COMPUTATIONAL FLUID DYNAMICS:MODELING THE SOFTMIXER®

Prepared For:

Donald F. Gerson, Ph.D. Rütten Engineering Inc.

Prepared by:

Karen Splinter Rob Wall

David LamChris Simpson Haskins

Submitted March 31, 2003.

TECHNOLOGY, ENGINEERING AND MANAGEMENTDEPARTMENT OF CHEMICAL ENGINEERING

QUEEN’S UNIVERSITY AT KINGSTON, ONTARIO, CANADA

TEAM SOFTMIXER® 2003

Karen Splinter - Client Contact Chemical Engineering, Queen’s University Karen was the primary liaison between the client (Rütten Engineering) and the TEAM Softmixer® 2003. She was also be the main contact liaison with the technical advisors (Dr. Khan at Fluent Inc. and Dr. Marchilon) as well as with the course coordinators Barrie Jackson and Annette Bergeron.

Rob Wall - Logistics Manager Chemical Engineering, Queen’s University Rob managed the group timetable and was aware of the availability and whereabouts of each member. The logistics manager prepared agendas for meetings and presentations, and made arrangements for meeting room reservations, travel and equipment.

Chris Simpson Haskins – Treasurer and Documentation Manager Robotics and Technology, Sir Standford Fleming College Chris was the experimental and software guru. He was also responsible for preparing the budget and managing all information collected by the group through literature searches and results.

David Lam - Visual and Written Communication Manager Mathematics and Engineering (Process Control), Queen’s University David was the editor and was responsible for the production of visual and written work.

ACKNOWLEDGEMENTS

The group would like to thank Annette Bergeron and Barrie Jackson, course coordinators

for Technology, Engineering and Management (APSC 400) and Donald F. Gerson, Ph.D.

TEAM Softmixer® would also like to thank the staff at the High Performance

Computing Virtual Laboratory (HPCVL) including Dr. Hartmut Schmider for their

efforts in terms of access to higher computing resources. Furthermore, the group would

also like to thank the team technical advisor, Dr. Keith Marchilon from DuPont Canada

for his invaluable support and expertise.

Finally, the team would like to acknowledge Dr. Rafiqul Khan from Fluent Inc. for his

continual direction, advice and technical support throughout the project with respect to

the challenges of CFD modeling.

ABSTRACT

The project objective was to conduct Computational fluid dynamic (CFD) analysis on the

Softmixer® provided by Rütten Engineering and to verify the results with physical

experimentation.

The CFD analysis was completed on the Softmixer®, a low shear mixer that

utilizes a vertically oscillating perforated disk. A physical model of the mixer was created

(2D and 3D) in the pre-processor Gambit 2.0, involving geometry creation and the

discretization of volumes through a meshing scheme. The resulting model was imported

to Fluent 6.1, and simulations completed to produce animations of flow fields indicating

mixing patterns, the degree of mixing, dead zones and shear stress via the generation of

shear rate, velocity magnitude and pressure profiles within the mixing tank. This was

possible through the use of moving dynamic mesh (MDM) schemes created with generous

support from the technical staff at Fluent Inc.

The 2D model was modeled as the vertical cross-section of Softmixer®, while the

3D model was taken to be a quarter section of the volume. The results obtained from the

2D model does not provide significant insight into mixing properties due to the

complexity involved in CFD modeling, but was chosen as an integral first step. The

results obtained from the 3D model provides additional information concerning the

mixing properties, constrained within a quarter section of the model; only a full model

would yield the complex mixing patterns, but the quarter section model relies on the

periodicity of the cylindrical vessel to reduce the cell count and computation time. The

geometry for the 3D model was completed, but simulations were not completed due to

the extensive computing power (1 GB and 1 GHz) required for meshing. Additional

computing power was available through access to the High Performance Computing

Virtual Lab (HPCVL), but was not completed due to time constraints and system

compatibility issues with respect to the software Gambit 2.0 and Fluent 6.1.

The 2D model was completed and the results analyzed. The fluid in the mixer was

modeled as water, although it is expected that viscosity would increase for biological

systems. The model was simulated at frequencies from 0.1-30 Hz and amplitudes from

0.001 –0.3 m. The results were analyzed and verified by physical experimentation using the

Video Grid Rendering (VGR) Method; tracking the location of a tracer ball during mixing

trials. The VGR system involved the development of software (using Visual Basic) to

automate tracking the tracer balls.

It was determined, as expected, that increases in frequency and amplitude led to a

higher degree of mixing that were indicated through a higher distribution of velocity

magnitude profiles within the tank in the 2D simulations. However, trials at 10 Hz and 300

mm and at 30 Hz and 100 mm indicated similar profiles; thus it was concluded that a

specified degree of mixing may be obtained at a lower frequencies by increasing the

amplitude. It was also determined, however, that the strain rate (related to the shear

stress), increased exponentially, seen as a linear relationship with respect to a logarithmic

scale, with respect to increasing frequency with constant amplitude and with respect to

increasing amplitude with respect to constant frequency.

The experimental verification was complicated by several factors discussed in the

report, but allowed general trends to be identified, reinforcing results obtained by the 2D

simulations. The location of the tracer ball was tracked quantitatively and seen to occupy

the outer edge of the tank more frequently. This higher probability of appearance

corresponds to the increased volume at larger radii. Furthermore, the ball occupied the

whole depth of the tank at a combination of higher frequencies and higher amplitudes.

Increasing this combination led to the dispersion in the frequency profile indicating a

higher degree of mixing.

TEAM Softmixer® 2003 has laid the foundation for CFD analysis of the Softmixer®

and hopes that future teams will complete the full 3D model and develop an alternative

technique for experimental verification or the fine tuning of the VGR Method.

TEAM Softmixer® 2003

Technology, Engineering And Management

Queen’s University, Kingston, ON

TABLE OF CONTENTS

1.0 Project Description 1

2.0 Background Information 2

2.1 Mixing 2

2.2 Shear Stress 5

2.3 Introduction to Computational Fluid Dynamics 7

3.0 Project Results 9

3.1 2D Simulation Results 9

3.2 3D Simulation Results 17

4.0 Experimental Verification 18

4.1 Experimental Design 19

4.2 Experimental Data Acquisition 21

4.3 Experimental Results and Analysis 24

4.4 Experimental Limitations 29

5.0 Conclusions 30

6.0 Recommendations 31

References

APPENDICES

A Softmixer® Equipment Specifications i

B A Brief Introduction to Gambit 2.0 iii

C Fluent 6.1 Convergence of Results vii

D 3D Model viii

E Alternative Experimental Techniques x

E.1 Video Grid Rendering (VGR) System x

E.2 Sound Delay System xii

E.3 Light Tracking System xiii

LIST OF FIGURES

Figure 1.1 Softmixer® Located in Dupuis Hall, Queen’s University 1

Figure 1.2 Mixing Agitator Disc 1

Figure 2.1 Turbulent Radial Mixing Impeller 3

Figure 2.2 Turbulent Axial Mixing Impellers 4

Figure 2.3 Laminar Helical Screw Impeller 4

Figure 2.4 Laminar Anchor Impeller 4

Figure 3.1 A Comparison of Two Velocity Magnitude Contours 10

Figure 3.2 A Comparison of Two Strain Rate Contours 11

Figure 3.3 Velocity Magnitude for Trail 31 (20 Hz and 50 mm) 13

Figure 3.4 Strain Rate for Trial 31 (20 Hz and 50 mm) 14

Figure 3.5 Shear Stress Flow Through the Disc Conical Holes 15

Figure 3.6 Frequency and Strain Rate at a Constant Amplitude (0.1 m) 15

Figure 3.7 Amplitude and Strain Rate at a Constant Frequency (10 Hz) 16

Figure 4.1 Experimental Setup 18

Figure 4.2 Operator Control Console for the Softmixer® 18

Figure 4.3 Tracer Ball Experiment 19

Figure 4.4 Recommended Experimental Setup 20

Figure 4.5 VGR System Display Console 22

Figure 4.6 Coordinate Acquisition from the VGR System 23

Figure 4.7 The Frequency Surface Area Plot 23

Figure 4.8 Trial 1: Frequency Plot at 20 Hz and 20 mm 24

Figure 4.9 Trial 2: Frequency Plot at 25 Hz and 25mm 25

Figure 4.10 Trial 3: Frequency Plot at 12 Hz and 50mm 25

Figure 4.11 Trial 4: Frequency Plot at 15Hz and 50mm 26

Figure 4.12 Trial 5: Frequency Plot at 16 Hz and 50 mm 26

Figure A.1 Dimensions of the Experimental Tank i

Figure A.2 Softmixer® Shaft and Agitator Disc ii

Figure B.1 Gambit 2.0 Screen Display v

Figure B.2 Fluent 6.1 Screen Display vi

Figure D.1 3D Wire-Frame Geometry viii

Figure D.2 Meshed Disc Section ix

Figure D.3 Meshing the 3D Model. ix

Figure E.1 Camera Positioning and the Original Tracer Ball xi

Figure E.2 Sensory Array xi

Figure E.3 Sound Receiving Unit xii

Figure E.4 Tracking System with Photo-Resistors xiv

Figure E.5 Light Diode Tracing Ball xiv

LIST OF TABLES

Table 3.1 2D Simulation Trials 9

Table 3.2 2D Simulation Trials for Experimental Verification 11

Table 4.1 Parameters of the Physical Trials Performed 20

Table 4.2 Frequency x Amplitude Chart for Experimental Trials 27

1.0 PROJECT DESCRIPTION

The report outlines the results of Computational Fluid Dynamic (CFD) simulations on the

Softmixer®, verified by physical experimentation. TEAM Softmixer® 2003 has

completed simulations using a simplified 2D model and has started the creation of a 3D

model. Furthermore, the team has attempted to verify the results using experimental data

through the creation of the Video Grid Rendering (VGR) system to track the location of

tracer balls in the mixing tank. The Softmixer® was provided courtesy of Rütten

Engineering and the CFD software available from Fluent Inc.

Figure 1.1 Softmixer® Located in Dupuis Hall, Queen’s University

Figure 1.2 Mixing Agitator Disc

1

2.0 BACKGROUND INFORMATION

2.1 MIXING

In conventional mixing applications, mild agitation requires 0.5 – 2.0 hp per 1000 US

gallons (Marchildon and Larocca, 2003). However, this represents a high degree of

agitation, requiring high power input and possibly causing damage to micro-organisms

(Harnby et. al., 1969); hence the emergence of laminar mixers.

The agitator diameter should be chosen, as a guideline (Marchildon and Larocca,

2003), by Equation 1:

ss TD 6.0 (1)

where Ds and Ts are the agitator and tank diameters respectively

so for the experimental setup, as Ts = 395 mm, Ds = 237 mm

Rotating laminar mixers require larger agitator diameters as fluid viscosity dissipates

inertial forces (Harnby et. al., 1969). In fact, increased fluid motion throughout the tank is

achieved as the diameter of the agitator approaches the diameter of the tank (Tatterson,

1991). However, with the available experimental setup, the actual agitator diameter is

approximately Ds = 148 mm, and as a result, the degree of mixing is not expected to be

optimal.

The other differences between turbulent and laminar mixers exist and are further

discussed. Typical turbine agitators have wall baffles to improve mixing performance

(Marchildon and Larocca, 2003); in laminar flow, these baffles may cause poor mixing

performance (Tatterson, 1991). Furthermore, in turbulent flow, flow patterns typically

correspond to the clearance, defined as the distance between the agitator and the tank

bottom. (Tatterson, 1991); but in laminar mixing, the clearance is defined as the distance

between the agitator and the tank wall, having a larger effect on flow patterns (Tatterson,

1991). Interestingly, turbulent mixers have both radial and axial impellers, as seen in

2

Figures 2.1-2.2, while laminar mixers tend to have radial flow regimes. For applications

involving mixing solutions containing biological cells, laminar mixing is preferred to

reduce cell subjugation to shear stress, possibly damaging cells. Typical laminar mixers

include the helical screw impeller and the anchor impeller as seen in Figure 2.3 and

Figure 2.4 respectively (Tatterson, 1991). Yet mild agitation in laminar mixing may still

produce negative effects.

The Softmixer® (Figure 1.1), proposes a different agitator that vibrates vertically.

Thus as laminar mixers differ from turbulent mixers in terms of agitator and motor

power, and mixing performance, the Softmixer® is also uniquely characterized from

traditional laminar mixers. The characterization of the Softmixer®, include factors such

as the mixing time; the time where the reactor contents have reached a specified degree

of uniformity from the initial start of mixing (Harnby et. al., 1969). This, according to

Harnby (1969), does not imply complete suspension, which exists when “…all particles

are in motion and no particle remains on the tank base for more than a short period, e.g.

1-2 s.” However, this is not necessarily desirable as relatively small regions of stagnation

may result in substantial power savings (Harnby et. al., 1969). This report attempted to

quantify, through CFD analysis, flow patterns characterized by velocity profiles, pressure

profiles and shear stress profiles. However, care must be taken to extend such results to

generalizations, as it should be noted from Tatterson (1991), that “…mixing occurring at

one scale is most likely quite different from the mixing at another scale.”

Figure 2.1 Turbulent Radial Mixing Impeller (Tatterson, 1991)

3

Figure 2.2 Turbulent Axial Mixing Impellers (Tatterson, 1991)

Figure 2.3 Laminar Helical Screw Impeller (Tatterson, 1991)

Figure 2.4 Laminar Anchor Impeller (Tatterson, 1991)

4

2.2 SHEAR STRESS ON MAMMALIAN CELLS

All cells in a moving fluid with a velocity gradient endure shear stress. The magnitude of

the shear stress is proportional to the fluid velocity gradients, the dynamic viscosity of the

fluid and the size of the cell. Compared to microorganisms, animal cells are very fragile.

This is because animal cells are comparatively large but lack a cell wall. Shear

susceptibility is also related to cell line, culture age and history and maintenance

conditions. Studies on M. citrifolia, Beta vulgaris and C. roseus showed that even mild

agitation was detrimental to culture performance (Kieran et al., 1984). However, low

agitation rates provided sub-optimal mixing. Poor mixing and oxygen deprivation can

account for the failure of suspensions to grow, regardless of shear stresses. Traditional

mixers that work fine for microorganisms are not appropriate for some mammalian cell

applications.

Shear forces result from spatial differences in momentum across material stream

lines in a moving body of fluid. If the flow is laminar, fluid elements move along parallel

stream lines so the shear stress can be predicted from the velocity gradient. In a stirred

tank shear forces arise from collisions with the vessel wall, collisions with the agitator,

gas bubbles bursting and from foaming. The Softmixer® does not have an agitator but

shear forces will still arise from collisions with the oscillating disk. Also, the disk

oscillates at much lower frequencies than agitators revolve so the magnitude of the

collision force is expected to be smaller in the Softmixer®.

Newton’s equation states that shear stress ( , N/m2) is proportional to the dynamic

viscosity ( , N.s/m2), the fluid velocity gradient (dv/dx, s-1) or shear rate ( , s-1) as shown

in Equation 2:

dxdv (2)

Newton’s equation is appropriate for dilute aqueous media (Goosen et al., 1984)

5

The cultivation of animal cells should avoid the vigorous agitation used in microbial

systems. Most works cite the effect of shear from the agitator as the source of damage

(e.g. cell disruption) to the cells. However, there exists very little quantitative data about

shear effect. In mouse and human cell experiments, wall shear stresses of 100 N/m2 over

0.5 seconds residence time cause a significant death rate (Harbour et al., 1984). Studies

on human embryonic kidney cells showed that shear stresses of less than 0.26 N/m2

caused a slight reduction in viability and no change in cell morphology. Using urokinase

production as a marker, kidney cells had maximum production at an applied shear stress

of 0.65 N/m2 (Harbour et al., 1984).

Other experiments have also shown that shear damage is a strong function of

shearing time as well as shearing force. These factors correlate with shear stress is the

following manner:

Gdtd

dydu (3)

Where µ is the shear viscosity, is the imposed stress, d /dt is the time change in the

stress and G is the shear modulus of elasticity. Typical reported values of G and µ for red

blood cells are 6*105 N/m and 10-3 Pa.s respectively.

Even for well-defined flow fields, it is difficult to compare results collected under

different conditions. This is complicated by a variety of physiologically and

morphologically distinct cell lines and by using any of a number of stress indicators.

Other studies have also shown that shear forces may exert more subtle forces than the

blatant rupture of cells, such as inhibition of cell mitosis and the synthesis of products

due to leakage of essential metabolites. In the end, the basic study of shear stress using a

range of cell lines under defined experimental conditions is warranted and of direct

relevance to scale up studies. Specific experiments should be performed on a cell line in

order to adequately know the maximum shear stress of the cell line under desired

operating conditions.

6

2.3 INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS

Computational fluid dynamics (CFD) numerically solves equations governing fluid flow

and heat transfer by the brute force method of integration and iteration. The equations

related to the process include the conservation of energy (4), mass (5) and momentum (6)

as well as the Navier-Stokes Equation (7-10) used to model fluid flow, various

thermodynamic equations of state and user specified reaction mechanisms (Fluent Inc.,

2002b). From a system consisting of these equations, the resulting pressure and

temperature profiles may be determined, simulating fluid flow through the reactor.

(Rate of Increase of Energy of Fluid Particle) = (Net Rate of Heat Added) + (Net Rate of Work) (4)

(Rate of Increase of Mass in Fluid Element) = (Net Rate of Flow of Mass into Fluid Element) (5)

(Rate of Increase of Momentum of Fluid Particle) = (Sum of Forces on Fluid Particle) (6)

xMSxw

zu

zxv

yu

yudiv

xu

xxdtdu 2 (7)

yMSyw

zv

zudiv

yv

yxv

yu

xydtdv 2 (8)

zMSudivzw

zyw

zu

yxw

zu

xxdtdw 2 (9)

where the divergence is defined as:

zw

yv

xuudiv (10)

7

32 (for gases) represents the viscosity due to volumetric deformation, the

dynamic viscosity, the density, (x,y,z) the direction of flow, u = (u,v,w) the velocity, and the surface stresses due to body forces such as gravity where ,

iMS 0xMS 0

yMS

and gSzM (Versteeg, 1995)

Commonly, the resulting systems of equations are interlinked and require partial

differential analysis. The solution, if one exists, may be approximated through numerical

methods via discretization of the equations into algebraic form, calculated at specific

locations. Methods developed include the finite difference method (FDM), the finite

element method (FEM) and the finite volume method (FVM), with the latter two more

commonly used. Focusing on the FVM, with advantages in computer memory and speed,

the physical system is divided into control volumes and the solution approximated for

each volume element minimizing the residuals (the change in value associated with each

variable of interest in successive iterations). Adding to the residuals are errors resulting

from the interpolation of nonlinear processes between control volumes, indicating that the

solution may be dependent on the model resolution (Fluent Inc., 2002b). Furthermore, the

solution may be compromised by computer round-off errors. Thus solution existence is

difficult to establish theoretically and furthermore, solution uniqueness is not guaranteed,

with possible solution convergence conditional on initial conditions. In any case, solution

accuracy may be verified through grid independence, in which the solution no longer

changes significantly with changes in mesh sizing. Yet there are no explicit rules to

ensure model accuracy (without experimentation) with respect to observed actual

conditions in the physical setup.

Despite the limitations in numerical approximations in complex systems, the

application of CFD analysis may be found in various industrial sectors including

aerospace and defense (missile systems), the automotive industry (internal combustion

engines, windshield washer nozzles), the electronics industry (electronic equipment

cooling), in environmental systems (pumps, scrubbers, fuel cells), in mixing technologies

(static mixers, CSTR), in consumer appliances (fans, mixers, lawn mowers, vacuum

cleaners, refrigerators), and in chemical processes such as oil and gas extraction, nuclear

power generation, polymer extrusion and reactor design (Fluent Inc., 2002a).

8

3.0 PROJECT RESULTS

Simplified models of the Softmixer® were simulated and CFD analysis conducted. The

CFD software available from Fluent Inc. requires “wire frame geometry” and mesh

creation in the pre-processor Gambit 2.0 followed by the actual computation and

boundary model specifications in Fluent 6.1*. The wire frame geometry outlines the

physical model dimensions while the mesh creation discretizes this volume. Finally, this

may be solved in Fluent 6.1*. The 2D and 3D model and results are described below.

3.1 2D SIMULATION RESULTS

Twenty simulations were performed at varying frequencies and amplitudes as seen in

Table 3.1. Frequencies varied from 0.01 Hz to 30 Hz and amplitudes varied from 1 mm

to 300 mm (Table 3.1). In order to analyze the trials after the simulations were complete,

data files were saved every 10 time steps and contour plots were saved every time step

including plots for the velocity magnitude, velocity vectors, strain rate and absolute

pressure. The velocity magnitude plots were used to assess the degree of mixing, and

strain rate plots to assess the shear stress profiles developed in the tank.

Table 3.1 2D Simulation Trials

Amplitude (mm)

Frequency (Hz) 1 10 100 300

0.01 Trial 19 Trial 18 Trial 17 Trial 25

0.10 Trial 15 Trial 14 Trial 3 Trial 21

1 Trial 10 Trial 12 Trial 13 Trial 16

10 Trial 7 Trial 5 Trial 4 Trial 22

30 Trial 9 Trial 8 Trial 11 Trial 24

9

Several trials indicated a low degree of mixing; amplitudes less than 10 mm and

frequencies less than 1 Hz were unable to cause sufficient fluid flow throughout the

mixer. The trial at 10 Hz and 300 mm indicated a high degree of radial and axial mixing

approximately halfway up the tank, similar to the trial simulated at 30 Hz and 100 mm

(Figure 3.1). The strain rate was also analyzed for these two trials, and it was observed

that the two trials exerted approximately the same magnitude and distribution of shear

stress within the mixing tank (Figure 3.2). This observation is important because

experimental trials found that amplitudes of 300 mm could not be performed with the

current linear motor used in the Softmixer®. The model results indicate that, if necessary,

smaller amplitudes may be substituted by increasing frequency proportionally, without

sacrificing the degree of mixing and without increasing the strain rate.

Figure 3.1 A Comparison of Two Velocity Magnitude Contours

10

Figure 3.2 A Comparison of Two Strain Rate Contours

In order to compare the 2D model with experimental results, five additional trials were

conducted as shown in Table 3.2. There were slight differences between the simulated

model and the experimental runs. These will be discussed in the Experimental

Verification section.

Table 3.2 2D Simulation Trials for Experimental Verification

Trial Frequency (Hz) Amplitude (mm)

Trial 26 8 50

Trial 29 12 50

Trial 27 15 50

Trial 28 20 20

Trial 30/31 20 50

11

12

Trial 30 (20 Hz and 50 mm) was simulated for an extended period of time with 8000 time

steps recorded. This extended trial (Trial 31), took over approximately 20 hours of real

time. The time step between iterations was 10-4 seconds, so the 8000 time steps

represented only 0.8 seconds of real time data. At a frequency of 20 Hz, this

corresponded to 16 cycles for the oscillating disk. The velocity magnitude contours for 9

time steps is seen in Figure 3.3, indicating that the mixer is generating high velocity

profiles above the disk, but low velocity profiles below the disk due to the conical shape

of the holes in the oscillating disk.

A: 35 B: 1000 C: 2000 D: 3000 E: 4000 F: 5000 G: 6000 H: 7000 I: 8000

Each timestep is 10-4 s

Figure 3.3 Velocity Magnitude for Trail 31 (20 Hz and 50 mm)

13

It should be noted that the high velocity seen above the middle of the disk will not exist

in reality due to the presence of the mixing disc shaft. The shaft was omitted in the model

to simplify the design and reduce simulation time. The strain rate progression for Trial 31

is seen in Figure 3.4 for three time steps. The maximum strain occurs at the disk, over a

small area.

Figure 3.4 Strain Rate for Trial 31 (20 Hz and 50 mm)

A schematic of how the strain rate increases as fluid flows through the disk is shown in

Figure 3.5. The trials indicated that the maximum strain rate occurred over a small area

through the conical holes as the disk plunges upward. Minimal shear was observed

elsewhere in the mixer.

14

Figure 3.5 Shear Stress Flow Through the Disc Conical Holes

The relationship of strain rate with increasing frequency and amplitude was of great

interest. Using the strain rate contours from each trial, the maximum strain rate was

recorded and plotted; Figure 3.6 demonstrates strain rate increasing with increasing

frequency, compiled from the five trials simulated at an amplitude of 0.1 m. Figure 3.6

shows a logarithmic relationship between strain rate and frequency, at frequencies greater

than 1 Hz.

Amplitude = 0.1m

0100200300400500600700800900

1000

0.01 0.1 1 10 100

Frequency (Hz)

Stra

in R

ate

(s-1

)

Figure 3.6 Frequency and Strain Rate at a Constant Amplitude (0.1 m)

15

Similarly, Figure 3.7 demonstrates the strain rate increasing with increasing amplitude,

compiled from the four trials at a frequency of 10 Hz. Figure 3.7 shows a logarithmic

relationship between strain rate and amplitude, at amplitudes greater than 0.01 m. The

logarithmic trend was not observed at frequencies less than 1 Hz and amplitudes less than

0.01 m; a result of a low degree of mixing at these parameters.

Frequency = 10 Hz

0100200300400500600700800900

1000

0.001 0.01 0.1 1

Amplitude (m)

Stra

in R

ate

(s-1

)

Figure 3.7 Amplitude and Strain Rate at a Constant Frequency (10 Hz)

16

3.1 3D SIMULATION RESULTS

A 3D model simulation would have provided insight into the flow patterns of the

Softmixer® but due to computing constraints, a quarter section of the model was

attempted (see Figures D.1-D.3 in Appendix D).

Creation of the wire frame geometry model was completed in Gambit 2.0, but

difficulties were encountered during mesh application. The model requires small cell

sizes around the oscillating disk due to expected high gradients in the area of movement,

thus increasing solution accuracy through additional calculations. Unfortunately, the

concentrated mesh scheme increases the number of cells and hence computing power

required. The TEAM was able to mesh approximately 80% of the model before memory

requirements exceed the 512 megabytes of RAM available. The original plan was to

have the Gambit portion of the 3D model completed by February 17th.

The TEAM decided to proceed with the 3D analysis using a parallel computing

network high higher memory and RAM support, available via the High Performance

Computing Virtual Laboratory (HPCVL) at Queen’s University. Access to these facilities

was not available until March 10th, and was plagued by security issues and additional

software to access the HPCVL, not completed until March 13th. Once the system was

setup, the model was imported to the HPCVL yet files were corrupted with embedded

references specific to the Windows operating system, not compatible with the Unix

system within the HPCVL. An attempt to reconstruct the model through the Unix system

was further complicated by software incompatibility with the grid buffering system

within the HPCVL and Gambit 2.0 was not functioning properly despite extensive

technical support from technical support at the HPCVL. Due to time constraints, further

work on the 3D model was abandoned.

17

4.0 EXPERIMENTAL VERIFICATION

Figure 4.1 Experimental Setup

Figure 4.2 Operator Control Console for the Softmixer®

18

4.1 Experimental Design

Physical trials were conducted to verify the accuracy of the CFD simulations, by

quantifying the fluid flow patterns in the Softmixer®. A PlexiGlass reactor was

available, with approximately the same dimensions as the Softmixer® stainless steel

tank, differing only in the shape of the reactor bottom. A large mixing bowl was used for

the clear tank and was caulked to prevent leakage. Several alternative experimental

techniques were considered (see Appendix E), but within budget and resource

constraints, TEAM Softmixer® 2003 decided to pursue the Video Grid Rendering system

(VGR). This method requires two video cameras, tracer balls and a backdrop to increase

the ability to view the tracer balls. The two video cameras were setup (Figure 4.3)

approximately 1.5 m from the tank at a relative position of 90°.

Figure 4.3 Tracer Ball Experiment

Tracer balls with a diameter of 0.8 cm were chosen, such that these balls were smaller

than the diameter of the holes in the oscillating disk (11.6 mm) yet these balls were also

large enough to be recorded by the cameras. The lowest density tracer ball available was

19

1.06 g/cm3, and hence the difference in density between the balls and the fluid medium

(water) must be considered. It was determined that the balls would have a terminal

velocity of approximately 1cm/s in water. This value was expected to significantly affect

the degree of mixing. To overcome this density difference corn syrup was added to

increase the density. Typical reactors are filled approximately 66%; for the experimental

setup, this corresponds to 53.6 L of water and 6 L of corn syrup (BeeHive Golden Corn

Syrup), resulting in a fluid density of approximately 1.04 g/cm3. The viscosity of the

mixture was not significantly affected by this addition as the bulk of the fluid was water.

Once the Softmixer® setup was completed (Figure 4.1-4.3) and the cameras in

position, the amplitude and frequency of the Softmixer® was varied via the operator

control console (Figure 4.2). It was interesting to note that at low frequencies and/or at

low amplitude, the tracer balls remained on the bottom of the mix bowl and could not be

seen by the video recorders. The trials that were conducted are listed below in Table 4.1.

Table 4.1 Parameters of the Physical Trials Performed

Trial 1 2 3 4 5 6* 7* 8* 9* 10*

Amplitude (mm) 20 25 50 50 50 20 50 20 15 8

Frequency (Hz) 20 25 12 15 16 12 20 5 2.5 50

*trials were not analyzed due to data corruption and loss of resolution

Figure 4.4 Recommended Experimental Setup

20

It should be noted that the actual experimentation was completed using a fluid medium

mixture of water and corn syrup. This reduced the clarity of the medium hindering data

acquisition. A possible improvement would be the use of clear glucose (seen in Figure

4.4), and coloured balls to allow multiple tracking within each trial.

4.2 Experimental Data Acquisition

Once physical experimental trials were conducted, the data was digitalized and analyzed

using the Video Grid Rendering Software (VGR) as seen in Figure 4.5, developed

through Visual Basic by a member of TEAM Softmixer® 2003.

The video recording from the two views of the mixing tank was digitized using a

video capturing card, but resulting in decreased resolution. The resulting digitized video

is then divided into frames, each a 20th of a second apart. Thus, for a two minute video

clip, six hundred frames were captured for each view. The two views fully specify the

location of the tracer ball in Euclidean space (R3). The time step chosen was arbitrarily

set at 0.05 s, considering the labour intensive procedure required in the number of

pictures to be analyzed.

The digitalized clips were then imported into the VGR system, to capture the X

and Z coordinates from the front view, and the Y and Z coordinates from the side view.

The VGR system automates the loading and coordinate calculation for each image, but

requires the manual location of the tracer ball within the image itself (Figure 4.6). Once

coordinates have been obtained for all frames, a save feature transfers results into Excel.

With the coordinates in Excel, where the origin was located at the left-hand bottom of the

transparent tank (not considering the bowl section), the Cartesian coordinate system was

translated to a cylindrical coordinate system with the origin located at the center of the

tank at the top of the liquid level, assumed to be constant. Thus the X and Y coordinates

were converted into a radial distance R with depth preserved (Z coordinates). Excel then

produces a tally of the number of times the bead appears in each arbitrary radial section

21

over the entire depth. Thus a surface area plot may be created showing the 2D view of

half the tank, and the frequency of the ball appearing within that vertical cross-sectional

area.

Figure 4.5 VGR System Display Console

22

Figure 4.6 Coordinate Acquisition from the VGR System

Figure 4.7 The Frequency Surface Area Plot

23

4.3 Experimental Results and Analysis

Several experimental runs were completed and digitalized. However, due to the loss in

resolution from the VGR method, the results for only the most significant trials are

shown below.

1 4 7 10 13 16 19

14710131619222528313437404346

5-64-53-42-31-20-1

Figure 4.8 Trial 1: Frequency Plot at 20 Hz and 20 mm

24

1 4 7 10 13 16 19

15913

172125293337

4145

5-64-53-42-31-20-10

345

21

Figure 4.9 Trial 2: Frequency Plot at 25 Hz and 25mm

1 4 7 10 13 16 19

1

4

7

10

13

16

19

22

25

28

31

34

37

40

43

46

5-64-53-42-31-20-1

543210

Figure 4.10 Trial 3: Frequency Plot at 12 Hz and 50mm

25

Figure 4.11 Trial 4: Frequency Plot at 15Hz and 50mm

1 4 7 10 13 16 19

14710131619222528313437404346

5-64-53-42-31-20-1

Figure 4.12 Trial 5: Frequency Plot at 16 Hz and 50 mm

26

The Frequency-Position plots (Figures 4.8-4.12) record the frequency of appearance of

the tracer ball in each coordinate space. Half the tank was analyzed assuming that the

results would be axial-symmetric, to correspond with the 3D simulation assumption. This

reduces the amount of data to be analyzed, but one would eventually hope to conduct

simulations and verification of the full model. Despite the limitations in the experimental

setup, the TEAM was able to extract some meaningful results.

The Video Grid Rendering system (VGR) only recorded the ball at certain

locations, but the path traveled between the two points within the time step may be

interpolated, though not exact. This approximation results in increased variance at higher

frequencies and amplitudes, or rather at higher velocities. A general trend apparent

through Figures 4.8-4.12, is the increased frequency of the ball appearing at larger radii.

This trend was expected because the horizontal cross-sectional area increases radially,

thus increasing the probability of the ball appearing in the region closer to the vessel wall.

This is consistent with expectations for a well-mixed reactor.

Another trend observed was the increased vertical distance the ball traveled at a

combination of higher frequency and amplitude (Table 4.1) as seen in Figure 4.11-4.12,

and slightly from Figure 4.9 compared to Figure 4.8. Since there was a slight density

difference between the ball and the water/corn syrup solution there was a small force

acting in the downward direction, hindering the ball from traveling towards the top of the

tank. Although trials with varying amplitude and constant frequency were conducted

(Trials 6-10 in Table 4.1), the video quality was insufficient for data acquisition;

however, the trends were reinforced by visual observation. For low frequency and

amplitude trials, visual observations noted that the tracer balls were less active and rarely

traveled beyond the upper half of the vessel. Furthermore, none of the low frequency-

low amplitude trials were able to overcome the gravitational forces, and the ball simply

settled to the tank bottom.

Table 4.2 Frequency x Amplitude Chart for Experimental Analysis Trials

Trial 1 2 3 4 5

Frequency (Hz) x Amplitude (mm) 400 625 600 750 800

27

As seen in Figure 4.12, the frequency plot indicated a well-mixed reactor with a well

dispersed distribution with rapid random motion. The plot does not have large frequency

gradients indicating short residence time within a given specified location.

Although it is difficult to compare these results to the CFD 2D simulations,

TEAM Softmixer® 2003 attempted to verify the results with the trends described above.

The simulated model used water as the mixing medium with a density of 1 g/cm3 while

the experimental runs were completed with a mixture of water and corn syrup with a

density of 1.04 g/cm3. However, more importantly, the oscillating disk was located much

lower in the tank than in the simulations. This was a result of parallel efforts to conduct

simulations and to verify the model with experimentation. A more accurate technique

would have been to design experimental trials and simulate a model based on

experimental parameters as several physical limitations were encountered during physical

testing that were not anticipated. Furthermore, the lower portion of the mixing tank was

semi-spherical, and not a flat bottom as depicted in the 2D model. This semi-sphere aids

in fluid motion on the bottom of the mixer, propelling the liquid up towards the

oscillating disk and may produce slightly different flow patterns. Finally, it was hoped to

use the 3D model in its full form to compare results, or at the quarter section results for

comparison, but this was not possible due to the computational difficulties encountered

with the mesh scheme.

28

4.4 Experimental Limitations

Video Grid Referencing is a new method of determining the degree of mixing. There are

some limitations with the current configuration; specifically, the curvature of the mixing

vessel in combination with lighting glare and reflection, caused difficultly identifying the

location of the tracer balls close to the vessel walls. Also, the mixing bowl (bottom

portion of the PlexiGlass vessel) is opaque and it was not possible to view the tracer balls

in this region. Furthermore, the corn syrup introduced to increase the density of the tank

medium, transformed the transparent medium into a translucent medium. The data

acquisition VGR system also further reduced video resolution during the digital

conversion for analysis, sometimes resulting in less than 50% in terms of useful data

extraction. However, in the future, the last two problems could be alleviated by using

clear corn syrup (glucose) and digital cameras recording. Finally, the arbitrarily chosen

time step for frame to frame analysis could not accurately track the ball’s movement

during high velocities. Thus, tracer ball tracking proved difficult and alternative methods

may be investigated in the future.

Experimental runs were completed at a range of frequencies and amplitudes, but

experimental analysis was further complicated by the poor quality in data extraction. The

loss in data resulted in reduced information from trials and visual observations were most

pronounced for high frequency and high amplitude runs. Although the use of the

Softmixer® relies heavily on low frequency and low amplitude operation, the

experimental setup required conditions such that ball movement may be observed. Thus,

CFD simulations were conducted and compared to these conditions for verification, while

simulations were also run for low frequency and low amplitude operation. Ideal

operation of the Softmixer® is at the minimum combination of frequency and amplitude

that is adequate to fully mix the vessel.

29

5.0 CONCLUSIONS

The 2D model does provide some insight into the fluid mechanics of the vessel.

Specifically, velocity profiles and strain rates were obtained indicating a well mixed

vessel at higher frequencies and amplitudes. Since the strain rates were relatively low,

the Softmixer® represents promise for the growth of mammalian cell cultures. The 3D

CFD model requires significantly more computer resources than were available, and was

not completed within the limited timeline.

Although there are some problems with VGR experimentation, specifically

resolution and time step problems. The group feels the results obtained were still valid.

The results of the VGR experimental trials supported the results of the 2D CFD model.

The mixer produced good radial mixing as seen by the increased ball frequency in the

radial direction. This result is expected due to the increased cross sectional area present

away from the center of the reactor. Increased amplitude and frequency result in better

axial mixing as recorded by increased ball frequency higher up in the reactor under these

operating conditions. Both of these results were supported by visual observations during

the trials.

30

31

6.0 RECOMMENDATIONS

A more accurate 2D model should be created and tested. Specifically the simplifications

made in the disk geometry and vessel geometry could be improved upon.

More computing power is required to finish creating the 3D model and to perform

CFD trials. More computing power would also decrease the time required to run trials on

the 2D model thereby increasing the amount of data that could be obtained.

The use of tracer balls to evaluate mixing should be pursued, with the following up-

grades to the technique:

Clear corn syrup should be used to raise the density of the fluid in the reactor.

Digital cameras should be used for recording the VGR input. This would

alleviate resolution problems that were encountered.

Smaller time steps could be used for the VGR system. Unfortunately, this would

increase the amount of time required for data acquisition.

The spreadsheets used for the VGR could be updated to record the velocity of the

tracer balls.

REFERENCES

Fluent Inc. 2002a. http://www.fluent.com.

Fluent Inc. 2002b. Basic Review of CFD.

Fluent Inc. 2002c. Fluent 6.0 Training Notes: Challenge Us with your Application.

Fluent Inc. 2002d. Gambit 2.0 Training Notes: CFD Preprocessor.

Gary B. Tatterson. Fluid Mixing and Gas Dispersion in Agitated Tanks. New York: McGraw-Hill Inc., 1991.

Harbour, Barford and Low. 1984. Process Development for Hybridoma Cells. Advancesin Biochemical Engineering. Vol. 29. New York: Springer-Verlag, 1984.

N. Harnby, M. F. Edwards, and A.W. Niewnow, eds. Mixing in the process Industries. London: Butterworths, 1969.

H.K. Versteeg and W. Malalasekera. 1995. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. London: Pearson Education Limited.

Keith Marchildon and Miguel Larocca. 2003. Flow and Energy Systems Part III: Agitation and Mixing. Kingston: Research and Business Development, DuPont Canada Inc.

Goosen, M., Daugulis, A. and P. Faulkner. 1993. Insect Cell Culture Engineering. Marcel Dekker, New York.

Kieran, Malone and MacLoughlin. 1984. Effects of Hydrodynamic and Interfacial Forces on Plant Cell Suspension Systems. Advances in Biochemical Engineering. Vol. 29. New York: Springer-Verlag, 1984.

Rafiqul Khan. 2003. Fluent Training Session, New Hampshire, US.

Rütten Engineering. 2003. Rütten Softmixer®. http://www.rutten.com/rutten_softmixers.htm.

Appendices

APPENDIX A

SOFTMIXER® EQUIPMENT SPECIFICATIONS

The Softmixer® was located in the Dupuis Laboratory at Queen’s University. The

specifications are shown below for the experimental setup. The schematics for the actual

Softmixer® stainless steel tank are similar but are not included.

Figure A.1 Dimensions of the Experimental Tank

It should be noted that the tank dimensions represent the actual physical dimensions (the

water level is thus not shown in Figure A.1).

i

Figure A.2 Softmixer® Shaft and Agitator Disc

The Softmixer® specifications are provided by Rütten Engineering (2003):

Design Frequency Range: 0-6 Hz

Design Amplitude Range: 0.5-60 mm

Typical Capacity: 100-1500 L

Motor Dimensions: 750 x 130 x 130 mm

Motor Weight: 9 kg

ii

APPENDIX B A BRIEF INTRODUCTION TO GAMBIT 2.0

Gambit is an integrated pre-processor for CFD analysis, consisting of four functions that

the user must complete before actual CFD analysis can be completed:

Geometry Construction o shapes and orientations must be created

Mesh Generation o a mesh is used to divide the created volumes into solvable cells

Mesh Quality Examinationo the mesh created can be examined and optimized

Boundary Zone Assignmento the faces and edges that have been created are labeled for analysis in

Fluent

Each of these functions forms an essential part of CFD analysis as mistakes or oversights

in the geometric model will be reflected and possibly magnified in the analysis. The

construction of the physical model is straightforward. The user must decide upon a

coordinate reference and Gambit creates fundamental geometries including cubes,

cylinders, spheres, and cones, and requires information for the placement of these 3D

volumes. Furthermore, once the volume has been created it can be selected and moved.

In this fashion it is very easy to create a relatively complex volume from small volumes

of different shapes. Alternate methods of volume creation are available, allowing the

user to create geometries in a bottom-up approach, using vertices, edge, and face

creation, later united together in the proper geometry, allowing the user to make more

complex objects.

Once volumes are put together, they can be united. Gambit offers three Boolean

functions for intersecting volumes or faces: unite, subtract and intersect. Unite merges

the two volumes and combines any shared volume. Subtract removes one volume (user

selected) but also removes any spaces formerly occupied by both volumes. Intersect

removes both volumes and leaves the space formerly occupied by both volumes.

iii

At this point it may be useful to define vertex, edge, face, and volume. A vertex is a point

and an edge is a curve that is defined by at least 1 vertex. In the case of one vertex the

edge forms a loop. A face is a surface (not necessarily planar) bounded by at least 1 edge,

while a volume is a geometric solid that can be thought of as a set of bounding faces.

Once a physical model is created, the user must apply a meshing scheme. The

mesh sets the boundaries for the control volumes that the model will be divided into.

Since Fluent solves the boundary conditions for each of these cells, Gambit allows the

user to control the cell size distribution. Discretization is the method of approximating

the differential equations by a system of algebraic equations for the variables at some set

of discrete locations in space and time, where the discrete locations in our model are the

cells created by the mesh (Fluent Inc. 2002b). An objective of controlling the size of the

cells is to ensure that there is not a significant size jump between adjacent cells; reducing

skewness.

Gambit allows the user to specify the meshing size, cell count per edge and

grading ratios. Each of these functions enables the user to control the creation of the

mesh directly, and additionally, there are several different meshing schemes and

elements. A variety of Hexahedron schemes are available that can adjust for shape

changes on the mapping face. Other schemes available include Tetrahedral/Hybrid

meshing which creates prism structures in boundary areas to capture viscous effects. The

last is Hex/Wedge (Cooper) meshing. Cooper meshing projects or extrudes a face mesh

(or a set of face meshes) from one end of the volume to the other and then divides up the

extruded mesh to form the volume mesh, requiring side edges/faces to be MAP meshed.

Meshing schemes must also take into consideration the size of mesh; it is advantageous to

reduce the number of mesh cells due to computer memory and calculation time

constraints without compromising solution accuracy, especially close to abrupt gradient

changes. The optimization of meshing is generally completed through experience and in

this project, with the direction of technical support at Fluent Inc. Furthermore, the

meshing is computationally intensive and requires significant computer power and time;

this has been reflected through the difficulties in the 3D model creation as discussed in

the report.

iv

Now that a meshing scheme has been applied and the volume has been divided

into a number of cells, the quality of the cell creation can be examined. The cells can be

examined based on their skewness. Skewness is a rapid change in cell volume between

adjacent cells, ideally 0 (implying that all cells are the same size) but ranging from [0,1].

Gambit displays a histogram with the distribution of skewness divided into intervals of

0.1; a “good” mesh will have a larger proportion of cells on the left side of the histogram,

with skewness [0,0.70] (Khan, 2003). The histogram display allows the user to

determine where cells with high skewness are located in the model. This allows the user

to go back and re-mesh the volume to create a “better” mesh scheme; this may require

changing the mesh pattern, reducing the mesh volume size and/or using a different face to

start the meshing.

Once a sufficient meshing scheme has been created, the boundary zones of the

model must be defined in Gambit before they can be solved in Fluent. The selecting of

zone type is important because these boundary conditions are required in Fluent. The

continuum type must also be selected for the model, with only three types of continuum

available: solid, fluid and porous. The resulting geometry and mesh scheme may then be

imported into Fluent for CFD analysis.

Figure B.1 Gambit 2.0 Screen Display

v

Figure B.2 Fluent 6.1 Screen Display

vi

APPENDIX C FLUENT 6.1 CONVERGENCE OF RESULTS

The CFD Fluent analysis was conducted using the convergence criteria for residuals of

0.01 for continuity and velocity terms and of 1.0 x 10-5 for energy as required for the

segregated solver (Fluent Inc., 2002c). The convergence criteria were chosen arbitrarily

to reduce simulation time as the team was not given specified tolerance levels. The

tolerance levels reflected the acceptable degree of error resulting from numerical

approximation techniques. However, despite ensuring the convergence of the residuals to

the arbitrary tolerance level, the team inspected the residuals graphically and ensured the

net mass imbalance was less than 1% of the total inlet mass as recommended by Fluent

Inc. (2002c).

%8023.0%10089.188

9668269.54822783.7M

It should be noted that diverging residuals did not necessarily imply solution divergence,

but rather indicated an increasing imbalance in the conservation equations (Fluent Inc.,

2002c). Hence, due to the complexities involved in residual analysis and convergence

determination, the team did not pursue further analysis of the precision and accuracy of

the results obtained. In more detailed studies, several models with refined mesh sizes

would be completed to ensure the solution is grid independent (the solution is not

dependent on the mesh size).

vii

APPENDIX D 3D MODEL

Figure D.1 3D Wire-Frame Geometry

viii

Figure D.2 Meshed Disc Section

Figure D.3 Meshing the 3D Model.

ix

APPENDIX E

ALTERNATIVE EXPERIMENTAL TECHNIQUES

Several alternative experimental techniques were considered and the top three presented

below. Other possibilities briefly discussed included using the Mixmeter® for limited

pressure profiles at particular locations, pH stabilization (to indicate the degree of

mixing), colour change reactions (also to indicate the degree of mixing), and the

radioactive tracing of flow patterns. These techniques were not pursued due to resource

concerns as well as the qualitative nature of characterizing the degree of mixing.

The VGR system was chosen as the most viable option; the Sound Delay was not

possible due to external vibrations of construction within the Dupuis Laboratory, and the

Light Tracking System was expected to be difficult considering the reflection of light in

the stainless steel vessel and the refraction of light in water as well as the obstruction of

cameras.

E.1 Video Grid Rendering (VGR) System

A grid is laid out in the video receiver, charting the path of the ball over an elapsed

period of time as seen in Figure E.2. Two cameras are to be mounted inside the tank at a

relative position of 90˚ (Figure E.1). The actual arrangement involved using a clear tank

and moving the cameras outside the vessel to enable a larger range of visibility and

removing the need for waterproofing.

Using a glowing ball will aid in the detection the ball. For a light source inside the

ball I recommend just a light bulb unless the Light Sensing Array is used. If that is the

case the same ball may be used cutting coast.

x

Figure E.1 Camera Positioning and the Original Tracer Ball

Figure E.2 Sensory Array

Equipment Required

Video Cameras (two minimum)

Visual Basic software (for data analysis automation)

Miscellaneous Parts (wire, glue, cauking)

Basic Stamp and Programming kit for the control of the camera system, timing, and

power supply (optional; not used in this report)

Light bulb and socket (optional to make the tracer ball glow for easier tracking; not used

due to the required size of the tracer ball)

xi

Limitations

The camera views will be slightly distorted due to the refraction of light from the liquid

medium and vessel wall, as well as the angle of the camera with respect to the horizon.

Furthermore, there will be areas of reduced visibility due to the shaft and plate as well as

the bottom portion of the tank (metal mixing bowl). This method is difficult to implement

and to extract data (as discussed in the report) and is less accurate than the Sound delay

and Light tracking System, but was chosen due to resource limitations.

Cost

Quantity Amount Optional

Stamp Kit 1 $177.00 YES

Colour Camera 2 $298.00

Light Bulb 1 $3.60 YES

Miscellaneous $65.00

Total in US Funds $543.60

E.2 Sound Delay System

A tracing ball emits a pulse, hitting receivers at different time intervals and the time delay

is used to calculate the distance from each sensor by triangulation.

Figure E.3 Sound Receiving Unit

xii

Equipment Required

Ultrasonic Range Finder (sound wave receiver)

Pulse Emitting Balls

Miscellaneous Parts (wire, glue, cauking)

Basic Stamp and Programming kit for the control of the camera system, timing, and

power supply (optional)

Limitations

The Sound Delay System is complicated by the effects of echo caused by the reflection

off the vessel walls. Furthermore, external noise may corrupt data and resonance of the

tank and contents must be considered. Finally, the flow of liquid in the tank may affect

sound waves resulting in distorted data.

E.3 Light Tracking System

This approach requires internal darkness, with a light emitting tracer ball (Figure E.5)

flowing within the tank. Photo-sensors, attached to two servo motors, are mounted on the

side of the tank (Figure E.4) to track the position of the ball as it moves within the tank.

These servo motors ensure that the sensor unit is pointed at the tracer ball, and from the

position of the two separate photo-sensor arrays, a 3D plot of the ball position can be

derived.

xiii

Figure E.4 Tracking System with Photo-Resistors

Figure E.5 Light Diode Tracing Ball

Equipment Required

Light Emitting Tracer Balls (photo-diode)

Photo-Resistor Sensors (detects the intensity of light)

Servo Motors and Control (control the motion of the sensory array)

Motor Control Mounting Board

Stamp and Programming kit for the control of camera system, timing, and power supply

Miscellaneous Parts (wire, glue, cauking)

xiv

xv

Limitations

The Light Tracking System is complicated by the refraction of light within the liquid

medium and reflection off the plate and shaft. Furthermore, photo-diodes may not be

measured if not directed at the photo-resistors.

Cost

Quantity Amount

Stamp Kit 1 $236.00

Motor 4 $39.96

Motor Board 2 $118.00

Photo Resistor 8 $14.40

Photo-Diode 4 $26.40

Miscellaneous $89.90

Total in US Funds $524.66