/6) B> 45

Pitch blade turbine (w/d=l/5)

7) Motor and drive design criteria:

RPM range - approximately 50 to 1000

viscosity - 1 to 20000 cp

D/T - .25 to .5 <3 steps)

Z/T - .8 to 2.0 <1.5 for 24" tank)

Power - to at least 15 Hp/1000 gal

C/T - 0 to .5

motor - prefer AC (possibility of adjustable

frequency drive), but is not essential

105
TANK DESIGN

18" Plexiglass Tank

36" length of 18" ID plexiglass pipe d/4-3/8" wall

thickness)

1/2" thick bottom plate notched for 18" ID pipe*

off center drain hole* plate to be glued and screwed to

pipe

1/2" thick top ring notched for 18" ID pipe (screwed

into place)

1/2" thick additional ring for midposi tion up pipe

length (if necessary)

106
Preliminary

Structural

Design

for

Mixing

Facility

107

Design

is

for

two

mixing

systems
Appendix III

Computer Program

for Laboratory Scale

Batch Mixing Experiments

The computer program's use is outlined in the procedure section of this paper.

For further information concerning the computer program or a listing of the

program, please contact the author.

108
Appendix IV

Immiscible Liquid

Dispersion Experiment

109
Immiscible Liquid Dispersion Experiment

Materials :

Organic Phase: Methylene Chloride

Surfactant: Sodium Dodecyl Sulfate

Purpose :

To determine the affect of different power levels of mixing on an organic

phase dispersed in an acqueous phase. Further, to test the affect of a surfactant on that dispersion.

Procedure :

1) Fill the tank with a 50Z organic solution (Z/T 1.0).

2) Place impeller In the organic phase (CH2 CI2 spgr.* 1.33).

3) Photograph the dispersion at various RPM values and different tank

levels.

4) Repeat using a surfactant.

Analysis :

Enlarge photographs and manually determine droplet size and number/area being

studied.
Appendix V

Flow Visualization

Experimentation

111
FLOW VISUALIZATION

Flow visualization studies were performed in the laboratory equipment

under various conditions of rpm, C/T and impeller type. The purpose of the

study was to gain a basic understanding of the mixing process, determine con- ditions that produced either axial or radial flow, and enhance general mixing

knowledge needed for appropriate experimental design.

Flow visualization tests were done using a red acrylic modeling powder

in water. Rotation rates from 50 to 600 rpm were observed. A flat blade turbine and a pitch (45 deg) blade turbine were used at C/T values ranging from

0.13 to 0.50. Observation of the flow patterns were observed visually and

recorded with video recording equipment. Knowledge gained from these tests was used to help design the experiments.

oo

Radial Flow

112
Appendix VI

Mixtime Data

113
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Appendix VIII

Fluid Mixing Statistics

119
FLUID MIXING STATISTICS

D. Ginley and D. Friday (12/84)

The fluid mixing problem is, from a statistical perspective a non- standard application. Most of existing statistical methodology is non- applicable due to the time dependent nature of the experiment. Furthermore,

almost all of the time series methodology, the statistical area most relevant

to the mixing problems, assumes stationarity and linearity or very specific

forms of non-stationarity or non-linearity. As a consequence very little of

existing methodology is applicable to the analysis of the laboratory data. It was therefore necessary to adapt existing statistical concepts as far as possible and then to develop new procedures specifically for the mixing problems.

The results, which are only partially described here, provide a thorough and

efficient description of the experimental results and minimize the use of the

subjective reasoning which is characteristic of past work in this area. There were three basic objectives in the statistical analysis. The first

is to provide an effective statistical summary of the large amounts of data

which result from mixing experiments. The second objective is to provide an estimate of the mixing time which is both statistically and physically sound.

That is, an estimate uniquely determined from the data, which has optimal statistical properties, which is applicable to data from a wide variety of experimental conditions, which is compatible with mixing theories, and is in agreement with visual observation of the mixing waveform. The only investigated

previous attempt to replace human judgement required the assumption of a very

restrictive sinusoidal-exponential model (Khang, Levenspiel, 1976). Finally

we hoped to obtain a general statistical model which could adequately describe

the time dependence of the experimental results and thereby provide another

parallel approach to achieving the first two objectives.

Statistical Summary of Experimental Results:

The summary of the data combined statistical concepts and graphics, utilizing to advantage the high resolution graphics hardware/software which was available. The simplest graph is a time plot which exhibits the central location and the dispersion of a set of replications of an experiment under identical experimental conditions at each point in time. The only underlying

assumptions are that all the replications fluctuate about some "norm" for the

120
given experimental conditions and that their deviations from this norm are random and independent of the outcomes of the other replications. These as- sumptions appear to be reasonable. Note that there is a clear time dependence

in the random component but this property does not affect the interpretation

of the plots. These plots can be implemented in various ways. The most

common is to use the arithmetic average for each epoch of time, average across replications, as the location component of the plot. The dispersion component

of the plot then gives information on how variable the repetitions of the

experiment are, with respect to the location estimate, at each point in time.

The most common such estimate is the sample variance. A plot of the average

with upper and lower bounds (avg. ± variance) exhibiting the time pattern of

the changing variance proved to very very informative (see fig. A).

In traditional statistical applications the mean and variance estimate is

used to develop confidence intervals. In this case not enough repetitions

were obtained of a single experiment to ascertain distributional properties

over time. This is a necessary assumption in developing confidence intervals

and we therefore did not develop confidence time plots. They are a possible

future extension, however, given sufficient data on a single experimental con- figuration. The mean-variance plot is by no means the only such plot. Threesigma bounds may be plotted, for example, as long as it is clear what is

plotted and that they are not used as confidence intervals. Another

possibility which was used is the median-extremes plot. The median is used

for the location plot and the maximum end minimum values are used as the upper

and lower bound. This plot has the advantage that the location plot is more robust to outliers than the average and the extremes are directly influenced

by the outliers. Therefore the typical mixing path is estimated clearly and

any extreme behavior is also apparent. Other possibilities are also reasonable

such as mean ± range, median ± order statistics, etc. These plots proved to

be a very useful way of summarizing the data and we advocate use of several of

them for exploratory purposes (see fig. B).

Another plot which proved useful is one we developed from some statistical

considerations called the cumulative successive squared difference (CSSD). It

involves taking successive difference on the data, then squaring this series

of differences and developing the partial sums. If c^ is the concentration at

time t = 0, 1,...,N then S(t) the CSSD at time t is given by (see fig. C):

t

s(t) = (c. - ; t = 1,

121
The reasoning behind such plots will be developed in a later publication.

Their interpretation, however, is to exhibit the dissipation over time of the

mixing energy in the experiment. Energy here is analogous to turbulence or variation in the observed data. It established another way of observing the

"quiet" periods before and after mixing with the additional advantage of providing quantiles over time. That is the percentage of energy in the mixing

experiment expended in any time interval can be measured and used for comparison with other experiments. It is conditional on the total energy in the

experiment however. If an experiment is run with a longer tail after the

mixing is completed then this small residual variation biases the estimates.

We have developed methods to compensate for this, however, for brevity we will

not discuss them at this time.

The location-dispersion plots and CSSD plots were not the only ones we found useful. Others exhibited variance decomposition, and structural information. These will be reported on later. A statistic which proved useful in

discriminating between different experimental conditions, such as probe location baffle position relative to probe location and stirring conditions, was

derived. It is related to the CSSD and showed marked differences between

different configurations. This will also be discussed further in a paper in

preparation.

Statistical studies also focused on mixtime estimation. All of these

approaches are non-parametric or model free. The intention was that they be

applicable to a wide range of mixing experiments and not be dependent on a particular, restrictive model. Two approaches to mixtime proved reasonable.

One is based on the CSSD plots and defines mixtime as the epoch after initiation at which the energy change falls into the background noise level. The

other approach is not related to the CSSD plots but to exceedance of the background noise level in reverse time. While both methods are reasonable statistically some practical problems were encountered due to the fact that the

background noise level is in the quantization region of the A/D converters.

The CSSD method is less affected by the quantizing and the effects of the

quantizing on the reverse-time method are being studies. When complete, the

details of the methods will be presented. The effort to remove the subjective

judgement from mixtime estimation we feel has been successful.

The final objective of modeling the sample paths from mixing experiments

and doing it in a very flexible and general way is in the research stage.

Some progress has been made and it is considered a difficult problem. We are

not prepared to report on this work at the present time.

122
RVERRGE

CONDUCTIVITY

VS

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Appendix IX

Experimental Test Procedure

125
TEST PROCEDURE

1) Select mixing vessel to be tested, and determine its ability to be filled

with deionized water, and to have a tracer of NaCl solution injected.

2) Determine the number of conductivity probes to be used (minimum of two).

Place these probes, one at the surface of the mixing fluid, and one away

from baffles at approximately the height of the impeller. Both probes

should be located near the vessel walls, with the surface probe above the

other one. Additional probes may be added to enhance information gained

from the test.

3) Fill the vessel with deionized water (Z/T = 1.0).

4) Record resistivity information from the conductivity probes. Data points

should be taken at no greater than 0.10 second intervals.

5) Inject the NaCl solution in the most realistic manner for the process

being studies (i.e., surface injection, injection by the impeller, etc.).

6) Record the data before the NaCl injection, and for a sufficiently long

time after the injection to insure that complete mixing has occurred.

7) For comparison to other work done, and to established correlations it is

necessary to measure the power. This may be done directly with a wattmeter, or by measuring the torque and rpm for the test performed.

Analysis of the data at this time is left to the individual. Further

details regarding experimental procedures and equipment may be found in

the 'apparatus' section of this report.

127
Appendix X Experimental Data

The following information is a representative example of the data obtainable

from the described experiments. For further information regarding specific

experimental setups and/or a more complete data set, please feel free to con- tact Douglas Ginley at the National Bureau of Standards (phone: (303)497-3521,

FTS 320-3521).

128
FINAL

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NBS-114A (REV. 2 -ao) U.S, DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 85-3030

2. Performing Organ. Report No. 3. Publication Date

July 1985

4. TITLE AND SUBTITLE

The Development of a Performance Test Procedure and Measurement Technique in a Batch Mixing System

5. AUTHOR(S)

Douglas Ginley

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gn Ificant Information. If document includes a significant

bibliography or literature survey, mention it here)

A performance test procedure and measurement technique for a batch mixing system

is described using conductivity probes. The design of the automated experimental

apparatus is described, and experimental procedures are given. Data collected

from the experiments are explained, and a mixtime analysis of the data is

performed. Conductivity probe response curves provide a good representation of

the system dynamics. Mixtime analysis allows for probe response comparisons to

evaluate system geometry and probe location.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

batch mixing; calibration techniques; conductivity probes; experimental apparatus;

mixtime analysis; torque measurements

13. AVAILABILITY

Uni i mi ted

1 1 For Official Distribution. Do Not Release to NTIS rn Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[X^Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

146

15. Price

* U.S. GOVERNMENT PRINTING OFFICE:1985— 580-051 / 25317 USCOMM-DC 6043-P80

. J