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Modelling, Testing and Optimization of a Passive
Solar Updraft Aeration System for Aquaculture in
the Developing World
by
Shakya Sur
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by Shakya Sur 2017
Modelling, Testing and Optimization of a Passive Solar Updraft Aeration System for
Aquaculture in the Developing World
Shakya Sur
Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
2017
Abstract
Pond aquaculture is major source of food security and income in the Asia-Pacific region. Over
70% of ponds are operated by smallholder farmers who do not have access to aeration technology for
proper management of dissolved oxygen levels. The Solar Updraft Aeration (SUpA) system was
developed to provide a low-cost, sustainable alternative to conventional aeration in resource-
constrained environments. This thesis presents a framework for identifying a suitable design of the
SUpA system for large-scale field testing. A comprehensive model was developed using computational
fluid dynamics (CFD) and validated in the bench-scale. The model was used to conduct a broad search
of the design space of each configuration. The inverted prism configuration was selected for further
optimization based on results from CFD and preliminary field tests. The optimized geometry showed
an improvement of 81% over a reference geometry based on previous designs and was selected for
testing in the future.
ii
Acknowledgements
Firstly, I would like to extend my sincere gratitude to my supervisor, Professor Amy M. Bilton,
for her unwavering support and guidance throughout my journey as a graduate student in the Water and
Energy Research Laboratory. Working on a research project with tangible, real-world impacts for
people living in underserved communities was a truly unique experience. She encouraged me to not
only grow as a researcher in the laboratory, but to also push myself outside my comfort zone and
develop a broad set of hands-on skills. I was privileged to have been part of a team that travelled to
Vietnam and Bangladesh multiple times over the last two years. Navigating the challenges and rewards
of working in the field greatly enriched my experience as a graduate student. I would also like to thank
Professor Bilton for giving me the opportunity to travel to Charlotte, North Carolina and present my
research at the ASME International Design Engineering Technical Conference in August, 2016.
I would also like to thank Professor Kamran Behdinan and Professor Fae Azhari for their
support and valuable feedback during the development of this thesis.
I am grateful to my colleagues at the Water and Energy Research Laboratory for offering
assistance, technical and moral support whenever needed. In particular, I would like to thank Mr. Jawad
Mirza for setting up the pH-indicated flow visualization apparatus and providing experimental data,
and Mr. Ahmed Mahmoud for conducting the first bench-scale experiments of the SUpA system.
I am also thankful to Elan Pavlov from Curiositate Inc and Matthew Comstock for their
continued technical advice and recommendations throughout the development of the SUpA technology.
I would like to acknowledge the support of Mr. Mohammed Yeasin, Mr. Tonmoy K. Biswas, Mr. F.
M. Kamrul Islam, Ms. Dewan Tashnuva Yeasmin, Mr. Baadruzzoha Sarker and other staff members at
the Bangladesh Rural Advancement Committee (BRAC) for providing regular updates from the field,
coordinating data collection and overseeing device installation in Bangladesh.
Finally, I thank my parents and my partner Meghan for their unconditional support and for
sticking with me through all the highs and lows of the last two years.
iii
Contents
Abstract ..................................................................................................................................... ii
Acknowledgements .................................................................................................................. iii
List of Tables .......................................................................................................................... viii
List of Figures .......................................................................................................................... ix
1. Introduction .................................................................................................................... 1
1.1 Importance of Aquaculture ......................................................................................... 1
1.2 Impact of Water Quality and Dissolved Oxygen on Aquaculture .............................. 2
1.3 Alleviating Stratification ............................................................................................ 5
1.4 Solar Updraft Aeration System................................................................................... 7
1.5 Thesis Objective & Contributions .............................................................................. 9
1.6 Thesis Organization .................................................................................................. 10
2. Literature Review ......................................................................................................... 11
2.1 Modelling of Pond Dynamics ................................................................................... 11
2.2 Natural Convection: An Overview ........................................................................... 13
2.3 Natural Convection in Enclosures ............................................................................ 15
2.4 CFD-Based Optimization ......................................................................................... 19
2.4.1 Design Sampling ................................................................................................. 19
2.4.2 Surrogate Modelling ............................................................................................ 21
2.4.3 Optimization ........................................................................................................ 23
2.5 Chapter Summary ..................................................................................................... 24
iv
3. Design Solutions ........................................................................................................... 26
3.1 Rod-Fin Design ........................................................................................................ 26
3.2 Bent-Fin Design........................................................................................................ 27
3.3 Inverted Prism Design .............................................................................................. 28
3.4 Metrics for Performance Characterization ............................................................... 29
4. SUpA System Modelling .............................................................................................. 30
4.1 Model Geometry ....................................................................................................... 30
4.2 Meshing .................................................................................................................... 31
4.3 Boundary Conditions ................................................................................................ 33
4.4 Solver Setup.............................................................................................................. 35
4.5 Results ...................................................................................................................... 36
4.5.1 Mass Flow Output ............................................................................................... 36
4.5.2 Velocity Distribution ........................................................................................... 40
4.6 Solution Independence from Solver Parameters....................................................... 42
4.6.1 Independence from Time Step Size ..................................................................... 42
4.6.2 Mesh Independence ............................................................................................. 43
4.7 Comparison with 3D Modelling ............................................................................... 45
4.8 Chapter Summary ..................................................................................................... 49
5. Model Validation .......................................................................................................... 50
5.1 Approach .................................................................................................................. 50
5.2 Bench-Scale Setup .................................................................................................... 51
v
5.2.1 Rod-Fin Geometry .................................................................................................. 51
5.2.2 Bent-Fin Geometry .............................................................................................. 54
5.3 CFD Modelling ......................................................................................................... 56
5.3.1 Geometry & Meshing .......................................................................................... 56
5.3.2 Boundary Conditions ........................................................................................... 56
5.3.3 CFD Results ........................................................................................................ 58
5.4 Comparison with Experimental Results ................................................................... 59
5.5 Inverted Prism .......................................................................................................... 61
5.6 Chapter Summary ..................................................................................................... 63
6. Design Space Exploration ............................................................................................ 64
6.1 Rod-Fin and Bent-Fin Geometries ........................................................................... 64
6.2 Inverted Prism Geometry ......................................................................................... 66
6.3 Results ...................................................................................................................... 67
6.3.1 Rod-Fin ................................................................................................................ 67
6.3.2 Bent-Fin ............................................................................................................... 68
6.3.3 Inverted Prism ..................................................................................................... 69
6.4 Chapter Summary ..................................................................................................... 70
7. Field Implementation .................................................................................................... 72
7.1 Vietnam .................................................................................................................... 72
7.2 Srimangal, Bangladesh ............................................................................................. 73
7.2.1 Device Sizing ...................................................................................................... 74
vi
7.2.2 Manufacturing ........................................................................................................ 75
7.2.2 Pond Installation .................................................................................................. 77
7.2.3 Results: Dissolved Oxygen .................................................................................. 78
7.3 Mymensingh ............................................................................................................. 80
7.3.1 Results ................................................................................................................. 83
7.4 Chapter Summary ..................................................................................................... 83
8. Design Optimization ..................................................................................................... 85
8.1 Problem Formulation ................................................................................................ 85
8.1.1 Design Variables ................................................................................................. 85
8.1.2 Objective Function .............................................................................................. 87
8.1.3 Constraints ........................................................................................................... 87
8.2 Optimization Approach ............................................................................................ 89
8.3 Design Space Sampling ............................................................................................ 90
8.4 Surrogate Model Evaluation and Results ................................................................. 91
8.5 Optimization ............................................................................................................. 94
8.6 Chapter Summary ................................................................................................... 104
9. Conclusion and Future Work ...................................................................................... 105
References ............................................................................................................................. 107
vii
List of Tables
Table 4-1: Boundary conditions applied to SUpA configurations for CFD evaluation ....................... 35
Table 4-2: Mass of water moved by the SUpA configurations ............................................................ 37
Table 5-1: Summary of boundary conditions applied to the different surfaces of the rod-fin and bent-
fin models ........................................................................................................................... 57
Table 7-1: Comparison of design parameters identified for the rod-fin geometry ............................... 74
Table 7-2: Comparison of design parameters selected for the bent-fin geometry ................................ 75
Table 7-3: Comparison of design parameters selected for the inverted prism geometry ..................... 81
Table 8-1: Parameterization of the inverted prism geometry used for shape optimization .................. 86
Table 8-2: Final optimized configuration determined from sensitivity study ...................................... 99
viii
List of Figures
Figure 1-1: Relative contribution of capture fisheries and aquaculture to fish used for human
consumption. Aquaculture accounted for more than half (52%) of the global share of fish
production in 2014 [2] ........................................................................................................ 1
Figure 1-2: Illustration of typical stratified conditions prevailing during the day [10]. Water near the
surface remains supersaturated while the bottom is starved of oxygen .............................. 4
Figure 1-3: A 1hp- paddle-wheel aerator installed at a hatchery in Srimangal, Bangladesh ................. 6
Figure 1-4: Oxygen tablets sold by ACI Animal Health in Mymensingh, Bangladesh. Tablets are the
only form of intervention for supplying oxygen accessible to smallholder ponds in the
region .................................................................................................................................. 7
Figure 1-5: Illustration of proposed SUpA concept. Solar thermal energy from the collector is
conducted to the bottom of the pond via the conduction element. Induced convection
currents help circulate oxygen-rich water from the epilimnion to the oxygen-deficient
regions in the hypolimnion ................................................................................................. 9
Figure 2-1: Vector plot of flow developed in the air-filled, differentially heated square cavity
experimentally analyzed by Tian et al. [25] ...................................................................... 16
Figure 2-2: A schematic of three possible CCD types based on 𝛂𝛂-value of star points for a 2-
dimensional design space. The star points exceed the design limits in the circumscribed
CCD. The original CCD points are scaled down in the inscribed CCD ........................... 20
Figure 3-1: Schematic of the rod-fin geometry. Vertical natural convection is induced from the
uninsulated surface of the cylindrical conduction element ............................................... 26
Figure 3-2: The bent-fin concept uses a single rectangular sheet of metal with the ends bent at right
angles. A rectangular updraft channel guides the convection current from the pond
bottom to the water surface ............................................................................................... 27
ix
Figure 3-3: A schematic of the inverted prism concept. Thermal energy captured by the angled walls
of the collector is transferred to the water through the thickness of the sheet metal ........ 28
Figure 4-1: Schematic of the (a) rod-fin, (b) bent-fin and (c) inverted prism geometries as constructed
using ANSYS DesignModeler 17.1 .................................................................................. 31
Figure 4-2: Illustration of the quadrilateral-dominant grids created for the three SUpA configurations
.......................................................................................................................................... 32
Figure 4-3: Example of a typical pond used for small-scale aquaculture in rural Bangladesh ............ 33
Figure 4-4: Transient mass flow profiles of the rod-fin, bent-fin and inverted prism geometries ....... 36
Figure 4-5: Contour plot of the thermal gradients observed in the (a)rod-fin, (b) bent-fin and (c)
inverted prism geometries. The highlighted dimensions indicate the lengths of the
conduction element where Δ𝑇𝑇 ≥ 1oC................................................................................ 39
Figure 4-6: Plot of velocity vectors observed in the bulk fluid region and updraft channel (inset)
during peak circulation in (a) rod-fin (b) bent-fin and (c) inverted prism models ............ 41
Figure 4-7: Mass flow rate profiles observed for three time-step sizes (dT) of the inverted-prism
model. Largest difference in the total mass of water moved was found to be 0.3%
between the case with dT = 10s and dT = 1s .................................................................... 43
Figure 4-8: Mass flow rate trends corresponding to different sizes of the core mesh elements. The
coarsest mesh with core size = 1.5in under-predicted the total mass flow output by 4%
compared to case with core size = 0.75in ......................................................................... 44
Figure 4-9: Mass flow rate profiles corresponding to different heights (t) of the first inflation layer
and number of layers (n) measured from the heat transfer wall ....................................... 45
Figure 4-10: Schematic of the 3D representation of the inverted prism geometry. Bilateral symmetry
was exploited to evaluate a quarter of the metal body for the 3D CFD model ................. 46
Figure 4-11: The mesh used to discretize the 3D modelling domain of the pond and inverted prism
configuration ..................................................................................................................... 46
x
Figure 4-12: Comparison of the mass flow profile with and without utilization of the ‘shell-
conduction’ feature within Fluent. Simulations were performed using a constant
irradiance of 1000Wm-2 for 1800s .................................................................................... 47
Figure 4-13: Velocity streamlines produced in the 2D and 3D CFD models at the time of occurrence
of peak mass flow rate ...................................................................................................... 48
Figure 4-14: Mass flow profiles observed in the 2D and 3D models of the inverted prism geometry. 49
Figure 5-1: CAD illustration of the bench-scale heating assembly used to validate the CFD model of
the rod-fin configuration ................................................................................................... 52
Figure 5-2: Schematic of the components used for pH-indicated flow visualization of the updraft
flow. The thymol blue indicator changed from yellow to blue at the cathode due to
localized increase in alkalinity when voltage was applied across the electrodes.............. 53
Figure 5-3: Bench-scale heating assembly representing the bent-fin configuration. The heating block
was used to provide uniform heat flux to the horizontal face of the bent metal plate ...... 54
Figure 5-4: Schematic of components used for pH-indicated electrolysis in the bent-fin apparatus. The
platinum wire was fixed on one updraft channel due to the assumption of flow symmetry
on both vertical fins .......................................................................................................... 55
Figure 5-5: 2D cross-section of the polyhedral mesh used for modelling the rod-fin (a) and bent-fin
(b) bench-scale setup ........................................................................................................ 56
Figure 5-6: Illustration of different surfaces of the rod-fin and bent-fin bench-scale models .............. 57
Figure 5-7: Distribution of velocity vectors obtained from the CFD evaluation of the rod-fin bench-
scale model. Peak velocity was found to be 19mm/s at the top of the updraft channel .... 58
Figure 5-8: Flow velocity distribution observed in the CFD model of the bent-fin bench-scale setup.
Peak velocity was 2.9mm/s at the top of the updraft channel ........................................... 59
Figure 5-9: (a), (c) - Cross-section profiles of the boundary layer at different heights (𝒚𝒚 ∗) along the
draft tube of the rod-fin and bent-fin models respectively (b), (d) – Experimentally
xi
measured velocity compared with peak and average velocities at each 𝒚𝒚 ∗ obtained from
CFD for the rod-fin and bent-fin geometries respectively ................................................ 60
Figure 5-10: Evolution of the natural convection flow in the bench-scale setup of the inverted-prism
geometry, visualized using food colouring injected at the base of the channel ................ 62
Figure 6-1: Geometry parameterization of the rod-fin configuration ................................................... 65
Figure 6-2: Definition of design variables of the bent-fin geometry .................................................... 65
Figure 6-3: Parameterization of the inverted prism geometry .............................................................. 66
Figure 6-4: Mean effects plot normalized by the average response of 27 configurations of the rod-fin
geometry generated using a Taguchi-based orthogonal array .......................................... 67
Figure 6-5: Normalized effects plot of the design space search of the bent-fin geometry ................... 68
Figure 6-6: Plot of normalized effects corresponding to the inverted-prism geometry........................ 69
Figure 7-1: CAD illustration of the rod-fin prototype tested in Vietnam in November 2015 .............. 73
Figure 7-2: Satellite image of the test pond located in the BRAC-operated hatchery in Srimangal .... 73
Figure 7-3: CAD illustrations of the rod-fin (a) and bent-fin (b) prototypes installed in Srimangal ... 76
Figure 7-4: The rod-fin device prior to being installed (left), and the bent-fin device being lowered
into the test pond by staff at the hatchery ......................................................................... 76
Figure 7-5: Difficulties in welding the solid 4in diameter aluminum rod to the thin aluminum sheet
resulted in poor contact between the collector and the conduction element ..................... 77
Figure 7-6: Instruments used for data collection from Srimangal - (a) optical DO logger probe (b)
ultrasonic anemometer (c) pyranometer ........................................................................... 78
Figure 7-7: The devices and weather station were installed along a diagonal across the test pond. The
SUpA devices were installed at opposite ends of the diagonal with the weather station
situated in the middle of the pond ..................................................................................... 78
Figure 7-8: Plot of DO data compared between measurements taken at the device and at a control
location for the rod-fin (top) and bent-fin (bottom) devices in Srimangal ....................... 79
Figure 7-9: Modified inverted prism with vertical updraft channel walls ............................................ 81
xii
Figure 7-10: Flow velocity vectors observed for the modified inverted prism geometry .................... 81
Figure 7-11: A prototype of the modified inverted prism being installed at a test location in
Mymensingh ..................................................................................................................... 83
Figure 8-1: Schematic of the design variables given in Table 8-1 ....................................................... 86
Figure 8-2: Geometric relationship between the solar hour angle and sloped length, base width and
collector angle of the inverted prism geometry ................................................................ 88
Figure 8-3: Illustration of approach and analysis tools used to arrive at an optimized configuration of
the inverted prism geometry ............................................................................................. 90
Figure 8-4: Distribution of the 54 design points generated by the enhanced CCD design sampling
method in ANSYS Workbench ......................................................................................... 91
Figure 8-5: Partial representation of the five-dimensional response surface generated using the
Kriging tool in ANSYS Workbench ................................................................................. 94
Figure 8-6: Convergence of mass flow output across generations ....................................................... 96
Figure 8-7: Plot of the eight candidate solutions obtained using the Multi-Objective Genetic
Algorithm .......................................................................................................................... 97
Figure 8-8: Summary of sensitivity study performed around Candidate #5. Decreasing updraft gap by
50% produced a 1% increase in mass flow output ............................................................ 98
Figure 8-9: Comparison of the mass flow rate profile of the optimized configuration (MOGA
Candidate) and the reference geometry defined in Section 4.1 ........................................ 99
Figure 8-10: Comparison of velocity vector distribution of (a) the reference geometry and (b) the
optimized design ............................................................................................................. 101
Figure 8-11: Comparison of the fluid and thermal boundary layers obtained at the mid-depth of the
inverted prism for the reference and optimized designs ................................................. 102
Figure 8-12: Dimensions of the 3D geometries and corresponding flattened sheet metal plan of (a)
the reference geometry and (b) the optimized design ..................................................... 103
xiii
1. Introduction
1.1 Importance of Aquaculture
Broadly defined as the cultivation of all forms of aquatic animals and plants, aquaculture is a key
source of income and food security to more than 20 million people worldwide [1]. It is one of the
fastest growing industries in the world, maintaining an annual rate of 7% between 1970 and 2000 and
6.2% between 2000 and 2012 [1]. In 2014, as shown in Figure 1-1, global aquaculture production
surpassed yields from capture fisheries for the first time [1], [2] .
Figure 1-1: Relative contribution of capture fisheries and aquaculture to fish used for human
consumption. Aquaculture accounted for more than half (52%) of the global share of fish
production in 2014 [2]
Developing countries, particularly those in the Asia-Pacific and South Asia, have played a
leading role in the rapid growth of the industry [1]. In 2010, Asia accounted for 53.1 million tonnes or
89% of the net global output from aquaculture [3]. Fish forms a staple diet of many countries in this
region, with countries such as Bangladesh and Cambodia obtaining 57% and 75% of their animal
0%
20%
40%
60%
80%
100%
1954 1964 1974 1984 1994 2004 2014
Sha
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f per
Cap
ita F
ish
Con
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Aquaculture Capture Fisheries
1
protein intake from fish respectively [4], [5]. The industry employs more than 17 million people across
the continent, representing more than 84% of all people engaged in aquaculture worldwide [1], [2],
[6]. In addition, the industry is a major economic driver in the region, contributing to 6% of the GDP
of Laos, 4.4% of the GDP in Bangladesh and 7.1% of the GDP of Vietnam [5], [7], [8].
A large proportion of the growth of the aquaculture sector is attributed to small-scale farmers,
estimated to comprise 70-80% of the total workforce in the sector in Asia and around the world [9].
‘Small-scale farmers’, in the context of aquaculture, generally refers to farmers managing low-yield
operations, usually on their own property. They are typically resource-poor and lack the technical and
financial capital of highly intensive, large-scale farmers. The ponds operated by these farmers are
homestead ponds, usually used for multiple purposes by the household. These ponds are generally not
managed and maintained for optimal fish production, and are often found to suffer from poor water
quality. As a result, the full potential of these ponds is not realized, constraining the productivity of
small-scale farmers in the region.
1.2 Impact of Water Quality and Dissolved Oxygen on Aquaculture
Lack of adequate water quality management has significant implications on the long-term
health and productivity of aquaculture ponds [10]. Water quality is a general term characterized by
levels of dissolved oxygen (DO), nutrients, organic matter, pH and salinity. DO is the most important
factor affecting the growth of fish after fish feed*. It directly impacts fish growth, metabolism and
resistance to disease. It is present in the water in the form of microscopic bubbles interspersed among
water molecules. The solubility of oxygen in water is quite low relative to the amount of oxygen in the
air and varies inversely with temperature. Oxygen enters the water through diffusion from the
atmosphere across the air-water interface, when the concentration of oxygen in the water is less than
the partial pressure of oxygen in the air.
The rate of diffusion of oxygen across the air-water interface is significantly faster than the
diffusion of oxygen within the water volume [10]. As a result, water can be under-saturated or
2
supersaturated with dissolved oxygen. Supersaturation of oxygen is often observed near the surface of
natural water bodies such as ponds and lakes due to the presence of microscopic plants known as
phytoplankton. During the day, with adequate amount of incident solar energy, phytoplankton release
large quantities of oxygen to the water via photosynthesis. This dissolved oxygen is then consumed
during respiration by all living organisms in the water column, including fish, aquatic plants, benthic
organisms dwelling in the pond bed, and the phytoplankton themselves. It is also used in the aerobic
decomposition of organic wastes. Dissolved oxygen levels in the pond are thus closely related to the
amount of solar energy received by the pond and changes in the pond’s thermal characteristics over the
course of the day.
During the day, the primary source of thermal energy in a water reservoir is solar radiation
incident on the water surface. Penetration of solar energy into the water column is governed by
Lambert’s law, which states that the amount of radiation absorbed by the water exponentially decreases
with distance from the surface. Two consequences arise as a result of this phenomenon. Firstly, only
the phytoplankton present near the surface receive sufficient sunlight for photosynthesis. Secondly, a
thermal gradient develops across the pond depth. The temperature of the water near the surface is
several degrees higher than water near the bottom of the pond. In the absence of wind or heavy rain, a
stable thermal stratification thus develops in the pond due to the warmer and less dense water present
above the colder, heavier water at the bottom. As a result, the oxygen produced by phytoplankton at
the surface remains confined to the upper stratum of the pond, leading to hyperoxic conditions at the
top and anoxic conditions at the pond bottom. The thermal stratification in turn creates a stable
dissolved oxygen stratification across the water column. This phenomenon is depicted in Figure 1-2.
The upper layer of the pond is commonly referred to as the epilimnion, while the bottom layer is known
as the hypolimnion. Water within the epilimnion undergoes some mixing due to the presence of winds
at the surface, resulting in nearly constant oxygen and temperature levels up to a finite depth. Beyond
this depth, surface effects diminish, resulting in a sharp decline in oxygen and temperature levels across
a narrow stratum known as the metalimnion or thermocline. Thermoclines are typically characterized
3
by a temperature gradient of at least 1oCm-1. Beyond the thermocline, in a layer known as the
hypolimnion, the gradients of both oxygen and temperature gradually decrease up to the pond bottom.
Figure 1-2: Illustration of typical stratified conditions prevailing during the day [10]. Water near
the surface remains supersaturated while the bottom is starved of oxygen
The stratification developed in a pond volume is not constant and is sensitive to changes in
solar irradiance, wind speeds, rainfall and amount of organic nutrients present in the pond. During the
day, water supersaturated with oxygen in the epilimnion loses oxygen to the atmosphere at a higher rate
than the diffusion of oxygen to subsurface layers. This deprives the lower depths of the oxygen needed
to sustain a healthy fish population. At night, with no photosynthetic production by the phytoplankton
and limited oxygen diffusion from the atmosphere being the only DO input to the pond, most of the
oxygen produced during the day is depleted during respiration by the pond biomass. This often results
in minimal oxygen levels around dawn throughout the pond. Some form of intervention is usually
required at this time to ensure a sufficient supply of DO.
Oxygen and temperature stratification has significant ramifications on the overall health of the
pond ecosystem. While tolerance to anoxic conditions varies with different fish species, regular
exposure to low dissolved oxygen increases the chances of fish stress and mortality. The lack of mixing
4
also leads to the accumulation of toxic gases such as ammonia produced from anaerobic decomposition
of organic wastes settling on the pond bottom. Stratification further increases the risk of a mass fish kill
due to a sudden pond turnover, a phenomenon that occurs when the cooler, anoxic water mixes
throughout the pond volume during high winds or severe storms.
1.3 Alleviating Stratification
Several strategies are used across the aquaculture industry to improve the availability and
distribution of dissolved oxygen throughout the pond. Some of these strategies aim to directly add
oxygen to the water, while others help redistribute DO throughout the pond. The most commonly used
method is aeration, the process of inducing oxygen transfer to water by increasing the surface area of
water in contact with air. Aeration is generally done at night when the DO levels are at their lowest.
The most commonly used types of aeration equipment for pond aquaculture include vertical pumps,
pump sprayers, propeller-aspirator-pumps, paddle wheels and diffused-air systems [11]. These devices
rely on electrical energy to increase the surface area of the water in contact with air, by splashing the
surface of water, forcing water into the air, or injecting a stream of air bubbles into the water.
Characterization of aeration performance and oxygen transfer rates of these systems is discussed in
[11]. Figure 1-3 shows a paddle wheel aerator typically installed in large-scale farms and hatcheries.
The example shown was installed at a hatchery in in Srimangal, Bangladesh.
5
Figure 1-3: A 1hp- paddle-wheel aerator installed at a hatchery in Srimangal, Bangladesh
Apart from increasing dissolved oxygen levels through diffusion, aerators also facilitate mixing
and destratification by moving oxygen-rich surface water to other regions of the pond [10]. This
movement of water indirectly helps increase overall oxygen availability by reducing diffusive losses to
the atmosphere from the supersaturated surface water. Among the aerators discussed above, Boyd et
al. found that propeller-aspirator type aerators induced the most circulation throughout the pond
volume. Various technologies dedicated to circulating water have also been devised, including air-lift
pumps, ‘water blenders’ [12], and axial impellers. Additional information on these systems can be
found in [10].
The aeration and circulation devices described above require reliable access to electricity and
feature complex systems with many moving parts. As such, they are typically used to supplement
intensive aquaculture in the developed countries and large scale commercial fish farms. In the context
of small-holder aquaculture in the developing world, these technologies are ill-suited for widespread
adoption. Surveys conducted in partnership with BRAC in Bangladesh revealed that out of 120 fish
farmers interviewed in the Mymensingh district, only 5 deployed an aeration system in their ponds. The
primary deterrent quoted by the farmers was high capital and operating costs of running an aeration
unit, typically a paddle-wheel system such as the example in Figure 1-3. The market opportunity for a
6
cost-effective aeration system was further proven as 93% of farmers also reported the occurrence of
fish kills in the last 5 years, out of whom 71% blamed disease and stress caused by low dissolved
oxygen levels. Furthermore, the present survey as well as previously published research [13], [14]
reported the widespread use of chemicals to control diseases and provide oxygen. Sold in containers
such as the example in Figure 1-4, oxygen tablets were usually added every two weeks and used for
emergency aeration when fish were observed to gasp for air at the water surface.
Figure 1-4: Oxygen tablets sold by ACI Animal Health in Mymensingh, Bangladesh. Tablets are
the only form of intervention for supplying oxygen accessible to smallholder ponds in the region
The average cost of each treatment was nearly $10 (USD). The tablets thus not only required
manual intervention by the farmer, but also accrued high operating costs with repeated use over the
long-term. Furthermore, as highlighted by Shamsuzzaman et al. [13], the long-term unregulated use of
chemicals in aquaculture posed significant environmental and health hazards, from increasing pH
imbalance in the pond to contamination of groundwater and food consumed by humans.
1.4 Solar Updraft Aeration System
The challenges facing small-scale aquaculture farmers described in this chapter present a
unique opportunity for a technological intervention that provides an alternative to expensive, high-
7
maintenance and mechanically complex aeration systems. Such an intervention would have to be
designed for implementation in resource-constrained settings such as rural Bangladesh and other
regions in the developing world. The Water and Energy Research Lab at the University of Toronto and
Curiositate Inc. in Massachusetts have developed such a concept known as the Solar Updraft Aeration
(SUpA) system. The SUpA system was conceived with the goal of reducing the adverse impact of pond
stratification in small-scale, homestead aquaculture in developing regions. Schematically shown in
Figure 1-5, the system consists of two main components: a solar collector and a conduction element.
The solar collector receives incident solar thermal irradiance �̇�𝑞𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠. At steady-state, a portion of this
incident heat flux, �̇�𝑞𝑐𝑐𝑠𝑠𝑐𝑐𝑐𝑐 is conducted to a conduction element, while the remainder, �̇�𝑞𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠, is lost to
radiation and/or convection from the surface of the collector. The conduction element then transfers the
heat flux �̇�𝑞𝑐𝑐𝑠𝑠𝑐𝑐𝑐𝑐 to the surrounding water via natural convection. The SUpA device has no moving parts
and relies solely on solar energy to induce mixing within the water column. Furthermore, it is a passive
system with nearly zero operating costs, requiring minimal maintenance following installation.
8
Figure 1-5: Illustration of proposed SUpA concept. Solar thermal energy from the collector is
conducted to the bottom of the pond via the conduction element. Induced convection currents
help circulate oxygen-rich water from the epilimnion to the oxygen-deficient regions in the
hypolimnion
1.5 Thesis Objective & Contributions
The overall objective of this work was to develop a framework to optimize the system design for
further evaluation of the SUpA technology in the field. In this framework, a range of three system
configurations were investigated. Comprehensive computational fluid dynamics (CFD) models of the
various designs were developed to characterize their performance. The overall modelling strategy was
validated using bench-scale experiments conducted in the laboratory. A broad search of the design
space of each system configuration was carried out to identify benchmark design parameters of each
geometry. The three configurations were evaluated based on the predictions of their CFD models as
well as their performance in preliminary field tests. The best performing design was optimized to further
9
improve system performance and determine a suitable configuration for implementation in further
testing in the future.
1.6 Thesis Organization
Following a review of published literature in Chapter 2, Chapter 3 introduces the three designs
of the SUpA system developed by the research team at the Water and Energy Research Laboratory,
University of Toronto. Chapter 4 discusses the development of CFD models of each design and
compares the performance of baseline geometries. Validation of these models using bench-scale
experiments is then discussed in Chapter 5. A broad, high-level search of the design space of each
geometry is conducted and analyzed in Chapter 6 to identify the best performing configuration of each
geometry. Chapter 7 reviews the performance of these designs in preliminary field tests conducted in
Bangladesh. Lastly, Chapter 8 discusses the optimization of the SUpA system to identify a
configuration for implementation in future, large-scale tests.
10
2. Literature Review
A review of published literature was performed to develop an efficient design, modelling and
optimization strategy for the SUpA system. The first section provides an overview of literature on
modelling of pond dynamics. The second section considers the parallel application of natural
convection in enclosures and discusses its relevance for modelling the SUpA device. The final section
of the literature review focuses on several examples of design optimization coupled with CFD codes.
2.1 Modelling of Pond Dynamics
As discussed in [11], naturally occurring water reservoirs such as ponds and lakes are highly
dynamic systems. There are complex interactions between physical, chemical and biological factors
that influence overall energy and dissolved oxygen characteristics over the course of a day. Changi et
al. [15] were among the first to numerically model natural convection turbulence and analyze its effect
on water circulation and changes in dissolved oxygen in water bodies. They characterized the stability
of a thermally-stratified water column using the Richardson number (Ri), a dimensionless quantity
given by
𝑅𝑅𝑅𝑅 =𝑔𝑔. (𝑑𝑑𝑑𝑑/𝑑𝑑𝑧𝑧)
𝑑𝑑(𝑑𝑑𝑑𝑑/𝑑𝑑𝑧𝑧)2 (Eq 2-1)
where 𝑔𝑔 is the acceleration due to gravity (980cm/s2), 𝑑𝑑 is the velocity of the convective
current (cm/s) given by 𝑑𝑑 = 0.48𝑤𝑤0.5 for a wind speed 𝑤𝑤(cm/s), 𝑑𝑑 is the fluid density(g/cm3) and 𝑧𝑧 is
the mixing depth being evaluated (cm). A Richardson number less than 0.25 was found to indicate an
unstable water column in which circulation was spontaneously induced both horizontally and vertically.
Lamoureux et al. [16] modelled temperature and energy dynamics of outdoor aquaculture ponds. They
developed a Pond Heat and Temperature Regulation (PHATR) model to predict the pond temperature
in heated and unheated ponds and quantify the magnitude of energy transfer mechanisms occurring
within those ponds. Daily solar irradiation, wind speed, ambient air temperature, and pond bed
temperature were used as meteorological data inputs to the model. A set of non-linear differential
11
equations representing heat transfer across a control volume defined in the pond was solved using a 4th-
order Runge-Kutta method. Their solutions showed that the long and shortwave radiation components
of the incident solar energy were the most dominant sources of heat in the case of unheated ponds.
Prior to the rapid advancement and accessibility to CFD software, modelling of hydrodynamics
in ponds was limited to complex numerical models such as those discussed above. Existing CFD-based
research typically focused on flow patterns occurring in wastewater treatment ponds. An overview of
the significant body of literature available on this topic can be found in [15], [17]. A recent example of
CFD modelling of wastewater ponds can be found in [18]. In this work, Karteris et al. simulated
convective flows occurring in a covered anaerobic sewage treatment pond using FLUENT and found
good agreement with physical measurements of flow velocities. Aspects of their modelling approach
are discussed in later sections. CFD has also been used to determine flow fields occurring in large
aerated lagoons used for secondary treatment of wastewater, as reported by Wu [19]. Submerged
impellers are used to aerate these lagoons by increasing exposure of the wastewater to aerobic
microorganisms. Wu analyzed the residence time and removal of biological oxygen demand (BOD)
based on different configurations of aerators in each pond.
Strategies used for modelling wastewater treatment ponds were adapted for aquaculture by
Peterson et al. [20]. They developed the first significant application of CFD to investigate fluid
dynamics in aquaculture ponds. They evaluated the impact of aerators on pond water circulation and
sediment shear stress in a 1-hectare, intensive shrimp culture pond. They compared the circulation
produced by paddle-wheel and propeller-aspirator aerators. A tool called ‘Automatic Pond Simulation
Methodology’ (AUTOPOND), developed previously by the authors, was used to spatially discretize a
three-dimensional representation of the shrimp pond. The CFD code was implemented using FIDAP, a
finite-element based solver. The authors compared CFD results to physical measurements taken at
various locations. They observed large discrepancies in flow velocities near the water surface due to
the presence of localized, unsteady winds. Higher fidelity was noted in the modelling of the pond
bottom where flow intrusions from surface effects were limited.
12
Another example of the use of CFD to model aeration systems is found in [21]. The authors
modelled paddle-wheel aerators installed in open raceway ponds for the large-scale cultivation of
microalgae. They analyzed the effect of aerator placement, bottom clearance and operating speed on
the vertical mixing of the water column. They adjusted these parameters to maintain a minimum vertical
flow velocity to prevent algae from settling at the bottom.
The literature survey above proves that CFD can be successfully used to simulate both natural
and artificially-induced flows in water reservoirs. However, the modelling of natural convection
specifically within aquaculture ponds was not found. The aeration systems used in aquaculture were
limited to paddle-wheels and propeller-aspirators. These systems were not deployed in resource-
constrained environments such as those found in the developing world. Furthermore, to the best of the
author’s knowledge, no literature on the modelling of aquaculture water circulation systems such as
those described in [10] or natural convection-based systems has been published.
2.2 Natural Convection: An Overview
Natural or free convection refers to the motion of fluid particles driven by buoyancy forces due
to temperature or density differences in the bulk fluid. Free convective flows are typically classified as
internal and external flows, depending on whether they are confined to a closed volume or are able to
move along a free surface. Natural convection flows are characterized by two dimensionless quantities
known as the Grashof Number and Rayleigh number, defined as
𝐺𝐺𝑟𝑟𝐿𝐿 =𝑔𝑔β(Ts − 𝑇𝑇∞)𝐿𝐿3
𝜈𝜈2 (Eq 2-2)
and
𝑅𝑅𝑎𝑎𝐿𝐿 =𝑔𝑔β(Ts − 𝑇𝑇∞)𝐿𝐿3
𝜈𝜈𝜈𝜈
(Eq 2-3)
where 𝑔𝑔 is the gravitational acceleration constant (m/s2), 𝛽𝛽 is the coefficient of volume
expansion of the fluid (1/K), 𝑇𝑇𝑠𝑠 is the temperature of the heated surface (oC), 𝑇𝑇∞ is the ambient
13
temperature in the fluid (oC), 𝐿𝐿 is the characteristic length of the geometry (m), and 𝜈𝜈 and 𝜈𝜈 are the
kinematic viscosity (m2/s) and thermal diffusivity (m2/s) of the fluid respectively. In the case of an
isoflux boundary condition on the heated surface, Eq 2-2 and Eq 2-3 are modified as
𝐺𝐺𝑟𝑟𝐿𝐿 =𝑔𝑔β�̇�𝑞𝑘𝑘𝜈𝜈2
𝐿𝐿4 (Eq 2-4)
and
𝑅𝑅𝑎𝑎𝐿𝐿 =𝑔𝑔β�̇�𝑞𝑘𝑘𝜈𝜈𝜈𝜈
𝐿𝐿4 (Eq 2-5)
where �̇�𝑞 is the uniform heat flux on the surface. 𝐺𝐺𝑟𝑟𝐿𝐿 and 𝑅𝑅𝑎𝑎𝐿𝐿 numbers are related as
𝑅𝑅𝑎𝑎𝐿𝐿 = 𝐺𝐺𝑟𝑟𝐿𝐿.𝑃𝑃𝑟𝑟
where 𝑃𝑃𝑟𝑟 is the Prandtl number of the fluid medium.
Flow characteristics of buoyancy-driven flows are obtained by the solution of the Navier-
Stokes equations governing continuity, momentum and energy of a fluid element. The Navier-Stokes
equations expressed in Cartesian and cylindrical coordinates can be found in [22], [23]. Adjustments
are made to the body force term in the momentum equation to reflect changes in fluid density with
temperature. The volume expansion coefficient, 𝛽𝛽, represents this variation of density with temperature
at a constant pressure [24]:
𝛽𝛽 =1𝑑𝑑�𝜕𝜕𝑑𝑑𝜕𝜕𝑇𝑇�𝑃𝑃
(Eq 2-6)
The above relationship is implemented as the ‘Boussinesq Approximation’ to expedite
computation in numerical flow solvers, wherein the partial derivative of density is replaced by finite
differences of the density and temperature. This leads to the following linear relationship at constant
pressure:
𝑑𝑑∞ − 𝑑𝑑 = 𝑑𝑑 .𝛽𝛽 . (𝑇𝑇 − 𝑇𝑇∞) (Eq 2-7)
where 𝑑𝑑∞ and 𝑇𝑇∞ are reference density and temperature values recorded at the film
temperature. The Boussinesq approximation is typically used when expected temperature difference
14
between the heated surface and the bulk fluid is less than 40oC. Using the Boussinesq approximation,
the velocity of a buoyancy-driven flow in the absence of viscous forces is expressed as
𝑣𝑣0 = �𝑔𝑔𝛽𝛽Δ𝑇𝑇𝑇𝑇 (Eq 2-8)
where Δ𝑇𝑇 is the positive difference in temperature between two points in a fluid along a vertical
height 𝑇𝑇[25].
Analogous to the Reynolds number in forced convective flows, the Grashof number governs
the nature of the flow regime in the free convection boundary layer. Flows beyond a critical 𝐺𝐺𝑟𝑟 exhibit
turbulence and flow instabilities in the flow field. The value of the critical 𝐺𝐺𝑟𝑟 depends on the geometry,
its orientation, surface temperature distribution and fluid properties. For example, for heated vertical
plates, the natural convection flow becomes fully turbulent for 𝐺𝐺𝑟𝑟 ≥ 109[24]. In the case of enclosures,
studies conducted by [25]–[27] show that the transition to turbulent flow occurs at 𝐺𝐺𝑟𝑟~107, with fully
turbulent flow observed at 𝐺𝐺𝑟𝑟~1011. Solution of the flow field in the turbulent regime necessitates the
use of a suitable model to accurately capture dynamics within the hydrodynamic and thermal boundary
layers. In the turbulent flow regime, the temperature and velocity terms in the Navier-Stokes equations
are represented by the sum of a mean value and a fluctuating component. Various models have been
developed to resolve the fluctuating terms in order to obtain a closed solution of the governing equation.
Variants of the 𝑘𝑘-𝜀𝜀 model and the 𝑘𝑘-𝜔𝜔 model are most commonly used, as described in [22], [28], [29].
2.3 Natural Convection in Enclosures
As demonstrated by [20], the surface of a pond can be adequately represented as a rigid wall
with zero roughness. Therefore, the fluid volume can be treated as a single fluid phase contained in an
enclosed domain. A large body of literature was found on the modelling of free convection in enclosures,
and was thus used to develop a robust CFD modelling strategy for the SUpA system. A review of some
of the most relevant findings is presented here.
A standard case frequently used to study convection in enclosures is a square, air-filled cavity
with differentially heated side walls [26]. Tian et al. [25] and Ampofo et al. [27] performed highly
15
controlled experiments with 𝑅𝑅𝑎𝑎 = 1.5 × 109 . These experiments provided benchmark data for
validating various turbulence modelling strategies. Figure 2-1 shows a plot of the vector distribution
observed by the authors at the mid-section of a differentially heated cavity. The authors noted the
confinement of the flow to the edges of the domain, and the relatively negligible movement in the core
fluid. They also observed the occurrence of secondary flows or flow reversals at the regions
approximately highlighted in the figure. Ampofo et al. compared the Large Eddy Simulation (LES) and
k-𝜀𝜀 turbulent models with their experimental results and found better prediction of turbulence quantities
using the LES model [27].
Figure 2-1: Vector plot of flow developed in the air-filled, differentially heated square cavity
experimentally analyzed by Tian et al. [25]
Zitzmann et al. [30] used the CFX-5 CFD code to compare the standard k-𝜔𝜔, SST (Shear-
Stress-Transport) k-𝜔𝜔 , LRR-IP (Launder-Reece-Rodi Isotropic Production) and SMC-𝜔𝜔 (Second
16
Moment Closure) turbulence models with the experimental results of [25]. Radiative heat transfer inside
the cavity was ignored. The authors found the best agreement with experimental data using the k-𝜔𝜔
model. They also investigated the influence of near-wall spatial resolution by varying the thickness of
the first inflation layer. They found that for Ra = 1.56 × 109 in the cavity given in [25], thickness of the
thermal boundary layer at the cavity midplane was 40mm. It was found that 13 inflation layers with a
first layer height equal to 0.1mm was adequate for reproducing the experimental results of [27]. Wu et
al. [28] also used the same data to evaluate the accuracy of the standard k-𝜀𝜀, RNG (renormalization
group) k-𝜀𝜀, realizable k-𝜀𝜀, standard k-𝜔𝜔, and SST k-𝜔𝜔 models. These models were implemented in
transient simulations computed up to 4000s. Simulation results were compared to experimental data
from [27] and data from Direct Numerical Simulation (DNS) published by [31]. The SST k-𝜔𝜔 model
gave the most accurate results for vertical velocities in the thermal boundary layer and in predicting the
extent of thermal stratification inside the enclosure. Contrary to the findings of [30], the standard k-𝜔𝜔
model was found to be the worst performer out of all five 2-equation models tested. Wu et al. [28] also
studied differences between 3D and 2D modelling as well as the significance of radiative heat transfer
within the cavity. They found that the use of a 3D model only slightly improved prediction of
temperature and velocity profiles at the mid-plane of the cavity. Accounting for heat transfer via
radiation reduced previously observed errors in predicting thermal stratification when measured
temperature profiles were used as boundary conditions on the horizontal walls. However, the effect of
radiation on flow rates and flow patterns was not discussed.
Buoyancy-driven flows in enclosures with different aspect ratios (cavity height/cavity length),
fluids and Rayleigh numbers have also been studied. Turan et al. [32] performed a set of simulations
for two-dimensional, steady-state laminar convection in cavities with aspect ratios ranging from 0.125
to 8, fluids with Prandtl numbers 0.71 to 7 and Rayleigh numbers ranging from 104 – 106. They reported
a direct relationship between the strength of convective circulation induced in the cavity and the cavity’s
aspect ratio. Since most ponds and water reservoirs have aspect ratios less than 1, tall enclosures are
17
not discussed further in this review. The reader is referred to [32] for additional information on this
topic. Convection in shallow enclosures was investigated by [33]–[35]. In [33], their transient
behaviour was examined and used to predict the onset of steady-state conditions. For an enclosure with
height ℎ and length 𝑙𝑙, a timescale for attaining steady-state was estimated from
𝑡𝑡𝑓𝑓 ~ ℎ𝑙𝑙/𝑘𝑘𝑅𝑅𝑎𝑎14 (Eq 2-9)
Bejan et al. [34] studied convection in a water-filled cavity with a low aspect ratio of 0.0625.
Temperatures of the vertical walls were controlled to maintain a Rayleigh number in the turbulent
regime of natural convection. At 𝑅𝑅𝑎𝑎 = 1.59 × 109, horizontal jets at the top and bottom of the cavity
were found to dominate the flow and some flow reversals were also observed.
Applications utilizing some of the modelling approaches described above can be found in [22],
[36], [37]. Ganguli et al. [22] and Gandhi et al. [37] and studied the hydrodynamics of convection in
liquid storage tanks. They modelled a cylindrical volume of water with a heating tube placed along the
cylinder’s axis. A 2D geometry utilizing the axial symmetry of the fluid domain was constructed. The
SST k-𝜔𝜔 turbulence model was used to conduct transient analyses of the system. The authors were able
to validate their model using PIV measurements with an error margin of 8%. Gandhi et al. also
performed simulations in the range of 𝑅𝑅𝑎𝑎 = 9.37 × 1010 to 𝑅𝑅𝑎𝑎 = 5.574 × 1013 for a two-phase fluid
domain within the same geometry. The authors studied the effect of adding draft tubes around the
central heating tube. The draft tubes were found to enhance circulation velocities and reduce overall
mixing times needed for complete destratification of the tank. Another example of the utilization of 2D
axisymmetry in the context of modelling natural convection in enclosures is presented in [36]. The
author modelled a heating oven as a 2D system in cylindrical coordinates. The simplified model was
compared with a complete 3D model and was comprehensively validated. It was then used to determine
an optimal configuration of the oven’s heaters to minimize internal temperature differences. Smolka
noted that the distribution of the Rayleigh number inside the oven chamber exceeded 109. The author
18
used the standard 𝑘𝑘 − 𝜀𝜀 turbulence model with enhanced wall treatment to forego high-resolution prism
layers on the wall surfaces [36].
2.4 CFD-Based Optimization
This section presents a review of the key steps involved in the preparation and execution of
optimization routines coupled with computational fluid dynamics. Strategies used for design sampling,
surrogate modelling and optimization are discussed in the context of various applications surveyed in
literature.
2.4.1 Design Sampling
Identification of the design space is typically the first step towards determining an optimal
system design. A number of design points or configurations are selected from the design space and
evaluated. This process of sampling points can be done in a systematic manner using a wide range of
strategies collectively known as ‘Design of Experiments’ (DOE) methods. These evaluations are
conducted prior to a solving a formal optimization problem, as they offer a means of quickly and
cheaply identifying the most influential variables within the system. This is particularly relevant in the
context of optimizing complex and highly non-linear systems in which relationships between input and
output parameters are not known beforehand. A significant volume of literature has been published
regarding various DOE techniques available to systematically sample a given design space. The reader
is referred to [38]–[40] for a comprehensive survey of these methods. The following section presents a
brief overview of the design sampling strategies used in the literature surveyed for this thesis.
Klimanek et al. [41] used a technique known as Central Composite Design (CCD) sampling
method to select 146 points from a nine-dimensional design space. The points were evaluated using
CFD to generate a response surface for optimizing vane positions in a mechanical cooling tower.
Mandloi et al. [42] also used CCD sampling. The authors performed design optimization of the intake
port of an internal combustion engine. The design space was defined by three variables. 15 design
points were selected using the CCD method to generate a surrogate model. Originally known as the
19
Box-Wilson Central Composite Design, the CCD sampling method uses a fractional factorial design
with center points that are combined with a group of ‘star points’ to estimate curvatures in the design
space [38]. Three combinations frequently used with different positions of the star points are shown in
Figure 2-2. Presently, several variations of these traditional CCD types are available, as reported in
[38], [40].
Figure 2-2: A schematic of three possible CCD types based on 𝛂𝛂-value of star points for a 2-
dimensional design space. The star points exceed the design limits in the circumscribed CCD.
The original CCD points are scaled down in the inscribed CCD
Dehghani et al. [43] utilized a Space-Filling Latin Hypercube structure based on the maximin
criterion. In the Latin Hypercube DOE method, the design space is divided into an orthogonal grid with
‘N’ sub-volumes having the same number of levels per variable. These elements are chosen so that only
one sub-volume is selected from each row and column of the grid. Points within these sub-volumes are
then sampled at random. The authors used the sampled points to optimize pressure recovery from
diffusers under laminar flow conditions. The diffuser geometry was parameterized in terms of control
points defined by a non-uniform rational basic spline (NURBS) applied to the diffuser wall.
20
Out of the design sampling techniques reviewed above, the CCD method was successfully used
in CFD-based applications such as in [44][45]. Furthermore, the enhanced face-centered CCD method
available in Workbench struck a balance between sampling at the extremities of the design space and
clustering around an expected region of interest. It was thus chosen for sampling the design space of
the SUpA system.
2.4.2 Surrogate Modelling
Surrogates or metamodels are cost-effective and computationally economical means of
approximating complex black box systems using mathematical relationships [39]. There have been
numerous advances in surrogate modelling techniques over the last two decades. These models utilize
the preliminary set of points tested using the DOE methods described in the previous section to generate
a response surface of the design space. Alternatively, these surrogate models are updated dynamically
as the optimization algorithm samples more points from the design space. The response surface
provides the system’s output parameters without having to perform time-consuming numerical analyses,
a significant benefit particularly when the optimization algorithm requires a large number of points to
be evaluated. Simpson et al. [46] provides a detailed review of metamodelling techniques commonly
used for design optimization across a range of applications.
Surrogate modelling techniques are broadly classified into parametric and non-parametric
models [47]. Parametric models, such as polynomial regression models and Kriging, are constructed
by tuning model parameters to fit the entire design space. On the other hand, non-parametric methods
such as artificial neural networks (ANNs), radial basis functions and inductive learning models use
different, localized models for different regions of the design space to build an overall global response
surface [47]. Non-parametric techniques are commonly employed in machine learning, speech
recognition, combat simulations and other applications where lower-order polynomials cannot
approximate the entire design space with sufficient accuracy [48]. These methods, however, require a
large number of initial data points with known responses to ‘train’ the metamodel [46]. Kriging, in
contrast, is a parametric approach that does not place such a requirement on a minimum number of
21
training points to be sampled from the design space. At the same time, it is more accurate than
polynomial regression models and is better equipped to model nonlinear systems [49]. The Kriging
method uses a combination of a polynomial response surface and estimations from a Gaussian spatial
correlation to evaluate an unknown point using information from known points in its vicinity. In this
way, the output 𝑦𝑦 for any design vector 𝒙𝒙 can be expressed as
𝑦𝑦(𝒙𝒙) = 𝑓𝑓(𝒙𝒙) + 𝑍𝑍(𝒙𝒙) (Eq 2-10)
where 𝑓𝑓 and 𝑍𝑍 are the polynomial curve and the localized deviations respectively.
Kriging can be conceived as a two-part process where the polynomial function is first
determined by fitting a curve through the known points across the design space. The second step
involves calculating the unknown parameters of the correlation function. The correlation function is a
normalized Gaussian distribution curve with zero mean and non-zero covariance. The Kriging tool in
ANSYS uses a correlation function of the form
𝑅𝑅�𝒙𝒙𝒊𝒊,𝒙𝒙𝒋𝒋� = exp �� 𝑁𝑁𝑠𝑠𝑘𝑘=1
𝜃𝜃𝑘𝑘 �𝑥𝑥𝑘𝑘𝑖𝑖 − 𝑥𝑥𝑘𝑘𝑗𝑗�2� (Eq 2-11)
where 𝜃𝜃𝑘𝑘 (𝑘𝑘 = 1,2. .𝑁𝑁𝑠𝑠) is the unknown parameter corresponding to the 𝑘𝑘𝑡𝑡ℎ dimension of the
𝑁𝑁𝑠𝑠 – dimensional design space, while 𝑥𝑥𝑘𝑘𝑖𝑖 and 𝑥𝑥𝑘𝑘𝑗𝑗 are the 𝑘𝑘𝑡𝑡ℎ components of the two sample points being
studied. Complex applications may require the parameterization of the exponent (2 in the above
equation) using a parameter 𝑝𝑝𝑘𝑘 . Together, 𝑝𝑝𝑘𝑘 and 𝜃𝜃𝑘𝑘fully define the shape of the Gaussian profile
between the 𝑘𝑘𝑡𝑡ℎ components of any two design points. The Kriging method also estimates of the
uncertainty associated with its prediction of the response at an unknown point. As a result, Kriging is
able to guide further sampling of the design space in an iterative manner. Additional detailed
discussions on the Kriging method can be found in [46], [50], [51].
Marais et al. [52] used the Kriging response surface method available in ANSYS Workbench’s
Design Explorer to model the moment coefficients of the heliostat as a function of the reflector’s angle
and aspect ratio. Dehghani et al. [43] also used Kriging to build a response surface model of the pressure
recovery of the diffuser corresponding to x- and y- coordinates of the spline control points along the
22
diffuser wall. Forrester et al. [50] found that in general, Kriging was particularly well-suited for
applications where determining the actual response was computationally expensive, such as CFD-based
calculations. Kriging was thus determined to be suitable for being used as a surrogate for the CFD
model of the SUpA system.
2.4.3 Optimization
The final step in the solution of a surrogate-based optimization problem is the evaluation of the
optimization algorithm itself. As observed in the case of surrogate modelling, a broad spectrum of
algorithms and solution approaches can be found in literature. A selection of these approaches is
reviewed here.
An optimization problem can be formally stated as
Minimize: 𝑓𝑓(𝒙𝒙)
Subject to: 𝑔𝑔𝑗𝑗(𝒙𝒙) ≤ 0 , 𝑗𝑗 = 1, …𝑚𝑚
ℎ𝑘𝑘(𝒙𝒙) = 0 , 𝑘𝑘 = 1,𝑝𝑝
𝑥𝑥𝑖𝑖𝐿𝐿 ≤ 𝑥𝑥𝑖𝑖 ≤ 𝑥𝑥𝑖𝑖𝑈𝑈 𝑅𝑅 = 1, . .𝑛𝑛
where 𝑓𝑓(𝒙𝒙) is the objective function corresponding to a design vector 𝒙𝒙,
𝑔𝑔𝑗𝑗(𝒙𝒙) is the 𝑗𝑗𝑡𝑡ℎ inequality constraint function,
ℎ𝑘𝑘(𝒙𝒙) is the 𝑘𝑘𝑡𝑡ℎ equality constraint function
𝒙𝒙𝒊𝒊𝑳𝑳 and 𝒙𝒙𝒊𝒊𝑩𝑩 are the lower and upper bounds of the 𝑅𝑅𝑡𝑡ℎ design variable
𝑚𝑚, 𝑝𝑝 and 𝑛𝑛 are the number of inequality constraints, equality constraints and number
of design variables for the given system
The above problem may be resolved using either gradient-based methods, heuristics, or a
hybrid approach involving both. Gradient-based techniques use a two-step process to iteratively narrow
the search for a minimum using gradient information from the response surface. Gradient-based
methods can solve large, multi-dimensional problems with relatively high efficiency and require little
problem-specific parameter tuning. However, these algorithms are prone to being trapped by local
23
minima and are not able to operate on multi-modal functions. In addition, they cannot be used to solve
problems involving discrete variables. As a result, heuristics-based techniques are more commonly
used to solve optimization problems associated with complex systems with little or no gradient
information available.
Many of the heuristics-based methods were inspired by naturally-occurring processes.
Evolutionary algorithms such as the Genetic Algorithm and Particle Swarm Optimization were based
on Darwin’s principle of survival of the fittest and the natural swarming behavior of flocking birds,
respectively [53], [54]. Other commonly used evolutionary algorithms such as Simulated Annealing
(SA) and Ant Colony Optimization are reviewed comprehensively in [55]. Genetic algorithms have
been widely used to determine an optimized system configuration for CFD-based applications. Marais
et al. [52] successfully utilized the Multi-Objective Genetic Algorithm (MOGA) integrated within
ANSYS Workbench to determine an optimized geometry of the heliostat’s reflector. Cavazutti et al.
[56] used MOGA to optimize the design of a vertical channel to maximize heat and mass transfer from
a natural convection current. Smolka [36] used a genetic algorithm to maximize the uniformity of
temperature distribution inside a convection-based heating oven. Lee et al. [57] employed a genetic
algorithm to minimize energy consumption of an HVAC system used for indoor climate control by
coupling the optimizer with CFD. A detailed review of the genetic algorithm can be found in [53]–[55].
2.5 Chapter Summary
Based on the findings in some of the literature reviewed above, several approaches were
identified for the purpose of modelling the SUpA system. Experimental and numerical analyses
conducted by both [22] and [36] showed that the solar collector and conduction element could be
approximated as an axisymmetric geometry to expedite computation. The meshing strategy used by
[30] indicated that a minimum first layer thickness of approximately 0.01% of the width of the cavity
could capture near wall effects with sufficient accuracy at high Rayleigh numbers. Further, the use of
temperature profiles as boundary conditions was validated by the results of both [28] and [30]. The
24
turbulence models evaluated in the present literature survey did not yield a clear winner in terms of
overall accuracy and robustness. However, the SST k-𝜔𝜔 model was the only model to have been
successfully implemented and validated in cylindrical coordinates as demonstrated by [22], [58]. Since
the SUpA geometry would also be evaluated to study circulation due to natural convection in an
axisymmetric, 2D domain, the SST k-𝜔𝜔 model was identified as the appropriate turbulence viscosity
model. Finally, it was found that optimization using genetic algorithms has been previously performed
entirely within the ANSYS Workbench environment, and could thus be used to identify and test an
optimal SUpA configuration prior to future field installations.
The literature review undertaken in this chapter shows that a range of options is available for
the purposes of modelling, validating and optimizing the SUpA technology. The review of parallel
applications involving the modelling of natural convection demonstrated the validity of employing the
2D axisymmetric model, use of the k-𝜔𝜔 SST turbulence for resolving turbulent and transitional natural
convection flows and the utilization of the optimization tool integrated within ANSYS Workbench.
However, to date, literature on successful technological interventions in pond aquaculture in remote,
underdeveloped communities, was not available. In addition, no published research on the development
of experimentally validated models and optimization of such systems was found.
25
3. Design Solutions
The three designs being evaluated in this study are introduced. Metrics used for characterization
of performance of the designs are discussed.
3.1 Rod-Fin Design
In the first iteration of the SUpA system, referred to as the ‘rod-fin’ design, a flat sheet of metal
was utilized as the solar collector while a solid cylindrical rod served as the conduction element. Both
components are made of a thermally conductive metal such as aluminum. The conduction element was
welded to the underside of the collector. The surface of the collector was glazed with plastic or glass to
prevent heat losses via wind-induced forced convection. The bottom face of the collector and a
submerged portion of the rod were insulated to preserve conduction of heat to the bottom of the rod.
The updraft channel was implemented as a circular tube positioned around the rod. A schematic of the
design is given in Figure 3-1. As shown in the figure, incident thermal energy was conducted from the
collector to the uninsulated part of the rod before being transferred to the surrounding water via natural
convection.
Figure 3-1: Schematic of the rod-fin geometry. Vertical natural convection is induced from the
uninsulated surface of the cylindrical conduction element
26
3.2 Bent-Fin Design
The second version of the SUpA device was motivated by the goal of reducing heat loss at the
contact region between the rod and the collector in the rod-fin geometry. This design consisted of a
single rectangular sheet of metal with both ends bent by 90 degrees. The bent surfaces of the metal
were immersed in water to form the conduction element, while the horizontal face served as the solar
collector. No welding was thus required during construction. Thermal energy from the solar collector
was conducted to the bent fins across the cross-section of the sheet metal. As was the case in the rod-
fin design, the solar collector was glazed. In addition, insulation was applied to the underside of the
solar collector and to the conduction element up to a specified depth. The updraft structure in this design
consisted of a rectangular channel constructed around each fin. An illustration of the bent-fin design is
given in Figure 3-2.
Figure 3-2: The bent-fin concept uses a single rectangular sheet of metal with the ends bent at
right angles. A rectangular updraft channel guides the convection current from the pond bottom
to the water surface
27
3.3 Inverted Prism Design
The inverted prism design, shown in Figure 3-3, was conceived with the goal of reducing losses
during conductive heat transfer through the metal while maintaining convective heat transfer to the
lower depths. Similar to the bent-fin geometry, this design also utilized a single piece of sheet metal
for its construction. The sheet metal was formed into a cavity in the shape of an inverted prism. The
opening to the cavity at the top was covered and sealed with a clear, transparent material. When
submerged in water, thermal energy from solar radiation incident on the angled inner walls was
conducted to the surrounding water across the thickness of the metal. The metal structure functioned
simultaneously as the solar collector and the conduction element. The updraft channel around the
inverted prism consisted of a vertical section at the bottom and an angled section parallel to the walls
at the top. When convective currents were set up, water entered the channel at the bottom before rising
along the angled section and emerging near the water surface.
Figure 3-3: A schematic of the inverted prism concept. Thermal energy captured by the angled
walls of the collector is transferred to the water through the thickness of the sheet metal
28
3.4 Metrics for Performance Characterization
Performance of the designs was evaluated using both results of CFD predictions as well as
preliminary field trials. CFD models were used to determine the impact of the designs on mass flow
rates of circulation in the water volume. This was done by creating a virtual surface within the updraft
channel and monitoring the mass flow rate across the surface over time. In addition to the mass of water
moved, the velocity of the convective current and thermal gradients developed in the modelling domain
were also evaluated.
In order to assess device operation in the field, changes in dissolved oxygen levels measured
in the pond during device operation were analyzed. The compatibility of the designs with
implementation in a resource constrained environment was also assessed in terms of cost, availability
of materials and challenges faced during manufacturing and installation.
29
4. SUpA System Modelling
The development and implementation of the CFD model of the rod-fin, bent-fin and inverted-
prism geometries are discussed in this chapter. The modelling domain is first defined in terms of
characteristics of the pond environment and ambient conditions. The performance of each design in
this environment is then evaluated in terms of the mass flow rate of water and peak velocity attained in
the circulation induced by natural convection.
4.1 Model Geometry
In 2010, the average area of ponds used for homestead aquaculture in the Mymensingh district
of Bangladesh, where field trials of the SUpA system are being conducted, was 0.06 ha (610m2) [59].
A pond with half of this area was chosen as the modelling environment for the SUpA system. One
device was installed in the center of this pond in the CFD model.
The device and pond was modelled as a two-dimensional (2D), axisymmetric geometry in the
interest of reducing computational costs. A large number of CFD evaluations were required for
performing mesh and time-step independence studies as well as the design studies discussed in Chapters
6 and 9. The 2D models required less than 2.5 hours per simulation for the different SUpA
configurations on a desktop PC with 16GB memory and 8-core Intel® Xeon® E5-1620 processor. On
the other hand, the number of mesh elements needed to spatially discretize a three-dimensional (3D)
model of the pond was of the order of 106 elements, requiring more than 24 hours per simulation.
Further, as discussed in Section 2.3, the validity of the axisymmetric assumption for approximating a
3D geometry was previously investigated and demonstrated by [22], [28], [36].
The fluid domain was thus modelled as a planar representation of a cylinder with radius 10m,
for a pond surface area of 314m2 or 0.03ha. The pond was assumed to have a depth of 1.25m, equal to
the average depth observed during visits to the test ponds in Mymensingh. ANSYS DesignModeler
v17.0 was used to construct 2D geometries of the SUpA designs, shown in Figure 4-1. The solar
collector and conduction element were merged into a single body representing a continuous metal
30
domain, while another body was created to model the surrounding water. Partitions were made within
the water domain to facilitate the use of quadrilateral mesh elements during the meshing process. The
dimensions of the rod-fin, bent-fin and inverted prism geometries given in the figure are based on
prototypes used in preliminary field trials. They are used as reference designs to demonstrate the overall
CFD modelling approach discussed in the following sections.
Figure 4-1: Schematic of the (a) rod-fin, (b) bent-fin and (c) inverted prism geometries as
constructed using ANSYS DesignModeler 17.1
4.2 Meshing
Meshing was accomplished using the ANSYS Meshing software integrated within the ANSYS
Workbench environment. A mesh topology consisting of both triangular and quadrilateral elements was
utilized and implemented by the proximity function. This allowed for a progressive refinement of cells
near the corners and edges of the geometry. A mapped quadrilateral face mesh was applied to the blocks
created inside the geometry in DesignModeler. Triangular elements were generated between the
blocked regions and the inflation layers. The size of elements in the core of the fluid region was 1.5in.
Based on the findings of [30], 20 prism layers were generated in the annulus between the conduction
element and the walls of the updraft channel and propagated to the water surface. A virtual monitor
surface was created between the draft tube and the conduction element to record the mass flow rate of
31
water rising along the updraft channel. An illustration of the grids used for the three SUpA designs is
shown in Figure 4-2.
Figure 4-2: Illustration of the quadrilateral-dominant grids created for the three SUpA
configurations
32
4.3 Boundary Conditions
The mesh of the SUpA geometry was translated to ANSYS Fluent to generate the CFD model.
The side wall and bottom of the pond were modelled as rigid walls with a roughness constant of 0.5.
The water surface was modelled as a rigid wall with zero roughness or a ‘free-slip’ boundary condition.
This was based on the recommendations of [20] and the implementation of this approach in [22].
Modelling of thermal stratification across the pond depth was not included in the scope of the current
work, as the process of coupling a numerical temperature model presented in [60] with the CFD code
is being investigated. For the analyses discussed in this thesis, an isothermal boundary condition with
a temperature 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓 equal to 23oC was applied to the water surface. The remaining sides of the pond
were modelled as no-slip, adiabatic walls. Peterson et al. [20] found that a more accurate representation
of the boundary conditions present on the pond walls and bed could be achieved by selectively altering
the roughness height on these walls. However, the pond modelled by the authors had a well-defined
shape with lined sidewalls and pond bed, unlike the typical homestead aquaculture pond found in rural
areas. The banks of these ponds are irregular and often lined with vegetation, such as in the example
shown in Figure 4-3. Construction of an accurate model of the dynamics of heat and mass transfer
across the pond banks was not investigated in the current work.
Figure 4-3: Example of a typical pond used for small-scale aquaculture in rural Bangladesh
33
Boundary conditions on the SUpA devices were modelled as follows. Solar irradiance was
modelled as a transient heat flux input applied uniformly incident on the surface of the collector. A
theoretical, time-varying profile of the solar irradiation with a peak irradiance of 1000Wm-2 was
implemented using a user-defined function (UDF) in Fluent. In the case of the inverted prism geometry,
the incident heat flux was reduced by a factor of the cosine of the collector angle, as given by the
following equation:
�̇�𝑄𝑒𝑒𝑓𝑓𝑓𝑓 = �̇�𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∗ cos (𝜈𝜈) (Eq 4-1)
where �̇�𝑄𝑒𝑒𝑓𝑓𝑓𝑓 is the effective thermal energy input, �̇�𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the instantaneous solar irradiation
(W/m2) and 𝜈𝜈 is the angle of inclination of the collector.
External radiation loss from the surface of the solar collector was defined using an external
emissivity 𝜀𝜀 of 0.5 for the surface of aluminum painted black. The sky temperature 𝑇𝑇𝑠𝑠𝑘𝑘𝑠𝑠 was found to
be 285K based on typical weather conditions in the summer in Bangladesh. Since the solar collector
was to be glazed, convection losses from the collector surface to the ambient air were not modelled.
The underside of the solar collector in the rod-fin and bent-fin configurations was treated as an adiabatic
wall. For the baseline geometries currently investigated, no insulation was applied to the submerged
portion of the conduction element. Thus, the entire surface of the conduction element was modelled as
a no-slip, conjugate heat-transfer boundary for all the geometries. A ‘shadow’ wall was automatically
generated by Fluent on the heat-transfer surface to model the transition from conductive heat transfer
within the metal to natural convection at the metal-water interface. The model was initialized as a
stationary fluid with a uniform temperature of 23oC throughout the domain. The model was simulated
for 12 hours while recording the mass flow rate of water through the updraft channel. A summary of
these boundary conditions is given in Table 4-1.
34
Table 4-1: Boundary conditions applied to SUpA configurations for CFD evaluation
Boundary Momentum Thermal
Collector Surface N/A �̇�𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝜀𝜀 = 0.5
𝑇𝑇𝑠𝑠𝑘𝑘𝑠𝑠 = 285K
Collector Underside N/A Adiabatic
Conduction Element No-slip Coupled Wall
Water Surface Free-slip Isothermal (𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓 = 295K)
Updraft Channel No-slip Adiabatic
Pond Walls No-slip Adiabatic
4.4 Solver Setup
Following the definition of the boundary conditions, the Fluent CFD solver was set up to carry
out a transient analysis of the SUpA system. The SST k-ω turbulence model was chosen to model the
eddy-viscosity term in the RANS equations, based on the literature reviewed in Chapter 2. Material
properties of the fluid were defined at a film temperature obtained from the average of the bulk fluid
temperature and the average temperature measured on the submerged part of the rod. Boussinesq’s
approximation was used to model the variation of water density with temperature as a linear function
as explained in Section 2.2. The material was chosen based on the nature of conductive heat transfer in
between the collector and conduction element. In the rod-fin and bent-fin geometries, thermal energy
travelled from the collector to the submerged conduction element. In the inverted prism configuration,
conductive heat transfer took place directly across the metal thickness of the collector. Thus, in the rod-
fin and bent-fin designs, aluminum was used for its high thermal conductivity, while steel was used in
the inverted prism geometry due to its significantly lower cost. The pressure-based solver with the
Pressure Implicit with Splitting of Operators (PISO) algorithm was used to solve discretized numerical
equations for continuity, energy, and momentum. The second order upwind scheme was used for spatial
discretization for energy and momentum, while a second order implicit formulation was used for the
35
transient analysis. Spatial discretization of pressure was achieved using the PRESTO scheme. The
under-relaxation factor (URF) applied to the energy and momentum equations was 0.9 and 0.1
respectively, based on recommendations for facilitating convergence in natural convection CFD
models.. The convergence monitor residual for energy was reduced by a factor of 10-3 from its default
value, while those for continuity, 𝑥𝑥 and 𝑦𝑦 momentum were reduced by a factor of 10-1.
4.5 Results
4.5.1 Mass Flow Output
The mass flow rate of the three designs was monitored over the course of the simulation. The
flow rate was calculated over a virtual monitor surface created within the updraft channel at each time-
step. The total mass of water moved in the circulation current was found by integrating under the mass
flow rate profile. The profiles of the three designs is shown in Figure 4-4 . The input irradiance on the
solar collector is plotted over the same period. The corresponding values of the total mass of water
moved by each configuration is given in Table 4-2.
Figure 4-4: Transient mass flow profiles of the rod-fin, bent-fin and inverted prism geometries
36
Table 4-2: Mass of water moved by the SUpA configurations
Configuration Mass of Water Moved in 12 Hours (kg)
Rod-Fin 790
Bent-Fin 2230
Inverted Prism 4045
As seen in the figure, the three profiles exhibit different characteristics. The flow profile
produced by the rod-fin geometry was found to have a smooth increase that followed the transient trend
of the input heat flux on the solar collector. The flow was observed to peak at 0.02kg/s around the 6-
hour mark at the same time as solar noon. In the case of the bent-fin geometry, the mass flow rate
peaked at the very end of the transient period, nearly 6 hours after maximum irradiance. This was
attributed to a delayed increase in circulation momentum in the interior of the bent-fin geometry,
resulting from the representation of the bent-fin in cylindrical coordinates. In the case of the inverted
prism, the mass flow rate was found to peak at 0.106kg/s at roughly the same time as solar noon. This
peak was 60% higher than that of the bent-fin geometry, and 420% higher than the rod-fin design. In
addition, as observed in Table 4-2, the net mass of water moved by the inverted prism design was found
to be 81% higher than the bent-fin design, and 412% higher than the rod-fin design. The inverted prism
was also the only configuration to feature a second, smaller peak in the flow rate in the first 30 minutes
of the simulation. This secondary peak occurred when the model responded to the initial jump in solar
irradiance from 0Wm-2 to 120Wm-2. The mass flow rate temporarily increased rapidly as the water
current near the surface reached the opposite wall. This was followed by a dip in the flow rate as the
interaction with the wall caused counter-flows and disturbances in the bulk volume. The increasing
irradiance then induced greater circulation, overcoming the temporary dip and causing the overall mass
flow rate to rise again.
37
The differences in performance of the three designs in terms of their mass flow output was
correlated to differences in water uptake volume, surface area of heat transfer and time-scales of heat
conduction through the metal body. As shown in the temperature contour distribution of Figure 4-5, the
temperature difference Δ𝑇𝑇 between the metal surface and the bulk fluid region was not uniform across
the submerged depths of the three conduction elements. As a result, the fraction of surface area of the
conduction element participating in convective heat transfer varied across the configurations. The
effective area of heat transfer was 54% and 4% of the total submerged surface area of the rod-fin and
bent-fin geometries respectively. However, the cross-section area of the updraft channel in the bent-fin
was nearly 10 times larger than that of the rod-fin design, resulting in a significantly greater volume of
water uptake. In addition, the area of contact between the conduction element and the solar collector in
the rod-fin design was less than 50% of the contact area in the bent-fin design. This resulted in a slower
rate of heat conduction to the exposed surface of the rod. In the inverted prism configuration, 100% of
the submerged portion of the conduction element surface area participated in convective heat transfer
to the surrounding water. In addition, the effective area of contact between the solar collector and the
convective heat transfer surface was equal to the entire submerged surface area, as the two surfaces
were part of the same metal body.
The mass flow rates at the end of the simulation period were observed to be non-zero in all
three designs. This indicated the effect of strong thermal inertia due to the large heat capacity of water.
In addition, at the end of the irradiation period, the momentum of the water circulation gained during
the day continues to generate movement through the updraft channel. However, this flow was not
monitored, as its contribution to the net mass of water moved during the day was found to be negligible.
The flow rate of water was also utilized in the numerical DO model to quantify the effect of the SUpA
device on DO levels throughout the pond. The development of the DO model and incorporation of mass
flow outputs from the CFD models was covered by [60] and was not included in the scope of this work.
38
Figure 4-5: Contour plot of the thermal gradients observed in the (a)rod-fin, (b) bent-fin and (c)
inverted prism geometries. The highlighted dimensions indicate the lengths of the conduction
element where 𝚫𝚫𝑻𝑻 ≥ 𝟏𝟏o𝐂𝐂
39
4.5.2 Velocity Distribution
In addition to the mass flow response of the three SUpA design configurations, characteristics
of the circulation induced in the immediate vicinity of the device as well as the bulk of the fluid volume
were also evaluated. The flow velocity outside the device was used as a measure of the relative
robustness of each design and its ability to counter local disturbances within the pond volume. Figure
4-6 (a), (b) and (c) show the distribution of velocity vectors of the rod-fin, bent-fin and inverted prism
designs. The vector plots were obtained at the time of peak circulation induced by each configuration,
determined from the maximum mass flow rates obtained from Figure 4-4.
In all three configurations investigated, the flow in the bulk volume of the fluid was
characterized by a single large circulation cell. A smaller, secondary circulation was observed at the far
end of the pond in the vector distribution of the rod-fin geometry. The greatest updraft velocity was
recorded in the draft tube of the rod-fin configuration, where the flow attained a velocity of 16mm/s.
The smallest peak updraft velocity was observed in the updraft channel of the bent-fin geometry. These
observations were consistent with the differences in temperature between the surface of the metal and
the ambient water, Δ𝑇𝑇, among the three geometries. As given in Eq 2-8, large values of Δ𝑇𝑇 correlate
directly with free convection flow velocities. In the rod-fin geometry, the small cross-section area of
the conduction element combined with the low water uptake capacity resulted in limited removal of
heat via natural convection compared to the other designs. This caused an accumulation of heat within
the cylindrical rod, resulting in large values of Δ𝑇𝑇 occurring on 54% of the submerged surface area, as
seen in Figure 4-5(a). In comparison, only 4% of the submerged area of the bent-fin had a temperature
difference greater than 1oC, as shown in Figure 4-5(b). In turn, these variations in Δ𝑇𝑇 caused the
differences in flow velocities observed in Figure 4-6 (a)-(c).
40
Figure 4-6: Plot of velocity vectors observed in the bulk fluid region and updraft channel (inset)
during peak circulation in (a) rod-fin (b) bent-fin and (c) inverted prism models
41
4.6 Solution Independence from Solver Parameters
The accuracy of the above results was checked to ensure independence from the size of the
time-step used for the transient analyses as well as the size of key features within the mesh. The inverted
prism geometry was used as a model for the time-step and mesh independence studies. Results from
these studies were utilized in the analyses of the rod-fin and bent-fin geometries. The net mass of water
moved as well as the nature of the mass flow rate profiles were analyzed to identify a suitable mesh
configuration and time-step size.
4.6.1 Independence from Time Step Size
Time-step sizes of 1s, 5s and 10s were tested to identify the step size for which convergence of
the total mass flow output was achieved. Results of the study are shown in Figure 4-7. It was found that
the output mass flow profiles were nearly identical for all three time-step sizes investigated. The total
mass of water moved was 4054kg, 4055kg and 4066kg for steps sizes equal to 10s, 5s and 1s
respectively, resulting in a maximum deviation of 0.3% from the reference geometry with a time step
size of 10s. The negligible variation in output was attributed to the large difference in time scales
between the developing flow and thermal energy input to the system. For most of the simulated period,
the flow was characterized by a single, slow-moving circulation cell occupying the bulk of the fluid
volume, as illustrated in Figure 4-6. In the absence of any localized regions of turbulence with large
velocities, the overall rate of change of flow velocity was smaller than the rate of change of heat flux
into the water. Thus, the larger time-step sizes of 5s and 10s were able to closely match the response of
the system evaluated with a time-step size of 1s. A step size of 10s was therefore deemed to be
sufficiently accurate for modelling the given geometry and used for all future analyses.
42
Figure 4-7: Mass flow rate profiles observed for three time-step sizes (dT) of the inverted-prism
model. Largest difference in the total mass of water moved was found to be 0.3% between the
case with dT = 10s and dT = 1s
4.6.2 Mesh Independence
Following the identification of a suitable time-step size, grid independence from the core prism
size and height of the first inflation layer was evaluated. The core prism size influenced the size of the
mesh elements in the bulk volume of the fluid domain, while the first inflation layer thickness affected
the resolution of the natural convection boundary layer adjacent to the heat transfer surface [30]. Three
levels of each parameter were evaluated. Figure 4-8 shows a plot of the mass flow profiles
corresponding to the core prism sizes 0.75in, 1in and 1.5in. All three cases were evaluated with 20
inflation layers in the updraft channel. The total mass outputs of water were 4045kg, 4154kg and
4214kg for core sizes 1.5in, 1in and 0.75in respectively, indicating a maximum negative deviation of
4% between the finest and coarsest meshes. The core size of 1.5in was thus found to be sufficient for
discretizing the bulk region of the fluid.
43
Figure 4-8: Mass flow rate trends corresponding to different sizes of the core mesh elements. The
coarsest mesh with core size = 1.5in under-predicted the total mass flow output by 4% compared
to case with core size = 0.75in
Figure 4-9 shows the mass flow profiles corresponding to different resolutions of the inflation
layer within the updraft channel. Three cases were evaluated with 5, 12, and 20 inflation layers,
corresponding to first layer heights of 2.6mm, 0.6mm and 0.13mm respectively. These values were
motivated by the inflation parameters investigated in [30]. A core-prism size of 1in was used in the
study. The total mass flow outputs were 4154kg, 4027kg and 4235kg for first-layer heights 0.1mm,
0.6mm and 2.6mm respectively. The variation between the coarsest and finest mesh was 2%. Although
the inflation layer height of 2.6mm was found to predict the mass output within 2% for the given
geometry, a first layer height of 0.1mm corresponding to 20 layers was chosen for subsequent analyses
to provide sufficient resolution for visualizing momentum and thermal profiles within the boundary
layer.
44
Figure 4-9: Mass flow rate profiles corresponding to different heights (t) of the first inflation
layer and number of layers (n) measured from the heat transfer wall
4.7 Comparison with 3D Modelling
In addition to developing a mesh and time-step independent model, the 2D axisymmetric
geometry was compared to an equivalent 3D model of the inverted prism. This was done to validate
the assumption that the 2D model was able to accurately capture critical aspects of fluid dynamics and
heat transfer from the device, and that the effects on fluid flow from the corners of a three-dimensional
geometry were negligible. The width of the base of the 3D model was adjusted to create a geometry
with the same surface area available for heat transfer. The inclination angle of the collector and its
sloped length were also preserved in both models. This allowed the 3D model to have the same effective
surface area for heat transfer while maintaining flow orientation and length in the updraft channel.
Figure 4-10 shows an illustration of the inverted prism concept modelled in 3D. Bilateral symmetry of
the model in two orthogonal planes, as highlighted in the figure, allowed for the modelling of only a
quarter of the device.
45
Figure 4-10: Schematic of the 3D representation of the inverted prism geometry. Bilateral
symmetry was exploited to evaluate a quarter of the metal body for the 3D CFD model
Figure 4-11 shows a 3D model of the quartered collector placed at the centre of a cylindrical
pond with the same dimensions as the axisymmetric model. The cylindrical shape of the pond was
preserved to allow for a controlled comparison between the two representations of the inverted prism
structure. Attempts were made to preserve the overall mesh topology in both models by sweeping the
2D mesh by 90o across 30 intervals. However, these resulted in large mesh sizes with over 1 million
elements, which placed significant demands on computational resources for simulating 12 hours of
device operation. Thus, fewer cells were added in the radial direction in the swept mesh. Hexahedral
elements were utilized in the bulk fluid region. The total number of elements in the final mesh was
281,390. Further improvement of the 3D mesh and development of a grid-independent 3D model was
beyond the scope of the current work.
Figure 4-11: The mesh used to discretize the 3D modelling domain of the pond and inverted
prism configuration
46
Unlike the 2D axisymmetric grid, the 3D mesh was modified to omit the generation of mesh
elements within the metal body of the collector. Regular meshing of the solar collector face using the
proximity function led to the formation of a large concentration of cells within the solid. Due to the
small thickness of the sheet metal, only a single layer of cells was used to model heat transfer across
the metal surface. However, creating these cells resulted in cells with large aspect ratios, which in turn
caused difficulties in solution convergence. As an alternative, the Shell Conduction feature in FLUENT
allowed the creation of a ‘virtual’ layer of cells that did not require the elements to be physically
meshed. This eliminated the solid metal body from the model domain. The validity of this approach
was proven in cylindrical coordinates by comparing its resulting mass flow profile with that of the
original 2D model. The results shown in Figure 4-12 indicate that the use of the virtual wall model
produced a difference of only 1% in the peak flow rate. It was thus assumed to be a valid approximation
for the 3D model.
Figure 4-12: Comparison of the mass flow profile with and without utilization of the ‘shell-
conduction’ feature within Fluent. Simulations were performed using a constant irradiance of
1000Wm-2 for 1800s
The results of the 3D simulation are presented in the following sections. Figure 4-13 shows a
comparison between the flow streamlines observed for the two geometries at solar noon. Differences
are noted in the shape of the circulation cell developed in the fluid volume. However, these differences
47
occurring away from the device were found to be insignificant as flow velocities were of the order of
10-4 m/s. The radial distance up to which velocities were greater than 1mm/s were found to be 3.5m and
2.5m in the 2D and 3D models respectively, indicating a difference of 20%. In the region close to the
device, effects of the 3D geometry were more significant than in the regions farther away. Momentum
transport occurred non-uniformly in the z-direction in the periphery of the device in the 3D model,
resulting in the lower velocity of the flow modelled in 3D.
Figure 4-13: Velocity streamlines produced in the 2D and 3D CFD models at the time of
occurrence of peak mass flow rate
The transient mass flow profiles of the two models are presented in Figure 4-14. It was found
that representing the device in two dimensions over-predicted the total mass of water moved by 10%
when compared to the device modelled in 3D. Based on the similarity of the flow patterns and mass
flow profiles produced by the two models, it was assumed that the relative trends in the response of
different points in 3D and 2D was the same. The 10% difference in the net mass of water moved was
thus deemed to be within an acceptable range of uncertainty. Furthermore, the significant savings in
time and computational costs offered by the 2D model were found to outweigh the observed
discrepancies in modelling the flow.
48
Figure 4-14: Mass flow profiles observed in the 2D and 3D models of the inverted prism geometry
4.8 Chapter Summary
The construction of unsteady CFD models of the SUpA design configurations was presented
in this chapter. The three configurations were modelled using 2D, axisymmetric reference geometries.
The mass flow profile, velocity and thermal gradients associated with each design were evaluated. It
was found that the net mass of water moved by the inverted prism geometry was predicted to be 81%
higher than the bent-fin design over a 12-hour period. The average flow velocity of the updraft current
of both the rod-fin and inverted prism geometries was more than twice as large as that of the bent-fin
configuration. The largest thermal gradient was observed in the rod-fin geometry. The CFD model was
tested and found to be independent from the size of the time step, core mesh size and height of first
inflation layer of the mesh. Lastly, the 2D model was compared to a preliminary 3D model developed
for the inverted prism geometry. In the present work, the 3D model was not evaluated further to obtain
a model independent from grid features and the size of the time-step. The flow patterns were observed
to be qualitatively similar in both models and the mass flow output was overestimated by the 2D model
by 10%. It was concluded that the 2D axisymmetric model was adequate for the purposes of modelling
the SUpA system for future tests.
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5. Model Validation
Evaluation of the modelling accuracy of the model in the previous chapter using experimental
methods is discussed. A bench-scale experiment was set up to simulate the heat transfer mechanism of
the rod-fin and bent-fin geometries. Flow visualization was performed using pH-indicated electrolysis.
The prediction of flow velocity at different positions along the vertical updraft channel is compared
between the CFD model and the experimental measurements. A qualitative bench-scale setup of the
inverted-prism geometry is also presented.
5.1 Approach
Development of the SUpA system began with proof-of-concept tests to investigate the
movement of water due to natural convection in an enclosure. Mahmoud [60] discusses these
preliminary tests in greater detail. Water in an aquarium tank was used to model the pond volume. A
solid cylindrical rod made of aluminum or steel was used as the conduction element. Thermal energy
input was supplied by two 36W ceramic cartridge heaters connected to a DC power supply. The heaters
were inserted into the top of the rod. Dye was added to the base of the tank to visualize the flow after
the exposed portion of the heated rod had attained a steady temperature. Preliminary tests showed that
the dye travelled upwards along the rod and spread over the water surface, indicating the formation of
a natural convection current. Subsequent tests utilized a draft tube placed around the metal rod. The
draft tube controlled the depth of water uptake from the bottom of the tank and entrained the flow rising
around the rod. While these tests gave a visual demonstration of the working principle of the SUpA
system, they provided limited quantitative information about the flow. The food colouring revealed the
general appearance and structure of the flow, but it was difficult to control the dye concentration for
each experiment and track the flow accurately. This in turn hindered efforts to validate the CFD model
being developed for the SUpA system. Therefore, an alternative to the dye-based visualization method
was implemented by the team at the Water and Energy Research Lab. This technique involved the use
of electrolysis and pH-indicated flow visualization to obtain a quantitative characterization of the lab-
50
scale system. Results from these tests were used to validate the overall modelling approach of the SUpA
device. A brief overview of these tests and a comparison of simulated and experimental results are
presented in the following sections.
Visual estimates of the updraft velocity obtained from the food-colouring tests were of the
order of millimetres per second. The pH-indicated flow visualization technique is often used for
visualizing flows in that range, as reported in [61]. This method uses a two-step process. First, a 0.01%-
by-weight concentration of thymol blue in distilled water is prepared in the tank. An alkali such as
sodium hydroxide (NaOH) is used to titrate the solution to its end point, followed by the addition of
concentrated hydrochloric acid (HCl). The final pH of the bulk fluid is just under 7, causing the solution
to appear yellow. At this point, the slightly skewed balance between hydroxide (OH-) and H+ ion
concentrations is highly sensitive to fluctuations caused by external inputs. The second part of the
process involves electrolysis to further offset these ion concentrations at the cathode and anode.
Oxidation occurs at the anode and H+ ions are added to the solution. This increases the pH locally and
the thymol blue solution remains yellow. On the other hand, reduction occurs at the cathode and OH-
ions are released into the solution. This increases the local alkalinity of the solution, causing the
indicator to turn blue around the cathode. The amount of coloured solution produced around the cathode
is controlled by changing the voltage applied across the electrodes. When the cathode is placed near a
stream of moving fluid, the coloured solution propagates with the flow and allows for direct flow
visualization.
5.2 Bench-Scale Setup
5.2.1 Rod-Fin Geometry
The lab-scale setup used to implement the pH-indicated visualization technique is shown in
Figure 5-1. The heating assembly consisted of same components as those used in the dye tests - a
partially insulated, cylindrical aluminum rod with a diameter of 1in was placed inside a draft tube of
diameter 1.5in. The rod was heated by two cartridge heaters at the top. Insulation was added around the
51
upper portion of the rod to prevent heat losses during conduction to the bottom. A 0.003in-thick sheet
of ceramic paper was used as the insulating material.
Figure 5-1: CAD illustration of the bench-scale heating assembly used to validate the CFD model
of the rod-fin configuration
A platinum wire with diameter 0.025mm was stretched across the bottom of the draft tube to
form the cathode. A 20-gauge copper wire was submerged in the tank away from the heating assembly
to serve as the anode. The electrodes were connected to a variable DC power supply. Two Minco S667
waterproof resistance temperature detectors (RTDs) were used to obtain temperature readings at the
locations on shown in Figure 5-2. Data from the RTD was processed by an Arduino Leonardo board.
The bulk temperature of the water away from the heating assembly was recorded using a digital
temperature probe. A Canon EOS DSLR camera was used to record the flow in the draft tube.
52
Figure 5-2: Schematic of the components used for pH-indicated flow visualization of the updraft
flow. The thymol blue indicator changed from yellow to blue at the cathode due to localized
increase in alkalinity when voltage was applied across the electrodes
After power supply to the cartridge heaters was turned on, temperature readings from the RTDs
were monitored until a steady state was attained at 32oC at the second RTD location. At this point, the
electrolysis circuit was switched on. 5V was supplied to the electrodes. Water around the platinum wire
at the bottom of the draft tube began to turn blue. The current passing through the electrodes was pulsed
to prevent accumulation of hydrogen gas around the cathode. The coloured-solution was then observed
to rise up along the rod.
Footage from the camera was analyzed to track the leading edge of the flow in the boundary
layer at several points along the vertical axis. Instantaneous velocities at these locations were calculated
by measuring vertical displacements of the leading edge over 10-second intervals. However, in the case
of the rod-fin setup, measuring these instantaneous velocities was challenging due to out-of-plane flow
diffusion and distortion of light caused by the curved walls of the draft tube. Therefore, a single average
53
updraft velocity was calculated by measuring the total transit time from the bottom to the top of the
tank. The updraft velocity was determined to be 8.5±0.2mm/s from the results of five trials.
5.2.2 Bent-Fin Geometry
Figure 5-3: Bench-scale heating assembly representing the bent-fin configuration. The heating
block was used to provide uniform heat flux to the horizontal face of the bent metal plate
To model the bent-fin geometry, the heating assembly consisting of the rod and cylindrical
draft tube was replaced by a 17in × 4in sheet of aluminum bent at either end by 90o, as shown in Figure
5-3. An updraft channel with a rectangular cross-section was supported around one of the vertical metal
fins. A 150mm × 150mm rectangular grid with 5mm × 5mm spacing was etched onto one face of the
draft tube to serve as a scale for measuring the instantaneous updraft velocity. The cartridge heaters
were inserted into a heating block placed above the top face of the bent metal. The heating block was
54
used to uniformly distribute the thermal energy input to the metal. The portions of the bent metal
exposed to air were insulated using the ceramic paper. Temperature sensors were mounted at the
locations shown. The thymol blue solution was titrated and prepared for electrolysis. The platinum
wire was stretched across the bottom of the draft tube at three locations. Figure 5-4 shows the position
of the different parts of the bench-scale setup used for flow visualization of the bent-fin geometry.
Figure 5-4: Schematic of components used for pH-indicated electrolysis in the bent-fin apparatus.
The platinum wire was fixed on one updraft channel due to the assumption of flow symmetry on
both vertical fins
5V was pulsed across the electrodes when the heating block and submerged fin attained a steady
state. The thymol blue solution was observed to rise up through the gap between the metal and the draft
tube. The leading edges of the flow streams were tracked against the backdrop of the etched grid. Due
to the flat walls, it was possible to measure instantaneous flow velocities with greater accuracy than in
the lab-scale prototype of the rod-fin geometry. The updraft velocity was measured in 10-second
intervals at 12 positions along the vertical channel.
55
5.3 CFD Modelling
5.3.1 Geometry & Meshing
Taking advantage of the symmetry of both systems about their middle plane, one half of the
bench-top setup was modelled as a three-dimensional geometry in ANSYS DesignModeler. ANSYS
Meshing was used to create an unstructured, tetrahedral mesh of each geometry. 20 prism layers were
generated in the annulus between the rod and the draft tube. These prism layers were propagated to the
water surface and walls of the tank. To improve computational efficiency, the 3D tetrahedral cells were
converted to polyhedral elements in ANSYS Fluent. Conversion to polyhedral elements is a common
strategy used to significantly reduce the total number of cells in complex geometries. The total number
of elements in the final grid used by Fluent was 975,265 for the rod-fin model and 677,741 for the bent-
fin model. Figure 5-5 shows the polyhedral mesh employed by Fluent for each setup.
Figure 5-5: 2D cross-section of the polyhedral mesh used for modelling the rod-fin (a) and bent-
fin (b) bench-scale setup
5.3.2 Boundary Conditions
A summary of the boundary conditions for each part of the modelling domain is given in Table
Table 5-1. The corresponding surfaces are labelled in Figure 5-6. Since heat loss from the exposed
surfaces of the conduction element, water surface and tank walls could not be accurately quantified,
56
temperature readings from the RTD at the top were incorporated into a user-defined temperature profile
for both systems. The water surface was treated as a free-slip boundary maintained at the ambient
temperature of the lab environment. The sides and bottom of the tank were assumed to be adiabatic,
no-slip walls. The uninsulated section of the rod was modelled as a coupled wall to allow convective
heat transfer to the surrounding water.
Table 5-1: Summary of boundary conditions applied to the different surfaces of the rod-fin and
bent-fin models
Boundary Description
A. Heating Cartridge Transient temperature profile measured from experiment
B. Water surface Free-slip, adiabatic
C. Insulated surface No-slip, adiabatic
D. Uninsulated surface No-slip, coupled wall
E. Updraft channel No-slip, adiabatic
F. Tank walls No-slip, adiabatic
Figure 5-6: Illustration of different surfaces of the rod-fin and bent-fin bench-scale models
57
5.3.3 CFD Results
The same modelling approach incorporating the turbulence model, material properties and
solution discretization schemes used for the 2D CFD models of the SUpA system discussed in Chapter
4 was employed to model the bench-scale versions of both geometries. Contour and vector plots of
velocity distribution obtained at the same time as the occurrence of steady-state conditions for the rod-
fin and bent-fin models are given in Figure 5-7 and Figure 5-8 respectively. Small regions of secondary
flow were observed near the top of the draft tube. The contour plot shows that the updraft velocity in
the annulus ranged from approximately 5mm/s near the bottom to 19mm/s. In the case of the bent-fin
setup, it was observed that the average updraft velocity ranged from 1mm/s to 2.9mm/s. This range was
significantly lower than that recorded in the cylindrical annulus of the rod-fin assembly.
Figure 5-7: Distribution of velocity vectors obtained from the CFD evaluation of the rod-fin
bench-scale model. Peak velocity was found to be 19mm/s at the top of the updraft channel
58
Figure 5-8: Flow velocity distribution observed in the CFD model of the bent-fin bench-scale
setup. Peak velocity was 2.9mm/s at the top of the updraft channel
5.4 Comparison with Experimental Results
The contour plot did not provide sufficient resolution of the boundary layer development along
the draft tube for comparison with an experimental validation. Therefore, horizontal profiles of the
boundary layer at different positions along the y-direction were recorded in the CFD model. Flow
velocity was determined by tracking the peak of the boundary layer in each profile. A comparison of
these results from the CFD and experimental tests is given in Figure 5-9 (a) – (b) for the rod-fin
geometry and Figure 5-9 (c) – (d) for the bent-fin geometry. Figure 5-9(a) shows the development of
the convective boundary layer profile at different positions along the updraft channel of the rod-fin
setup. The positions are indicated by the dimensionless quantity 𝑦𝑦∗ = 𝑦𝑦/𝐿𝐿 , representing the y-
coordinate of each profile normalized by the fin depth 𝐿𝐿 submerged inside the draft tube. The first
section corresponding to 𝑦𝑦∗ = 0 was defined at the bottom of the draft tube. The markers along each
profile represent the nodes at which the y-velocity was measured. With increasing height, the shape of
59
the boundary layer was found to change from a nearly parabolic curve at 𝑦𝑦∗ = 0 to the boundary layer
typically observed in natural convection currents. The position of the peak velocity approached the
surface of the rod with increasing 𝑦𝑦∗, reflecting higher rates of heat transfer closer to the water surface.
Figure 5-9: (a), (c) - Cross-section profiles of the boundary layer at different heights (𝒚𝒚∗) along
the draft tube of the rod-fin and bent-fin models respectively
(b), (d) – Experimentally measured velocity compared with peak and average velocities at each
𝒚𝒚∗ obtained from CFD for the rod-fin and bent-fin geometries respectively
In Figure 5-9(b), peak and average y-velocities at each section are plotted and compared with
experimental results. It is observed that the average flow velocity of the thymol blue solution lies
between the peak and average velocities of each profile predicted by the model. At any of the monitored
profiles, the leading edge of the thymol blue solution had a velocity that was necessarily greater than
60
zero but less than or equal to the peak velocity of the boundary layer. The peak and average velocities
given by the CFD model are also observed to be greater and less than the velocity of the leading edge,
respectively. Therefore, the range of numerically estimated values overlapped with the uncertainty
limits of the physical measurements. This indicated that the CFD code was able to accurately predict
the range of flow speeds in the updraft current.
For the bent-fin setup, the boundary layer profiles were recorded at the same 12 positions at
which experimental measurements were made. Six of these profiles are plotted in Figure 5-9(c). The
development of the natural convection boundary layer was observed as the flow rose upwards in the
draft tube. At 𝑦𝑦∗ = 0.93, a small part of the boundary layer was affected by the intrusion of a secondary
flow into the draft tube and consequently showed a negative velocity near the draft tube surface. In
Figure 5-9(d), peak and average velocities predicted by the model are compared with the measured
velocities of the thymol blue solution. As previously observed in Figure 5-9(b) in the case of the rod-
fin setup, the range of velocities given by the model was found to lie within possible limits of the flow
in the physical system. The model was thus able to successfully predict the updraft flow velocities along
the draft tube.
5.5 Inverted Prism
A bench-scale experiment of the inverted prism was conducted as a qualitative, proof-of-
concept test using food colouring to visualize the flow. A 0.05in-thick rectangular aluminum plate bent
by 90o was immersed in a tank filled with water. The sides of the bent plate were sealed to prevent
intrusion of water into the cavity. A 150W lamp was used to model solar irradiation incident on the
surface of the aluminum. Figure 5-10 shows the evolution of the flow as the blue dye was slowly added
to the water at the bottom of the channel inlet. After 1 minute, multiple streaks of food colouring in the
shape of the free convection boundary layer were observed inside the channel. Although the exact
velocity of the convective current was not determined, the bench-scale experiment confirmed that this
61
design was capable of generating a convective circulation in a given water volume with thermal energy
input to the angled collector.
Figure 5-10: Evolution of the natural convection flow in the bench-scale setup of the inverted-
prism geometry, visualized using food colouring injected at the base of the channel
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5.6 Chapter Summary
The validation of the CFD models of the SUpA system was presented. The natural convection
flow was visualized in a controlled manner for the first time. pH-indicated electrolysis using thymol
blue indicator was used to produce a coloured stream of fluid transported by the convection current in
the bench-scale setup. CFD models of the bench-scale of the rod-fin and bent-fin apparatus were
evaluated. Predicted flow velocities were found to agree with experimental results at all measurement
locations along the updraft channel of both the rod-fin and bent-fin geometries. A major challenge faced
during experimentation was the accurate tracking of the leading edge of the convective flow. This was
caused by optical distortion by the clear plastic components of the bench-scale assembly. Accurate
tracking was further hampered by the tendency of the coloured flow-stream to deviate from the vertical
plane of the cathode wire, resulting in erroneous readings from the camera footage. Lastly, the inverted
prism geometry was tested in a similar bench-scale setup in the lab using food colouring for flow
visualization. The test was purely qualitative. It showed that the new design was able to induce natural
convection currents in the water tank when heated from a distance by an electrical lamp. It demonstrated
an opportunity for a more rigorous validation of the inverted prism model in the future.
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6. Design Space Exploration
A broad search of the design spaces of the different geometries was conducted to identify the
influence of design variables on the performance of the SUpA device. Taguchi orthogonal arrays were
utilized to systematically sample the design space. Results of the design studies are discussed.
6.1 Rod-Fin and Bent-Fin Geometries
The parameterization of the rod-fin and bent-fin geometries is given in Figure 6-1 and Figure
6-2 respectively. Three levels were chosen for each parameter. Dimensions of the solar collector and
conduction element were chosen based on standard, commercially-available stock sizes of sheet metal
and metal rods. In addition, the devices were sized so that they could be carried by two people. The
upper and lower bounds of the design space were defined after taking these factors into consideration.
The insulation factor ‘D’ was defined as the ratio
𝐷𝐷 = �𝐼𝐼 − 𝐹𝐹𝐶𝐶
� (Eq 6-1)
where 𝐼𝐼 was the actual depth up to which insulation was applied on the conduction element and
𝐹𝐹 and 𝐶𝐶 were the gap above the updraft channel and fin depth respectively.
A systematic search of the design space was then performed. Out of the full factorial design
consisting of 38 = 6561 points, 27 configurations based on a Taguchi orthogonal array were identified.
These points were evaluated using CFD. A full-scale, 2D axisymmetric model was used for all the
configurations. The design studies presented for the rod-fin and bent-fin geometries were carried out
during early stages of the CFD model development of the SUpA system. Thus, the setup of the model
used to test the design points differed from the model used for the inverted prism geometry. Firstly, the
output parameter was defined as the absolute mass flow rate of water moved by the device through the
updraft channel at the end of the simulation. Secondly, since an efficient mesh such as that shown in
Figure 4-2 had not yet been developed, a smaller pond domain with a radius of 1.5m was used. The
height of the solar collector above the water was fixed at 0.15m.
64
Figure 6-1: Geometry parameterization of the rod-fin configuration
Figure 6-2: Definition of design variables of the bent-fin geometry
65
6.2 Inverted Prism Geometry
Figure 6-3: Parameterization of the inverted prism geometry
The parameters identified for the initial design study of the inverted prism geometry are shown
in Figure 6-3. They include the sloped length of the collector, the angle of inclination of the collector,
the updraft gap, the width of the horizontal bottom of the inverted structure, the thickness of the metal,
the gap between the top of the draft tube and the water surface, the insulation factor and a vertical depth
factor 𝑇𝑇, defined as the ratio of the height of the bottom section of the updraft channel to the height of
the water column below the base of the device:
𝑇𝑇 =ℎ
𝑑𝑑 − 𝐷𝐷 ∗ cos (𝐴𝐴)
(Eq 6-2)
where ℎ is the height of the bottom section of the updraft channel, 𝑑𝑑 is the pond depth, and 𝐷𝐷
and 𝐴𝐴 represent the sloped length of the collector and angle of inclination, respectively. The
dimensions of the pond, orientation of the updraft channel and gap between the pond bed and the bottom
of the draft tube were held constant as shown in the figure. The output monitored for each of the 27
configurations was the total mass of water moved by convection through the draft tube gap normalized
by the volume of metal used for each geometry, recorded after 1 hour of simulation time.
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6.3 Results
6.3.1 Rod-Fin
Figure 6-4: Mean effects plot normalized by the average response of 27 configurations of the rod-
fin geometry generated using a Taguchi-based orthogonal array
The mean effects plot in Figure 6-4 shows the results of the twenty-seven evaluations
performed for the rod-fin geometry. The most influential parameters are discussed here. The length and
diameter of the submerged conduction element were found to have the largest impact on the mass flow
rate. This was expected as the larger surface area allowed for a higher rate of heat transfer to the
surrounding water, while a larger diameter reduced the conductive heat loss from the solar collector to
the conduction rod. A smaller annulus size was also found to enhance the updraft mass flow rate.
Although the reduced annulus limited the volume of the water uptake, the smaller gap between the
surface of the rod and the inner wall of the draft tube prevented secondary flow cells and vortex
shedding from developing inside the draft tube.
These secondary flow cells were found to divert water from the circulation current and decrease
the overall mass flow output. The reduction in water uptake volume had a smaller impact on the device
performance than the detrimental effect of vortices forming in the annulus. Similarly, a narrower gap
67
between the top of the draft tube and the water surface was amenable to higher flow rates as it limited
the amount of water that could cause localized regions of flow reversal inside the draft tube. The
insulation penetration factor was found to exhibit a peak at 33% penetration, resulting from a trade-off
between the amount of thermal energy retained for convective heat transfer and the amount of heat
consumed within the rod. The gap between the pond bed and bottom of the draft tube and the thickness
of the solar collector were observed to have a minimal impact on the mass flow output of the device.
6.3.2 Bent-Fin
Figure 6-5: Normalized effects plot of the design space search of the bent-fin geometry
As noted in the results of the design study carried out for the rod-fin geometry, the depth of the
submerged conduction element had the greatest effect on the mass flow rate of water, as the exposed
surface area on the bent fin directly affected the amount of heat transfer to the surrounding water. This
design study also showed that the spacing between the water surface and the top of the draft tube as
well as the updraft channel width were inversely related to the mass uptake, as occurrence of flow
reversals in the updraft region was reduced. The insulation penetration factor was found to vary directly
with the mass uptake of water. This was explained by the larger retention of heat transferred from the
solar collector to the conduction element. The thickness of the metal used and collector surface area,
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represented by the length of the plate in the axisymmetric system, also showed positive correlations
with the mass flow rate of water. The larger collector area allowed for a larger amount of thermal energy
input into the device. The larger metal thicknesses corresponded to greater cross-sectional areas,
enabling a higher rate of heat transfer to the vertical fins via conduction.
6.3.3 Inverted Prism
Figure 6-6: Plot of normalized effects corresponding to the inverted-prism geometry
Figure 6-6 shows the mean effects plot of the mass flow rate per unit volume of metal used in
each configuration of the inverted prism geometry. The results indicate that the base width, updraft gap
and metal thickness have the greatest effect on the mass flow rate normalized by the volume of metal,
𝑉𝑉, given by
𝑉𝑉 = 𝜋𝜋 �(𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝜈𝜈 + 𝑏𝑏) �𝑙𝑙 +𝑏𝑏
cos𝜈𝜈� − �
𝑏𝑏2
cos𝜈𝜈�+ 𝑏𝑏2� 𝑡𝑡 (Eq 6-3)
where 𝑙𝑙, 𝑏𝑏, 𝜈𝜈 and 𝑡𝑡 are the sloped length, base width, collector angle and metal thickness
respectively. The metal thickness was inversely related to the volume-normalized mass flow rate, as
69
thinner metal allowed for more efficient heat transfer to the water while also resulting in a smaller metal
volume. The largest base-width value was observed to have an average increase of 35% from the mean
response of all configurations. As observed in the schematic given in Figure 6-1, the base width was
the radius of a cylinder below the collector with a height equal to the vertical segment of the updraft
channel. Since the volume of a cylinder is directly proportional to the square of its radius, a 60%
increase in the base-width resulted in a 156% increase in the volume of water being drawn into the
updraft channel per unit time, which outweighed the corresponding increase in metal volume. The
collector angle was also directly related to the normalized mass flow rate, indicating that the reduction
in effective thermal input given by Eq 6-3 was more than offset by the resulting decrease in volume of
the metal. The minimal effect of the sloped length showed that the effect of the increase in heat transfer
surface area was almost matched by that of the increase in metal volume. The gaps in the updraft
channel and between the top of the draft tube and water surface played the same role as in the design
studies of the rod-fin and bent-fin geometries, where the smaller gap prevented significant intrusion of
secondary flows into the channel. However, a trade-off between flow interference and flow capacity
was also noted, as the larger gap was found to allow a greater uptake of water from the bottom. It was
noted that the insulation factor changed the response by only 5% from the mean, and favoured the
smallest fraction of penetration into the updraft channel. This indicated that the inverted prism geometry
performed better when the entire surface area of the angled collector walls was available for heat
transfer. Finally, it was observed that a smaller height of the vertical section of the updraft channel
favoured higher performance as it allowed for greater uptake of water.
6.4 Chapter Summary
A high-level exploration of the design space was performed for the three SUpA configurations
being evaluated to quantify the relationship between device performance and design variables. In
general, it was found that increasing the surface area available for heat transfer correlated with an
increase in the mass flow rate of the convective circulation. Increasing the spacing inside the updraft
70
channel and between the water surface and the updraft opening was found to negatively impact the
flow. The presence of insulation was most significant in the rod-fin and bent-fin geometries, where a
larger insulation penetration into the updraft channel was correlated with an increase in flow circulation.
The inverted prism geometry was evaluated with a different output parameter defined by the mass flow
rate normalized by the volume of the metal of each configuration. It was found that a geometry with a
large collector angle, large base-width and minimum metal thickness yielded the highest mass flow
rate.
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7. Field Implementation
The performance of the SUpA candidates was assessed in terms of their overall feasibility of
implementation in the field using the results of preliminary trials. Dissolved oxygen data from the pond
bottom was analyzed for each design. Challenges faced during manufacturing and installation were also
evaluated.
7.1 Vietnam
The first field trials were carried out in the Bac Ninh province of Vietnam, near the city of
Hanoi. The trials were conducted in a collaboration with the National Institute of Science and
Technology Policy And Strategy Studies (NISTPASS). The test pond was part of an agricultural
research facility. It measured approximately 90m × 15m in area and had an average depth of 2m. Prior
to device installation, a weather station for monitoring wind speed, solar irradiance and ambient
temperature was set up next to the pond. Baseline dissolved oxygen readings and water temperature
were also obtained from the test pond at several depths. These measurements were used as inputs for
numerical models of dissolved oxygen and temperature dynamics in the pond, similar to those
developed by [16] and [20]. Two prototypes of the SUpA system based on the rod-fin geometry were
installed in the test pond. The devices were sized by sampling 27 points within an 8-dimensional design
space using a Taguchi orthogonal array. A CAD model of one of the devices is shown in Figure 7-1.
Dissolved oxygen levels at the bottom of the pond at a control location were compared to those
next to the device. Initially, the pond was found to be too large for the two devices to create any
statistically significant difference in DO. A part of the pond was then sectioned and the devices were
brought closer together. Data obtained from the test pond after the sectioning indicated improvements
of up to 18% at the bottom of the pond next to the device. The field trials in Vietnam were the focus of
the work of A. Mahmoud. The reader is referred to [60] for detailed information on device
manufacturing, installation, the data acquisition process as well as challenges faced during testing.
72
Figure 7-1: CAD illustration of the rod-fin prototype tested in Vietnam in November 2015
7.2 Srimangal, Bangladesh
The field trials and device sizing discussed here begin with the second round of testing of the
SUpA device in Srimangal, a town in the northeastern region of Bangladesh. The project was
undertaken in collaboration with BRAC, the largest NGO in the world in terms of staff [62]. The tests
were carried out in a 0.1ha pond at a hatchery owned and operated by BRAC in Srimangal, shown in
Figure 7-2. The rod-fin and bent-fin configurations were installed and evaluated in the test pond shown.
Device sizing, manufacture and results obtained from these tests are presented in this section.
Figure 7-2: Satellite image of the test pond located in the BRAC-operated hatchery in Srimangal
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7.2.1 Device Sizing
Sizing of the device for the field test was informed by both the results of the high-level design
space exploration discussed in Chapter 6 as well as overall feasibility of manufacturing and installation
in remote areas in the developing world. The best performing configuration from the DOE was modified
for implementation in the field and is tabulated in Table 7-1 and Table 7-2 for the rod-fin and bent-fin
geometries respectively.
Table 7-1: Comparison of design parameters identified for the rod-fin geometry
Parameter Value from DOE Value in the Field
*Fin radius (in) 3 2
Updraft Gap (in) 1 1
Fin Depth (in) 24 24
Insulation Factor 0.33 0.33
Bottom Gap (in) 4 4
Top Gap (in) 2 2
Collector Length (in) 24 24
*Collector Thickness (in) 0.125 0.375
In the above table, the parameters marked with an asterisk (*) were modified for field
installation. In the case of the rod-fin geometry, the radius of the rod and thickness of the collector were
changed. Although the design study predicted improved flow rates with a rod of radius 3in, it was found
to be too heavy to be securely welded to the thin sheet used for the collector. A rod with a 2in radius
was used instead. The thickness of the collector was increased from 0.125in to 0.375in in order to
support the solid conduction rod.
74
Table 7-2: Comparison of design parameters selected for the bent-fin geometry
Parameter Value from DOE Value in the Field
Updraft Gap (in) 1 1
Fin Depth (in) 24 24
Insulation Factor 0.5 0.5
Top Gap (in) 2 2
Bottom Gap (in) 6 6
Collector Length (in) 24 24
*Metal Thickness (in) 0.25 0.1875
In the bent-fin configuration, the metal thickness was reduced to 0.1875in for manufacturing.
Although a higher thickness was correlated with improved performance due to higher rate of conduction
through the metal, it led to difficulties with bending the sheet metal by 90o on a brake.
7.2.2 Manufacturing
Figure 7-3 shows 3D CAD models of the devices sized for the field tests in Srimangal and
Figure 7-4 shows the completed devices before they were deployed in the pond. The devices
manufactured in Bangladesh were simplified compared to those in Vietnam. All materials utilized for
construction of the devices were sourced locally. Plastic barrels were used for flotation instead of buoys.
The steel frame structure supporting the draft tube was replaced by cords attached to the solar collector.
Styrofoam sheets were used to insulate the solar collectors as well as the bent fin surfaces of the second
device.
75
Figure 7-3: CAD illustrations of the rod-fin (a) and bent-fin (b) prototypes installed in Srimangal
Figure 7-4: The rod-fin device prior to being installed (left), and the bent-fin device being lowered
into the test pond by staff at the hatchery
Several opportunities for improving the manufacturability of the designs were identified.
Options for insulating materials were limited to styrofoam sheets, which were susceptible to
degradation with long-term exposure to ultraviolet light [63]. Both designs favoured metals with high
thermal conductivity to minimize losses during the conduction of heat from the collector to the
submerged conduction element; as a result, aluminum was used instead of cheaper and more widely
available metals such as steel. During the construction of the rod-fin device, welding the solid
aluminum rod with a 4in diameter to the 0.375in-thick aluminum sheet of the solar collector proved to
76
be challenging. The highly conductive aluminum sheet quickly dissipated heat away from the joint,
compromising the integrity of the weld. As seen in the photo, the finished weld had poor contact with
the sheet metal and resulted in a localized increase in thermal resistance.
Figure 7-5: Difficulties in welding the solid 4in diameter aluminum rod to the thin aluminum
sheet resulted in poor contact between the collector and the conduction element
7.2.2 Pond Installation
The two devices were installed at diagonally opposite ends of the pond. A pair of Onset U26
dissolved oxygen loggers was placed near the surface and pond bottom adjacent to both devices to
monitor DO levels in the vicinity of the device. Control loggers at corresponding depths were suspended
from a floating weather station located in the middle of the pond. The weather station recorded wind-
speed near the water surface using an ultrasonic anemometer. Global solar irradiance (GSR) and
photosynthetically active radiation (PAR) were measured using SP-212 and SP-215 pyranometers
respectively. Additional information about the implementation of these sensors and the significance of
PAR can be found in Mahmoud [60] and Boyd [10] respectively. Both dissolved oxygen and weather
station sensors recorded data at 15-minute intervals. These instruments are shown in Figure 7-6. The
layout of the devices and weather station is shown in Figure 7-7.
77
Figure 7-6: Instruments used for data collection from Srimangal - (a) optical DO logger probe (b)
ultrasonic anemometer (c) pyranometer
Figure 7-7: The devices and weather station were installed along a diagonal across the test pond.
The SUpA devices were installed at opposite ends of the diagonal with the weather station
situated in the middle of the pond
7.2.3 Results: Dissolved Oxygen
Figure 7-8 shows a sample of the data from the two devices obtained over a four-day period
from the tests conducted in Srimangal. The dissolved oxygen measurements at the bottom of the pond
near the device are compared to those from the bottom of the pond at the control location. The daily
solar irradiance during the same period is also plotted. An average increase of 18% in dissolved oxygen
78
at the sensor near the rod-fin device is noted. Mahmoud [60] found this increase to be statistically
significant and found that the increase positively correlated to the presence of the device in the pond.
Figure 7-8: Plot of DO data compared between measurements taken at the device and at a control
location for the rod-fin (top) and bent-fin (bottom) devices in Srimangal
During the same period, the data from the logger next to the bent-fin device showed a negligible
difference of 2% with the logger at the control location. This difference in impact on local DO levels
between the two designs was hypothesized to be the result of updraft flows with insufficient
momentum. As demonstrated in both the CFD models as well as the bench-scale experiments, the peak
flow velocity in the updraft channel of the bent-fin geometry was less than 25% of the corresponding
velocity in the rod-fin design. The average velocity in the updraft channel of the full-scale device was
79
predicted by the CFD model to be less than 5mm/s. This may have caused any convective currents to
be dominated by local, naturally-occurring currents within the water volume. Further investigation of
the potential issues with the bent-fin device was hampered by several challenges that arose during the
weeks following the installation. The sensors at the bottom of the pond began to show signs of severe
fouling due to the large concentration of biomass and sediments suspended in the water column. There
was some improvement in the quality of data when pieces of tarp were placed below the sensors at the
bottom. However, much of this data received afterwards could not then be evaluated rigorously due to
power supply issues on the weather station platform.
7.3 Mymensingh
The third round of field testing commenced in the Mymensingh district of Bangladesh in
February 2017. A modified version of the inverted prism geometry was installed in five test ponds. In
this version, the original updraft channel consisting of a vertical section at the bottom and an angled
portion at the top was replaced by the single vertical structure as shown in Figure 7-9. This design
change was motivated by improved results of the CFD simulations and simplified manufacturing
process. The mass flow rate with the vertical updraft structure was found to be 50% higher than the
original design. CFD simulations showed that the vertical updraft channel walls resulted in a
significantly higher volume of water being drawn from the bottom of the device. In addition, the flow
was observed to remain stable and uniform from the bottom to the top of the updraft channel. This is
illustrated in a vector distribution plot in Figure 7-10.
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Figure 7-9: Modified inverted prism with vertical updraft channel walls
Figure 7-10: Flow velocity vectors observed for the modified inverted prism geometry
The prototypes for field testing were sized according to the design study performed on the
original inverted prism design as well as constraints associated with manufacturing the new geometry.
A summary of these design parameters is given in Table 7-3.
Table 7-3: Comparison of design parameters selected for the inverted prism geometry
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Parameter Value from DOE Value in the Field
*Collector Angle (deg) 75 45
*Sloped Length (in) 24 21
Insulation Factor 0.05 0
*Updraft Gap (in) 0.5 N/A
Top Gap (in) 2 2
Vertical Depth Factor (in) 0.5 0.5
*Base Width (in) 12 3
Metal Thickness (in) 0.05 0.05
Since the effect of shading had not been accounted for in the original search of the design space,
the collector angle was decreased from 75o to 45o to increase the range of solar irradiance it would be
able to receive during the day. The sloped length and base width were adjusted to allow the metal body
to be formed out of a stock sheet metal size of 48in × 48in in order to minimize wastage. The updraft
channel gap investigated in the previous design study was not translated into the new geometry as the
vertical structure resulted in a continuously varying channel cross-section. Figure 7-11 shows the
manufactured device being lowered into one of the test ponds belonging to a local farmer.
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Figure 7-11: A prototype of the modified inverted prism being installed at a test location in
Mymensingh
7.3.1 Results
Data gathered from the field tests in Mymensingh continues to be evaluated and is not included
in the present work. Several challenges were faced in the months following the installation. Severe
fouling was once again found to hamper data collection efforts from the dissolved oxygen loggers. The
ponds were reported to contain large amounts of fish feed, leading to a dense growth of phytoplankton
and biofouling agents. The onset of monsoon in the following months also impacted DO results, as it
was difficult to evaluate the device without a sustained period of thermally stratified conditions in the
pond.
7.4 Chapter Summary
Preliminary trials of the rod-fin geometry in Vietnam had demonstrated that the deployment of
the SUpA system correlated with increased dissolved oxygen levels at the bottom of a relatively small
section of the pond. The second set of trials in Srimangal also showed an 18% increase in bottom
dissolved oxygen when the rod-fin device was installed over a 4-day period. During the same period,
the bent-fin device did not show any statistically significant changes in dissolved oxygen levels at the
pond bottom. Longer term testing of the devices was compromised due to difficulties with data
collection and processing.
83
In terms of device manufacturing, there were two factors that negatively impacted the potential
of the rod-fin and bent-fin geometries to be used for large-scale adoption of the SUpA technology in
the future. The first was the requirement of a metal with high thermal conductivity such as aluminum.
The high thermal conductivity was an advantage over steel in promoting heat conduction through the
conduction element and solar collector; however, it also resulted in difficulties with welding the solid
rod to the sheet metal of the collector in the rod-fin device. The second factor was the need for adequate
thermal insulation on both the underside of the solar collector as well as the submerged section of the
conduction element. In a tropical region such as rural Bangladesh, acquiring insulation that did not
degrade with UV exposure and had a sufficiently high R-value was a difficult task.
In comparison, although the impact on dissolved oxygen levels has not yet been ascertained,
the inverted prism geometry was found to be easier to manufacture as it could utilize an all-steel
construction. Furthermore, it did not require insulation as the mechanism of heat transfer in the inverted
prism favoured greater exposure to the surrounding water to maximize convective heat transfer.
84
8. Design Optimization
The inverted prism geometry was identified as a suitable design configuration of the SUpA
system for further research and field trials. Shape optimization of the inverted-prism geometry was
performed to identify an improved configuration for future tests. Previous work in this thesis had
demonstrated a validated modelling approach in which the geometry could be easily adjusted to produce
the maximum possible flow rate of water under material and environmental constraints. Thus, an
optimization design study was performed on the inverted prism geometry and is discussed in this
chapter.
8.1 Problem Formulation
For a design space with 𝑛𝑛 design variables, the standard form of a non-linear programming
optimization problem is expressed as
Minimize �𝜙𝜙(𝐱𝐱)�
Subject to 𝑔𝑔𝑖𝑖(𝐱𝐱) ≤ 0 (𝑅𝑅 = 1, …𝑚𝑚)
and 𝐱𝐱𝐋𝐋 ≤ 𝐱𝐱 ≤ 𝐱𝐱𝐔𝐔
where 𝜙𝜙 represents the objective function evaluated at any design point 𝐱𝐱 given by 𝐱𝐱 =
𝑥𝑥𝑖𝑖 ∀ 𝑅𝑅 𝜖𝜖 (1, …𝑛𝑛) for 𝑛𝑛 design variables, 𝑔𝑔𝑖𝑖 represents the 𝑅𝑅𝑡𝑡ℎ constraint out of a total of 𝑚𝑚 constraints,
and 𝐱𝐱𝐋𝐋 and 𝐱𝐱𝐔𝐔 are vectors composed of the lower and upper bounds of each design variable 𝑥𝑥𝑖𝑖.
8.1.1 Design Variables
The geometry of the inverted prism device was decomposed into a set of design variables,
geometric constraints and model constants. The design space previously defined in Section 6.2 was
modified based on the main effects plot in Figure 6-6. Since the insulation factor and vertical depth
factor were found to have minimal impact on the average mass flow response, these were excluded
from the present design space. The new design space is illustrated in Figure 8-1. The boundaries of the
design space are given in Table 8-1.
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Table 8-1: Parameterization of the inverted prism geometry used for shape optimization
Parameter Lower Bound Upper Bound
Draft Tube Gap (in) 0.5 4.0
Collector Sloped Length (in) 12 30
Collector Angle (deg) 15 75
Base Width (in) 3 12
Metal Thickness (in) 0.050 0.125
Figure 8-1: Schematic of the design variables given in Table 8-1
Thus, for the optimization problem formulation of the inverted prism geometry, the design
vector 𝐱𝐱 was given by 𝐱𝐱 = (𝑥𝑥1, 𝑥𝑥2,𝑥𝑥3,𝑥𝑥4, 𝑥𝑥5), where the components of 𝐱𝐱 were the values of the 5
design variables described above.
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8.1.2 Objective Function
The objective function 𝜙𝜙(𝐱𝐱), which represented the output of the system for any input vector
𝐱𝐱, was then defined. The goal of improving the performance of the SUpA device was to increase fish
yields by redistributing dissolved oxygen levels throughout the pond. This is directly related to the
amount of water circulated by the device. Therefore, 𝜙𝜙(𝐱𝐱) was selected as the total mass of water
moved by the device during the day and was maximized in the optimization process.
8.1.3 Constraints
Two constraints were applied to the optimization problem based on limitations on the stock
sizes of sheet metal available and the effects of self-shading of the device due to the angled faces.
1. Surface Area
The size of sheet metal sold in the field locations was 8’ × 4’, with a total area of 4608in2. For
such a sheet made of steel with thickness 0.05in, utilizing the entire piece to manufacture the inverted
prism resulted in a large, cumbersome structure weighing more than 60kg. It was thus decided that the
metal was to be formed out of half of an 8’ × 4’ sheet, thereby producing two devices from a single
stock piece of sheet metal. This was incorporated in the optimization problem by requiring that the
surface area of the axisymmetric model be less than 2116in2, or half of the usable area of the stock
sheet. The usable area was given by the area of the metal remaining after forming a 1in-wide flange
around the perimeter for attaching the collector glazing. Mathematically, this was expressed as
𝜋𝜋 �(𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝜈𝜈 + 𝑏𝑏) �𝑙𝑙 +𝑏𝑏
cos𝜈𝜈� − �
𝑏𝑏2
cos𝜈𝜈�+ 𝑏𝑏2� − 2116 ≤ 0 (Eq 8-1)
where 𝑙𝑙,𝜈𝜈 and 𝑏𝑏 are the sloped length of the collector, angle of inclination of the collector and
the radius of the collector bottom.
2. Self-Shading
The angle of inclination of the collector resulted in shadows being cast on the inner faces at
various times of the day. This prevented incident solar thermal energy from being fully utilized for heat
transfer to the water. The effects of shading had not been incorporated into the boundary condition
87
applied on the solar collector surface in the CFD model. The incident heat flux had been applied
uniformly over the entire surface using an energy source term in a virtual layer of cells on the solar
collector. This would have resulted in configurations with smaller apertures receiving the same amount
of irradiation over the simulated period as those with larger apertures. Therefore, for the optimization
problem, a constraint was imposed to exclude those points which would not be able to capture at least
66% of the total irradiation on a given day. For the remaining points in the feasible region, it was
assumed that shading would only reduce the net irradiation received by each device without changing
their relative positions on the design space. The constraint was expressed by considering the geometry
given in Figure 8-2. The position of the sun is indicated by 𝜃𝜃0, which represents the minimum solar
hour angle at which the sun is visible from either vertex at the bottom of the inverted prism. At this
angle, the entire collector receives irradiation from the sun without shading. Based on the irradiation
profile given in Figure 4-4, it was found that 66% of the daily irradiation was available between the
hour angles 52.5o and 127.5o. Thus, 𝜃𝜃0 was defined as 52.5o. The shading constraint was then applied
to limit the design space to those configurations for which the aperture corresponded to 𝜃𝜃0 ≤ 52.5𝑠𝑠, or,
using the geometry shown in Figure 8-2,
tan−1 �𝑙𝑙𝑙𝑙𝑅𝑅𝑛𝑛𝜈𝜈
2𝑏𝑏 + 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝜈𝜈� − 52.5 ≤ 0 (Eq 8-2)
where 𝑏𝑏, 𝑙𝑙, and 𝜈𝜈 were the base width, sloped length and angle of inclination of the collector
respectively.
Figure 8-2: Geometric relationship between the solar hour angle and sloped length, base width
and collector angle of the inverted prism geometry
88
The problem formulation for the given system was thus stated as
Maximize 𝜙𝜙(𝐱𝐱), where 𝜙𝜙(𝐱𝐱) = net mass of water moved during day
Subject to 𝑔𝑔𝑖𝑖(𝐱𝐱) ≤ 0 (𝑅𝑅 = 1,2) , given by Eq 8-1 and Eq 8-2
and 𝐱𝐱𝐋𝐋 ≤ 𝐱𝐱 ≤ 𝐱𝐱𝐔𝐔, where 𝐱𝐱𝐋𝐋, 𝐱𝐱 and 𝐱𝐱𝐔𝐔 are the five design variables and
their ranges as given in Table 8-1
8.2 Optimization Approach
The optimization approach is outlined in Figure 8-3. A fraction of the design space was first
systematically sampled using the CFD model. A surrogate model of the CFD simulations was then
constructed by determining empirical relationships between the design inputs and known system
response at each of these sampled points. The optimization algorithm then used the surrogate model to
determine a set of candidate points ranked in order of their proximity to the global maximum. These
points were tested using the CFD code to validate the response surface constructed in the second step.
If the accuracy of the response surface was less than 90%, the candidate points were added to the initial
sample set to refine the surrogate model. The above steps were then repeated. After sufficient agreement
between the CFD and its surrogate was found, a sensitivity study was conducted at the global maximum
predicted by the optimization algorithm. Finally, the best performing design point from the sensitivity
study was identified as the optimal design configuration of the given geometry. The following sections
elaborate on each of these steps in greater detail.
89
Figure 8-3: Illustration of approach and analysis tools used to arrive at an optimized
configuration of the inverted prism geometry
8.3 Design Space Sampling
The construction of a suitable surrogate model of the CFD system required a set of training
points obtained from the design space defined in Table 8-1. As discussed in Section 2.4.1, while several
strategies have been employed for performing this initial sampling of the design space, the enhanced
face-centered Central Composite Design (CCD) method was used for its balance between sampling at
the extremities of the design space and clustering in the expected region of interest. For the five
parameters associate with the inverted prism geometry, the enhanced CCD method generated 54 design
points. Figure 8-4 graphically depicts the distribution of points generated by the CCD method for each
parameter. As seen in the figure, the number of design points were distributed across five ‘levels’ given
by L1, L2, L3, L4 and L5, where L1 and L5 corresponded to the lower and upper bounds of the
parameter respectively. The enhanced CCD method created 10 points for L1, 17 points for L3, and 9
points for each of the remaining levels.
90
Figure 8-4: Distribution of the 54 design points generated by the enhanced CCD design sampling
method in ANSYS Workbench
The total mass of water moved by each design configuration was evaluated using CFD. Each
simulation represented device operation over a 12-hour period. The time-varying solar irradiance
profile shown in Figure 4-4 was used as the heat flux boundary condition on the surface of the collector.
As demonstrated in Section 2.4.2, the heat flux profile was implemented using a user-defined function
(UDF). Since the collector tilt angle was one of the design variables being analyzed, separate UDFs
were written to obtain the effective heat flux for each tilt angle according to Eq 4-1. A Matlab script
was used to create the UDFs, load them into the simulation, save the simulation output files and switch
from one design point to the next.
8.4 Surrogate Model Evaluation and Results
A number of options for surrogate modelling are offered within ANSYS Workbench. These
include Sparse Grid, Artificial Neural Networks, Second Order Polynomial Response Surface, Non-
parametric Regression and Kriging. Out of these models, as discussed in Section 2.4.2, Kriging has
been used in a wide range of applications for its flexibility and ability to model complex, non-linear
systems with a small number of initial sample points [46]. In addition, Forrester et al. [50] found that it
0
4
8
12
16
20
L1 L2 L3 L4 L5
Num
ber o
f Poi
nts
Levels
91
was particularly well-suited for deterministic applications such as CFD. It was therefore selected for
constructing a surrogate of the CFD model of the SUpA system.
Figure 8-5 depicts a portion of the response surface showing the variation of the base width,
collector angle, updraft gap and metal thickness with the sloped length. The design points sampled
using the CCD method are also indicated. Trends in system response between different pairs of design
variables are discussed. For the response surface corresponding to each pair of design variables, the
three remaining parameters were held constant at their average values.
Figure 8-5(a) shows a positive correlation between the mass flow output and the base width
and angled length of the collector for the entire range of both variables. Since increasing both
parameters increased the overall size of the device, the shape of the response surface was attributed to
the direct relationship between the surface area of the metal in contact with the water and the rate of
convective heat transfer.
Figure 8-5 (b) shows the variation of the mass flow output with the angle of inclination and
sloped length. The response surface in this plot revealed a trade-off between the effective solar
irradiance received by the collector and friction encountered by the convective flow in the angled
section of the updraft channel. Configurations with smaller angles of inclination received greater
effective irradiance due to the presence of the cosine factor in Eq 4-1. However, these configurations
also resulted in a smaller vertical component of the flow velocity within the angled section of the updraft
channel. For sloped lengths less than 25in, the greater effective irradiance input to the collector more
than compensated for the loss in flow momentum due to wall friction in the updraft channel. However,
for longer sloped lengths, the effect of wall friction became more significant. The peak response thus
deviated from the lower limit of the inclination angle and was observed to occur at an angle of 30o at
the upper limit of the sloped length.
In Figure 8-5(c), the variation of the mass flow output with updraft gap and sloped length is
shown. The response surface in this case was the result of a trade-off between the volumetric capacity
of the updraft channel and the negative impact of flow reversals occurring within the channel. For
92
smaller sloped lengths, corresponding to smaller area of convective heat transfer, the peak flow rate
occurred at the upper limit of the updraft gap, which allowed for the uptake of a larger volume of water.
At greater sloped lengths, corresponding to larger convective surface areas, the negative impact of
secondary flows within larger channel widths prevailed over the increased water uptake capacity. As a
result of these competing factors, the peak flow rate was observed at an updraft gap equal to 1.8in for
a sloped length of 30in.
Figure 8-5(d) shows the response surface corresponding to the variation in sheet metal
thickness. It was found that for smaller collector sizes, the mass flow output varied inversely with the
thickness of the sheet metal. For larger collector sizes, however, this relationship was reversed. This
variation in the response of the inverted prism geometry was attributed to the significance of conductive
heat transfer occurring longitudinally within the metal body. As observed in the temperature contour
plot in Figure 4-5, the temperature inside the metal was higher at the base of the collector than along
the slanted walls. This occurred due to the accumulation of heated water below the base of the prism
and the removal of thermal energy via convection along the angled updraft channel. As a result, a
thermal gradient developed between the collector base and the rest of the metal body. For larger
collector surface areas, the conduction of heat across this thermal gradient aided convective heat
transfer from the angled walls. Thicker sheet metal promoted this internal heat conduction by increasing
the available cross-section area within the metal thickness. For designs with smaller sloped lengths and
collector surface areas, the best performing configurations were those that allowed the incident thermal
energy to be transferred to the water as quickly as possible, resulting in thinner sheet metal being
favoured in this case.
93
Figure 8-5: Partial representation of the five-dimensional response surface generated using the
Kriging tool in ANSYS Workbench
8.5 Optimization
As discussed in Section 2.4.3, genetic algorithms have been widely used for CFD-based
optimization in ANSYS Workbench. They offer a robust means of determining the global minimum
94
(or maximum) across the design space and can accommodate non-linear response surfaces as well as
integer variables [53]. The Multi-Objective Genetic Algorithm in ANSYS is a hybrid variant of the
Non-dominated Sorted Genetic Algorithm-II that can evaluate multiple goals and is compatible with
all types of input parameters [64]. Detailed information about the algorithm and its implementation
within the ANSYS Workbench environment can be found in [64]. A single-objective optimization was
implemented using the MOGA for the SUpA geometry in Workbench. The algorithm searched for a
global maxima of the objective function representing the total mass of water moved by a design point
over the simulated period. The algorithm was initialized using a population of 1000 individuals. The
minimum recommended initial size is 10 times the number of design parameters in order to provide
sufficient information about the response surface as an input to the algorithm[64]. Thus, an initial size
of 1000 individuals was deemed adequate for the given problem with 5 design variables. The number
of individuals to be evaluated in each generation was 100, set to the default value used in the
optimization setup in Workbench. The minimum convergence stability percentage was also set to the
default value of 2%. The convergence stability describes the variation of the average response and its
standard deviation from one population with respect to the population in the preceding generation[65].
It is given by the following ratios:
𝑆𝑆𝜇𝜇 =| 𝜇𝜇𝑖𝑖 − 𝜇𝜇𝑖𝑖−1|𝜙𝜙𝑚𝑚𝑠𝑠𝑚𝑚 − 𝜙𝜙𝑚𝑚𝑖𝑖𝑐𝑐
× 100 (Eq 8-3)
and
𝑆𝑆𝜎𝜎 =| 𝜎𝜎𝑖𝑖 − 𝜎𝜎𝑖𝑖−1|𝜙𝜙𝑚𝑚𝑠𝑠𝑚𝑚 − 𝜙𝜙𝑚𝑚𝑖𝑖𝑐𝑐
× 100 (Eq 8-4)
where
𝑆𝑆𝜇𝜇 is the stability in terms of the mean population response
𝑆𝑆𝜎𝜎 is the stability in terms of the standard deviation of the population response
𝜇𝜇𝑖𝑖 is the mean response of the 𝑅𝑅𝑡𝑡ℎ population
𝜎𝜎𝑖𝑖 is the standard deviation of the response across the 𝑅𝑅𝑡𝑡ℎ population
𝜙𝜙𝑚𝑚𝑠𝑠𝑚𝑚 is the maximum output value determined from the evaluation of the first generation
95
𝜙𝜙𝑚𝑚𝑖𝑖𝑐𝑐 is the minimum output value determined from the evaluation of the first generation
In the MOGA-based optimization used in ANSYS, the first population is not taken into account
when determining convergence stability, as it was not generated by the algorithm[65]. Thus, in Eq 8-3
and Eq 8-4 above, 𝑅𝑅 ≥ 3. Convergence was said to have occurred when both measures of stability, i.e.
𝑆𝑆𝜇𝜇 and 𝑆𝑆𝜎𝜎, were observed to be less than a user-defined threshold 𝑆𝑆.
Following the definition of these parameters, the algorithm executed the search for the global
maxima of the mass flow output response. A convergence plot of the output parameter towards a
maximum value is given in Figure 8-6. The decreasing stability or increasing convergence trend is also
shown. The algorithm was terminated when the minimum convergence stability of 2% was attained
after 13 generations.
Figure 8-6: Convergence of mass flow output across generations
The algorithm then generated a list of eight individuals ranked in order of their fitness. These
points belonged to the first pool of candidate points from which the final optimized configuration would
be determined upon successfully validating their response using CFD. Figure 8-7 graphically depicts
96
the eight design points and compares their responses to those obtained from the CFD evaluations. It
was found that the surrogate model had overestimated the response of Candidate #8 by 6%. The largest
difference between the responses of the CFD and surrogate models was noted in the case of Candidate
#5, where the response surface had under-predicted the mass flow output by 9%. Since the discrepancy
between the two responses was less than 10%, the surrogate model was not refined further.
Figure 8-7: Plot of the eight candidate solutions obtained using the Multi-Objective Genetic
Algorithm
As seen in Figure 8-7, Candidate #5 was also found to have the largest mass flow output of all
points in the candidate pool amounting to 7291kg of water moved. It was thus analyzed further and
selected for a parameter sensitivity study to confirm its location at the global maximum. The sensitivity
of the design space was checked along two dimensions defined by the updraft gap and the metal
thickness. The remaining design variables were associated with the prism geometry and were not tested
as the surface area of Candidate #5 was at its maximum possible value. The updraft gap and metal
97
thickness were both varied by ±50%. Three additional design points were generated and their responses
analyzed. The results are given in Figure 8-8. An additional improvement of 1% over the output of
Candidate #5 was observed when the updraft gap was reduced by 50%.
Figure 8-8: Summary of sensitivity study performed around Candidate #5. Decreasing updraft
gap by 50% produced a 1% increase in mass flow output
The sensitivity study showed that the baseline design corresponding to Candidate #5 was not
located at the global maximum predicted by the optimization algorithm. This discrepancy was attributed
to the 9% difference between the responses predicted by the surrogate model and the CFD
simulation at Candidate #5, as given in Figure 8-7. It was concluded that additional sampling of the
design space around this point would further reduce this difference and enable the optimization
algorithm to make a more accurate prediction of the global maximum. However, further refinement of
the surrogate model was not included in the scope of the current work. The 'optimized' design was thus
obtained from the sensitivity study in Figure 8-8, producing a mass flow output of 7358kg with the
6610
6917
7358
6909
-10.0% -8.0% -6.0% -4.0% -2.0% 0.0% 2.0%
Percentage Change in Mass Flow Output
Mass Flow Output(kg) with 50% Parameter Decrease
Mass Flow Output(kg) with 50% Parameter Increase
ThicknessValue at Candidate #5= 0.09in
Updraft GapValue at Candidate #5 = 1.8in
Candidate #5 Output = 7291kg
98
baseline updraft gap reduced by 50%. The corresponding design variables and their values are given in
Table 8-2.
Table 8-2: Final optimized configuration determined from sensitivity study
Parameter Optimized Value
Updraft Gap (in) 0.9
Collector Sloped Length (in) 15.8
Collector Angle (deg) 51.4
Base Width (in) 11.9
Metal Thickness (in) 0.09
The performance of the above point was evaluated in comparison with the reference
configuration presented in Chapter 4. Figure 8-9 shows the mass flow profiles of the two designs. The
mass flow output of the optimized design was 81% higher than that of the reference case (4045kg).
Figure 8-9: Comparison of the mass flow rate profile of the optimized configuration (MOGA
Candidate) and the reference geometry defined in Section 4.1
99
The overall improvement in performance was attributed to a combination of several factors that
distinguished the optimized design from the baseline geometry. These are illustrated in Figure 8-10,
which compares the distribution of velocity vectors observed under peak irradiance in the both designs.
Firstly, the width of the base of the collector was more than twice as large in the optimized design. This
allowed for a greater volume of water to be drawn into the vertical section of the updraft channel,
resulting in a larger overall mass flow rate. Secondly, the updraft channel width was reduced by 35%.
The narrower gap reduced the overall length of counter-flow intrusion into the channel, while
maintaining a sufficiently high flow rate of water. Finally, the steeper angle of inclination of the
collector reduced the horizontal component of the flow velocity near the water surface. This in turn
prevented the flow from reaching the opposite boundary wall before the solar irradiation increased,
resulting in the absence of the initial disturbance observed in the early stages of the baseline case.
100
Figure 8-10: Comparison of velocity vector distribution of (a) the reference geometry and (b) the
optimized design
Figure 8-11 shows a comparison of the hydrodynamic and thermal boundary layers in the
updraft channel of the two designs, recorded at the middle of the sloped face of the collector. Both
101
boundary layer profiles are plotted against the 𝑥𝑥-coordinate, representing distance from the metal
surface, normalized by the channel width 𝑑𝑑. In the optimized design, the thickness of the momentum
boundary layer was more than 50% of the channel, while it was less than half of the width in the baseline
geometry. Further, the peak velocity was 15% higher in the optimized design. The difference in the
thermal boundary layers of the two designs was less pronounced. The peak temperature difference
between the fluid and ambient temperature that occurred at the metal surface was identical in the two
cases. However, in the optimized geometry, the thermal boundary layer was 10% thicker, consistent
with the greater flow velocity and thicker momentum boundary layer.
Figure 8-11: Comparison of the fluid and thermal boundary layers obtained at the mid-depth of
the inverted prism for the reference and optimized designs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x/d
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Vel
ocity
(mm
/s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(T -
T) (
oC
)
Vre f
VM O G A
Tre f
TM O G A
102
Upon evaluation of the optimized geometry, an equivalent 3D version of the optimized design
was constructed. The angle of inclination of the collector measured along a mid-plane of the device
was the same as that of the 2D model. The ratio of the angled length of the collector to the base-width
was the same in both models. This resulted in the model shown in Figure 8-12. The 3D version of the
optimized design was not evaluated using CFD in the current work.
*length of sloped wall at mid-section
Figure 8-12: Dimensions of the 3D geometries and corresponding flattened sheet metal plan of
(a) the reference geometry and (b) the optimized design
The surface area of the optimized axisymmetric model was 2116in2, equal to the maximum
possible area available for manufacturing the device. However, forming the 3D prism geometry
required the elimination of material from the corners as given in the flattened sheet metal schematic in
103
Figure 8-12. As a result, the total surface area available for heat transfer did not translate to the 3D
representation. However, the total area of the baseline 3D model was 1646.4in2, while that of the
optimized design was 1861.6in2. Thus, when compared to the amount of metal used to make the 3D
version of the baseline geometry, the optimized design was found to reduce wastage of the available
sheet metal by 10.1%.
8.6 Chapter Summary
Design optimization of the inverted prism geometry was presented in this chapter. The goal of
the optimization problem was to identify a design configuration that was able to move the greatest
amount of water while respecting material constraints. The design space associated with the inverted
prism discussed was reformulated with fewer design variables than in previous studies. The design
space was systematically sampled at 54 locations using the enhanced CCD method within ANSYS
DesignExplorer. The sampled points were utilized in the construction of a surrogate of the CFD models
using Kriging. The response surface created by the surrogate model was used for the optimization of
the geometry. The genetic algorithm used by the MOGA tool in ANSYS was implemented. Constraints
were applied based on the surface area of stock sheet metal available in the field as well as internal
shading caused by the angled walls of the collector. The assumption that the effect of shading did not
change the relative position of points across the response surface needs to be verified. A set of eight
candidate design points generated by the optimization were validated with the CFD model and found
to agree within 10%. A parameter sensitivity study was carried out on the best performing point and a
further improvement of 1% was obtained when the updraft gap predicted by the algorithm was reduced
by half. The best performing configuration in the sensitivity study produced a mass flow output 81%
greater than that of the reference case. While the framework developed in this chapter yielded good
results, opportunities for further improving the overall process and reducing observed discrepancies
were identified. Ultimately, the optimized configuration determined using the present approach was
translated to 3D and adopted for further testing and validation in the field.
104
9. Conclusion and Future Work
Three configurations incorporating the principle of the SUpA technology were evaluated. CFD
models of the rod-fin, bent-fin and inverted prism configurations were developed and the flow
characteristics of the convective circulation were discussed. Among the three geometries, the inverted
prism design was found to circulate the greatest mass of water over a 12-hour period. The modelling
approach was validated using a pH-indicated flow visualization technique implemented on bench-top
models of the rod-fin and bent-fin geometries. The experimentally measured updraft velocity was found
to lie between the average and peak velocities predicted by the CFD model at all the measurement
locations along the updraft channel for both designs.
While the CFD model was validated in the bench-scale, several opportunities for improving the
model were identified. A key aspect of pond dynamics not included in the current work was the effect
of thermal stratification on the convective circulation induced by the SUpA throughout the water
column. Although numerical models have been developed by the SUpA research team for predicting
diurnal temperature changes in the pond, they are one-dimensional in nature and do not account for
spatial variations across the pond as a result of the SUpA operation. In addition, the 2D axisymmetric
model is limited to simulating the effects of only one SUpA device. In order to model a typical
homestead aquaculture pond with possible deployment of multiple SUpA devices, the development of
a grid-independent, computationally efficient 3D model needs to be investigated further. The overall
radius of influence of the device operation in a pond environment also requires further validation. The
flow velocities predicted by the CFD model are found to be in the 5-10mm/s range in the updraft
channel, and rapidly diminish beyond a radius of 2.5-3m, as given in the velocity distribution of the
inverted prism geometry. The circulation cell induced by the device at peak irradiance was found to
extend up to the edge of the pond; however, the extremely low velocities of the fluid in those regions
(of the order of 0.1mm/s) mean that the radius of influence would be significantly smaller in the
physical system.
105
Following the development of the CFD model, a broad search of the design space associated
with each configuration was performed to gain insights into the effect of various design parameters on
the mass flow output. The performance of the designs in the field was characterized using available
data on their impact on dissolved oxygen levels as well as overall manufacturability in resource-
constrained settings. The inverted prism concept was found to be the most suitable configuration for
large-scale field testing based on evaluations of the CFD model and preliminary field trials. It was thus
selected for further design analysis. Shape optimization of the inverted prism geometry was carried out
using a Kriging-based surrogate model and the MOGA optimization tool in ANSYS Workbench. The
optimization framework yielded a promising 81% increase in mass flow output compared to the
reference geometry of the inverted prism. At the same time, further improvement of the optimization
process in terms of refining the surrogate model and verifying the assumption used for the self-shading
constraint is required. In addition, following the development of an improved 3D model, the
optimization results need to be validated in 3D to inform future design modifications for field testing.
In summary, this thesis demonstrated the use of computational fluid dynamics, a systematic
search of the design space and surrogate-based optimization methods to significantly improve the
technological capabilities of the SUpA system. Moving forward, the improved design will be
manufactured and evaluated in the field as part of ongoing randomized control trials in Mymensingh,
Bangladesh. Along with further testing, the research presented in this thesis will support the
development of the SUpA technology and contribute towards its potential to improve the livelihoods
of smallholder fish farmers in the developing world.
106
References
[1] FAO, The state of world fisheries and aquaculture, vol. 2014. 2014.
[2] FAO, “The State of World Fisheries and Aquaculture 2016. Contributing to food security and
nutrition for all.,” p. 200, 2016.
[3] S. Funge-Smith, M. Briggs, and W. Miao, Regional overview of fisheries and aquaculture in
Asia and the Pacific 2012. 2012.
[4] High Level Panel of Experts on World Food Security, “Sustainable fisheries and aquaculture
for food security and nutrition,” Fao, no. June, pp. 1–119, 2014.
[5] R. Bhujel, “Small-scale aquaculture: Global and national perspectives,” Small-scale Aquac.
Rural Livelihoods, vol. 2030, pp. 10–18, 2012.
[6] WorldFish, “Fish Supply and Food Security in South Asia,” Fish Fish., pp. 1–4, 2009.
[7] J. L. Fiedler, K. Lividini, E. Drummond, and S. H. Thilsted, “Strengthening the contribution of
aquaculture to food and nutrition security: The potential of a vitamin A-rich, small fish in
Bangladesh,” Aquaculture, vol. 452, pp. 291–303, 2016.
[8] N. Van Huong and T. H. Cuong, “Freshwater aquaculture’s contribution to food security in
Vietnam: A case study of freshwater tilapia aquaculture in Hai Duong province,” J. Int. Soc.
Southeast Asian Agric. Sci., vol. 18, no. 1, pp. 6–17, 2012.
[9] R. Subasinghe, I. Ahmad, L. Kassam, S. Krishnan, B. Nyandat, A. Padiyar, M. Phillips, M.
Reantaso, W. Miao, and K. Yamamoto, “Protecting small-scale farmers: a reality within a
globalized economy?,” Farming Waters People Food, vol. 1, pp. 705–717, 2012.
[10] C. E. Boyd and C. S. Tucker, Pond Aquaculture Water Quality Management, 1st ed. Kluwer
Academic Publishers, 1998.
[11] C. E. Boyd, “Pond water aeration systems,” vol. 18, no. February, pp. 9–40, 1998.
[12] C. D. Busch and R. K. Goodman ’, “ENGINEERING SESSION I WATER CIRCULATION--
AN ALTERNATIVE TO EMERGENCY AERATION,” J. World Maricul. SOC, vol. 12, no.
107
1, pp. 13–19, 1981.
[13] M. Mostafa Shamsuzzaman and T. Kumar Biswas, “Aqua chemicals in shrimp farm: A study
from south-west coast of Bangladesh,” Egypt. J. Aquat. Res., vol. 38, no. 4, pp. 275–285,
2012.
[14] K. M. Jahan, B. Belton, A. Hazrat, C. D. Goutam, and I. Ara, “Aquaculture technologies in
Bangladesh: An assessment of technical and economic performance and producer behavior,”
p. 123, 2015.
[15] W. Y. B. Changi and H. A. I. Ouyang, “Dynamics of Dissolved Oxygen and Vertical
Circulation in Fish Ponds,” vol. 74, pp. 263–276, 1988.
[16] J. Lamoureux, T. R. Tiersch, and S. G. Hall, “Pond heat and temperature regulation (PHATR):
Modeling temperature and energy balances in earthen outdoor aquaculture ponds,” Aquac.
Eng., vol. 34, no. 2, pp. 103–116, 2006.
[17] R. G. Passos, D. F. C. Dias, and M. von Sperling, “Review of practical aspects for modelling
of stabilization ponds using Computational Fluid Dynamics,” Environ. Technol. Rev., vol. 5,
no. 1, pp. 78–102, 2016.
[18] A. Karteris, A. Papadopoulos, and G. Balafoutas, “Modeling the temperature pattern of a
covered anaerobic pond with computational fluid dynamics,” Water. Air. Soil Pollut., vol. 162,
no. 1–4, pp. 107–125, 2005.
[19] B. Wu, “CFD Analysis of Mixing in Large Aerated Lagoons,” Eng. Appl. Comput. Fluid
Mech., vol. 4, no. 1, pp. 127–138, 2010.
[20] E. L. Peterson, J. A. Harris, and L. C. Wadhwa, “CFD modelling pond dynamic processes,”
vol. 23, pp. 61–93, 2000.
[21] R. Pandey and M. Premalatha, “Design and analysis of flow velocity distribution inside a
raceway pond using computational fluid dynamics,” Bioprocess Biosyst. Eng., vol. 40, no. 3,
pp. 439–450, 2016.
[22] A. a. Ganguli, A. B. Pandit, J. B. Joshi, and P. K. Vijayan, “Hydrodynamic and heat transfer
108
characteristics of a centrally heated cylindrical enclosure: CFD simulations and experimental
measurements,” Chem. Eng. Res. Des., vol. 89, no. 10, pp. 2024–2037, 2011.
[23] A. Mahmoud, T. N. Quang, E. Pavlov, and A. Bilton, “Development of a Solar Updraft
Aeration System for Pond Aquaculture in Resource-Constrained Environments,” Proc. IEEE
2014 Glob. Humanit. Technol. Conf., 2015.
[24] Y. a. Cengel, “Heat Transfer: A Practical Approach,” Mc Graw-Hill, pp. 785–841, 2003.
[25] Y. S. Tian and T. G. Karayiannis, “Low turbulence natural convection in an air filled square
cavity. Part I: The thermal and fluid flow fields,” Int. J. Heat Mass Transf., vol. 43, pp. 849–
866, 2000.
[26] S. A. Omranian, “The computation of turbulent natural convection flows,” Thesis, pp. 1–438,
2011.
[27] F. Ampofo and T. G. Karayiannis, “Experimental benchmark data for turbulent natural
convection in an air filled square cavity,” Int. J. Heat Mass Transf., vol. 46, no. 19, pp. 3551–
3572, 2003.
[28] T. Wu and C. Lei, “On numerical modelling of conjugate turbulent natural convection and
radiation in a differentially heated cavity,” Int. J. Heat Mass Transf., vol. 91, pp. 454–466,
2015.
[29] I. Ansys, “ANSYS Fluent Theory Guide,” vol. 15317, no. November, p. 514, 2013.
[30] T. Zitzmann, M. Cook, P. Pfrommer, S. Rees, and L. Marjanovic, “Simulation of steady-state
natural convection using CFD,” 9th Int. IBPSA Conf., pp. 1449–1456, 2005.
[31] J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, and P. Le Quéré, “Experimental and
numerical investigation of turbulent natural convection in a large air-filled cavity,” Int. J. Heat
Fluid Flow, vol. 25, no. 5, pp. 824–832, 2004.
[32] O. Turan, R. J. Poole, and N. Chakraborty, “Aspect ratio effects in laminar natural convection
of Bingham fluids in rectangular enclosures with differentially heated side walls,” Int. J. Heat
Mass Transf., vol. 80, no. 1, pp. 727–736, 2015.
109
[33] J. Patterson and J. Imberger, “Unsteady natural convection in a rectangular cavity,” J. Fluid
Mech., vol. 100, no. 1, p. 65, 1980.
[34] A. Bejan, A. A. Al-Homoud, and J. Imberger, “Experimental study of high-Rayleigh-number
convection i n a horizontal cavity with Merent end temperatures,” 1981.
[35] J. Imberger, “Natural convection in a shallow cavity with differentially heated end walls. Part
3. Experimental results,” J. Fluid Mech., vol. 65, no. 2, p. 247, 1974.
[36] J. Smolka, “Genetic algorithm shape optimisation of a natural air circulation heating oven
based on an experimentally validated 3-D CFD model,” Int. J. Therm. Sci., vol. 71, pp. 128–
139, 2013.
[37] M. S. Gandhi, J. B. Joshi, and P. K. Vijayan, “Study of two phase thermal stratification in
cylindrical vessels: CFD simulations and PIV measurements,” Chem. Eng. Sci., vol. 98, pp.
125–151, 2013.
[38] T. W. Simpson, D. K. J. Lin, and W. Chen, “Title: Sampling Strategies for Computer
Experiments: Design and Analysis.”
[39] G. G. Wang and S. Shan, “Review of Metamodeling Techniques in Support of Engineering
Design Optimization,” J. Mech. Des., vol. 129, no. 4, p. 370, 2007.
[40] nanoComposix, Uv/Vis/Ir Spectroscopy Analysis of Nanoparticles, vol. 1.1. 2012.
[41] A. Klimanek, T. Musioł, and A. Stechman, “Optimization of guide vane positions in bended
inflow of mechanical draft wet-cooling tower,” Arch. Thermodyn., vol. 32, no. 3, pp. 263–272,
2011.
[42] P. Mandloi and G. Verma, “Design Optimization of an in-Cylinder Engine Intake Port,”
Nafems World Congr. 2009, 2009.
[43] M. Dehghani, H. Ajam, and S. Farahat, “Automated diffuser shape optimization based on
CFD simulations and surrogate modeling,” J. Appl. Fluid Mech., vol. 9, no. 5, pp. 2527–2535,
2016.
[44] U.-H. Jung, J.-H. Kim, J.-H. Kim, C.-H. Park, S.-O. Jun, and Y.-S. Choi, “Optimum design of
110
diffuser in a small high-speed centrifugal fan using CFD & DOE,” J. Mech. Sci. Technol.,
vol. 30, no. 3, pp. 1171–1184, 2016.
[45] V. K. Srinivasa, S. Renjith, and B. Shome, “Design of experiments enabled CFD approach for
optimizing cooling fan performance,” SAE 2014 World Congr. Exhib., vol. 1, no. April 2014,
2014.
[46] T. W. Simpson, J. D. Poplinski, P. N. Koch, and J. K. Allen, “Metamodels for Computer-
based Engineering Design: Survey and recommendations,” Eng. Comput., vol. 17, no. 2, pp.
129–150, 2001.
[47] N. V. Queipo, R. T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, and P. Kevin Tucker,
“Surrogate-based analysis and optimization,” Prog. Aerosp. Sci., vol. 41, no. 1, pp. 1–28,
2005.
[48] F. M. Alam, K. R. McNaught, and T. J. Ringrose, “A comparison of experimental designs in
the development of a neural network simulation metamodel,” Simul. Model. Pract. Theory,
vol. 12, no. 7–8 SPEC. ISS., pp. 559–578, 2004.
[49] G. G. Wang and S. Shan, “Review of Metamodeling Techniques in Support of Engineering
Design Optimization,” J. Mech. Des., vol. 129, no. 4, p. 370, 2007.
[50] A. I. J. Forrester and A. J. Keane, “Recent advances in surrogate-based optimization,” Prog.
Aerosp. Sci., vol. 45, no. 1–3, pp. 50–79, 2009.
[51] B. Zhang, B. Song, Z. Mao, W. Tian, B. Li, and B. Li, “A novel parametric modeling method
and optimal design for Savonius wind turbines,” Energies, vol. 10, no. 3, 2017.
[52] M. D. Marais, K. J. Craig, and J. P. Meyer, “Computational Flow Optimization of Heliostat
Aspect Ratio for Wind Direction and Elevation Angle,” Energy Procedia, vol. 69, pp. 148–
157, 2015.
[53] G. Venter, “Review of Optimization Techniques,” Encycl. Aerosp. Eng., pp. 1–12, 2010.
[54] T. Bartz-Beielstein, J. Branke, J. Mehnen, and O. Mersmann, “Evolutionary Algorithms,”
Wiley Interdiscip. Rev. Data Min. Knowl. Discov., vol. 4, no. 3, pp. 178–195, 2014.
111
[55] N. Yusup, A. M. Zain, and S. Z. M. Hashim, “Evolutionary techniques in optimizing
machining parameters: Review and recent applications (2007-2011),” Expert Syst. Appl., vol.
39, no. 10, pp. 9909–9927, 2012.
[56] M. Cavazzuti and M. A. Corticelli, “Optimization of a buoyancy chimney with a heated ribbed
wall,” Heat Mass Transf. und Stoffuebertragung, vol. 44, no. 4, pp. 421–435, 2008.
[57] J. H. Lee, “Optimization of indoor climate conditioning with passive and active methods using
GA and CFD,” Build. Environ., vol. 42, no. 9, pp. 3333–3340, 2007.
[58] M. S. Gandhi, M. J. Sathe, J. B. Joshi, and P. K. Vijayan, “Two phase natural convection:
CFD simulations and PIV measurement,” Chem. Eng. Sci., vol. 66, no. 14, pp. 3152–3171,
2011.
[59] N. Ahmed and K. A. Toufique, “Greening the blue revolution of small-scale freshwater
aquaculture in Mymensingh, Bangladesh,” Aquac. Res., vol. 46, no. 10, pp. 2305–2322, 2015.
[60] A. H. Mahmoud, “A Passive Solar-Thermal Aeration System for Rural Pond Aquaculture by
A thesis submitted in conformity with the requirements Department of Mechanical and
Industrial Engineering Aquaculture,” 2016.
[61] D. J. Baker, “A technique for the precise measurement of small fluid velocities,” J. Fluid
Mech., vol. 26, no. 3, pp. 573–575, 1966.
[62] Y. Chen, “Microfinance program in BRAC — the largest NGO in the world,” 2013.
[63] M. J. Reiney, M. Tryon, and B. G. Achhammer, “Study of degradation of polystyrene, using
ultraviolet spectrophotometry,” J. Res. Natl. Bur. Stand. (1934)., vol. 51, no. 3, p. 155, 1953.
[64] “Multi-Objective Genetic Algorithm (MOGA),” SAS IP, Inc., 2015. [Online]. Available:
https://www.sharcnet.ca/Software/Ansys/15.0.7/en-us/help/wb_dx/dxBEMtemp11.html.
[Accessed: 23-Aug-2017].
[65] “Convergence Criteria in MOGA-Based Multi-Objective Optimization,” SAS IP, Inc., 2015.
[Online]. Available: https://www.sharcnet.ca/Software/Ansys/16.2.3/en-
us/help/wb_dx/dx_theory_MOOConverge.html. [Accessed: 23-Aug-2017].
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