Final Report Mainak Bhaumik - 26

7/28/2019 Final Report Mainak Bhaumik - 26

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CFD INVESTIGATION OF THERMOCLINE

BEHAVIOUR IN THERMAL STORAGE TANK

A PROJECT REPORT

Submitted by

MAINAK BHAUMIK

in partial fulfillment for the award of the degree

of

MASTERS OF ENGINEERING

IN

THERMAL ENGINEERING

UNDER THE GUIDANCE OF

Dr. R. S. MAURYA

BHARATIYA VIDYA BHAVANS

SARDAR PATEL COLLEGE OF ENGINEERING

MUNSHI NAGAR, ANDHERI (WEST)MUMBAI 400 058

UNIVERSITY OF MUMBAIMARCH 2012


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DISSERTATION APPROVAL

The dissertation entitled CFD Investigation of Thermocline Behavior in Thermal Storage

Tank by Mr. Mainak Bhaumik is being approved for the awardofMaster of Engineering

(Mechanical) in Thermal Engineering.

--------------------------- ------------------------------

Internal Examiner External Examiner

(Dr. R. S. Maurya)

----------------------------------------Head of the Department

Mechanical Engineering

----------------------------------------

PRINCIPAL

Date:

Place: MUMBAI


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CERTIFICATE

This is to certify that this dissertation titled CFD Investigation of Thermocline Behavior in

Thermal Storage Tank submitted by Mr. Mainak Bhaumik in partial fulfillment of

requirements for the degree of Master of Engineering (Mechanical) with Thermal Engineering

subjects, is a bona fide research work carried out by him under my supervision.

Dr. R. S. Maurya(Project Guide)


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ACKNOWLEDGMENTS

Its a great pleasure to acknowledge those whose active help and support make this thesis possible

in the present form. First, the author would like to thank the project guide Dr. R. S. Maurya, for his

endless guidance and constant encouragement.

The author gratefully acknowledges Dr. Roshini Easow for her valuable help and suggestions.

My sincere thanks to staff members of mechanical engineering department of Sardar Patel College

of Engineering, for their technical help that author received during the whole period.

Finally, no thanks will ever be enough for my parents, friends, colleagues and other members of

my family. It is their unconditional love, enthusiastic support and encouragement which remained

as the real source of inspiration to me and kept me going. Words would fail to express my

indebtedness, especially, to my parents, who have gone through many hardships in making me

what I am today.

Mainak Bhaumik


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ABSTRACT

Thermal stratified storage tanks are an effective method to improve the efficiency of thermal

storage devices that are commonly used in thermal systems when the available energy source isirregular or when a time lag exists between the production and the demand. Thermocline behavior

and thermal stratification of hot water storage tanks during the stagnation mode is investigated

using CFD tools. 2D CFD investigation of thermocline behavior in the hot water thermal storage

tank has been carried out. A commercial code ANSYS Fluent 6.3 has been used for solving and

post processing of the data.

The study addresses the change in water stratification due to thermocline layer growth during the

cool down of the water inside the storage tank of thermal systems in the 90 to 20 temperature

range, which lies within the operating range of most conventional and solar hot water and liquid

based heating systems.

The simulation is carried out with different cases in which the initial thermocline is set for different

height of the hot water storage tank with Fluent. Results are analyzed for cooling rate of water in

the storage tank and thermocline thickness development in the storage tank.


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CONTENTS

Acknowledgements iv

Abstract v

Contents viList of Figures viii

List of Tables x

Chapter No. Title Page No.

Chapter 1 Introduction 1

1.1 Energy Storage 1

1.2 Applications of Thermal Energy Storage (TES) Systems 2

1.2.1 Water Heating 2

1.2.2 Solar Heating 3

1.3 Thermal Stratification 6

1.4

1.4.1

1.4.2

1.4.3

Introduction to Computational Fluid Dynamics (CFD)

Applications of CFD

CFD Methodology

Processes in CFD

13

13

14

15

Chapter 2 Literature Review 17

2.1 Literature Review 17

2.2 Objective and Scope 21

2.3 Methodology 21

Chapter 3 Problem Definition 22

3.1 Problem Definition 22

3.2 Governing Equations 24

3.2.1 Continuity Equation 24

3.2.2 Energy Equation 253.2.3

3.3

Momentum Equation

Boundary conditions

25

Chapter 4

4.1

Numerical Implication

Computational Domain

26

26


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4.2

4.3

4.4

Mesh

Problem and Solution Set up in Fluent 6.3

Grid Independent Test

27

29

37

Chapter 5 Results and Discussions 38

5.0 Results and Discussions 38

5.1 Temperature contours 39

5.2 Buoyancy Driver Flow 54

5.3 Heat loss from Tank 58

5.4 Comparison of Case Results 63

Chapter 6 Conclusions

Future Scope

64

65

References 66


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List of Figures

Figure No. TitlePage

No.

Figure 1 Schematic diagram of SDHW System 5Figure 2 Schematic diagram of natural stratification of River and Ocean Water 7

Figure 3 Schematic diagram of thermal stratification of Water in the SDHW

Storage tank

8

Figure 4 Different levels of stratification within storage tank withequivalent

stored energy a) highly stratified, b) moderately stratified and c) fully

mixed unstratified storage tank

9

Figure 5 Destratification Factor 11

Figure 6 Control Volume 13

Figure 7 Basic structure of Fluent Solver 16

Figure 8 Schematic of the hot water storage tank under study 22

Figure 9 Computational Domain 26

Figure 10 Complete 2-D view of coarse mesh size is 18,360 28

Figure 11 Boundary conditions applied to case 1 34





Figure 16 Grid independent test 37

Figure 17 Computational model of storage tank at a time interval of 00hr 39

Figure 18 Case 01 transient temperature contour at 50% of tank height 41

Figure 19 Case 01 transient behavior of temperature profile v/s height of tank 42

Figure 20 Better visualization of thermocline plots of case 01 42

Figure 21 Case 02 transient behavior of temperature profile v/s height of tank 44

Figure 22

Figure 23

Figure 24

Case 02 comparison plots of temperature profile

Case 03 transient behavior of temperature profile v/s height of tank

Case 03 comparison plots of temperature profile

45

47

48


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Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Figure 31

Figure 32

Figure 33

Figure 34

Figure 35

Figure 36

Figure 37

Figure 38

Figure 39

Case 04 CFD calculated temperature profile in the tank

Case 04 CFD calculated temperature profile at different heights of the

tank

Case 04 CFD calculated velocity profile at different heights of the tank

Case 04 CFD comparison plots of temperature profile at one hour

interval

Case 04 CFD comparison plots of temperature profile at 24 hours

interval

Case 05 CFD calculated water temperatures in the tank with initially

uniform temperature

Case 05 CFD calculated temperature profile in the tank

Case 05 CFD calculated temperature profile at different heights

CFD calculated vertical fluid velocities at different heights

CFD calculated vertical fluid velocities at different times

Schematic diagram of a tank consisting of N layers

The influence of stratification on heat loss removal factor for cooling

starting with a uniform temperature of 900C (case 05)

The heat exchange between layers v/s temperature gradient in the tank

for cooling with a uniform temperature of 900C (case 05)

The influence of stratification on heat loss removal factor for cooling in

the stratified tank (case 04)

The heat exchange between layers v/s temperature gradient in the

stratified tank (case 04)

50

50

51

51

52

53

55

55

56

57

60

61

61

62

62


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List of Tables

Table No. Title Page No.

Table 1 Mesh information ..27Table 2 Problem Set up29

Table 3 Properties of water.......30

Table 4 Solution Set up.31

Table 5 Relaxation settings in FLUENT...32

Table 6 Boundary conditions applied to various cases..33


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CHAPTER 1- INTRODUCTION

1.1Energy Storage:Energy storage as a natural processis as old as the universe itself. The energy present at the

initial formation of the universe has been stored in stars such as Sun, and is now being used by

humans directly for example through solar heating or indirectly for example by growing crops or

conversion into electricity in solar cells.

As a purposeful activity, energy storage has existed since pre-history; through it was often

not explicitly recognized as such. An example of deliberate mechanical energy storage is the use of

logs or boulders were collected at the top of a hill or wall and the energy thus stored used to attack

invaders who came within range.

A more recent application is the control of waterways to drive water mills for processing

grain or powering machinery. Complex systems of reservoirs and dams were constructed to store

and release water and also potential energy is contained and can be used when required.

Types of Energy storage:

Energy storage can be in various forms like -

-Thermal Energy Storage

-Electrical Energy Storage-Mechanical Energy Storage

-Chemical Energy Storage.

Thermal energy storage:

The thermalenergy storage (TES) can be defined as the temporary storage of thermal heat

energy at high, medium or low temperature. The purpose of such storage is to store energy when it

is in excess of the requirement of an application and to make energy available for extraction when

the supply of energy is inadequate or absent. This thermal energy storage can reduce the time taken

to supply energy when there is peak demand of energy and also it plays an important role in energy

conservation. Thermal energy can be stored as sensible heat or as latent heat. Sensible heat

storage is usually done in an insulated container containing a liquid like water or a porous solid in

the form of pebbles or rocks. The first type is preferred with liquid collectors, while the second

type is compatible with air heaters. In the case of latent heat storage, heat is stored in a substance


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called phase change material (PCM). When PCM melts heat is released; heat is extracted and

stored when the PCM substance freezes or initially being in solid state. Sensible heat storage

systems operate over a range of temperatures, while latent heat storage systems operate essentially

at the temperature at which the phase change takes place.

Other forms of storage are possible if the application involves some energy conversion

process. For example, from internal conversion engine mechanical work is being obtained after

conversion of thermal energy. Here also energy storage can be done using large sized flywheel.

Similarly electrical power can be stored and being obtained after conversion. Electric energy can be

stored in the form of electric batteries. Many types of electric batteries are used for the purpose; the

most common being is the lead-acid batteries.

1.2Applications of Thermal Energy storage (TES) systems:The thermal energy storage applications are-

- Water Heating

- Space Heating

- Cooking

- Drying etc.

The topic ofwater heating is considered for study and it is explained further.

1.2.1 Water Heating:Water heating is a thermodynamic process using an energy source to heat water above its

initial temperature. Typical domestic uses of hot water are for cooking, cleaning, bathing, and

space heating. In industry, both hot water and water heated to steam have many uses.

Domestically, water is traditionally heated in vessels known as water heaters, kettles, pots etc.

These metal vessels heat a batch of water but do not produce a continual supply of heated water at apreset temperature. The temperature of hot water varies based on the consumption rate of hot water,

use of hot water and the cooling rate of hot water. Appliances for providing a more-or-less

constant supply of hot water are variously known as water heaters, hot water storage tanks,

boilers, heat exchangers, or geysers depending on whether they are heating potable or non-

potable water, in domestic or industrial use, their energy source, and in which part of the world


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they are found. In domestic installations, potable water heater is used which is known as domestic

hot water (DHW). There are two types of water heaters one is storage hot water system and the

other is instantaneous or continuous hot water flow systems. Both the system can use a variety

of energy sources to heat water. In hot water storage system water is heated and stored in an

insulated tank for use when it is required. This storage of hot water systems can operate on mains

pressure and from gravity feed constant pressure tank. Mains pressure tank delivers hot water at

a similar pressure and flow rate to cold water so more than one outlet can usually be turned on

without greatly affecting pressure. The storage tank is usually located at ground level inside or

outside the house. Mains pressure systems have been the most popular systems in recent decades.

While Constant pressure or gravity feed system delivers hot water at lower than mains

pressure from a tank which is located above the ground level in domestic cases mostly in the roof

of the house. Pressure depends on the height difference between the tank and the point of use. It is

thermosyphonic type and based on the density difference of water, the water flows. They are often

cheaper to purchase and last longer than mains pressure systems. For either type of system, storage

tanks may be made ofcopper, glass (enamel) lined steel or stainless steel. Copper and glass-lined

tanks typically have a sacrificial anode to reduce tank corrosion, which needs to be replaced every

few years.

Instantaneous water heater systems heat the water only when it is required and do not use

a storage tank. They can operate on natural gas, LPG or electricity. Gas models are available

with either electronic ignition or a pilot flame. They can be mounted internally or externally.

The various energy sources for heating water are- Solar energy, Electricity, Natural gas, LPG,

Coal, Coke, wood etc.

1.2.2 Solar heating:

Due to concerns about the size of petroleum and natural gas reserves and also about the

environmental impact of the combustion of fossil fuels, the search for more sustainable resources to

provide alternate sources of energy is intensifying. Solar energy is one of the most important

sources of renewable energy and can be used to produce electricity and heat.

Sun is radiating energy in the form of heat and light. A dark colored material surface, when

exposed to sun, absorbs most of the heat and the material gets heated up. As a result there would be

rise in temperature of the associated material by way of conduction. Since the dark colored material


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has attained higher temperature than the surrounding air, it will exchange heat with the air by way

of convection. Again, as the dark material is exposed to the atmosphere, it will exchange heat with

the atmosphere by way of radiation. Solar domestic hot water (SDHW) storage system can

provide up to ninety percent of hot water for free using the Suns energy. Only thing is it is

dependent on climatic condition. Solar systems cost more to buy and install initially but the extra

upfront cost will be recovered over the life of the system through reduced energy bills. Solar

systems will take longer to recover their costs in smaller households, in cooler parts of the country,

or where access to sunlight is restricted.

Solar domestic hot water (SDHW) systems:

Using solar energy to provide domestic hot water is not a new idea. In certain countries

black painted water tanks have been used as simple solar water heaters for centuries. Today,

millions of modern solar water heaters are in use. Solar water heating technology has improved

greatly in recent years. For example, modern solar water heaters work even when the outside

temperature is well below freezing and they are protected from overheating on hot, sunny days.

Many models also have their own built-in, back-up heaters, which can meet all of a user's hot water

needs, even when there is no sunshine. Solar water heating can reduce the demand for conventional

fuels. This, in turn, can reduce damage to the environment and reduce the amount of money spent

on oil imports, exploration, and new electrical generating capacity.

Operation of the SDHW system:

Solar water heaters perform three basic operations-collection, transfer and storage. The

Solar radiation is collected and converted to heat energy by a solar collector. Collected heat

energy circulates hot fluid through the pipelines and transfers the heat to a storage tank either

using a heat exchanger, internally or externally to the storage tank or without a heat exchanger. The

hot water is stored until needed for domestic use. Fig. 1 shows a schematic diagram of the system

containing these components.


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Fig.1: Schematic diagram of SDHW system.

Operation of SDHW Storage Tank:

Normally the hot water storage tank is a vertical vessel made of steel which is used to store

thermal energy in terms of water to fulfill the domestic hot water demands in the bathroom, kitchen

and laundry. The operation of SDHW Storage tank mainly is of two types forced convection

SDHW Storage system and natural convection SDHW type. Again in forced convection SDHW

system there is either direct mixing type or indirect mixing type SDHW system. In direct mixing

type the hot water enters into the tank normally from top or from top side of the tank from the solar

collector and cold make up water from the bottom of the tank. The required hot water is also

removed from the top or top side of the tank while the cold recyclable water is removed from the

bottom of the tank and proceeds towards the solar collector for heating and after heating to enter

into the tank due to lighter density of hot water. Here in direct mixing there is no involvement of

heat exchanger to exchange heat. In case of indirect mixing type the hot water from the solar


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collector enters into the tank through a heat exchanger it may shell and tube type or spiral coil type

or of mental tank. There is no direct contact of hot water of collector and the cold water of the tank.

The hot water remains within the heat exchanger itself and due to that more thermal stratification

within the tank can be achieved. Due to advantages of achieving more thermal stratification in the

tank, the indirect mixing heat exchanger type hot water tank is preferred. But only thing is there is

additional cost of heat exchanger and piping is increased. Natural convection SDHW storage

system is also called as thermosyphonic type storage tank as there is no involvement of pump in

this system to supply hot water into the tank. It works based on the temperature and density

difference of water, as the water gets heated up it becomes lighter and it rises up automatically and

enters into the top of the tank, while cold denser water from the bottom of the tank fills the empty

space within the collector and collector piping. Additional electric heater also can be placed inside

the tank to worm water during the summer season while sunlight is unavailable or at the night

while the stored hot water is not sufficient hot or to supply more extra demand of hot water.

1.3 Thermal Stratification:

Thermal stratification is a phenomenon of liquid and water in which cold water zone

remains at the bottom and hot water zone remains at the top of the water level due to density

difference. Along with cold zone and hot zone, there is one barrier zone also in between them,

which is called as thermocline zone. In the thermocline zone there is a gradient of temperature dueto heat transfer from hot and cold water. This thermal stratification of water is a natural

phenomenon in the pond, lake, river, sea and ocean. During day time while Sun light falls on the

top surface of the water in the lake, river, ocean etc., water gets heated up and maintains hot water

zone for a particular depth. Cold water zone remains at the bottom of the water level bed. This is

how the thermal stratification formed naturally in the water reservoir or sea or ocean. Fig.2

illustrates the natural thermal stratification in the ocean, river, lake, etc.


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Fig.2: Schematic diagram of natural thermal stratification of river and ocean water.

Thermal Stratification of water in the SDHW Storage Tank:

Due to gravitational effect and the buoyant force of liquid, a high-density fluid or cold

water will settle at the lower part of a tank and a low-density fluid or hot water at the upper part of

the storage tank. A thermal barrier available between a hot zone to a cold zone inside the tank and

maintains the stable vertical temperature or density gradient. This barrier region between hot and

cold region is called as Thermocline. The combination of all these three zones namely hot zone,

cold zone and thermocline zone is known as Thermal Stratification of tank. This thermal

stratification of water inside the tank is desired. Also the thermocline thickness should be less as

much as possible. Water is having the tendency to stratify naturally. Fig.2 represents the thermal

stratification of water as a natural behavior of water in the lake, ocean or river. While Fig.3illustrates the thermal stratification of water in the SDHW storage tank. It also illustrates the

thermocline movement up and down due to inlet and outlet of hot and cold water. The significance

and the movement of thermocline behavior in the storage tank can be better visualized from the

Fig.4.


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Fig.3: Schematic diagram of thermal stratification of water in the SDHW storage

tank.


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a)

b)

c)

Fig. 4: Different levels of stratification within storage tank with equivalent stored energy

(a) highly stratified, (b) moderately stratified and (c) a fully mixed, unstratified storage

tank.


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Importance of thermal stratification:

Thermal stratification allows an optimal use of the stored thermal energy with minimized

heat losses. It also ensures that the collector inlet temperature is as low as possible. High degree of

thermal stratification increases thermal performance of solar hot water systems because return

temperature to the solar collector is lower from the lower part of the tank. A lower return

temperature to the solar collector will increase the efficiency of the solar collector.

Necessary requirements to achieve thermal stratification:

Stable thermal stratification within the tank can be achieved by various means. It can be

achieved by a large aspect ratio (H/D); advisable is in between 3 and 4 to enhance storage tank

performance. A good thermal stratification can be achieved by charging the tank from the top of the

tank or from the top side of the tank with an inlet temperature much higher than the surrounding

water temperature. Moreover, injecting at low flow rate does not disturb cold store water in the

lower part of the tank and hence a thermal stratification can be easily maintained.

Degradation of thermal stratification (destratification):

The process of thermal energy transfer from the storage tank which affects the thermal

stratification of tank leads to degradation of thermal stratification of tank. Such thermal energy

transfers are- convective input and output flows, water and envelop conduction, Convective

exchange between water and envelop and envelop and surrounding, radiative exchange between

external envelop or walls, heat losses to ambient through the tank envelope, heat conduction from

the hot layer to cold layer. Vertical conduction in the tank wall, which losses heat to the

environment and produces convective currents that promote mixing and influences destratification

of tank through walls of the tank, even though tank is insulated as there is no such insulating

material which is hundred percent heat resistant proof. Fig. 5 explains the destratification factors.

The degradation of thermal stratification can be reduced but it cannot be designed for perfectly

100% stratified tank. By controlling the temperature difference of upper and lower tank water

volume (hot and cold water temperature) that is by maintaining a constant different hot and cold

temperature zone, thermal destratification can be controlled. Optimum insulation thickness to the


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tank and all tank attachments helps to reduce destratification. Choosing a right type of insulation is

also a cause to avoid destratification of tank.

Fig. 5: Destratification Factors.

Thermocline thickness development:

Thermocline thickness develops in the tank due to natural convection of hot and cold zone

in the tank. Also the thermocline thickness develops due to continuous inflow of hot and cold

liquid in the tank. The thickness of thermocline indicates the extent of mixing occurred due to

inflow streams during the cycle. This thermocline thickness is not desired one. But it cannot be

avoided and no such design of tank can be done without thermocline thickness development.

Thermocline thickness is determined based on water temperature distribution inside the tank. In the

stratified water tank the water temperature distribution profile formed could move either upward or

downward during charging or discharging cycles of water.


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Importance of thermocline thickness:

Thermocline thickness influences the degradation of stratification which leads to the heat

transfer losses from the tank. So a thinner thermocline thickness is desired since a thicker

thermocline thickness indicates larger degradation of stratification which is not the desired one.

This thermocline thickness indicates extent of mixing occurred. The development of thermocline

thickness is not required but it cannot be eliminated also fully, only we can reduce the thermocline

thickness up to some extent.

Investigation of thermal stratification and thermocline thickness:

The methods to assess performance in hot water thermal energy storage (TES) and

thermocline movement can be by using- experimental, analytical and numerical modeling.

Experimental methods are quite costly. While analytical models needs extensive assumptions

which render models incomplete but it is necessary as assumptions helps to avoid complication of

equations and easier to solve. Therefore there has been a growing need for numerical models to

describe TES systems, thereby allowing computational methods to help in solving governing

equations. Most fluid flow and heat transfer problems can be solved by using commercially

available numerical software and computational codes. These are mainly of two types- finite

element methods (FEMs) and finite volume methods (FVMs). The FEM divides the domain into

a number of elements or nodes (points), while the FVM separates the domain into volumes or cells.

Both the methods use various techniques in order to achieve convergence. The FVM has been used

extensively in computational fluid dynamics (CFD), since its conservative nature allows for a

good simulation of many fluid flow phenomena. There are several commercial CFD codes present

in the market like Ansys, CFX, and Fluent etc. In the present study of TES tank CFD Fluent 10.0

code used as a solver.


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1.4 Introduction to CFD:

Computational fluid dynamics (CFD) is a computer based tool for simulating the behavior

of system involving fluid flow, heat transfer and other related physical process. It works by solving

the equation of fluid flow over the region of interest with specified condition on the boundary of

that region. CFD implements a variety of technologies including mathematics, computer science,

engineering and physics, this discipline have to be brought together to provide the meaning of

modeling fluid flows.

CFD solvers are generally based on the finite volume method. Domain is discretized onto a

finite set of control volumes (or cells). General conservation (transport) equations for mass,

momentum, energy, species, etc. are solved on this set of control volumes. Partial differential

equations are discretized into a system of algebraic equations. All algebraic equations are then

solved numerically to render the solution field. Fluid region of pipe flow is discredited into a finite

set of control volumes (mesh).

Fig. 6: control volume

1.4.1 Applications of CFD:

CFD is useful in a wide variety of applications and here we note a few to give you an idea

of its use in industry. The simulations shown below have been performed using the FLUENT

software. CFD can be used to simulate the flow over a vehicle. For instance, it can be used to study

the interaction of propellers or rotors with the aircraft fuselage the following figure shows the

prediction of the pressure field induced by the interaction of the rotor with a helicopter fuselage in


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forward flight. Rotors and propellers can be represented with models of varying complexity. The

temperature distribution obtained from a CFD analysis of a mixing manifold is shown below. This

mixing manifold is part of the passenger cabin ventilation system on the Boeing 767. The CFD

analysis showed the effectiveness of a simpler manifold design without the need for field testing.

Bio-medical engineering is a rapidly growing field and uses CFD to study the circulatory and

respiratory systems. The following figure shows pressure contours and a cutaway view that reveals

velocity vectors in a blood pump that assumes the role of heart in open-heart surgery.

CFD is attractive to industry since it is more cost-effective than physical testing. However, one

must note that complex flow simulations are challenging and error-prone and it takes a lot of

engineering expertise to obtain validated solutions.

A CFD technique is powerful and spans a wide range of industrial and non industrial

application areas. It is also used by engineers and scientist in a wide range of fields. Typical

applications include:

Process industry : mixing vessels , chemical reactors Building services: ventilation of building, such as atria. Health and safety : investigating the effects of fire and smoke Motor industries: combustion modeling, car aerodynamics. Turbo machinery: flow inside rotating passages, nozzles, diffusers etc. Electrical and electronics: heat transfer within and around circuit boards, transformers and

other electrical appliances.

Environmental: dispersion of pollutants in air or water.

1.4.2 CFD methodology:

The basic procedure followed for solving any CFD problem is.

1. The geometry (physical bounds) of the problem is defined.2. The volume occupied by the fluid is divided into discrete cells (the mesh).

3. The physical modeling is defined - for example, the equations of motions + enthalpy +

species conservation.


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4. Boundary conditions are defined. This involves specifying the fluid behavior and properties

at the boundaries of the problem. For transient problems, the initial conditions are also

defined.

5. The equations are solved iteratively as a steady-state or transient case depending on the

physical situation.

6. Analysis and visualization of the resulting solution.

1.4.3 Processes in CFD:

Preprocessing Solving Post processing

Preprocessing:

This is the first step in building and analyzing a flow model. It includes building the model

within a computer-aided design (CAD) package, creating and applying a suitable computational

mesh, and entering the flow boundary conditions and fluid materials properties. There are used the

ICEM software for this purpose. CAD geometries are easily imported and adapted for CFD

solutions in ICEM.

Solving:

The CFD solver does the flow calculations and produces the results. There are four general-

purpose products: FLUENT, FloWizard, FIDAP, and POLYFLOW. There is used FLUENT CFD

code because it has extensive interactivity, so it can make changes to the analysis at any time

during the process. This saves time and enables to refine the designs more efficiently.

Post processing:

This is the final step in CFD analysis, and it involves the organization and interpretation of

the predicted flow data and the production of CFD images and animations. All of Fluent's software


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products include full post processing capabilities. Post processing tools enable to provide several

levels of reporting, so it can satisfy the needs in design process .

Fig.7: Basic Structure of FLUENT Solver.


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CHAPTER 2- LITERATURE REVIEW

2.1 Literature Review:

Numerous stratification performance measures have been proposed and no method is

widely accepted. The ideal case of stratification in the storage tank is when the hot and cold regions

are completely separate and the thermocline temperature gradient is infinite.

Lavan and Thompson (1977) experimentally studied thermally stratified hot water storage

tanks. The objective of their study was to determine a method of removing hot water from the

storage tank and adding cold water into it while maintaining a steep thermocline. The study had

concluded that improving the stratification of the stored water in solar energy systems can

significantly improve the collector and the system efficiency.

Sliwinski, et al. (1979) investigated the performance of stratified tanks during charging.

They found that the size of the region affected by jet mixing was a function of the Richardson

number (Ri). They concluded that stratification occurred at the storage inlet for Richardson

numbers as low as 0.24 and the degree of stratification was sensitive to the variation of the

Richardson number when the inverse of the Peclet number was low.

Jaluria and Gupta (1982) conducted an experimental study of the temperature decay in

thermally stratified water tank for solar energy storage. A tank was initially stratified by adding hot

water to the top of the cold fluid. It was found that the buoyancy-induced mixing that arose

maintained the upper layers essentially isothermal and gave rise to horizontal temperature

homogeneity in the water body. The decrease in the surface temperature was initially accompanied

by an increase in temperature in the bottom layers, followed by a decrease in temperature

throughout the water body at the later stages. The cooling process was found to depend strongly on

the initial temperature level and distribution.

Hollands and Lightstone (1989) reviewed low-flow, stratified-tank solar water heating

systems, to improve the solar collector efficiency. The authors stated that in a stratified tank the

interface between the hot and cold fluids would have zero thickness and deviations from this ideal

are clearly visible; however, in practice, destratification factors include inlet jet mixing, and plume

entrainment, and heat conduction and side losses can cause significant deviations from the ideal

stratification.


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Zurigat, et al. (1991) performed an analytical and an experimental investigation on the influence

of inlet geometry on mixing in stratified thermal energy storage. The authors found that the inlet

geometry had a significant influence on the thermal stratification in a storage tank for Richardson

numbers below 3.6 while the inlet geometry effect was negligible for Richardson numbers above 10.

A study by Al-Najem and El-Refaee (1997) concluded that the turbulent mixing (or eddy

conductivity) factor caused by hydrodynamic disturbances at the inlet and outlet ports of storage

tank played an important role in the performance of thermal stratification storage tanks. The

authors also investigated the tank inflow situations that included two configurations: the upper

inflow and the lower inflow. The authors found that the inlet hot water from the solar collector that

enters the tank from the top would easily build stratification, but colder inflow at the top of tank

would completely mix the temperature field inside the tank.

Eames and Norton (1998) performed a theoretical and experimental investigation into the

thermal performance of stratified hot water tanks. A finite volume based model was validated by

comparison with measured temperatures from a series of thirty-two experiments in which the inlet

velocity and temperature ranged between 25 to 90 mm/s and 11C to 52C, respectively, and

various permutations of inlet and outlet port locations and initial storage stratification profiles were

tested. A parametric analysis determined the effect of inlet and outlet port locations on storage

performance for a range of operating conditions. The effects of finite volume size on predicted

levels of entrainment and diffusion in the inlet region were reported. The results indicated that

storage tank charging was performed more efficiently for tall tanks with the inlet port near the top.

Andersen and Furbo (1999) measured mixing or destratification during hot water discharge

in solar tanks with different inlet designs. Based on measurements and on detailed simulation

models, the influence of mixing on the yearly thermal performance of solar storage tanks was

calculated. It was found that the decrease in the yearly thermal performance utilization of solar

energy was up to 23% due to mixing during hot water draw offs.

In the work done by Shah and Furbo (2003) the impact of the inlet design with different

baffle plates on the flow patterns in the tank were investigated using numerical method and

validated by experiments. A simple, straight pipe with no baffle, hemispherical baffle plate and a

large flat baffle plate were compared under different discharge times and flow rates (1 L/min or 10

L/min). The performance of the diffuser was characterized by the ability of the tank to maintain

stratification, when cold fluid was added to the tank. Entropy and availability analyses were used to


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evaluate the level of stratification. The results showed that the entropy changes and availability

changes in the storage during the draw-off were influenced by the Richardson number and initial

temperature difference between top and bottom of the tank.

Sensible cool thermal storage with chilled water as the storage medium is a widely used and

effective energy management technique that reduces energy cost through load shifting. John M et

al. (2004), performed parametric study of single pipe diffusers in stratified chilled water storage

tanks. The diffuser pipe is installed at the top of the tank from where hot water enters into the

storage tank. It was found that thermocline thickness used in the analysis of the data, a very large

range of thicknesses was obtained.

Altuntop, et al. (2005) studied the effect of using different baffles on thermal stratification

in a cylindrical hot water tank using various mathematical models. Later the findings were

validated by experimentation. Temperature distributions within the tank for 12 different baffles

were obtained. The results indicated that placing baffles in the tank provides better thermal

stratification compared to the no baffle case.

A CFD integrated analysis of a large-scale hot water seasonal heat store was numerically

studied by Panthalookaran et al. (2007), to identify the effects of aspect ratio, containment shape,

internal structures and containment size on their efficiency.

Numerical study of the aspect ratio effects on the stratification in water storage tanks

conducted by H. Aloui and C.Bouden, 2008. It was observed that the thermal performance of solar

heating systems is highly influenced by the thermal stratification in the heat storage. The purpose

of their study was to figure out the thermal stratification mechanism inside a water storage tank and

to study the influence of the aspect ratio and thereby to determine an optimum design of the tank.

Fan et al. (2009) did experimental and CFD analysis on thermal stratification in a hot water

tank established by heat loss from the tank. A vertical cylindrical hot water tank experimentally and

numerically investigated for thermal stratification and natural convection for standby periods. The

transient fluid flow and heat transfer in the tank during cooling caused by heat loss are investigated

by CFD calculations and by thermal measurements.

Temperature Profile and Thermocline Thickness of a stratified thermal energy storage tank

has been has been analyzed by Joko Waluyo et al. (2010). They have determined thermocline

thickness based on water temperature distribution inside the tank. The water temperature

distribution profile formed could move either upward or downward during charging or discharging


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cycles. Using continuous profile, thermocline thickness is accurately identified as asymptote

regions with limit points. Method used was discrete data of temperature distribution.

CFD analysis of a density dependent valve within a hot water system carried out by Helen

Smith et al. 2010. The purpose of the valve is to allow water to circulate within the system when

the temperature of the water rises above a critical valve. From Archimedes principle, a buoyancy

oat made from a given material will rise when below a critical temperature and sink when above a

critical temperature. Investigated the valves behavior under specific conditions to modulate the

flow rate and maximize thermal stratification of the renewable energy storage tank.

CFD solution and experimental testing of buoyancy driven convection caused by condensers

immersed in a water tank given by Z. Gao et al. In their study a straight and L shaped condenser

coils was used. However when the coil was built in an L shape, the water stratification

disappeared. Results from CFD simulation were compared with the experimental data and found to

be close to each other.

Michael et al. (2010) investigated Thermocline Movement Dynamics and Thermocline

Growth in Stratified Tanks for Heat Storage. An experimental and numerical study using a scale

model of an industrial stratified tank (aspect ratio 3.5) and a Perspex tank (aspect ratio 8.2) are

reported.

The height to diameter ratio (AR) is a factor that influences stratification. Abdul Jabbar et al.

(2011) did experimental study of temperature stratification in a thermal storage tank in the static

mode for different aspect ratios. Thermal behavior and stratification of hot water storage tank

during the stagnation or static mode investigated experimentally for three different aspect ratios

(AR) of the tank, namely 2, 1 and . They have concluded that a better thermal stratification can be

achieved by increasing the aspect ratio.

The paper Michael et al. has been taken for investigation. The transient analysis of static

stratified storage tank has been extended for better visualization and to capture thermocline growth

profile in insulated tank.


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Summary of Literature Review:

There is a great significance of thermal stratification in the hot water storage tank as the

efficiency of the sensible thermal energy storage system depends on the stratification of storage

tank. Stratification loss occurs due to thermocline movement which cannot be restricted. Various

studies and experiments performed on thermal stratification of storage tank. But no clear cut

investigations and results have been found on the thermocline movement within the storage tank

with adiabatic wall boundary condition at static mode. So for that it is decided to capture transient

behavior of thermocline movement on adiabatic wall storage tank at static mode condition.

2.2 Objective and Scope:

The objective of the project is to extend the transient state investigation on thermal

stratification and thermocline layer within the solar domestic hot water storage tank for longer

period of a week with available heating effect of hot water. Present work considers the static

stratified storage tank with insulation and without insulation. A real storage tank always provided

with some insulation to prolong the loss of thermal stratification. A transient study will be always

more useful and appropriate from practical point of view.

Realizing the importance of thermocline a thinner thermocline is desired since a thicker

thermocline indicates the larger degradation of stratification inside the storage tank. It is decided toinvestigate the problem at the fundamental level to predict its distinguishing features of

thermocline thickness and movement from zero time level to a time level of one hour. The

proposed work involves investigation of thermocline growth in the storage tank problem.

2.3 Methodology:

The methods carried out to solve the problem are as follows -

- Creating a model for the problem using ICEM Software.- Discritized the model using ICEM Software.- Solve the problem using Fluent 10.0 Software.


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CHAPTER 3- PROBLEM DEFINITION

3.1 Problem Definition:

Problem under the study contains a vertical hot water storage tank. The storage tank

contains 50% of cold water and 50% of hot water. Cold water is at the bottom of the tank and hot

water above the cold water. Temperature of cold and hot water are varied in between 20C and

80C. The Storage tank is at static mode, there is no inlet and outlet of energy that is heat and mass

that is water. Transient analysis of thermocline growth at the barrier region of cold and hot water is

carried out using commercial CFD Software. The walls of the tank are adiabatic wall. A schematic

of the model vertical cylindrical storage tank is as shown in Fig. 8. The storage tank is having

height of 1276mm, diameter 360mm and thickness 1.5mm. Inside the storage tank the water

experience heating and cooling process due to temperature gradient present there.

Fig.8: Schematic of the Hot Water Storage Tank under study.


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Selected cases for analysis:

The main outcome of this project is to investigate the thermal stratification of SDHW

storage tank and the thermocline movement and the effect of thermocline movement on thermal

stratification storage tank. Three different cases of adiabatic wall and nonadiabatic wall of SDHW

storage tank are selected for analysis. The cases selected are based on practical and theoretical

possibilities.

Case1:

In case1 SDHW storage tank is considered as an adiabatic wall and having with different

hot and cold water zone. Initial thermocline is set at 50% of the tank height. Hot water initial

temperature is 80C at the above of thermocline and cold water initial temperature is 20C below

the thermocline line. Heat diffusion occurred due to natural convection in between hot and cold

water zone are captured for transient state. Tank wall is theoretical adiabatic wall with no heat loss

from the tank walls and no heat generation from the walls.

Case2:







Case3:








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Case 4:

In case4 SDHW storage tank is considered as a nonadiabatic wall and having with

different hot and cold water zone. Tank wall is uninsulated, so heat loss from the tank wall and the

heat diffusion from thermocline line set at 50% of tank height are captured for transient state. Hot

zone is at 80 while cold water is at 20 in between thermocline layer is set at 50% of tank

height from where thermocline growth occurs.

Case 5: with nonadiabatic wall condition of storage tank:

In case5 also SDHW storage tank is considered as a nonadiabatic wall. Natural heat

convection occurs from the uninsulated walls of the tank are captured for unsteady condition, while

the entire tank is filled with a constant hot water temperature of 90.

3.2 Governing equations:

All of CFD, in one form or another, is based on the fundamental governing equations of

fluid dynamics the continuity, momentum and energy equations. They are the mathematical

statements of three fundamental physical principles upon which all of fluid dynamics is based:

1. Mass is conserved. (Continuity equations)2. Energy is conserved. (Energy equation)3. Momentum equation. (Newtons second law of motion)

3.2.1 Continuity equation:

Unsteady 2-D mass conservation or continuity equation for tank incompressible fluid which

is water is given by-

u

x+

v

y= 0 (1)


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3.2.2 Energy equation:

The energy equation is derived from the first law of thermodynamics which states that a

rate of change of energy of a fluid particle is equal to the rate of heat addition to the fluid particle.

+ v

=

(2)

3.2.3 Momentum equation:

Newton second law states that the rate of change of momentum of a fluid particle equals to

the sum of forces on the particle.

+v

=

2

(3)

3.3 Boundary conditions:

The wall of the tank is considered as an adiabatic wall while the tank is insulated and

nonadiabatic wall while tank is considered as uninsulated tank. Inside the tank fluid is water. The

temperature of water inside the tank considered as hot water at the top half portion of the tank at

80 while bottom half of the tank is considered as cold room water temperature at 20. Central

part of the tank is considered as perfect thermocline and later on thermocline thickness increases

due to natural diffusion of hot and cold water temperature. The implied boundary conditions are

illustrated in the Fig.19. For case1 of insulated wall the boundary condition given as adiabatic wall,

the wall is given as stationary wall with no slip. Also under thermal condition of the wall it is given

as no heat flux and no heat generation within the wall. In case2 the tank is uninsulated wall, the

boundary condition given for wall is nonadiabatic stationary wall. Under thermal boundary

condition from the wall, natural convection is given. Natural convection heat transfer co-efficient

(h) from wall to the atmospheric air is given as 10w/m2k and free stream atmospheric temperature

(T) given as 20 (293k). No heat generation from the wall. Wall thickness considered as 1.5mm.

Inside fluid is water having different temperatures of hot and cold above and below the set

thermocline line. Hot water temperature applied as 80 above the thermocline line and cold water

temperature is 20 below the thermocline line.Case3 is also nonadiabatic wall with all the

boundary conditions given for nonadiabatic wall in case2. Only thing is the inside fluid which is

water is considered at a same uniform temperature throughout the tank as 90. Water temperature

drop from inside the tank and heat convection from all the four walls to be calculated.


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CHAPTER.4. NUMERICAL IMPLIMENTATION

4.1 Computational domain:

Chosen computational domain contains a two dimensional rectangular area. The storage

tank geometry is simple and inside the tank water temperature is symmetric from the centre of the

tank, so two dimensional domain is considered instead of three dimensional domain. It is also quite

easier to make two dimensional domain, to choose and create mesh in two dimensional, and also to

check the domain than three dimensional domain. Inside the computational domain there is 50%

cold water and remaining 50% is filled with hot water. The percentage of hot and cold water varied

for different cases but the domain area is fixed where the CFD investigation is done. Also there is

one case considered in which the entire tank is filled with full hot water. Fig.9 shows the

computational domain.

Dimensions: Height = 1276mm

Width = 360mm

Fig.9: Computational Domain.


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4.2 Mesh:

The dimensions of initial model have been taken for analysis from Fig.8 of problem

definition. By using the dimensions from the considered model, the geometry has been created in

ICEM. The standard commands like point, arc, and mesh are used to create the complete geometry.

Meshing also known as grid generation, is a discretization of model into smaller regions

called as grids or elements. Generated grid has a significant effect on rate of convergence (or even

lack of convergence), accuracy and computation time. So it is important to select appropriate

elements type, meshing scheme and grid density. When we mesh any topological entity (except

vertex), ICEM creates mesh nodes throughout it according to the specified meshing parameters like

meshing scheme, spacing between nodes etc. The main task in meshing was to create a complete

orthogonal structure grid. In meshing model scheme, hexahedral map meshing is used. The

complete two dimensional coarse mesh model of mesh size 18360 is as shown in the Fig.10 to

describe how the mesh is created for complete model. The same domain mesh size is refined for

very fine mesh of mesh size 73,440. After grid independent test with eight different grids and out

of that four grids those are giving the similar results and coinciding with the results of each other

are accepted. Very fine mesh of mesh size 36,780 is used in the following simulations. Table 1

gives the details of domain and grid size. While Fig. 10 shows the pictorial view of CFD meshed

model of the computational domain.

Table 1: Mesh information

Domain Number of Grids

Storage Tank 18,360


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Fig.10: Complete 2-D view of Coarse Mesh size is 18,360.


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4.3 Problem and Solution Setup in Fluent 6.3:

To obtain correct converged results by the Fluent 6.0 software for the various cases of the

selected problem some problem and solution setups are done. Those are further explained as

Problem setup:Software need problem data set up is configured as per different cases of problem.

Basically problem consists of solid area in which incompressible fluid water is there. Pressure

based solver is selected to solve transient heat transfer of selected incompressible fluid. CFD

implicit scheme is adopted to solve the problem. The geometry of the problem is 2 dimensional.

Unsteady temperature behavior of water need to be obtained from the problem. All such problem

setup data is tabulated in the Table 2. The properties of water at a temperature of 27 are also

listed down in Table 3.

Table 2: Problem Setup

Sr. NoDefine problem Setup

OptionsProblem Setup Adopted

01 Solver Pressure Based Solver

02 Formulation Implicit

03 Spatial discretization 2D

04 Temporal discretization unsteady

05 Fluid Material water

06 Cell zone material water


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Table 3: Properties of water

Property Value

Specific heat 4187.7 J / kg. k

Dynamic viscosity, ( ) 0.000653 kg / m. s

Thermal expansion, ( ) 0.003 k-1

Density, ( ) 997.044 kg / m3

Thermal conductivity, (k) 0.618 w/m k.

Solution setup:

Natural-convection flow is modeled with Boussinesq approximation during CFD

simulation. The buoyancy for an incompressible fluid with constant fluid properties is modeled by

using the Boussinesq approximation in ANSYS FLUENT 6.3. The model uses a constant density

fluid model but applies a local gravitational body force throughout the physical domain which is a

linear function of the fluid thermal expansion coefficient () and the local temperature differencerelative to a datum called the buoyancy reference temperature. The Boussinesq approximation

models the change in density using eq.4.

( ref) = ref. (T Tref) (4)

Where, Tis the local temperature in K,

Trefis the buoyancy reference temperature in K,

is the thermal expansion coefficient in K-1,

refis the density of water in kg/m3 and

is the local density in kg/m3

A zero velocity field is assumed at the start of all simulations. The calculation is considered

convergent for the continuity equation, the momentum equations and energy equations. The


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simulation runs with a time step of 1second and a duration of 1 hour and 24 hours. Table 3 gives

solution control and solution setup.

Table 4: Solution Setup

Sr. No Solution Control Parameters Solution Setup Adopted

01 Pressure PRESTO and SIMPLE

02 Energy equation activation Second Order Upwind

03 Momentum equation activation Second Order Upwind

04 Time step 01s

Relaxation:

Each of the variables (mass, moment, density) represents an equation the solver is trying to

solve. Each iteration values obtained for the variables should get closer and closer together.

Relaxation factors make solution take a lot longer to converge. Because of the nonlinearity of the

equation set being solved by FLUENT, it is necessary to control the change of. This is typically

achieved by under-relaxation, which reduces the change of produced during each iteration. In a

simple form, the new value of the variable within a cell depends upon the old value, old, the

computed change in , , and the under-relaxation factor, , as follows:

= old + (5)

The relaxation settings are tabulated in Table 4.


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Table 5: Relaxation settings in Fluent

Variable Relaxation Factor

Pressure 0.30

Density 1.0

Body Forces 1.0

Momentum 0.70

Energy 1.0

Boundary conditions:

The equations relating to fluid flow can be closed (numerically) by the specification of

conditions on the external boundaries of a domain. It is the boundary conditions that produce

different solutions for a given geometry and set of physical models. Hence boundary conditions

determine to a large extent the characteristics of the solution we obtain. Therefore, it is important to

set boundary conditions that accurately reflect the real situation to obtain accurate results. Various

boundary conditions as per need applied to the problem cases are tabulated in the table 3.


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Table 6: Boundary conditions applied to various cases

Sr.

No

Boundary

ConditionsCase 01 Case 02 Case 03 Case 04 Case 05

01 Adiabaticwall

Yes Yes Yes No No

02

Thermocline

set within the

tank height

Thermocline

set at 50% of

tank heightThermocline

set at 80% of


set at 20% of


set at 50% of

tank heightWhole tank

is at constant

temp

03Initial Hot

water temp80 80 80 80 90

04Initial Cold

water temp20 20 20 20 No coldwater inside

the tank

05

Free stream

air temp (T)---------- ---------- ---------- 293 K 293 K


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Fig. 11: Boundary conditions applied to Case 1 Fig. 12: Boundary conditions applied to Case 2


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Fig. 13: Boundary conditions applied to Case 3 Fig. 14: Boundary conditions implied to Case 4


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Fig.15: Boundary conditions implied to Case 5.


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4.4 Grid independent test:

Investigations are carried out to detect the optimal time step and grid density. To check grid

independence, six different sizes of grids viz., 12,680, 18,360, 22,236, 36,780, 45,090 and 73,440

are taken. These entire six grid mesh domain are simulated for one hour. The thermocline thickness

developed in grid number 12,680, 18,360, 22,236, 36,780, 45,090 and 73,440 are 550mm, 600mm,

550mm, 600mm, 550mm and 400mm respectively. The values of thermocline thickness developed

for one hour simulation from the central point of the tank and the grid numbers of the mesh are

plotted in a graph to compare the results of thermocline thickness developed by different grid

numbers. From the plotted graph it is found that the grid size 18,360 and 36,780 are grid

independent. The grid number 18,360 is used for all the cases. Fig.16 represents pictorial view of

grid independent test result.

Fig.16: Grid independent test

0

100

200

300

400

500

600

700

0 10000 20000 30000 40000 50000 60000 70000 80000

Thermoclinethicknessinmm

Grid Size

Grid indepentent test result


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CHAPTER 5: RESULTS AND DISCUSSION

5.0 Results and Discussion:

Present work uses ICEM for solid modeling and meshing purpose. Fluent 6.3 has been used

as solver. The investigation starts with grid sensitivity test and obtained simulated results has been

validated with the available experimental and CFD data. The work contains a parametric study of

thermocline thickness. Fig.17 is the computational model of storage tank in which thermocline is

set at the centre of the tank in between cold and hot water for zero time intervals. From here the

further unsteady analysis is carried out at a time interval of one hour. CFD Simulated results are

illustrated in the Fig. 18 for a time interval of one hour. Graphical representation of thermocline

movement of temperature v/s tank height of every after one hour and up to seven hours are plotted

together for comparison and better visualization of changes in thermocline growth in Fig.19 and

Fig.20.The three different thermocline set in the storage tank based on the tank height those are at

50% of tank height, 80% of tank height and 20% of tank height and thermocline growth are

recorded using CFD Software. The thermocline at 50% of tank height is the best as far as the

thermal efficiency of the storage tank is considered. Considering the same we had simulated and

extended the transient time thermocline movement at 50% of tank height. The results are validated

with the experimental and CFD results of Michael et al. (2010) and grid independence test alsobeen done. As it was found that the 50% thermocline set up is the best one for the optimal thermal

stratification of storage tank is concerned at static mode so with this intension, for better

visualization and identification of fully mixed unstratified uniform temperature for an optimum

time period simulation has been extended. Also the effects on thermocline by varying different

temperature is simulated and recorded. The simulated results shows that the movement of

thermocline at initial time is more as compared to same in later time because of decrease in thermal

gradient. The results are validated with the experimental and CFD results of Michael et al. (2010).

Simulation is extended for more time period of increased hours and for a week to note done the

change in stratification from highly stratified tank to moderately stratified tank and then mixed

unstratified storage tank.


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5.1 Temperature contours:

In this section contours of temperature for all the cases are shown. For each case figure are

shown which gives information about temperature contour and change in thermocline behavior. A

contour line (also isoclines) is a function of variables is a curve along which the function has a

constant value.

Fig.17: Computational Model of Storage Tank at a time interval of 00hr.

Case 01 CFD Result:

Transient analysis of the case1 is carried out. The analysis is validated with the

experimental and CFD results and then extended for a day and also for a week to find out the

thermocline behavioral change as the time increases. The result includes the temperature contours

and height v/s temperature plots for the thermocline growth from initial thermocline set at 50% of

the tank. Fig.18 includes transient temperature contour from initial 00 hours time period to seven


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hours time period. The Fig. 19 illustrates plots of temperature along a line drawn in the centre of

geometry of storage tank (vertical line) for different time steps, thermocline set at 50% of tank

height. The Fig.19 shows that the x-abscissa temperature along the y-co-ordinate that is distance

from the bottom of the storage tank changes nears the thermocline. In this graph it can be seen very

easily that the movement of thermocline is faster at the initial times. Just to have a better

visualization Fig.20 shows a section of Fig.19.


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Fig. a: Case 01 Temp Contour after 00hrs. Fig. b: Case 01 Temp Contour after 01hrs

Fig. c: Case 01 Temp Contour after 04 hrs. Fig d: Case 01 Temp Contour after 07 hrs.

Fig.18: Case 01Transient temperature contour at 50% of tank height


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Fig.19: Case 01 Transient behavior of Temperature profile v/s height of tank.

Fig. 20: Better visualization of thermocline plots of case 01.


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Case 02 CFD Results:

In this case initial thermocline height set, is changed from 50% of tank height to 80% of

tank height. Transient temperature contours are shown in Fig.17 and plots of tank height v/s

temperature are plotted in Fig.18. Due to lesser volume of hot water and the buoyancy effect of

water the initial thermocline thickness moved downward. Thermal stratification of water in the tank

looses after a period of 24 hours and the entire tank water temperature becomes mixed uniform

temperature of 38.


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Fig. a: Case 02 Temp Contour after 00 sec Fig. b: Case 02 Temp Contour after 60 sec.

Fig. c: Case 02 Temp Contour after 05 mints. Fig. d: Case 02 Temp Contour after 01 hrs.

Fig. 21: Case 02 Transient behavior of Temperature profile v/s height of tank.


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Fig. 22: Case 02 Comparison plots of temperature profile.


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Similarly like case2 in this case the initial thermocline height set, is changed from 50% of

tank height to 20% of tank height. Temperature contours and tank height v/s temperature plots for

transient state are illustrated in Fig. 23 and Fig. 24 respectively. It takes more time to lose thermal

stratification of water. After of 48 hours uniform mixed constant hot water temperature of 62 is

formed throughout the tank height. Thermocline thickness shifted upward and bottom cold water

became hotter.


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Fig. a: Case 03 Temp Contour after 00 sec Fig. b: Case 03 Temp Contour after 60 sec.

Fig. c: Case 03 Temp Contour after 05 mints. Fig. d: Case 03 Temp Contour after 01 hr.

Fig. 23: Case 03 Transient behavior of Temperature profile v/s height of tank.


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Fig. 24: Case 03 Comparison plot of temperature profile.


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This case is also similar like case 01only thing is that the tank is uninsulated. The main

intension to investigate this case is to capture heat diffusion effect internally in between hot and

cold water zone and along with that natural convection heat loss due to uninsulation of tank from

the tank walls. Thermocline is set at the centre of the tank that is at 50% of tank height but the tank

considered is uninsulated and so natural convection heat loss occurs to the atmosphere through

walls of the tank. Such study of heat loss from uninsulated tank can be utilized to slightly worm the

room temperature during winter season. Hot and cold water zone temperatures taken as 80 and

20 respectively. The buoyancy driven flow in this stratified tank is investigated. Fig. 25

represents temperature profile in the tank at 3 hours after the start. At the upper part of the tank

there is a uniform temperature of approximately 87 while the water temperature at the bottom of

the tank is almost constant at 20. In the middle part of the tank there is a strong thermal

stratification of increased temperature approximately 59 from 0.58m height to 1.25m height of

the tank. From Fig. 26 and Fig. 27 it is observed that there is a downward flow of up to 0.0069 m/s

along the tank wall at the height of 1.25m. It is also found that water in the central parts of the tank

is flowing downwards and upwards due to the heat loss from the top of the tank. At the height of

0.638m, there is very weak downward flow due to presence of more hot water at the top of the

tank. At 0.58m height, there is a weak upward flow close to the tank wall. The rising flow has the

magnitude of approximately 0.004 m/s. that means there is a negative heat loss of the tank which

heats up the fluid adjacent to the wall, creating upward flow. At the lower part of the tank a strong

thermal stratification exists with a colder water of 20 from 0.58 meter height to the bottom of the

tank. Fig. 28 and Fig. 29 represent plots of tank height v/s tank temperature profile from 1hour to 7

hours and from 1 day to 7days respectively. After of 6 days onwards thermal stratification

disappears and forms a constant cold water temperature of 10.


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Fig. 25: Case 04 CFD calculated temperature profile in the tank.

Fig. 26: Case 04 CFD calculated temperature profile at different heights of the tank.


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Fig. 27: Case 04 CFD calculated velocity profile at different heights of the tank.

Fig. 28: Case 04 Comparison plots of temperature profile at one hour interval.


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Fig. 29: Case 4 Comparison plots of temperature profile at 24 hours interval.

Case 5 CFD Result:

The tank is full of hot water. Hot water initialize temperature taken is 90. The transient

behavior of heat and temperature of water due to heat flow inside the tank and heat loss to the

atmosphere due to uninsulation of wall are captured. The measurements of temperature of water are

started with an initial uniform tank water temperature of 90. Due to uninsulation of tank the heat

loss from the tank walls started. Such heat loss can be utilized to slightly worm the room

temperature during the winter season. The tank inside temperature is initially 90 which is

constant and uniform throughout the entire tank. The ambient air temperature is 20. Heat transfer

co-efficient of air is 20 w/m2k. Natural convection heat loss occurs due to uninsulation of tank,

which is exposed to the ambient air to raise the room air temperature during winter season. After 1

hour, the water temperature at the top and the middle parts of the tank is uniformly 87.25. There

is a gradual decrease of temperature from 87.25 to 85.5 from the tank height of 1.2m. The

maximum temperature difference between the top and bottom of the tank is noted as 4.5.

Temperature after 6 hours decreases to 72 at the top part of the tank, while the temperature water


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at the bottom of the tank decreases to 62. The temperature difference between tank top and the

tank bottom increases to 10. After 24 hours from the start of simulation, the water temperature at

the bottom of the tank decreased down to 38. Constant isothermal tank water gets gradually

stratified with respect to time, as the cold water flows down along the tank wall. The heat loss of

water from the walls of the uninsulated water tank gets settled down at the lower part of the tank.

The validity of the CFD model for an initial condition a tank filled with water at constant

temperature is investigated well and validated with the experimental and CFD results of Fan J. and

Furbo S.

Fig. 30: Case 05 CFD calculated water temperatures in the tank with initially uniform

temperature.


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The tank is left to be cooled down with an ambient air temperature of 20. The initial

temperature profile at the start of the measurement is as shown in Fig. 30. It can be seen that the

CFD model predicts well the water temperature at different times very accurately.

5.2 Buoyancy Driven Flow:

The buoyancy driven flow in the tank due to heat loss from the tank is investigated by CFD

calculations. The temperature profile of the tank were examined at 12 hours after the start of a

standby period for the tank with a uniform temperature of 90, refer Fig. 31. From Fig. 31 it is

observed that the water temperature is almost same from 1.10 meters height to the top of the tank.

There is a temperature decrease of 5 from 1.25m to 0.56m of tank height. At the bottom part of

the tank slowly thermal stratification occurs with a temperature decrease of 20 from 0.2m to the

bottom of tank. The CFD calculated temperatures and vertical fluid velocities at different heights of

the tank are shown in Fig. 32 and Fig. 33 respectively. Due to the relative lower temperature of

the fluid close to the tank wall, there is a downward flow with a vertical velocity of up to 0.005

m/s. In the bulk of the tank there are two flow circulations which bring fluid of lower temperature

downwards and fluid of higher temperature upwards. The strong flow circulation is caused by the

heat loss from the top of the tank. At 2/3rd of tank height (0.8m), the fluid temperature drops to

82 in the tank boundaries. In the area close to the tank wall the fluid flows downwards with a

velocity slightly higher than the fluid at the height of 1.25m. At 1/3rd of tank bottom height, the

downward flow slows down with a velocity of 0.002m/s due to the presence of thermal

stratification in the tank. In the middle of the tank there is an upward flow of -0.0005m/s which

means that the warmer fluid rises up. Fig. 34 shows the vertical fluid velocity profile at 0.38m

from the bottom of the tank as the tank water is cooling down. It is observed that the maximum

downward flow is 0.009 m/s at 01 hour after the start. The buoyancy driven flow gradually

decreases to 0.004 m/s. That means there is decreasing of temperature and increasing of thermal

stratification of water inside the tank.


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Fig. 31: Case 05 CFD calculated temperature profile in the tank.

Fig. 32: Case 05CFD calculated temperature profile at different heights.


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Fig. 33: CFD calculated vertical fluid velocities at different heights.


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a)

b)

Fig. 34: CFD calculated vertical fluid velocities at different times.


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5.3 Heat loss from tank:

As the case 05 is uninsulated, so heat loss takes place from the walls. The heat loss is

calculated by using heat transfer equations. To analyze the magnitude of the buoyancy driven flow

and the influence of the flow on thermal stratification, the tank is equally divided into a number of

layers (N=10). The divided parts are numbered sequentially from the bottom to the top of the tank

refer Fig. 35. Heat loss from the side of the layer I is defined as Q loss(I). It is calculated based on

traditional heat transfer theory. The heat loss moving from the layer above (I+1) to the layer (I)

due to the buoyancy driven flow which is defined as Qflow(I). A heat loss removal factor a(I) for

surface I is defined as the ratio between the heat loss moved down by natural convection, refer eq.

6 and the total amount of heat loss of the layer. The heat loss of the layer includes both heat loss

from the side of the tank and the heat loss moved down from the layer above.

= . . (6)

Where,

h = Convective heat transfer co-efficient 20 w/m2 k

A = Area of each layer in m2

= Average temperature difference of each layer in 0C

T hot = Average hot water temperature in each layer

T cold = Ambient atmospheric temperature 200C

( ) =()

()()(7)

For the top layer N, the heat loss moving from the layer above is replaced by the heat loss from the

top of the tank.

( 1) =()

()(8)

Thermal stratification in the tank is characterized by a temperature gradient Gr(I).


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( ) =()()

()()(9)

Where Tlayer(I) is the average fluid temperature of layer I in k, while H layer(I) is the average height

of layer I in m measured from the bottom of the tank.

The heat loss removal factor a(I) is calculated for all the 9inter-layer surfaces and shown in Fig 35.

for a cooling test starting with a uniform tank water temperature of 90. At 3 hours after the start,

the temperature gradient, Gr(I) is very small for the most part of the tank,0.2-0.9K/m for the upper

7 inter-layer surfaces, showing that there is almost no thermal stratification at the middle and upper

parts of the tank. At the lower part of the tank the temperature gradient, Gr(I) increases to 2.4 K/m

and 16 K/m for the second and the first surface respectively, indicating thermal stratification at the

lower part of the tank. The heat loss removal factor is greatly influenced by the temperature

gradient at small values. a(I) is approximately 0.55, meaning is that 55% of the apparent heat loss

of the layer placed above the surface plus the heat loss transferred from the upper parts of the tank

to the layer placed above the surface is transferred down to the layer below the surface. At the

lower part of the tank, the heat loss removal factor drops to 0.16 and 0.08 for the second and first

surface respectively. It is the thermal stratification in the lower part of the tank that stops the cooled

water from flowing downwards. The heat loss removal factor is calculated for different time steps

and is shown in Fig.36. A tendency observed that the heat loss removal factor goes to a lower level

at the lower part of the tank as the time goes. It happens due to the gradual cooling down of the

tank and due to the thermal stratification established at the lower part of the tank.

The heat exchange between layers by natural convection is shown in Fig.37. At the upper

part of the tank the heat exchange between the layers is in the range of 4-16 W. as long as there is

no thermal stratification, the heat transferred upwards is equal to or higher than the calculated heat

loss from one layer (6-10.4 W from 1/10 of the tank side). While at the lower part of the tank the

heat exchange is significantly reduced to a value smaller than 1 W.

The heat exchange between layers for a stratified tank is given in Fig. 38. A heat

exchange of 4-11 W can be observed at the upper part of the tank. The heat exchange decrease

dramatically at the middle part of the tank when the temperature gradient increases from 10 to up to

130 K/m. The strong thermal stratification suppresses the buoyancy driven flow and therefore


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reduces the heat exchange by natural convection to a value lower than 1 W. the heat exchange is in

the range of (-0.15, 0.15) W at the lower part of the tank which could be due to disturbed flow of

the water. The heat loss removal factor is calculated for all the surfaces at different time steps with

a heat exchange higher than 1 W to obtain a good accuracy.

Fig. 35: Schematic diagram of a tank consisting of N layers.


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Fig. 36: The influence of stratification on heat loss removal factor for cooling starting with a

uniform temperature of 90 (case 05)

.

Fig. 37: The heat exchange between layers versus temperature gradient in the tank for

cooling with a uniform temperature of 90 (case 05)


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Fig. 38: The influence of stratification on heat loss removal factor for cooling in the stratified

tank (case 04)

Fig. 39: The heat exchange between layers versus temperature gradient in the stratified tank

Documents

Final Report Mainak Bhaumik - 26