AN ANALYSIS AND SIMULATION OF SOLAR WATER DESALINATION SYSTEMS

by

AHMED GHADHBAN

B.S., University of Basrah, 2005

A thesis submitted to the

Faculty of the Graduate School of the

University of Colorado in partial fulfillment

of the requirements for the degree of

Master of Science

Mechanical Engineering Program

2017

ii

This thesis for the Master of Science degree by

Ahmed Salim Hial Ghadhban

has been approved for the

Mechanical Engineering Program

by

Peter Jenkins, Chair

Kannan Permnath

Maryam Derbeheshti

Date: May 13, 2017

iii

Ghadhban, Ahmed (M.S., Mechanical Engineering Program)

An Analysis and Simulation of Solar Water Desalination Systems

Thesis directed by Professor Peter Jenkins

ABSTRACT

This dissertation presents theoretical analysis and simulations used to improve the

performance of desalination systems and compares several solar desalination processes. This

research demonstrates how to use modular approaches for the dynamic simulation and steady

state analysis of desalination by using MATLAB r2016a Simulink. Data from NIST

(National Institute of Standard and Technology) and from SAM Advisor (System Advisor

Model) were used in this study. Three types of distilled water (pipe water, heavy water, and

seawater) were used to compare the distilled fresh water produced from each solar

desalination system. The potable water production rate from heating the feed water was

calculated using empirical and theoretical modeling. Results of the modeling and

experimental results were compared for both processes. The simulations, modeling, and

optimization of desalination processes using computer design technology are discussed. The

results from this research could be used to predict the operating conditions of desalination

systems.

The form and content of this abstract are approved. I recommend its publication.

Approved: Peter Jenkins

iv

ACKNOWLEDGMENTS

I would like to thank my advisor, Professor Jenkins, for giving me the chance to work

on this project. I am thankful for his help and patience. I also would like to thank my

committee members: Dr. Premnath and Dr. Darbeheshti. Each one of them has provided me

with opportunities to advance my study and provided encouragement along the way. Also, I

appreciate the people who have supported me, especially my family, my parents, my wife

and my friends. Moreover, I would like to thank the Department of Mechanical Engineering

for allowing me to utilize the library and labs to complete my research. I greatly appreciate

the Mechanical Department workshop for the construction of the PV Solar desalination

system. Finally, I am grateful to everyone who has encouraged me to pursue my project.

v

TABLE OF CONTENTS

CHAPTER

I INTRODUCTION ........................................................................................ 1

1.1 Background ........................................................................................... 1

1.2 Water Crises .......................................................................................... 1

1.3 Research Motivation ............................................................................. 2

1.4 Research Objectives .............................................................................. 2

1.4.1 Neural Networks for Modeling ........................................................ 3

1.4.2 Steady State and Dynamic Simulations ........................................... 3

1.4.3 Comparing Results .......................................................................... 3

1.5 Research Methods ................................................................................. 4

II PROPERTIES OF WATER ......................................................................... 5

2.1 Produced Water ..................................................................................... 5

2.2 Feed Water ............................................................................................ 6

2.2.1 Brackish Water ................................................................................ 6

2.2.2 Seawater........................................................................................... 7

III DESALINATION ..................................................................................... 10

3.1 Desalination Use. ................................................................................ 10

3.2 Desalination Background .................................................................... 12

3.3 Desalination Process Classifications ................................................... 13

vi

3.3.1 Membrane Process ......................................................................... 13

3.3.2 Thermal Process ............................................................................ 14

IV SOLAR ENERGY .................................................................................... 20

4.1 Introduction of Solar Energy ............................................................... 20

4.2 Sun-Earth relationships ....................................................................... 20

4.3 Solar Radiation Definition .................................................................. 21

4.4 Solar Energy applications.................................................................... 22

4.4.1 Sun’s energy capture ways ............................................................ 24

V PROJECT DESCRIBTION AND ANALYSIS ......................................... 27

5.1 PV Solar Powered Desalination ............................................................. 27

5.1.1 System Outline ................................................................................ 28

5.1.2 Develop PV Solar Array and Batteries ............................................ 31

5.1.3 Size Heating Source ......................................................................... 38

5.1.4 Provide Heat to the Water ............................................................... 41

5.1.5 Condensing the Vapor. .................................................................... 50

5.2 Solar Still ................................................................................................ 53

5.2.1 Solar Still Elements ......................................................................... 53

5.2.2 Energy Balance ................................................................................ 54

5.2.2.1 External Heat Transfer ....................................................... 55

5.2.2.2 Internal Heat Transfer ........................................................ 59

vii

VI RESULT ................................................................................................... 63

6.1 PV Solar Powered Desalination Results .............................................. 63

6.2 Solar Still Results ................................................................................... 78

6.3 Comparing the results............................................................................. 81

VII DISCUSSION AND CONCLUSION ..................................................... 84

7.1 Discussion .............................................................................................. 84

7.2 Conclusion .............................................................................................. 85

7.3 Future Direction ..................................................................................... 85

REFERENCES ……………………….........…………………………………………86

viii

LIST OF TABLES

TABLE

1. Drinkable water standard of water ............................................................................ 5

2. Water saline category ................................................................................................ 7

3. Major ion concentration in seawater. ........................................................................ 9

4. PV solar electrical characteristics .......................................................................... .36

5. Thermophysical properties of air ............................................................................ 41

6. Feed water types yield ............................................................................................ 76

ix

LIST OF FIGURES

FIGURE

2.1. Ions concentration in seawater ...................................................................................... 8

3.1. Chart shows a fraction of the worldwide capacity of the desalination plants by regions.

.................................................................................................................................... 11

3.2. Installed desalination plants’ capacity in the USA and worldwide from 1950 to 200612

3.3. Thermal desalination process diagram........................................................................ 14

3.4. Schematic diagram of multi-stage flash ...................................................................... 15

3.5. Schematic diagram of multiple-effect distillation. ...................................................... 16

3.6. Schematic diagram of vapor compression distillation ................................................ 17

3.7. Global distribution of installed water desalination capacity by the technolog.. ......... 18

4.1. Sun-Earth relationships ............................................................................................... 21

4.2. Variation of the solar radiation with the year ............................................................. 22

4.3. Available solar energy in the United States ................................................................ 24

4.4. Photovoltaic cell panel. ............................................................................................... 26

5.1. PV solar desalination system. ..................................................................................... 27

5.2. PV solar powered desalination schematic................................................................... 30

5.3. PV Module and batteries modeling in MATLAB/ Simulink ...................................... 31

5.4. Ideal PV circuit ........................................................................................................... 32

5.5. Equivalent circuit for PV module ............................................................................... 33

5.6. Typical P_V and I_V curve for PV module................................................................ 36

5.7. Heating source sizing in MATLAB/Simulink ............................................................ 39

5.8. Schematic of water evaporative in MATLAB/Simulink ............................................ 45

x

5.9. Two-Phase fluid properties block. …….…...………………………………………45

5.10. Water properties data (picture is taken from MATLAB). ........................................ 46

5.11. Rigid pipe block ……….……………..……………………………………………46

5.12. Heat balance for condensate ..................................................................................... 51

5.13. Schematic of water condensate in MATLAB/Simulink. .......................................... 52

5.14. Solar still basin .......................................................................................................... 54

5.15. Overall energy balance ............................................................................................. 55

5.16. Schematic of solar still desalination ......................................................................... 62

6.1. P-V curve characteristic .............................................................................................. 63

6.2. I-V curve characteristic. .............................................................................................. 64

6.3. PV Array characteristics for P–V and I-V curves ....................................................... 65

6.4. Photovoltaic panel characteristics for different irradiance values (1000, 500, and 100)66

6.5. Actual power output in June in Denver for one PV panel. ......................................... 67

6.6. Actual power output in June in Denver for three PV Panels ...................................... 67

6.7. Water distilled flow rate for piped water. ................................................................... 68

6.8. Vapor-Water distilled temperature for piped water. ................................................... 69

6.9. Piped Water vapor fraction. ........................................................................................ 70

6.10. Piped Water distilled production in one hour. .......................................................... 70

6.11. Piped Water distilled curve. ...................................................................................... 71

6.12. Heavy Water distilled flow rate. ............................................................................... 71

6.13. Vapor and water distilled temperature for heavy water. ........................................... 72

6.14. Heavy Water production in one hour. ....................................................................... 72

6.15. Heavy Water distilled curve. ..................................................................................... 73

xi

6.16. Heavy Water vapor fraction. ..................................................................................... 73

6.17. Seawater distilled flow rate. ...................................................................................... 74

6.18. Seawater distilled production in one hour. ............................................................... 75

6.19. Comparing modeling results of water distilled from three water types. ................... 76

6.20. Distilled Seawater production done experimentally in one hour. ............................. 77

6.21. Comparing freshwater productivity for Seawater from experiment and modeling of PV

solar method. .............................................................................................................. 78

6.22. Solar Still modeling yield. ........................................................................................ 79

6.23. Water temperature and glass temperature. ................................................................ 80

6.24. Reference experimental Solar Still distilled water .................................................... 81

6.25. Comparing the freshwater results from the PV Solar modeling approach with the

freshwater from Solar Stills modeling for Seawater. ................................................. 82

6.26. Comparing the freshwater results from the PV Solar experimental approach with the

freshwater from Solar Stills experimental for Seawater. ........................................... 83

1

CHAPTER I

INTRODUCTION

1.1 Background

The growing world population is rapidly increasing the demand for fresh water. Only

about 2.5% of water that exists on earth is fresh water [27], and this water is not distributed

equally. Groundwater constitutes 30% of the fresh water resources [4], but in arid and semi-

arid areas, underground water is difficult to obtain and expensive to ship. Therefore, it’s

necessary to develop alternatives to produce potable water from salt water. Fresh water is

required for industrial, agricultural, and domestic uses. Clean water shortages are a major

factor in economic development. The oceans provide 96.5% of earth’s water [27], but the salt

concentration renders this water not suitable for human use. Salt concentration in oceans

ranges from 33-37 ppt [7]. Seawater desalination is considered the best option to meet the

demands of fresh water globally. Desalination has already been successfully implemented in

several countries: Europe, southern and western parts of the US, and North Africa.

1.2 Water Crises

Many countries lack natural sources of drinkable water, and consequently, 1 billion

humans cannot access clean water [35]. The potable water shortage has the world’s attention

because water is necessary for the economic development and health to maintain the

ecosystems [12]. Continued efforts are made to develop methods to get fresh water from

different sources to provide water to people, farmers, and factories. However, fresh water

sources are limited, and retaining a balance in social and economic development results in an

imbalance between water supply and demand, putting pressure on many countries’ water

resources. The situation is further complicated because of the increasing rate of water

2

consumption, due to population growth and the social and economic development. Therefore,

it’s crucial to increase the global availability of water sources.

In response to this water crisis, the desalination of seawater has become a main

resource of water for the long-term, and has already been implemented in several countries.

Among desalination processes, solar desalination is much more practical than other

processes, especially in arid areas where many water resources are available but suffer from a

lack of a power supply. In spite of its high cost, solar desalination has an advantage that

satisfies a variety of demands, and it is a clean source of energy.

Because of the potential to produce fresh water and support life on earth, developing

desalination processes is very important. Solar desalination, in particular, requires immediate

and significant efforts to design improvements and controls for establishing the costs

associated with producing this technology.

1.3 Research Motivation

The importance of desalinated water will only increase as the natural water sources

are depleted. In order to solve the fresh water problem, new water resources should be

discovered, and new techniques developed.

Desalination is considered a satisfactory technique for purifying conventional water

sources. In several countries, fossil fuel has been used to provide power to water desalination

systems. For small systems, low-cost, solar-powered water desalination may be preferred.

1.4 Research Objectives

The following topics will be analyzed in this research project:

a. Neural networks for the predictive modeling of water desalination.

b. Dynamic and steady-state simulations of a flash desalination system.

3

c. Comparison of the results between different types of solar desalination processes.

1.4.1 Neural Networks for Modeling

Applying artificial intelligence to the design and operation of desalination systems

will lead to better designs and enhanced operation of these systems. This process is a good

choice for neutral networks because of the complexity of the process.

The behavior is nonlinear with some degrees of freedom, and this nonlinearity is due

to the physical properties of streams depending on the pressure, temperature, and salinity.

The amount of mass flow and heat transfer also contribute to the nonlinear behavior

of the models in the thermal process. The neural network provides a suitable prediction

model for the desalination modeling.

1.4.2 Steady State and Dynamic Simulations

The goals of simulation and modeling for the industrial processes are improved and

optimized in this project. Steady state models are developed that involve algebraic equations.

The dynamic models are primarily applicable to estimate the performance and

optimization of the system. The dynamic models involve differential and algebraic equations,

which describe the process’s time-dependent behavior. Dynamic models are appropriate for

the transient behavior simulations, though they could also be used to analyze the system

behavior under dynamic conditions. The motivation of system for this system simulation was

to determine any enhancements to the system for increasing the production of distilled water.

1.4.3 Comparing Results

In this research, the water produced from the solar-powered desalination system was

determined by two methods: PV solar-powered system and a solar still.

The methods used were:

4

1. Compare the fresh water results from PV Solar modeling simulation to the

results from modeling the solar still.

2. Compare the fresh water results from PV solar experimental approach to the

results from the experimental solar still.

1.5 Research Methods

This research will use two different methods for the production of the distilled water.

The first method was the photovoltaic solar powered desalination system. Computer software

program was used to estimate the production for three types of water systems based on the

NIST (National Institute and Standards Technology) fluid properties. MATLAB Simulink

was used to simulate the desalination processes, and the SAM software was used to obtain

the radiation properties.

The second method was the solar still, which was simulated by using MATLAB

r2016a.

5

CHAPTER II

PROPERTIES OF WATER

2.1 Produced Water

Chemical substances may be found in drinking water supplied from pipe water, but

they are not dangerous to humans.

The following table presents a list of chemical substances in drinkable water, and the

approximate safe levels (the levels more than the level‘s value in the table may cause a

serious trouble) [9].

Table 1 Drinkable water standard of water

Substance Nature of Trouble Level (mg/l)

Chloride Taste and corrosion in hot

water systems

200-600

Nitrate Methaemoglobinaemia for

infants

50-100

Copper Taste, discoloration and

corrosion of pipes, and

utensils

0.05-3

Iron Taste and growth of iron

bacteria

0.1

Manganese Taste, discoloration, and

turbidity.

0.05

Phenolic compounds Taste, particularly in

chlorinated water

Less than 0.001

Zinc Astringent taste, and sand

like deposits

5

Magnesium Hardness taste 30-150 (or up to 250 if

sulfate exists)

Sulfate Irritation when combined

with magnesium or sodium

250

Hydrogen Sulfide Taste 0.05

6

2.2 Feed Water

Feed water compositions are important for several reasons:

a. They are necessary for the production of physical properties data used for design.

b. To operation the system without scale formation, the compositions of scale

constituting ions are important. Seawater may have three times the salinity of

brackish water, yet the some ions concentration in brackish water may be higher than

seawater and produce more scale.

c. In general, desalination processes, such as reverse osmosis and electrodialysis, are

dependent on salinity, and as a result, the membrane process is used with brackish

water more than with seawater.

2.2.1 Brackish Water

Brackish water is water that has a higher saline concentration than fresh water but less

than seawater.

Brackish water may form from the mixing of fresh water and seawater in bodies such

as estuaries [34].

Generally, the make up of brackish water lies between fresh water and seawater.

Brackish water could be used safely and used for an environmental advantage for crop

irrigation in arid areas.

Technically, the salt concentration of slightly brackish water to brackish is between

500-2000 ppm, and it is only cautiously used for irrigation.

There are some classifications of salty water based on the salt concentration in water.

Table 2 shows some of the salt water classifications based on salt concentrations [17].

7

Table 2 Water saline category

Designation Total dissolved salts

(ppm)

Category

Fresh water <500 Using for drinking and

irrigation.

Slightly brackish 500-1000 Irrigation.

Brackish 1000-2000 Using for irrigation with

caution.

Moderately saline 2000-5000 Primary drainage

Saline 5000-10000 Secondary drainage and

saline groundwater.

Highly saline 1000-35000 Very saline groundwater

source

Brine >35000 Seawater

2.2.2 Seawater

Precipitation contains CO2 dissolved from air, whose carbonic acid causes the

rainfall to be slightly acidic because of the carbonic acid that was formed from CO2. As

rainwater erodes rocks, acids in the rainfall breaks down the rocks. This process generates

ions that flow into rivers, streams and oceans. The most dominant ions in seawater are

chlorine and sodium. Together, they form a less than 90% of the dissolved ions in oceans

[21]. The salinity (concentration of salt in seawater) is about 35 ppt (part per thousand) [8],

[13].

In most marine areas, salinity is measured as a total of all the salts dissolved in the

water. 35 ppt is not a highly concentrated ratio, but the water in the oceans or seas, which

have 35 ppt, is very salty. The interesting characteristic of salt concentrated in water is that

the dissolved salts are made up of the same type of minerals and salts, and they always

appear in the same concentration ratio to each other (even if the salt concentration is different

8

from the average concentration)[8]. The majority of salt in seawater is sodium and chlorine,

but other salts exist as well.

Figure 2.1 Ions concentration in seawater

Figure 2.1 shows the major ions in seawater[8]. The major ions are those components

whose seawater concentration is more than 1 ppm (part per million). The reason for using

this definition of major ions is that salinity is reported to 1 ppm [33]. Therefore, the major

9

ions are the ones which contribute to the salinity. According to the definition, there are

eleven major ions in seawater.

Table 3 indicates those ions and their concentrations (from Pilson, 1998)

Table 3 Major ion concentration in seawater.

Ion Concentration (g/kg)

Na 10.781

K 0.399

Mg 1.284

Ca 0.4119

Sr 0.00794

Cl 19.353

SO4 2.712

HCO3 0.126

Br 0.0673

B(OH)3 0.0257

F 0.0013

Totals 35.169

10

CHAPTER III

DESALINATION

3.1 Desalination Use.

Desalination specifically refers to the removal of minerals and contaminated

substances from salt water.

Water sources can include seawater, brackish, rivers and streams, process water and

industrial feed, and wastewater. Because of the saline, this water is not appropriate for human

usage, and it should be desalinated to use safely. Desalination is already being used

internationally for the following reasons:

1. Fresh water scarcity and natural sources cannot fulfill the growing request for low

salinity water.

2. The industrial requirement for pure water, such as for petroleum processing and

power plants.

3. There is a deterioration of the quality of potable water resources. The rapid decrease

of underground aquifers and increase of the salinity concentration in those non-

renewable resources exacerbates the global water deficiency problem.

4. As technologies develop, water desalination becomes easier, and there are many types

of desalination processes.

The desalination process has improved rapidly, and it is used by several regions. It is

already a satisfactory solution to water scarcity in the world, and it is now approved as a

trustworthy resource for fresh water.

According to IDA (International Desalination Association), the number of

desalination plants operated in the world in 2015 was 18,426. These plants provided more

11

than 22.9 billion US gallons daily, and supplied fresh water for about 300 million people in

150 countries [1].

At present, about 1% of people in the world are depending on desalinated water to for

daily requirements, but according to United Nations, 14% of the people in the world will be

suffering from water scarcity by 2025 [2].

Figure (3-1), shows desalination distributions in the world basing to the regions [19].

Figure 3.1 Chart shows a fraction of the worldwide capacity of the desalination plants by

regions.

12

3.2 Desalination Background

Desalination is a natural phenomenon that has already been occurring on the earth for

billions of years. The natural water cycle (water evaporating from the sea and then

condensing to form pure rainfall) is the clearest example of the water desalination process.

Creek sailors heated water to evaporate fresh water from the saline water. In 1804, the first

public water plant built in Scotland by Robert Thom was based on slow sand filtration [5].

Since 1960, the worldwide capacity for desalinated water has grown exponentially [3].

The following figure shows the worldwide desalinated water capacity since 1960.

Figure 3.2 Installed desalination plants’ capacity in the USA and worldwide from

1950 to 2006 [3].

13

3.3 Desalination Process Classifications

Desalination is an energy intensive system and involves expensive infrastructures.

Thus, several desalination methods have been industrialized over the years to yield potable

water from saline water economically. Desalination processes can be classified, based on the

separating system that is applied, into physical, thermal, and chemical processes. There are

two major types of desalination methods: membrane and thermal.

3.3.1 Membrane Process

The membrane separation process includes the passage of water into a semipermeable

film under a pressure. Pressurization reverses the natural transport of water that occurs from

a dilute side to a more concentrated side to balance the fluid’s energy. The membrane process

needs driving forces such as electrical potential, vapor, and pressure to overcome the natural

osmotic pressures and effectively force water through membrane processes.

The membrane process is subdivided into two types [26]:

a. Reverse Osmosis (RO)

b. Electrodialysis (ED)

Reverse Osmosis is a pressure-driven process. The operating pressure range of RO is

from 3.4-68 bar [10]. RO was commercially presented in the 1970s, and currently, RO is the

largest desalination process method used in the USA. RO is used for desalinating feed water

with a salt concentration more than 15,000 ppm [26].

Electrodialysis is a direct current-driven process. Electrical power is used to transfer

the salts’ ions throughout a membrane, and then separate them to create potable water as a

product. ED was commercialized in the 1960s [26]. ED was initially considered a seawater

desalination method, but it has largely been used for desalinating salty or brackish water.

14

Because of the essential features of the electrical methods used in Electrodialysis systems,

ED is typically used to treat brackish water rather than seawater.

3.3.2 Thermal Process

The thermal process technology, as the term indicates, involves heating saline water

to its boiling temperature to produce vapor, and then condensing the vapor to obtain fresh

water. The thermal process is one of the oldest and most common techniques used. Thermal

technologies are used with seawater, but have seldom been used with brackish water due to

high costs.

In the thermal process, thermal energy could be obtained from conventional

hydrocarbon sources or nonconventional solar energy sources. Therefore, the thermal process

involves a source of energy to give the system enough power for operation. The source could

be a fossil fuel source, or a renewable energy source such as solar power.

Figure 3.3 Thermal desalination process diagram

15

I. Conventional Hydrocarbon Sources

The thermal process uses fossil fuels to heat saline water and form a vapor. There are

many types of desalination processes which use the conventional energy, such as [26]:

a. Multi-Stage Flash Distillation (MSF).

b. Multiple-Effect Distillation (MED).

c. Vapor Compression Distillation (VCD).

Multi-Stage Flash Distillation

MSF is one of the thermal desalination types which has been in use since about the

1950s. MSF facilities involve a number of chambers connected together. MSF is the process

which has a stream that flows through a bottom of stages (chambers), with each successive

stage operating at a sequentially lower pressure [26]. A proportion of the stream of brine

flashes into vapor and will be condensed and collected as fresh water. In MSF distillation,

feed water is heated in sequenced stages. A MSF plant could contain from 4 to 40 stages

[24], [36].

Figure 3.4 Schematic Diagram of Multi-Stage Flash [36]. Figure 3.4 Schematic diagram of multi-stage flash [36].

16

Multiple-Effect Distillation

The MED is a thermal process method which has been used over 100 years, making it

the oldest desalination technique which is still used. The MED desalination technique occurs

in series of effects (vessels) and it reduces the pressure in successive steps. In a typical plant,

there are from 8 to 16 steps [24]. The Multiple-Effect distillation is similar to Multi-Stage

Flash distillation, which uses an evaporative technique that occurs in a series of effects or

chambers. However, the MED differs from the MSF in which the steam formed in one step

condenses in the next one. Also, in a multi-effect distillation, feed water could be sprayed

onto a tube bundle or flow onto vertical surfaces to promote a fast boiling and evaporation.

Vapor, which is generated in the first step, heats up the second step for evaporation and is

condensed in the tubes. These evaporation and condensation processes occur continuously

for several steps.

Figure 3.5 Schematic diagram of multiple-effect distillation.

17

Vapor Compression Distillation

The VCD has been used for medium and small scale units, and it is based on the

principles of decreasing the boiling point temperature by reducing the pressure. The heat

used to evaporate the feed water comes from compressing the vapor. Steam jets and

mechanical compression systems are commonly used to condense steam to produce enough

energy to evaporate the incoming feed water.

Vapor compression distillation has a comparatively high thermal performance and

could be applied in the desalination of highly concentrated salt water. VCD is typically used

in medium and small capacity applications. The following diagram provides a simple

illustration of the vapor compression desalination system. The VCD is used in combination

with another thermal distillation process [24], [11], [36].

Figure 3.6 Schematic diagram of vapor compression distillation [36].

18

The following figure shows the global desalination capacity distribution according to

the technology that is used.

II. Nonconventional Solar Sources.

Solar desalination or solar distillation is one of the available methods that is currently

satisfying global water needs in several regions. Solar desalination is a suitable solution for

small communities where sources of electricity are not available, and there is a plenty of

solar radiation. Furthermore, solar energy is considered a clean source of power, and it is an

environmentally friendly and a highly promising technology. Solar desalination has the

advantage of cost savings due to the fact that solar energy is a limitless power source and is

easily accessible.

Figure 3.7 Global Distribution of Installed Water Desalination Capacity by

Technology [37].

Figure 3.7 Global distribution of installed water desalination capacity by

technology [37].

19

Solar energy is an appropriate energy source for water desalination and is currently a

popular area of research. Therefore, it’s important for solar-powered water desalination to be

considered in the techniques for salt water desalination. Solar energy is one of a number

forms of thermal energy that could be used for providing power for desalination processes.

The Performance of solar desalination systems depends upon the design and climate

conditions. Several efforts have been made to improve and develop the performance of solar

distillation. Solar energy can be used for desalinating water in an indirect way, where the

power from a solar energy device system is supplied to a distilled unit, or in a direct way

through solar stills.

There are two processes for the solar powered desalination techniques:

a. Using photovoltaic cells to get the enough energy to heat the feed water.

b. Solar stills

Using photovoltaic cells (PV)

The PV system is a simple approach involving the use of PV solar cells to generate

enough electricity to supply power to a heating source to heat the feed water. The PV solar

desalination technique uses solar energy as an indirect energy source. Photovoltaic cells can

convert solar energy to electricity to heat feed water which can then be combined with

storage batteries.

Solar Stills

The solar still is one of the solar desalination methods that is used for distilled water

from salt water. Solar stills use direct sun radiation to evaporate feed water, and can be used

with a large or small system. A solar still may be designed to meet the water needs of a single

family, and it is relatively inexpensive systems, especially when used for small groups.

20

CHAPTER IV

SOLAR ENERGY

4.1 Introduction of Solar Energy

Solar radiation is a term for electromagnetic radiation, which is received from the

sun. Solar radiation can be converted to useful energy such as electricity or heat.

The Total Solar Irradiance (TSI) depends only on the distance between the sun and

the earth and the total sun energy per second (time) [29].

Not all of the sun’s radiation are absorbed by the earth: 29% of the energy is

reflected, and the other 71% is absorbed by the oceans, land, buildings, and atmosphere [42].

4.2 Sun-Earth relationships

The sun is a sphere of hot gasses, and its temperature is 5777° K. The mean distance

between the earth and the sun is 1.495 * 1011 m [29].

The radiation emitted from the sun to the earth is a nearly constant amount, and it is

called the solar constant (G) [29].

The solar constant is the energy which is emitted from the sun per a time unit that is

receive on the unit area of a surface perpendicular to a direction of the spread of the radiation

at the mean earth-sun distance. The absorbed radiation contains visible light and infrared

radiation.

According to the World Radiation Center (WRC), the value of the Solar Constant (G)

is 1367 w/m2 [29].

The following figure shows the solar constant, and the average distance between the

sun and the earth. As well as, the figure 4.1 shows the angle of solar radiation on the earth.

21

Figure 4.1 Sun-Earth relationships [29].

4.3 Solar Radiation Definition

For engineering purposes, it is important to understand the differences between types

of solar radiation such as beam radiation, diffuse radiation, total solar radiation, and

irradiance [29].

Beam radiation is received directly from the sun without have been changed by

scattering over the earth’s atmosphere, and it is also referred to as direct radiation. To avoid

confusion between the direct solar radiation and diffuse radiation, the term of beam radiation

is used [29].

Diffuse radiation is the radiation that is received from the sun after it is scattered by

the earth’s atmosphere. In some meteorological literature, diffuse radiation refers to sky

radiation [29].

22

Total solar radiation is a sum of the solar diffuse radiation and the solar beam

radiation on a horizontal surface. Total solar radiation is also known as global radiation [29].

Irradiance is the rate at which the radiant energy is incident on a unit area of a surface

The Solar radiation which is received from the sun to the earth is a variety with a time of the

year. The following figure appears the variation of the extraterrestrial solar radiation with

time.

For engineering purposes, the energy that is received from the sun could be

considered constant [29].

4.4 Solar Energy Applications

Solar energy or solar power is a form of energy harnessed from the heat and power of

the sun. Solar energy is renewable, and thus a “green” (eco-friendly) energy source, just like

wind power. These green energies are virtually inexhaustible, unlike expendable fossil fuels.

Figure 4.2 Variation of the solar radiation with the year [29].

23

However, solar power is reliant upon the weather and the sunshine present in a

location. Areas which lack sunlight or experience cloudy weather may have difficulties using

solar power effectively.

Fortunately, most areas that suffer from water scarcity are located in regions that

have an abundance of sunshine. Every hour, the sun emits enough power to deliver enough

energy for a whole year across the globe [45]. Solar energy is used to create large amounts of

power on a utility scale and to provide individual businesses and residences with electricity.

Because sunlight is available almost everywhere, and it does not require fuel or

connection to a power grid, solar energy is useful for providing power to remote regions and

for various portable devices.

A common way of harnessing power from the sun’s rays is through photovoltaic (PV)

panels. The PV panels operate as conductors that take the sun’s lights, heat up, and generate

energy (and electricity). Since technologies are developing and the ingredients of the

materials used in the photovoltaic panels are becoming greener, the PV technique is

becoming more accessible.

Most solar panels that are used today have an average life expectancy of 20-40 years

[45]. However, solar power generation is not a new technology; it has been used for more

than 50 years.

Most of solar energy use is on a small scale, and most of the large-scale generation

was developed in the 1970s and 1980s [32].

There are many applications for using the solar energy:

1. Heating residential buildings.

2. Electric power generation

24

3. Water heating uses.

Some areas in the United States are more apt for solar power than others. In 2009,

California had the most solar power capacity, followed by New Jersey.

Almost all states in the USA receive sunlight per square mile more than German

[32].

4.4.1 Sun’s energy capture ways

Solar rays are distinguished according to their wavelengths. Infrared rays constitute

around 50% of light, while the visible light accounts for 40%. The remaining rays are

ultraviolet, which make up about 10%. Because most of the infrared rays are short waves,

they are not considered warm radiation rays. The wavelength of infrared rays is less than

3000 nanometers [38].

Figure 4.3 Available solar energy in the United States [32].

25

Using sunlight in buildings has the potential to significantly decrease energy

consumption. This area of development is called day-lighting, and it is one of the methods

used to decrease energy consumption in buildings.

Solar energy is easily converted into heat through absorption by liquid, gaseous or

solid materials. Heat can then be used in sanitary water heating, water evaporation, and other

purposes. Heat can also easily be converted into electricity, and it could run or facilitate

physical or chemical transformations.

Solar radiation could also be observed as a flux of photons or electromagnetic

particles. Photons that come from the sun are highly energetic, and they could promote

photoreactions such as generating electrons’ conduction in semiconductors or enabling the

transformation of sunlight into electricity. Note that the two fundamental approaches to

capture the sun’s energy – photoreaction and heat – could also be combined in a number of

methods to provide combined energy vectors, e.g. electricity and heat. Therefore, from the

two basic methods (heat and photoreaction), we can distinguish some main domains of

applications such as photovoltaic electricity and thermal power.

Solar cells are made from semiconductor materials. When the sunlight is incident on

the PV arrays, it knocks electrons in the PV cells’ material atoms. As the electrons flow

throughout the cells, electricity is generated [32].

Modern PV solar cells were developed in the 40s and 50s from the last century, and

the technology has improved over the past years. The space programs of some countries such

as the United States use photovoltaic solar cells as an energy source to generate power for

spacecraft and satellites [32]. PV panels have also been used for supplying electricity to

remote areas that lack local electricity, such as arid areas.

26

Solar cells are organized onto the solar panel. This solar panel is coated to protect the

solar cells (usually coated on glass). Several panels are organized into an array that can be

scaled to give enough energy. A single cell can produce electricity to power an emergency

telephone, though larger arrays are needed to power buildings

Figure 4.4 Photovoltaic cell panel.

27

CHAPTER V

PROJECT DESCRIBTION AND ANALYSIS

5.1 PV Solar Powered Desalination

PV Solar Desalination is a simple method which uses a Photovoltaic cell (PV) to

generate electricity. The PVs supply enough power for the heating source (heater) to deliver

a required thermal energy to boil the feed water to generate vapor and then this vapor is

condensed to produce fresh water. The sun radiation is collected by the PV solar cells for

producing the electricity which is stored in batteries.

The purpose of using the batteries with this system is to store extra power for use at

night or in cloudy days.

Figure 5.1 PV solar desalination system.

28

5.1.1 System Outline

Compared with other desalination systems, the PV Solar desalination has several

differences. Because prototyping testing is costly and time consuming, it is difficult to

predict the performance of the system.

Therefore, modeling and simulation are important for concept evaluation,

prototyping, and analysis of PV solar desalination systems. Furthermore, the modeling

process could model not only the thermally simulated modules, but also the embedded

software which was used to control all the required components.

MATLAB/Simulink is a general-purpose modeling and simulation package used in

science and engineering design and research for the modeling of engineering systems.

MATLAB, Simulink, and Simscape were used for modeling the desalination system.

Simscape enables the designer to build models of physical systems in the Simulink

environment rapidly. Simscape could also be used to build component models based on a

physical connection which directly integrates with other modeling diagrams. Simscape

provides a complex component and analysis capability. It also helps to test the system and

develop the system’s control. The models can be parameterized using MATLAB r2016a

expressions and variables [6].

The inputs for running this project after completing the design depend on weather

conditions and the amount of feed water. The weather conditions include the sun’s radiation

and the temperature of the day.

To design and test the solar desalination, the PV panel, heat system, and condensate

system were modeled in MATLAB r2016a and the Simulink environment. The model was

29

developed using physical principles and empirical data. Emphasis was given on maintain

simple component models.

The model was developed to determine the distilled water production from feed water

by using Matlabr2016a Simulink/Simscape simulation.

To facilitate the modeling process, the project was divided into four steps to simulate

the process.

Develop PV Solar Array and Batteries.

Size Heating Source (Heater).

Provide Heat to the Water.

Vapor Condensing.

The following schematic represents the outline of the system that was designed using

MATLAB r2016 Simulink/Simscape.

The design depends on the physical properties of water according to the National

Institute of Standard and Technology (NIST) software, which is related to MATLAB r2016a

environment software.

Each of the four outline’s steps were connected with each other by Simulink blocks

obtained from the Simscape library, which was especially useful for simulating thermal

fluids. Some data of the components that exist in the MATLAB library were used.

The process (modeling) was arranged with successive steps from the modeling of the

photovoltaic system to the production of water.

Simulink models were assembled as connected blocks which were structured

hierarchically.

30

Fig

ure

5.2

PV

sola

r po

wer

ed d

esal

inat

ion s

chem

atic

31

5.1.2 Develop PV Solar Array and Batteries

The PV Solar panel was the main component in the solar power system which

generated electricity that was stored in batteries. The panels were integrated with charged

batteries to give the system stability and continuity. As a result, the production of water was

more consistent.

Figure 5.3 PV module and batteries modeling in MATLAB/ Simulink

32

The first step was to determine the Photovoltaic solar module data.

1. For an ideal PV Circuit, the following parameters are used in the model:

𝐈 = 𝐈𝐩𝐯 – 𝐈𝐃 [16], [18] (1)

𝐈𝐃 = 𝐈𝐨 ∗ [𝐞𝐱𝐩 (𝐕

𝛂.𝐕𝐓) − 𝟏] [16] (2)

𝐕𝐓 =𝐍𝐬 𝐊 𝐓

𝐪 [16] (3)

I is the PV output current.

VTis the thermal voltage

K is the Boltzmann’s constant, and it is equal to 1.398 *10-23 J/K.

𝑞 = 1.602 *10-19 coulomb.

Ns is the PV cells’ number.

T is the PV cells’ temperature.

Figure 5.4 Ideal PV circuit

33

𝑎 is modified ideality factor.

Ipv is the current generated by the incidence of light.

Io is the diode reverse bias saturation current.

At a short circuit;

I = ISC, and I = Ipv

V = 0

At an open circuit;

I=0

𝐕 = 𝐕𝐎𝐂 = 𝛂 𝐕𝐓 ∗ 𝐥𝐧 ( 𝟏 +𝐈𝐒𝐂

𝐈𝐎) [16] (4)

2. For an equivalent circuit with series and parallel resistances:

The power output from the electrical circuit is expresses by the relation;

𝐏 = 𝐈 𝐕 [29]

𝐈 = 𝐈𝐋 − 𝐈𝐃 − 𝐈𝐬𝐡 [29] (5)

Figure 5.5 Equivalent circuit for PV module

34

𝐈𝐬𝐡 =𝐕+𝐈∗𝐑𝐬

𝐑𝐬𝐡 [29] (6)

IL is the current generated by the incidence of light.

ISh is the shunt current.

Rs is the series resistance.

Rsh is the shunt resistance.

ID is expressed in the same way of the equation (2)

Thus, the circuit needs five parameters to operate (IL, ID, Rs, Rsh, and a)

Modified ideality factor a is related to the known physical parameters (k, T, Ns, and

q) and the unknown parameter n by the equation [29];

𝐚 =

𝐧𝐤𝐓𝐍𝐬

𝐪 [29] (7)

n is the ideality factor.

For an ideal diode, n=1.

For real diode, n is between 1 and 2.

The five parameters (IL, ID, Rs, Rsh, and α) were obtained by using the measured

characteristics of the voltage and current of the module at the reference conditions that are

supplied by a manufacturer.

The power-voltage measurements were made at a cell temperature 25o C, incident

radiation 1000 W/m2, and spectral air mass equal to 1.5 [29].

The current-voltage measurements at the reference conditions were available from the

manufacturer at maximum power, short circuit conditions, and open-circuit conditions. The

manufacturer also supplied the temperature coefficient (µ𝐼, 𝑠𝑐 ) of short-circuit current, and

the temperature coefficient (µ𝑉, 𝑜𝑐) of open circuit voltage [29]

35

𝐈𝐋 =𝐒

𝐒𝐫𝐞𝐟∗ (𝐈𝐋,𝐫𝐞𝐟 + µ𝐈, 𝐬𝐜 ∗ (𝐓𝐜– 𝐓(𝐜,𝐫𝐞𝐟))) [29] (8)

Tc is the PV cell temperature.

Tc,ref is the PV cell reference temperature.

S

Sref is the effective absorbed solar ratio.

S = Sref [29].

The value of the diode current is given by [29];

𝐈𝐨

𝐈𝐨, 𝐫𝐞𝐟= (

𝐓𝐜

𝐓(𝐜,𝐫𝐞𝐟))

𝟑

𝐞𝐱 𝐩 (𝐄𝐠

𝐤 𝐓│Tc,ref

−𝐄𝐠

𝐤 𝐓│𝐓𝐜

) (9)

Eg is a bandgap energy of a material which is;

Eg / (Eg,ref )= 𝟏 − 𝐂 (T-Tc,ref) [29] (10)

For silicon;

Eg= 1.794 * 10-19 J.

C= 0.0002677.

The series resistance Rs does not depend on the temperature or the solar radiation;

Rs=Rs,ref [29]. The shunt resistance Rsh depends on the absorbed solar radiation and does

not depend on the temperature;

Rsh/R(sh,ref ) =Sref/𝐒 [29] (11)

Based on Rauschenbach (1980), the negative inverse of the shunt resistance was

approximately equal to the slope of I-V curve at the condition of open circuit voltage.

𝐝𝐈/𝐝𝐕 = −𝟏/𝐑𝐬𝐡 [29] (12)

a/aref = Tc/Tc,ref [29] (13)

The following table presents the PV module electrical characteristics that were

obtained from the manufacturer.

36

Table 4 PV solar electrical characteristics

Maximum Power Pmax. 320 w

Vmp 54.7 V

Imp 5.86 A

Voc 64.8 V

Isc 6.24 A

Efficiency 19.6 %

Total number of series cell Ns 96

PV Solar module data for Sunpower SPR-E19-320.

For this project, the data which shows in Table 5.1 were used to design the PV Array, and it

was chosen because of the high module efficiency, which was more than 19%.

For estimating the PV solar panel daily operation, it was important to know the daily

peak sunshine hour (PSSH) for the location where the PV Array was installed.

Figure 5.6 Typical P_V and I_V curve for PV module [29].

37

PSSH refers to the solar radiation which a particular location could receive if the sun

is shining at its maximum rate for a certain number of hours.

The average PSSH in Denver, Co. =5.5 hour/day for fixed tilted array at latitude [41].

The following parameters were used;

The required load energy for operating the desalination system per day is El.

The PV array losses efficiencies are η.

The PV array thermal factor is Fth.

Then,

Equation (14) expresses the power that the PV array should generate for a

desalination system that operates with El energy per day.

For estimating the number of PV arrays that is required for system’s operating, it

should know the power that is generated from the PV array module which was used in the

desalination system.

Number of PV Array =

Peak Power for PV Array

PV Module Power (15)

Because of the variations in the PV power resulting from the change in weather, the

system could have operational problems.

Thus, the battery storage was necessary to stabilize the energy input to the system,

especially when the desired system’s operation was longer than the daily peak sunshine hour.

For sizing the batteries, there were two parameters to be estimated: the battery

capacity rating (AH) and the battery voltage.

The maximum depth of discharge for battery is DOD [23].

Peak Power for PV Array (kW) =El

PSSH ∗ η ∗ Fth [22] (14)

38

Battery Capacity (kW h) =El

DOD∗ηb [23] (16)

Where; ηb is the battery efficiency.

The output voltage which was required from the battery was Vr.

Thus,

The battery capacity (AH) was given by;

Battery Capacity (AH) = Battery Capacity (kw h)

Vr [23] (17)

For the project, the output voltage which was required from the battery was 24 volts.

Therefore, the battery capacity could be obtained with only a 24-volt battery or two of 12-

volt batteries.

However, using four batteries with 6-volt battery was preferred since the 12-volt, and

24-volt batteries were heavy.

Using more than four batteries might cause an unbalance in the battery charging and

discharging.

5.1.3 Size Heating Source

The electric heater was designed as a cylinder around a pipe to generate a uniform

heat at a specified temperature.

The initial temperature was the ambient temperature, and a thermostat was designed

to limit the heater’s temperature.

By controlling the power input to the heater, a uniform heat production of the heater

was also obtained. Therefore, the heater’s temperature to the feed water was constant with

the time.

The following figure is a schematic diagram which illustrates the heater modeling in

MATLAB/Simulink.

39

The Power comes from the PV Array and Batteries storage assembly. The final

temperature was the temperature which was delivered to heat the feed water.

This heating simulation was built using the following analysis which represents the

heat production by the coil heater with a uniform heat generation and a constant temperature.

The cylinder heater has diameter Dh, and length Lh in (m). The heat capacity (specific

heat) is Cp,h in (j/kg.C), and the heater’s density is ρ in kg/m3.

The heater surface area, S, was for an open sided cylinder with a thin thickness (th) and given

as: S= π *Dh *Lh

Thus;

Vol is the heater’s volume in m3,

𝐦 = ρ ∗ Vol (19)

Where;

𝐕𝐨𝐥 = 𝛑 ∗

𝐃𝐡𝟐 − (𝐃𝐡 − 𝐭𝐡)𝟐

𝟒∗ 𝐋𝐡 (18)

Figure 5.7 Heating source sizing in MATLAB/Simulink

40

m was the heater’s mass.

The useful heat which was generated by the heater was Qh,

𝐐𝐡 = 𝐦 𝐂𝐩,𝐡 ∆𝐓 (20)

∆𝐓 = 𝐓𝐡 − 𝐓𝐢 (21)

The power inputs to the heater was P, and it was the same power that was delivered

by the batteries.

The total heat which was generated from the power P was Q.

𝐐 = 𝐏 ∗ 𝐭 (22)

The heater’s losses to the ambient was Ls.

Thus,

𝐐 = 𝐐𝐡 + 𝐋𝐬 (23)

𝐋𝐬 = 𝐡𝐚 𝐀 (𝐓𝐡 − 𝐓𝐚) (24)

Where;

Th is the heater’s temperature.

Ti is the heater’s initial temperature.

Ta is the ambient temperature.

A is the heater’s surface area.

ha is the heat convective coefficient of the ambient air.

𝐡𝐚 =

𝐍𝐮 ∗ 𝐊𝐚

𝐃𝐡 (25)

Ka is the heat conductive coefficient of air.

𝐍𝐮 = 𝟏. 𝟏𝟓 𝐑𝐞,𝐃

𝟏/𝟐 (𝐏𝐫)

𝟏

𝟑 [20] (26)

For Pr ≥ 0.6 [20]

41

Pr is Prandtl number, and Re is Reynolds number.

𝐑𝐞,𝐃 = (𝐕𝐚 ∗ 𝐃𝐡)/𝛎 [29] (27)

Va is the wind speed, ν is the air kinematic viscosity.

Thus,

𝐏 ∗ 𝐭 = 𝐦 𝐂𝐩,𝐡 (𝐓𝐡 − 𝐓𝐢) + 𝐡𝐚 𝐀 (𝐓𝐡 − 𝐓𝐢) (28)

The Pr, Ka, and ν of air are taking according to the bellow table

Table 5 Thermophysical properties of air [20].

Temperature

(k) 𝝂 . 𝟏𝟎𝟔

(𝒎𝟐

𝒔)

𝐊. 𝟏𝟎𝟑

(𝒘

𝒎. 𝒌)

Pr

100 2.00 9.34 0.786

150 4.426 13.8 0.758

200 7.59 18.1 0.737

250 11.44 22.3 0.720

300 15.89 26.3 0.707

350 20.92 30 0.7

400 26.41 33.8 0.69

Incropera, Frank P.; DeWitt, David P. (2002)

5.1.4 Provide Heat to the Water

Heat that transfers from the heater to the pipe by radiation, and it is expressed by

Stefan-Boltzmann law:

𝐐 = 𝛆 𝛔 𝐀 𝚫𝐓𝟒 [20] (29)

Assume the shape factor was equal to one [14].

The heat that transfers between the coil heater and the feed water’s pipe was given by

[20];

42

𝐐𝐫𝐚𝐝. = 𝛔 𝐀

𝐓𝐡𝟒 − 𝐓𝐩

𝟒

(𝟏Ԑ) + (

𝟏 − ԐԐ ) ∗ (

𝐃𝐩

𝐃𝐡)

[20] (30)

Where;

σ = 5.6703 * 10-8 is the Stefan-Boltzmann constant.

ε is the emissivity coefficient.

Dp is the feed water’s pipe outer diameter.

Tp is the pipe’s outer wall temperature.

The heat that transfers into the pipe to heat the feed water was transferred by

conduction and convection.

A. The energy conducted through the pipe was expressed by Fourier’s law

𝐪 = −𝐊 ∆𝐓 [20] (31)

𝐪 = −𝐊 (𝐢

𝛛𝐓

𝛛𝐫+ 𝐣 (

𝟏

𝐫) (

𝛛𝐓

𝛛Ø) + 𝐤

𝛛𝐓

𝛛𝐳) [20]

(32)

Assuming the heat transfer is in one dimension and steady state and has constant

properties.

Thus, Fourier’ law in one dimension is:

𝐪 = − 𝐊 𝐀 𝐝𝐓

𝐝𝐫 [20] (33)

Assuming the heat transfers in (r) dimension.

K is the heat transfer conductive coefficient of the pipe

For Quasi-steady state without heat generation for cylindrical coordinates;

𝟏

𝐫∗

𝐝

𝐝𝐫(𝐊𝐫

𝐝𝐓

𝐝𝐫) = 𝟎 [20] (34)

By solving the above equation, we get;

43

𝐓(𝐫) = 𝐂𝟏 𝐥𝐧 𝐫 + 𝐂𝟐 (35)

Where;

C1 and C2 are constants.

Solving equation (35) at the boundary conditions,

T(r) = Tpo at ro and T(r) = Tpi at ri.

After solving the values of constants (C1 and C2), the temperature distribution equation in

the pipe is;

𝐓(𝐫) =

𝐓𝐩𝐢 − 𝐓𝐩𝐨

𝐥 𝐧 (𝐫𝐢

𝐫𝐨)

∗ 𝐥 𝐧 (𝐫

𝐫𝐨) + 𝐓𝐩𝐨 (36)

Thus, equation (33) will become

𝐪 =

𝟐𝛑 𝐋𝐩 𝐊 (𝐓𝐩𝐨 − 𝐓𝐩𝐢)

𝐥 𝐧 (𝐫𝐨

𝐫𝐢)

(37)

Tpo, and Tpi are the pipe’s outer wall temperature, and inside wall temperature.

ro, and ri, are the pipe’s outer radius, and inner radius.

Lp is the pipe’s length.

B. The energy which is transferred by convection from the pipe to feed water is expressed

by Newton’s law;

𝐐 = 𝐡𝐰 𝐀 ∆𝐓 (38)

𝐡𝐰 =

𝐍𝐮 ∗ 𝐊𝐰

𝐃𝐢

(39)

∆T is the temperature difference between the water before heating and after heating.

Kw is water’s heat transfer conductive coefficient.

hw is water’s heat transfer convective coefficient.

A is the pipe’s inside surface area.

44

Di is the pipe’s inner diameter.

For calculation Nusselt number Nu, Re must be determined as,

𝐑𝐞 =

𝐕𝐰 𝐃𝐢

𝛎𝐰 (40)

Vw is the water’s velocity.

νw is the water’s kinematic viscosity.

Water flux or water flow rate is equal to water velocity multiplying the area’s cross section.

��𝐰 = 𝛑 ∗

𝐃𝐢𝟐

𝟒∗ 𝐕𝐰 (41)

From equation (41), the water velocity Vw is obtained (water flow rate is known).

Choosing the tube wetting ratio perimeter for the flow between 0.03-0.14,

𝐰𝐫 =

��𝐰

𝐋𝐩 [25] (42)

wr is the wetting rate, which is the feed water flow rate per pipe unit length.

For laminar flow with a constant surface temperature, the Nusselt number could be

estimated as follow:

Nu=3.66 for Re≤ 2300 [20].

For turbulent flow,

Nu = 0.023Re0.8 ∗ Pr0.4 for Re>2300 [20].

The required heat energy for evaporating the m mass of water is given by,

𝐐𝐫𝐞 = ��𝐰 𝐂𝐩𝐰(𝐓𝐛 − 𝐓) + ��𝐰 𝐋 (43)

Qre is the required energy to evaporate the mass of water.

T is the water temperature in the initial state.

Tb is the water boiling temperature.

Cpw is the water specific heat j/kg.C.

45

L is the latent heat evaporation of water j/kg.

mw is the water flow rate kg/s.

The above figure presents the heating water assembly schematic which was simulated

in MATALB/Simulink.

The process was simulated in MATLAB/Simulink by using the water properties

based on the NIST software.

Figure 5.9 Two-Phase fluid properties block

The block above was used to determine fluid properties in the MATLAB/Simulink. It

provides thermo-physical properties of two-phase fluid. This block parameterizes the

properties of fluid in terms of a normalize internal energy and pressure.

Figure 5.8 Schematic of water evaporative in MATLAB/Simulink

46

𝐔𝐧 =𝐮−𝐮𝐦𝐢𝐧

𝐮𝐋𝐬𝐚𝐭(𝐩)−𝐮𝐦𝐢𝐧− 1 (From MATLAB)

Un is the normalize internal energy, u is the fluid specific internal energy, uLsat(p) is

the fluid specific internal energy of the liquid phase at saturated, umin is the minimum

internal energy of the fluid in the 2 phase state

The following models the water flow inside the rigid pipe.

Figure 5.11 Rigid pipe block

The ports A and B represent the inlet and outlet of the pipe. The port H represents the

thermal port for the heat transfer between the pipe and the surroundings.

The total thermal energy is equal to the sum of internal energy and kinetic energy.

𝐄 = 𝐌 (𝐮𝟏 +𝟏

𝟐[

𝐦𝟏𝐋𝐩

𝐌]

𝟐

) (From MATLAB)

Figure 5.10 Water properties data (picture is taken from MATLAB).

47

E is the total energy of water, u1 is the water internal energy, M is the total water

mass in the pipe, m1 is the water mass flow rate into the pipe through the port A and B (the

above equation is from MATLAB).

For understand the evaporation state, it is important to understand the Vapor-Liquid

Equilibrium concept.

The Vapor-Liquid Equilibrium (VLE) condition is that the Gibbs energy is minimized

at a known pressure and temperature. This means that the Gibbs energy is constant for any

small perturbation [44].

(dG)T, p = 0

𝐝𝐆 = (𝐆𝐠𝐰 − 𝐆𝐥𝐰)𝐝𝐧𝐰 = 𝟎 [44] (44)

So, Ggw = Glw.

Ggw is the Gibbs energy in a vapor (gas) phase, Glw is the Gibbs energy in a liquid phase, and

dnw is the small water amount.

When the temperature increases, the water molecules in the liquid phase move more

rapidly and it becomes more likely to convert into the gas (vapor) phase. Thus, the pressure

of the vapor increases with temperature.

The relation between vapor temperature and pressure is given by Clapeyron equation;

𝐝𝐩𝐬𝐚𝐭

𝐝𝐓=

𝐋

𝐓∆𝐕 [44] (45)

∆V= Vg – Vl

Psat is the saturated vapor pressure.

Vg is the volume of the vapor phase.

Vl is the volume of the liquid phase.

48

In most cases, Vg is greater than Vl, and for ideal gas pV = RT(treated the vapor as

an ideal gas) [44].

So, the Clapeyron equation becomes;

𝐝𝐩𝐬𝐚𝐭

𝐝𝐓=

𝐋

𝐓𝟐 𝐑𝐩

[44] (46)

R is the ideal gas constant.

𝐝𝐥𝐧𝐩(𝐓)

𝐝𝐓=

𝐋(𝐓)

𝐓𝟐𝐑 [44] (47)

Since 1/p dp= d lnp.

Equation (47) is Clausius - Clapeyron equation, which applies at low pressures (less

than 10 bar). It is used to calculate the vapor pressure at a given temperature.

A more practical equation that is used for computing the vapor pressure is the

Antoine Equation;

𝐥𝐧 𝐩𝐬𝐚𝐭(𝐓) = 𝐀 −

𝐁

𝐓 + 𝐂 [44] (48)

A, B, and C are the Antoine parameters for fluid.

Seawater is a mixture of water and several compositions (more than 85% of the

mixture is sodium and chloride, as shown in Figure 2.1).

For any seawater component, the partial pressure of any component equals to the

vapor pressure of the component multiplied by its mole fraction [44].

𝐩𝐢 = 𝐱𝐢 𝐩𝐢,𝐬𝐚𝐭(𝐓) [44] (49)

𝐩𝐢 = 𝐲𝐢 𝐩 [44] (50)

p and pi are the seawater pressure and component partial pressure in the liquid phase.

49

xi and yi are the mole fraction of the component in the liquid phase and the vapor phase in

vapor-liquid equilibrium.

Also,

𝐲𝐢 𝐩 = 𝐱𝐢 𝐩𝐢,𝐬𝐚𝐭 (𝐓) [44] (51)

Equation (51) is the Raoult’s law.

The variable Kvalue equals to yi / xi

Substitute Kvalue in Raoult’s law and rearranged it.

𝐊𝐯𝐚𝐥𝐮𝐞 =

𝐩𝐢,𝐬𝐚𝐭(𝐓)

𝐩 [44] (52)

The sum of the all vapor components mole fraction is equal to 1.

∑𝐢 𝐲𝐢 = 𝟏 [44] (53)

Also,

∑𝐢 𝐊𝐯𝐚𝐥𝐮𝐞 𝐱𝐢 = 𝟏 [44] (54)

For ideal gas;

∑𝐢 𝐩𝐢 = 𝐩 [44] (55)

For any component, the feed water (F) fraction is z. The heated feed water has a

vapor (V) fraction y and residual liquid (L) fraction x.

𝐅 𝐳𝐢 = 𝐋 𝐱𝐢 + 𝐕 𝐲𝐢 [44] (56)

Substitute Kvalue value in equation (56).

𝐅 𝐳𝐢 = 𝐋 𝐱𝐢 + 𝐕 (𝐊𝐯𝐚𝐥𝐮𝐞 𝐱𝐢) [44] (57)

𝐱𝐢 =

𝐅 𝐳𝐢

𝐋 + 𝐕 𝐊𝐯𝐚𝐥𝐮𝐞 [44]

(58)

Since L= F-V,

Then;

50

Since ∑𝐢𝐱𝐢 = 𝟏 and ∑𝐢 𝐲𝐢 = ∑𝐢 𝐊𝐯𝐚𝐥𝐮𝐞 𝐱𝐢 = 𝟏

Use the relation ∑𝐢 (𝐲𝐢 − 𝐱𝐢) = 𝟏 − 𝟏 = 𝟎. ,

∑

(𝐊𝐯𝐚𝐥𝐮𝐞 − 𝟏)𝐳𝐢

𝟏 + (𝐕𝐅) (𝐊𝐯𝐚𝐥𝐮𝐞 − 𝟏)𝒊

= 𝟎 [44] (60)

The above expression is Rachford-Rice equation.

The boiling point of mixture fluid such as seawater is different from the boiling point

of pure fluid such as water.

Therefore, the boiling point elevation of seawater is given by the following equation;

∆Tb is the boiling point elevation.

Tb is the normal water boiling point temperature.

xb is the mole fraction of the compositions that exist in the sweater.

L is the water’s latent heat evaporation.

R is the ideal gas constant.

5.1.5 Condensing the Vapor.

Condensation is a process in which water vapor is converted to liquid when the

temperature of the vapor falls below its saturation temperature.

The condensation process occurs when vapor molecules come in contact with cooler

molecules. The vapor will lose energy when the heat transfer of energy occurs and the vapor

will convert to liquid. The energy balance of condensate the vapor is the same energy balance

for evaporated the water but in the opposite direction.

𝐱𝐢 =𝐳𝐢

𝟏 + (𝐕𝐅) (𝐊𝐯𝐚𝐥𝐮𝐞 − 𝟏)

(59)

∆𝐓𝐛 =

𝐑(𝐓𝐛)𝟐𝐱𝐛

𝐋 [44] (61)

51

Figure 5.12 Heat balance for condensate [20].

The energy that is released from condensation process is expressed by [20]:

𝐪𝐫𝐞𝐥 = 𝐔𝐀 (𝐓∞𝟏 − 𝐓∞𝟐 ) [20] (62)

qrel is the energy released.

T∞1 is the water condensed temperature.

T∞2 is the cooling temperature.

𝐔 =

𝟏

𝐑𝐭𝐨𝐭𝐚𝐥 [20] (63)

Rtotal is the total heat transfer resistances.

𝐑𝐭𝐨𝐭𝐚𝐥 =𝟏

𝟐 𝛑 𝐫𝟏𝐋𝐩𝐡𝟏+

𝐥𝐧 (𝐫𝟐

𝐫𝟏)

𝟐𝛑 𝐊𝐰𝐋𝐩+

𝟏

𝟐 𝛑 𝐫𝟐𝐋𝐩 𝐡𝟐 [20] (64)

r1 and r2 are the inner and outer pipe radius,

h1 and h2 are the heat convective coefficient of water and air respectively.

𝐡𝟏 =

𝐍𝐮 𝐊𝐰

𝐃𝟏 [20] (65)

For constant temperature equals and Pr ≥ 0.6.

52

Nu= 3.66 [20].

𝐡𝟐 =

𝐍𝐮 𝐊𝐚

𝐃𝟐 [20] (66)

Nu is estimated in the same way in the equation (26).

𝐍𝐮 = 𝟏. 𝟏𝟓 𝐑𝐞,𝐃𝟏/𝟐

(𝐏𝐫)𝟏𝟑

𝐑𝐞𝐃 =

𝐕𝐚𝐃𝟐

𝛎 (67)

The Raoult’s law is expressed by [44];

∑ (

𝐲𝐢

𝐩𝐢,𝐬𝐚𝐭(𝐓))

𝐢

=𝟏

𝐩 (68)

Also, considering the following equation.

∑𝐢𝐱𝐢 = 𝟏 (69)

Figure 5.13 Schematic of water condensate in MATLAB/Simulink.

53

∑𝐲𝐢

𝐊𝐯𝐚𝐥𝐮𝐞𝐢

= 𝟏 [44] (70)

Replace pi,sat(T) in the Antoine equation (equation (48)):

So, Antoine equation will become;

𝐩𝐢,𝐬𝐚𝐭(𝐓) = 𝟏𝟎 𝐀−

𝐁

𝐓+𝐂 [44] (71)

Substituting the above equation into Raoult’s law (equation (68)) to estimate the

condensation temperature, and this condensation temperature is used to calculate the

saturated pressure pi,sat(T).

Finally, the condensate mole fraction is given by,

𝐱𝐢

𝐲𝐢=

𝐩

𝐩𝐢,𝐬𝐚𝐭(𝐓) [44] (72)

5.2 Solar Still

The basic principles of solar still distillation are simple but effective, as the sun's

energy heats the feed water to the point of evaporation. As the water evaporates, this vapor

rises and condenses on the solar still’s cover for collection. This process eliminates

impurities such as minerals, and removes microbiological organisms. The result is fresh

water. Thus, the solar stills desalination process uses the sun’s radiation to evaporate the salt

water and then condenses it. The clean water is collected as drinkable water. Modeling was

used to predict the operation of the thermal system design for the solar still desalination

process.

5.2.1 Solar Still Elements

The essential elements of Solar Still are:

1) Feed water basin.

2) Incoming radiation.

54

3) A transparent cover (glass or plastic).

4) Collection pipes that collect the condensate water.

5) Other miscellaneous parts such as sensors

The sun’s radiation heats the water in the basin and evaporates the water. The water

then condenses under the transparent cover as droplets. These droplets flow down into the

collecting pipes

Figure 5.14 Solar still basin

5.2.2 Energy Balance

To model the energy balance of the solar still, the following process was followed.

The sunlight passes through the cover of the still and is absorbed in the seawater layer and by

the black cover in the basin, heating the basin and seawater. Also, the seawater is heated by

55

the black surface by conduction heat transfer. As a result, the seawater temperature increases.

Vaporization will take place on the surface of the seawater. The seawater surface is semi-

permeable which that means the mass flux of one component is zero. For example, the water

that evaporates from the surface evaporates into an adjoining air stream. Therefore, the

saturated air at the interface is transported by diffusion because of the partial pressure

differences and by convection because of the natural convection of the air from the feed

water interface into the air inside the basin. Based on a quasi-steady state energy balance, the

air inside the basin is also saturated. Thus, the saturated air inside the basin will condense at

the cover.

5.2.2.1 External Heat Transfer

The external energy balance on the solar still includes the cover and the basin bottom

losses. Assume there is no temperature gradient along the cover.

𝐈(𝐭) = 𝐈(𝐭)𝐑𝐠 + 𝐈(𝐭)𝛂𝐠 + 𝐈(𝐭)𝐑𝐰 + 𝐈(𝐭)𝛂𝐰 + 𝐈(𝐭)𝛂𝐛 (73)

I (t), αw, Rw, αg, Rg, and αb are the solar radiation intensity, water absorptivity and

reflectivity, the glass cover absorptivity and reflectivity, and basin bottom absorptivity.

Figure 5.15 Overall energy balance

56

𝐈(𝐭)𝛂𝐠 + ( 𝐪𝐞𝐰 + 𝐪𝐜𝐰 + 𝐪𝐫𝐰) = (𝐪𝐫𝐠 + 𝐪𝐜𝐠) [39] (74)

𝐈(𝐭) 𝛂𝐰 = ��𝐰 𝐂𝐩𝐰

𝐝𝐓𝐰

𝐝𝐭+ 𝐪𝐞𝐰 + 𝐪𝐜𝐰 + 𝐪𝐫𝐰 − 𝐪𝐛 [39]

(75)

𝐈(𝐭)𝛂𝐛 = 𝐪𝐛 + 𝐪𝐜𝐛 + 𝐪𝐬

𝐀𝐬

𝐀𝐛 [39]

(76)

Where;

Cpw is water specific heat capacity.

mw is the distilled water mass.

qb is the basin heat transfer, qcb is the basin bottom heat losses, and qs is the heat losses from

the side.

The heat losses from the solar still occur on the cover, the bottom, and sides to the

ambient by convection, radiation, and conduction.

The heat losses from the solar still that occur on the cover, the bottom, and sides to

the ambient are by convection, radiation, and conduction.

I. Losses from the cover:

The cover’s losses are by convection and radiation.

Convection heat transfer losses from the cover to the ambient is given by,

𝐪𝐜𝐠 = 𝐡𝐜𝐠(𝐓𝐠 − 𝐓𝐚) [39] (77)

Ta is the ambient temperature.

Tg is the glass cover temperature.

hcg is the glass cover heat transfer convective coefficient.

Radiation heat losses are given by [39],

𝐪𝐫𝐠 = 𝐡𝐫𝐠(𝐓𝐠 − 𝐓𝐚) [39] (78)

hrg is the heat transfer radiative coefficient.

57

𝐡𝐫𝐠 =𝛆 𝛔 ((𝐓𝐠)

𝟒− (𝐓𝐬𝐤𝐲)

𝟒)

𝐓𝐠 − 𝐓𝐚 [39] (79)

Tsky is the sky temperature which is given by [28],

𝐓𝐬𝐤𝐲 = 𝟎. 𝟎𝟓𝟓𝟐(𝐓𝐚)𝟏.𝟓 [28] (80)

ε is the glass cover emissivity.

σ is the Stefan-Boltzmann constant.

The overall glass heat transfer by radiating and convection is qg.

𝐪𝐠 = 𝐡𝐭𝐠(𝐓𝐠 − 𝐓𝐚) [39] (81)

𝐪𝐠 = 𝐪𝐜𝐠 + 𝐪𝐫𝐠 [39] (82)

And;

𝐡𝐭𝐠 = 𝐡𝐜𝐠 + 𝐡𝐫𝐠 [39] (83)

Where;

htg is the total heat transfer losses coefficient from ambient to glass. It expressed according to

J. H. Watmuff, 1977.

𝐡𝐭𝐠 = 𝟐. 𝟖 + 𝟑 𝐕𝐚 [31], [15] (84)

II. Losses from the bottom and sides:

Losses from the bottom and sides are by radiation, conduction, and convection.

𝐪𝐛𝐬 = 𝐪𝐛 + 𝐪𝐜𝐛 + 𝐪𝐬 (85)

𝐪𝐛𝐬 = 𝐔𝐨(𝐓𝐛 − 𝐓𝐚) (86)

qbs is the total losses from bottom and sides.

Tb and Ta are the temperature of the basin and ambient respectively.

Uo is the basin overall heat loss coefficient.

𝐔𝐨 = 𝐔𝐛 + 𝐔𝐞 (87)

58

Where;

Ub and Ue are the heat loss coefficient of bottom and sides respectively.

𝐔𝐛 =

𝟏

(𝟏

𝐡𝐰) + (

𝟏𝐡𝐛

) [39]

(88)

𝐡𝐛 =

𝟏

𝐋𝐢𝐧𝐬

𝐊𝐢𝐧𝐬+

𝐡𝐜𝐛 + 𝐡𝐫𝐛

𝐡𝐜𝐛𝐡𝐫𝐛

[39] (89)

Where;

Lins and Kins are the still’s insulation thickness and thermal conductive coefficient.

hcb and hrb are the basin heat transfer convective and radiative coefficient.

On the bottom, there is no wind speed, thus, hcb+hrb=htb and it estimated such as

equation (84) with wind speed is zero. Therefore, hcb+hrb= 2.8 w/m2.

hw is the water heat transfer convective coefficient.

The Nusselt number inside the still between the water and glass cover is given by Dunkle

[30], [43],

𝐍𝐮 = 𝐂(𝐆𝐫 𝐏𝐫)𝐧 [30], [43] (90)

C and n depend on the Gr.

C=0.21, n= 1/4 for 104 < Gr < 3.2 ∗ 105

C=0.075, n=1/3 for 3.2 ∗ 105 < Gr < 107

Gr is Grashof number and is expressed by,

𝐆𝐫 =

𝐠 𝐁 ∆𝐓 (𝐋𝐛)𝟑

𝛎𝟐 [20] (91)

B, g, Lb, and ν are the volumetric coefficient of expansion, gravitational constant,

space between the glass cover and water, and the kinematic viscosity respectively.

59

∆T = (Tw − Tgi)

Pr = ν/αα [20]

αα is the thermal diffusivity.

𝐔𝐞 = 𝐔𝐛 (

𝐀𝐬

𝐀𝐛) [39] (92)

Ab and As are the basin bottom area and the basin side area.

With As ≫ Ab, the Ue was ignored [39].

5.2.2.2 Internal Heat Transfer

Internal energy balance means that the heat transfer occurs inside the solar still

between the feed water surface and the cover by radiation, convection, and evaporation [39].

Figure 5.14 shows the model of the distilled water in a typical solar still

I. Irradiative heat transfer

The rate of heat radiation from the water surface to the cover is,

𝐪𝐫𝐰 = 𝐡𝐫𝐰(𝐓𝐰 − 𝐓𝐠) [39] (93)

hrw is the irradiative heat coefficient, and it is given by [39],

𝐡𝐫𝐰 = 𝛆𝐞𝐟𝐟. 𝛔 [((𝐓𝐰)𝟐 + (𝐓𝐠)𝟐

) (𝐓𝐰 + 𝐓𝐠)] [39] (94)

The effective emissivity is given by,

𝛆𝐞𝐟𝐟. =

𝟏

(𝟏

𝛆𝐰) + (

𝟏𝛆𝐠

) − 𝟏 [39]

(95)

εw and εg are the water and the glass cover emissivity.

II. Convective heat transfer

The general convective heat transfer equation is given by,

𝐪𝐜𝐰 = 𝐡𝐜𝐰(𝐓𝐰 − 𝐓𝐠) [28], [39] (96)

60

hcw is the heat convective coefficient between the basin bottom and ambient, and it is given

by [30].

𝐡𝐜𝐰 = 𝟎. 𝟖𝟖𝟒 [(𝐓𝐰 − 𝐓𝐠) + ((𝐩𝐰 − 𝐩𝐠)(𝐓𝐰 + 𝟐𝟕𝟑. 𝟏𝟓)

𝟐𝟖𝟔. 𝟗 ∗ 𝟏𝟎𝟑 − 𝐩𝐰)]

𝟏𝟑

(97)

Where,

pw is the partial pressure at the water surface.

pg is the partial pressure at the glass cover.

𝐩𝐰 = 𝐞

𝟐𝟓.𝟑𝟏𝟕−(𝟓𝟏𝟒𝟒

𝐓𝐰) [28], [39] (98)

𝐩𝐠 = 𝐞

𝟐𝟓.𝟑𝟏𝟕−(𝟓𝟏𝟒𝟒

𝐓𝐠) [28], [39]

(99)

III. Evaporative heat transfer

The general evaporative heat transfer equation is given by,

𝐪𝐞𝐰 = 𝐡𝐞𝐯𝐚(𝐓𝐰 − 𝐓𝐠) [39] (100)

heva is the evaporative heat transfer and it is given by (based on Dunkle’s) [30], [39].

𝐡𝐞𝐯𝐚 = 𝟏𝟔. 𝟐𝟕𝟑 ∗ 𝟏𝟎−𝟑𝐡𝐜𝐰 (

𝐩𝐰 − 𝐩𝐠

𝐓𝐰 − 𝐓𝐠) [30], [39] (101)

The hourly yield is given by [18];

𝐦 = (𝐪𝐞𝐰

𝐋) ∗ 𝟑𝟔𝟎𝟎 [18] (102)

Where;

m is the hourly distilled water from the solar still.

L is the latent heat vaporization.

The overall heat coefficient loss between the glass cover and water surface given by;

𝐡𝐭𝐰 = 𝐡𝐫𝐰 + 𝐡𝐜𝐰 + 𝐡𝐞𝐯𝐚. [39] (103)

61

Solar still overall loss (U) is given by following equations [39];

𝐔 = 𝐔𝐭 + 𝐔𝐛 (104)

Ut the solar still’s top overall losses.

𝐔𝐭 =

𝟏

𝐑𝐭 (105)

𝐑𝐭 =

𝟏

𝐡𝐭𝐰+

𝟏

𝐡𝐭𝐠

(106)

Thus,

𝐔𝐭 =

𝐡𝐭𝐰𝐡𝐭𝐠

𝐡𝐭𝐰 + 𝐡𝐭𝐠 (107)

The water temperature Tw is given by [39];

𝐓𝐰 =

𝐟

𝐚𝐚[𝟏 − 𝐞𝐱𝐩(−𝐚𝐚 𝐭) + 𝐓𝐰𝐨 𝐞𝐱𝐩(− 𝐚𝐚 𝐭)] [39] (108)

Where, f is a function, and it is given by;

𝐟 =

(𝛂𝛕)𝐞𝐟𝐟. 𝐈(𝐭) + 𝐔 𝐓𝐚

𝐦𝐂𝐩𝐰 [39] (109)

The value of (ατ)eff is obtained from the following equation.

(𝛂𝛕)𝐞𝐟𝐟. = 𝛂𝐛

𝐡𝐰

𝐡𝐰 + 𝐡𝐛+ 𝛂𝐰 + 𝛂𝐠

𝐡𝐭𝐰

𝐡𝐭𝐠 + 𝐡𝐭𝐰 [39] (110)

Where;

aa is constant and equal to U/(mw * Cpw).

Two is the initial basin water temperature at time t=0

The glass temperature is assumed to have no gradient and expressed by [39];

𝐓𝐠 =

𝐈(𝐭)𝛂𝐠 + 𝐡𝐭𝐰𝐓𝐰 + 𝐡𝐭𝐠𝐓𝐚

𝐡𝐭𝐰 + 𝐡𝐭𝐠 [39] (111)

Where;

62

Tw is the water temperature.

Tg is the glass cover temperature.

For the theoretical calculation, assume there is no temperature gradient in the glass

cover and water.

The following figure represents the modeling of the solar still desalination system that

was designed using MATLAB r2016 Simulink.

Figure 5.16 Schematic of solar still desalination

63

CHAPTER VI

RESULT

In this section, it will show the simulated results which were developed by

MATLABr2016a and compare the simulation with the experimental results of the project.

Also, a comparison is made between the several solar desalination processes.

6.1 PV Solar Powered Desalination Results

The simulated results for the Photovoltaic Array were based on the information from

Sunpowers Company for their SPR-E19-320 module. The following figures show the relation

between the output power with the voltage (P-V Curve) and the Ampere-Voltage relation (I-

V Curve).

Figure 6.1 P-V curve characteristic

64

Figure 6.1 illustrates the relation between the power output from the PV Solar and

Voltage.

The maximum power output (Pmax.) occurs at the voltage (Vmp.) and Current (Imp).

For this module,

Pmax. =320.27 W at the Vmp = 54.6.

As seen in the following figure, Voltage (Vmp.) occurs at a Current Imp=5.86.

𝐏𝐦𝐚𝐱. = 𝐈𝐦𝐩 ∗ 𝐕𝐦𝐩 [29] (112)

Figure 6.2 I-V curve characteristic.

65

The following figure shows the relationship among the Pmax, Imp., and Vmp, for a PV

Array.

The above figures are based on a 1000 𝑤

𝑚2 irradiance. However, the solar irradiance is

not constant throughout the day.

Figure 6.4 shows the PV Array characteristics for three irradiance values 1000, 500,

and 100𝑤

𝑚2. In this project the theoretical calculations used the maximum operating point

characteristics for estimating the output power.

Figure 6.3 PV Array characteristics for P–V and I-V curves

66

The following figure shows the PV Solar output power for an average June day in

Denver, Colorado, USA. The values for that day were obtained from the System Advisor

Model (SAM) program. It is clear that the actual power output from the PV solar was not

adequate to give the required estimated power of 320 W. Thus, using more than one PV

panel was needed to provide the required power. In this project, three PV panels were used.

Figure 6.4 Photovoltaic panel characteristics for different irradiance values (1000,

500, and 100)

67

Figure 6.5 Actual power output in June in Denver for one PV panel.

Figure 6.6 Actual power output in June in Denver for three PV panels

68

From figure 6.6, it is clear that the PVs Array does not provide enough power to

operate the system from about 6 pm to 8 am. Therefore, batteries were needed to keep the

system working continuously. The batteries were charged from the PV during the period

from 8 am to 6 pm and discharged from 6 pm to 8 am. to give the system the continuous

required operating power.

The distilled water obtained from the piped water, heavy water, and sea water are

shown in the following figures.

In the figures for the distilled feed water, production flow rate was for a sample of 6

minutes.

The distilled water was measured in kg/s or (liter/s) and with time in seconds.

Figure 6.7 Water distilled flow rate for Piped Water.

As shown in the above figure the production started after about 50 seconds. Initially,

the distilled water flow rate was high and then decreased over time. The reason for the initial

69

high value was that the condensation pipe at the beginning of the operation was not warm

and because of the vacuum pressure that occurred during the starting of the distillation

process. Thus, this initial period was neglected in estimating the production of the water.

Figure 6.8 shows the vapor and water temperatures inside the heating and

condensation pipes.

Figure 6.8 Vapor-Water distilled temperature for Piped Water.

In Figure 6.8, the difference in temperature between the vapor (red line) and the water

distilled (blue line) at the beginning of production was the largest. Also, the difference in the

temperature of the water and vapor throughout the period when the unstable production

occurred was zero. Therefore, the vacuum pressure caused the unstable production.

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The system stabilized after about 70 seconds and started to give stable distilled water.

Figure 6.7 shows the uniform system flow rate measured in kg/s. The production of uniform

water was the goal of using this system which was connected to batteries.

Figure 6.9 Piped Water vapor fraction.

Figure 6.9 shows the ratio of the vapor after heating and condensation process. The

red line refers to the vapor ratio after the heating process while the blue line refers to the

vapor ratio after condensation process.

The production for one hour is shown in the figure 6.10.

Figure 6.10 Piped Water distilled production in one hour.

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The amount of production of uniform distilled water is shown in figure 6.11. The

amount of water was about 1.843 liters per hour.

Figure 6.11 Piped Water distilled curve.

For heavy water, the feed water was preheated.

Figure 6.12 Heavy Water distilled flow rate.

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Figure 6.13 Vapor and water distilled temperature for heavy water.

As seen in the above figure, the temperature of the water distilled was the same

temperature of the vapor which means the system was operating in the vapor-liquid

equilibrium (VLE) zone.

The water distilled in one hour was about 1.773 liters.

Figure 6.14 Heavy Water production in one hour.

The heavy water distilled curve was also uniform and is shown in the following

figure.

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Figure 6.15 Heavy Water distilled curve.

Figure 6.16 Heavy water vapor fraction.

74

The vapor fraction was uniform for the heavy water desalination.

The seawater desalination behavior was similar to the previous water desalination

types. The distilled sea water flow rate was less than the other, which resulted from its higher

boiling temperature.

Tbb = ∆Tb+373.15.

Tbb is the seawater boiling temperature, and ∆Tb is the boiling point elevation (the

difference between normal water boiling temperature and seawater boiling temperature).

∆Tb =0.5942

Thus, Tbb = 373.74

Sea water distilled production flow rate was constant with the time.

Figure 6.17 Seawater distilled flow rate.

75

From the above figure, it can be seen the time to start the desalination production was

longer than for the piped and heavy water. The reason for this delay is that the seawater

consists of more compositions than the piped and heavy water.

The hourly production was 1.409 liters per hour.

Figure 6.18 Seawater distilled production in one hour.

The distilled water curves for piped water, heavy water, and seawater per hour are a

linear relation, and the expression could be written mathematically as,

Y= C (X-td)

Where;

td is the time when the distilled starts.

C is a constant.

76

Table 6 Feed water types yield

For piped water, the boundary condition at X= 3600 and Y=1.843

C= 1.843/(3600-50) = 0.00519.

And for heavy water, the boundary condition at X=3600 and Y=1.773

C=1.773/(3600-64) = 0.00501

And for seawater, the boundary condition at X=3600 and Y=1.409

C= 1.409/(3600-107) = 0.00403.

Figure 6.19 comparing modeling results of water distilled from three water types.

The experiment was done for seawater, and the results are shown in the following figure.

Feed Water Desalination starts Time

(s)

Yield water per hour

(liter)

Piped water 50 1.843

Heavy water 64 1.773

Seawater 107 1.409

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Figure 6.20 Distilled Seawater production done experimentally in one hour.

The experimental water production had an approximate linear behavior. There was a

difference between the theoretical solution of the distilled water production which was

obtained from simulation of the MATLAB software and the experiment. This difference was

because the software simulation had the assumption that the weather conditions such as

constant wind speed and temperature during one hour, while in actual testing, there were

differences in the weather conditions during one hour. The difference in wind speed was not

taken into account in the numerical estimation. The average wind speed was taken as 5 m/s.

The distilled water from the experiment was about 1.19 liter per hour.

The following figure shows the difference between the modeling and experimental

distillation of seawater. It shows a small difference in the linear relation for the production of

78

water. Both production curves might be more similar if the testing had been done indoor

without the effects of wind.

Figure 6.21 Comparing fresh water productivity for Seawater from experiment and modeling

of PV solar method.

6.2 Solar Still Results

The data used in theoretical calculation which was made by the MATLAB simulation

were taken from 8 am to 5 pm.

The calculation does not estimate the data from 5 pm to 8 am since there was not

enough solar energy available. It was assumed that there was no temperature gradient

throughout the cover due to a small thickness of the cover. The testing was done for sea

water only.

79

Figure 6.22 Solar Still modeling yield.

From the above figure it can be seen that the distilled water increased with time until it

reached a peak value, and then decreased. The reason for the increase was that the solar

energy was increasing in the morning and that led to an increase in the water production,

while in the afternoon there was a decrease in production according to the change in solar

energy.

When the solar energy was increasing, the energy absorbed by the system increased,

which led more heat transfer to the feed water. This increased heat transfer consequently

increased the water temperature, causing the rate of evaporated water to increase, resulting in

80

an overall increase in distilled water. Increasing the difference between the water temperature

and cover temperature led to an increase in the distilled water.

Figure 6.23 Water temperature and glass temperature.

For the experiment, reference data was taken as,

Experiment time is from 9 am to 4 pm.

Feed water depth in the basin=1 cm.

Glass cover slope = 38 degrees.

The basin box was 2 m length and 0.5 m width;

Area of the basin =2*0.5=1m2.

The glass cover area was 1.4m2.

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The glass cover thickness was 4 mm.

There was no temperature gradient through the cover due to the small thickness.

The experiment was done on a cloudy day.

Figure 6.24 Reference experimental Solar Still distilled water [40].

The distilled water in this reference experiment fluctuated due to fluctuation in the

weather conditions during the experiment. The data taken was in (ml) per hour

6.3 Comparing the results

Comparison of the modeling results of the PV solar powered desalination approach

and Solar Still approach are given in the figure 6.25, and the comparison of the experimental

results of the both approaches are shown in the figure 6.26.

The mass of the feed water used in the solar still approach was constant;

mf = 0.01 m * 1 m2 = 0.1 m3.

= 10 liters.

82

While, the feed water flow rate in the PV powered desalination approach was 0.018

kg/s.

mf =0.018 kg/s * 3600 s/hr= 64.8 kg/hr.

= 64.8 liter/hr. in one hour.

Figure 6.25 Comparing the freshwater results from the PV solar modeling approach with the

freshwater from Solar Stills modeling for Seawater.

The modeling of the distilled water of PV-powered approach was done in the same

period that the modeling of the solar still was done (8 am to 5 pm). It can be seen that the two

approaches have a different behavior with time. The water production from the PV powered

system method was not affected by ambient conditions because it was connected to the

batteries, which compensated for the solar energy available. On the other hand, in the solar

still method, the system’s capacity was affected by change in the solar energy available.

83

In the experiment, the difference between the two approaches was observed. The

experiments for both methods were done in the same weather conditions.The experiments

were made in a cloudy day to study the system’s performance.

Figure 6.26 Comparing the freshwater results from the PV solar experimental approach with

the freshwater from Solar Stills experimental for Seawater.

As seen in the above figure, each approach had difference results. The difference

between the two methods was caused by a variation in the weather conditions during the day.

It can also be seen that the fresh water production from the PV-powered desalination method

was approximately linear and gave a steady daily production, while the solar still daily

production fluctuated with the time due to the weather conditions.

84

CHAPTER VII

DISCUSSION AND CONCLUSION

7.1 Discussion

In this research project, the numerical analysis of the basic solar desalination

approaches was established and the theoretical results were compared with results obtained

from the experiment.

Using the results from this research, the following could be concluded:

The essential factor affecting the productivity of the solar still was the available solar

energy. The water from the solar still increased in proportion to the amount of available solar

energy. The performance of the PV solar-powered desalination method was not affected by

the variation of solar radiation, because it was connected to batteries to compensate the

variation in available solar energy. When the temperature differences between the water

interface and the glass cover in the solar still increased, the amount of the fresh water

production increased.

The maximum amount of the fresh water obtained from the solar still occurred during

the period when the solar radiation was highest, while the distilled water from the PV solar

method was approximately constant.

The deviation between the experimental and theoretical results for the solar

desalination was due to the following reasons. The equations that were used in the

calculations did not consider the heat losses due to the saturated water leakage from the solar

still. When the vapor pressure in the solar still was more than the ambient pressure, the

saturated air leaked to the outside. The incoming air from the surroundings to the still was

not saturated and it took time to be heated and then saturated. This led to a reducution of the

85

distilled water of solar still. This was not considered in the numerical solution that predicted

the production rates. And the numerical calculations of the PV solar approach did not

consider the changes in wind speed during the one hour testing period.

7.2 Conclusion

Using the PV solar desalination system could provide a steady quantity of drinkable

water for a small community and for people who live in regions with impure water sources.

Additionally, communities having difficulty in accessing local electricity or a lack of

electrical power would benefit from solar desalination. Also, the PV solar desalination was a

continuously operating system throughout the day and it could be running continuously

throughout the year.

7.3 Future Direction

This research represents a basic step and study towards the development of a solar

desalination system. In the future, the study should consider the following points:

Scaling the systems to increase the water flow rate produces from the system.

Determine the system’s efficiencies.

Calculate and comparing the system’s cost.

86

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