Final Report Majorproject

8/11/2019 Final Report Majorproject

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CONTENTS

Declaration

Certificate

Acknowledgement

Contents

List of Figures

Nomenclature

Abstract

NOMENCLATURE ...................................................................................................... 10

1. INTRODUCTION .................................................................................................. 14

DIRECT AND INDIRECT REFRIGERATION SYSTEM .............................. 141.1

1.1.1. ADVANTAGES OF INDIRECT REFRIGERATION SYSTEMS ............ 15

1.1.2. DISADVANTAGES OF INDIRECT REFRIGERATION SYSTEMS ...... 16

1.2. NATURAL CIRCULATION LOOPS ............................................................. 16

1.2.1. ADVANTAGES OF NCL ........................................................................ 17

1.2.2. DISADVANTAGES OF NCL .................................................................. 17

1.3. NANOFLUIDS ............................................................................................... 18

1.3.1. ADVANTAGES OF NANOFLUID ......................................................... 19

1.3.2. DISADVANTAGE OF NANOFLUIDS ................................................... 19

1.4. OBJECTIVES ................................................................................................. 19

1.5. APPROACH ................................................................................................... 20

2. LITERATURE REVIEW ....................................................................................... 21


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2.1. NANOFLUIDS: .............................................................................................. 21

2.2. NANOFLUIDS BASED NATURAL CIRCULATION LOOP: ....................... 23

3. MODELS FOR TURBULENCE ANALYSIS-TRANSPORT EQUATIONS.......... 25

3.1. TRANSPORTATION EQUATIONS FOR STANDARD K- MODEL:......... 25

3.2. MODELLING TURBULENT VISCOSITY: ....................................................... 25

3.3. RNG k- EQUATIONS: ...................................................................................... 26

3.4. k- MIXTURE TURBULENCE MODELS..................................................... 28

3.5. k- DISPERSED TURBULENCE MODELS.................................................. 29

3.6. STANDARD k- MODEL:............................................................................. 30

3.7. Transport Equations for the SST k- Model.................................................... 31

3.8. TRANSPORT EQUATIONS FOR THE k-kl- MODEL:............................... 32

4. DESCRIPTION OF MULTIPHASE MODELS ...................................................... 33

4.1. THE MIXTURE MODEL ............................................................................... 33

4.1.1 OVERVIEW ............................................................................................ 33

4.1.2. LIMITATIONS ........................................................................................ 34

4.1.3. CONTINUITY EQUATION .................................................................... 35

4.1.4. MOMENTUM EQUATION ..................................................................... 36

4.1.5. ENERGY EQUATION ............................................................................ 36

4.1.6. RELATIVE SLIP VELOCITY AND THE DRIFT VELOCITY ............... 37

4.1.7. GRANULAR PROPERTIES .................................................................... 38

4.1.8. KINETIC VISCOSITY ............................................................................ 38

4.1.9. GRANULAR TEMPERATURE .............................................................. 38

4.1.10. INTERFACIAL AREA CONCENTRATION .......................................... 39

4.2. EULERIAN MODEL ...................................................................................... 41


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4.2.1. LIMITATION OF EULERIAN MODEL ................................................. 42

4.2.2. VOLUME OF FRACTION EQUATION ................................................. 42

4.2.3. EQUATIONS IN GENERAL FORM ....................................................... 43

4.3. VOLUME OF FLUID (VOF) MODEL THEORY ........................................... 47

4.3.1. OVERVIEW OF THE VOF MODEL: ...................................................... 47

4.3.2. LIMITATIONS OF THE VOF MODEL: ................................................. 47

4.3.3. STEADY-STATE AND TRANSIENT VOF CALCULATIONS: ............. 47

4.4. HOW TO CHOOSE A RIGHT MODEL? ....................................................... 51

5. PHYSICAL MODEL OF NCL ............................................................................... 53

5.1. PHYSICAL MODEL ...................................................................................... 53

5.2. GEOMETRIC AND MATERIAL SPECIFICATIONS FOR THE MODE ....... 53

5.3. GRID GENERATION ..................................................................................... 54

6. RESULTS .............................................................................................................. 55

6.1. COMPARITIVE STUDY OF DIFFERENT TURBULENT MODELS ............ 55

6.1.1. VALIDATION ......................................................................................... 58

6.1.2. INFERENCES ......................................................................................... 60

6.2. SIMULATIONS OF WATER BASED NANOFLUIDS (Results) ................... 61

6.2.1. ENHANCEMENT OF THERMAL CONDUCTIVITY AND HEAT

TRANSFER RATE. ............................................................................................... 61

6.2.2. VISCOSITY ............................................................................................. 62

6.2.3. MASS FLOW RATE VARIATION ......................................................... 62

6.2.4. VALIDATION ......................................................................................... 63

7. CONCLUSION ...................................................................................................... 66

8. FUTURE WORKS ................................................................................................. 67


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List of Figures

Fig 1: Indirect refrigeration system with forced circulation type secondary loop

Fig 2 : Rectangular NCL

Fig 3 : Which model chose

Fig.4 : Schematic of the Natural Circulation Loop employed in the model

Fig 5: Meshing of a cross section

Fig 6: Variation of heat transfer rate w.r.t temperature ()Fig 7: Variation of mass flow rate w.r.t temperature (

)

Fig 8: Variation of Turbulent intensity rate w.r.t temperature ()Fig 9 : Variation of turbulent kinetic energy transfer rate w.r.t temperature ()Fig 10 : Variation of Turbulent dissipation rate w.r.t temperature ()Fig 11 : Reynolds number v\s for various turbulence modelsFig 12: Specific heat variation of Co2 with Temperature

Fig 13 : Variation of Viscosity of Various nanofluids with Volume fraction

Fig 14 :Variation of the mass flow rate with Volume fraction

Fig 15 : Validation of Simulation results with Vijayans correlation(CuO)

Fig 16 : Validation of Simulation results with Vijayans correlation(Al2O3)

Fig 17 : Validation of Simulation results with Vijayans correlation(TiO2)


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NOMENCLATURE

generation of turbulence kinetic energy due to mean velocity gradientsAi,j cell face area of the u-control volume

CO2 carbon dioxide

d dimensionless channel gap width

D cross-diffusion term

Flength empirical correlation that controls the length of the transition region

Gb Generaration of turbulent kinetic energy due to buoyancy

gi component of the gravitational vector in theithdirection

kL laminar kinetic energy

kT turbulent kinetic energy

Pk is the production of kinetic energy

Pm dimensionless head pressure

Pr Prandlt number

Prt turbulent Prandtl number for energy (default value of Prt is 0.85)

Ra Rayleigh number

Rec critical Reynolds number

Rt transition Reynolds number

S modulus of the mean rate-of-strain tensor


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Skand Sare the source terms

T temperature, K

U dimensionless velocity alongX

V dimensionless velocity along Y

W loop width, m

X, Y dimensionless coordinates,X, Y

Yk,Y

dissipation of k and due to turbulence

thermal diffusivity, m2s-1

thermal expansion coefficient,K-1

kandeffective diffusivity for k and due to turbulence

dimensionless temperature difference

dimensionless time

inverse turbulent scale

vorticity magnitude momentum source term


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ABSTRACT

The growing popularity of nanofluid applications in diverse fields has drawn

attention of researchers to exploit its uses extensively. It is required to overcome the

drawbacks of conventional fluids in terms of heat and mass transfer, and explore this

field in order to find a working fluid having very good transport behaviour along with

sustainability. Stable suspension of nanofluids offers favourable features such as high

thermal conductivity at very low concentrations of nanoparticles. Nanoparticles do not

settle down quickly or damage the setup as in the case of micro-particle substrates, hence

overcomes the disadvantages of the latter. Nanofluids find applications in

microelectronics, nuclear reactor coolant and space technology as well.

This work presents the investigation of the behaviour of water based nanofluid

with cupric oxide and alumina as nanoparticles, which operates in a natural circulation

loop with isothermal source and sink under various operating conditions. This is

simulated in a commercial CFD software ANSYS (Fluent 14.5). The ability of

nanoparticles to drastically change the thermo-physical properties of fluids is utilized in

obtaining the desirable properties for the base fluid. The water based nanofluid isoperated in the natural circulation loop at different source and sink temperatures. Effect

of temperature variation on thermo physical properties of base fluid as well as

nanoparticles have been considered and suitable correlations [1]

are used to find thermo

physical properties of nanofluids. Boussinesq approximation has been employed in

energy equation to consider buoyancy effect caused by temperature difference. The K-

turbulence model is employed to catch the turbulence effects within the loop. Further

investigations are done on the effect of change in concentration of nanoparticles in the

base fluid. The results of the parameters such as heat transfer rate, friction factor and

pressure drop are noted and compared at every stage. Results show that there is increase

in heat transfer rate with increase in volume concentration of nanoparticles.


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Results obtained from simulation have been validated with published

experimental data[2]

and demonstrate good agreements. The results are compared for

different Rayleigh number and concentration of nano particles.

Keywords: Nanofluid, Natural circulation loop,CFD, Turbulence modelling.


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1.

INTRODUCTION

Due to an unprecedented improvement in technology, there has been rapidindustrial growth across the globe. This has also given rise to new concerns. In the

current scenario, global warming and ozone depletion have emerged as major source of

concern. Also the rising oil prices are a constant area of worry. The excess use of fossil

fuels is leading to their rapid exhaustion. Considering all these factors there is an urgent

need to make all the system energy efficient. Thermal systems like refrigerators consume

large amount of power. So, there is a large scope for development of nature friendly and

efficient refrigerants. Synthetic refrigerants are being phased out worldwide to combat

the twin menace of ozone layer depletion and global warming. The objective to attain

holistic environmental safety has facilitated the emergence of natural refrigerants as the

more benign working fluids in refrigeration and heating systems. Several natural

refrigerants are regaining their importance and are on a path of revival. However, many

of these natural refrigerants are either toxic or flammable or both. The rapid advances in

nano technology have led to new types of heat transfer fluids called nanofluids.

In such cases, it is desirable to reduce the amount of refrigerant used in the system

and restrict the refrigerant to the plant room. The addition of a secondary fluid loop to

transfer heat between the refrigeration plant and the refrigerated space fulfils both these

purposes. Reduction in the amount of refrigerant used also leads to faster pump-down and

defrost. Secondary fluid loops are widely used in various refrigeration, air conditioning

and heating applications [1]. A recent spurt in the universal interest to study alternatives

to the conventional direct refrigeration systems and use of natural refrigerants as

secondary fluids has been visible. Traditionally used secondary fluids are water, brines,

glycols, alcohols, etc.

DIRECT AND INDIRECT REFRIGERATION SYSTEM1.1

Refrigeration systems can be broadly classified into direct and indirect systems. The

difference between direct systems and indirect systems, also known as secondary loop

systems, lies in the physical separation between the primary loop, where the cooling


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effect is produced, and the secondary loop, where cooling takes place. An indirect

cooling system incorporates two different refrigerants (primary and secondary) to provide

cooling. In all these systems, the primary loop is a conventional refrigeration system that

uses a phase changing fluid as primary refrigerant, which is restricted to the plant room.

A separate fluid (secondary refrigerant) circulates in the secondary loop and transports

thermal energy between the refrigerated space and the refrigeration plant. An additional

heat exchanger is required to transfer heat between the conditioned space and plant room

via the secondary loop. The fluid used in the secondary loop is normally a safe and

environmentally benign fluid that does not undergo any phase change during the process

of heat transfer. However, it is possible to build indirect systems in which the secondaryfluid may also undergo phase change. A secondary loop integrated with a conventional

refrigeration system is shown in Fig. 1. As mentioned before, the indirect systems require

an additional heat exchanger (HHX) and a secondary refrigerant pump. This may result in

increased first cost and energy requirements compared to equivalent direct systems.

However, employing a NCL with suitable secondary fluid can eliminate the use of

secondary fluid pump.

Fig 1: Indirect refrigeration system with forced circulation type secondary loop

1.1.1. ADVANTAGES OF INDIRECT REFRIGERATION SYSTEMS

Since primary refrigerant is confined to the plant room, a flammable and/or toxic

but eco-friendly fluid can be used as primary refrigerant.


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Less refrigerant charge in the primary loop: reduces capital cost and refrigerant

leakage.

Smaller primary cooling loops further benefit in maintenance and checking

operations.

A secondary loop system is also simpler to modify.

1.1.2. DISADVANTAGES OF INDIRECT REFRIGERATION SYSTEMS

Additional heat exchanger and circulating pump increase initial cost.

An added temperature difference may result in lower efficiency. Selection of a suitable secondary fluid requires additional investigation

1.2.NATURAL CIRCULATION LOOPS

Heat transfer loops (secondary loops) are classified into two groups: forced

circulation loop (FCL) in which an external pump is used to drive the flow, and a natural

circulation loop (NCL). In NCLs circulation of fluid is maintained due to the buoyancy

effect caused by thermally generated density gradient, so that a pump is not required. In aNCL, the heat sink is located at a higher elevation than the heat source which establishes

an unstable density gradient in the system and hence, under the influence of gravity,

lighter (warmer) fluid rises up and heavier (cooler) fluid comes down. Hence thermal

energy can be transported from high temperature source to low temperature sink without

direct contact with each other and also without using any prime mover.


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Fig 2: Rectangular NCL

1.2.1. ADVANTAGES OF NCL

The main advantage of NCL is its simplicity and low cost. This is due to the fact that

pumps are eliminated. Also this is comparatively safer. With NCL there is improved flow

distribution and better two phase characteristics are observed.

1.2.2. DISADVANTAGES OF NCL

In a NCL, the driving head is low. Hence lower maximum power is available per

channel. There is also a high prevalence of instabilities. Specific start up procedure may

also be required.

i. Selection of working fluids for natural circulation loops

Selection of working fluid (secondary fluid) for NCLs are typically carried out based

on the following properties:

Low freezing point Low viscosity

High volumetric expansion coefficient

High volumetric heat capacity

High specific heat

High thermal conductivity


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High density

Chemically stable, non-toxic, non-corrosive nature

Environment friendliness

Cost, availability etc.

Low freezing point is the first criterion for selecting a secondary fluid for

refrigeration applications, and it should be well below the operating temperature of the

system. For the optimum design of secondary refrigeration system, it is essential to find

the right balance between viscosity, specific heat and thermal conductivity.

1.3.NANOFLUIDS

Suspension of nanomaterial in colloidal form in the range of 1-100nm in a carrier

fluid is known as nanofluids [2]. The nanoparticles used in nanofluids are typically made

of metals, oxides, carbides, or carbon nanotubes. Common base fluids include

water, ethylene glycol and oil.

Currently nanofluids are being intensely researched upon. The low thermal

conductivity of conventional heat transfer fluid has been a serious obstacle for

improvement of performance and compactness of the system. Studies on micro-meter

sized particles encountered a host of problems such as rapid settling of particles, clogging

and increased pressure drop in the fluid [2].

The nanofluids received intense scientific attention after large enhancement in

thermal conductivity of copper based nanofluids was reported at very low volume

fractions. After detailed investigations by a number of researchers, Brownian motion

induced convection and conduction through percolating nanoparticle paths are considered

to be the most probable causes for the increased value of thermal conductivity [3], [4] and

[5]. Some very recent works indicate conduction through the formation of agglomerates

as another significant factor [6], [7].


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1.3.1. ADVANTAGES OF NANOFLUID

High specific surface area and therefore more heat transfer surface between

particles and fluids.

High dispersion stability with predominant Brownian motion of particles.

Reduced pumping power as compared to pure liquid to achieve equivalent heattransfer intensification.

Reduced particle clogging as compared to conventional slurries, thuspromoting system miniaturization.

Adjustable properties, including thermal conductivity and surface wettability,by varying particle concentrations to suit different applications.

1.3.2. DISADVANTAGE OF NANOFLUIDS

Poor long term stability

Increased pressure drop

Lower Specific heat compared to base fluid

High production Cost of nanofluids

1.4. OBJECTIVES

The objectives of the present work are:

Comparative study of different turbulence models for the simulation of single

phase carbon-di-oxide in a rectangular natural circulation loop.

Steady state analysis employing a 3-Dimensional CFD model of water based

nanofluids (Alumina (Al2O3), Cupric Oxide (CuO)) in rectangular NCL with

isothermal heat source and sink as end heat exchangers.

To investigate their thermal performance by studying Thermal Conductivity (k),

Heat Transfer Rate (Q), Specific Heat (Cp).

To study the physical properties such as Viscosity, Density (), Volumetricexpansion ().

To compare results of Turbulent and Laminar flows for the given nanofluids.


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To understand the Multi-Phase Models available in FLUENT and selecting the

most appropriate one.

Further results are to be validated using previous works.

1.5.APPROACH

For carrying out this work FLUENT is used to model the given problem. The

simulation involves an understanding of the various turbulence models and the multi-

phase models available in FLUENT. The best model is identified for the given case

from previous research work carried out in this area. Also, many physical properties

are to be found out from available data to run the simulations.

The results are obtained by running simulations for the following cases:

Different Nanofluids (Al2O3, CuO)

Particle Size variation

Different Volume Fractions

Turbulent and Laminar flows


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2.

LITERATURE REVIEW

2.1.NANOFLUIDS:

Pastoriza-Gallego et al. (2010) analysed stability and dispersion of nanofluids

obtained by dispersing CuO nanoparticles in water. They found out that the particle size

has subtle but not negligible influence in density. The deviations from the ideal behaviour

increases with the nanofluid concentration. The differences in the viscosities are large

and must be taken into account for practical application. They described the differences

in the viscosities by considering the describing either the aggregation state or the particle

size distribution of nanofluid. They found out that the viscosity increases as the particle

size decreases.

Yu et al. (2009) measured the thermal conductivity and viscosity of ZnO

nanoparticles in ethylene glycol. It was found out that the setting time has no effect on

the thermal conductivity of the nanofluid. The thermal conductivity increased with

increase in temperature. The thermal conductivity of the nanofluid increased nonlinearly

with the particle concentration. The results were consistent with prediction values by the

Maxwell and Bruggeman models. It was also found out that the low particle

concentration nanofluids demonstrate Newtonian behaviour, and the high particle

concentration nanofluid demonstrate shear-shinning behaviour.

Hwang et al. (2005) measured thermal conductivities of nanofluids by hot wire

method. It was demonstrated that the effective thermal conductivity of nanofluid in base

fluid is much higher than that of the pure fluid. The thermal conductivity increases

linearly with the particle concentration. The thermal conductivity of nanofluid was found

to be function of thermal conductivities of both the nanoparticles and the base fluid.

Hwang et al. (2006) examined the effect of adding different nanoparticles in base

fluid on lubrication and thermal conductivity. They measured kinematic viscosity and

thermal conductivity to study thermo physical properties of nanofluids. It was found out


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that with increase in particle volume fraction the thermal conductivity of nanofluid

increases. They found out that the stability of nanofluids is influenced by the

characteristics between nanoparticles and the base fluid.

Xuan et al. (1999) demonstrated a method to prepare nanofluid by using

nanoparticles and base metal. They carried out theoretical study on the conductivity of

prepared nanofluids using hot wire method and proposed a model to describe thermal

conductivity and heat transfer number.

Chopkar et al. (2006) prepared a nanofluid by dispersing nanocrystallineparticles in ethylene glycol. They characterized the size of nanoparticles by transmissionelectron microscopy and X-ray diffraction, and measured thermal conductivity of

nanofluids using a purpose-built thermal comparator. The results showed that thermal

conductivity of nanofluids is around two times performance of the nanofluids. They also

derived some correlations for predicting Nusselt that of base fluid. Heat removal rate of

nanofluid was found to be better than base fluid. Hence, use of nanofluids was

recommended for automobiles.

Xuan et al. (2000) investigated the mechanism for heat transfer of nanofluids. Theyderived the heat transfer correlation of the nanofluid by using two different approaches.

Chandrasekar et al. (2009) presented friction factor and heat transfer characteristics

of nanofluid flowing through horizontal tube. The nusselt number wasfound to be increased for nanofluid compared with base fluid. The pressure loss was

found to be almost equal for nanofluid and base fluid. The correlations developed for

friction factor and Nusselt number was found to be in accordance with the experimental

data.

Chandrasekar et al. (2009) in another paper reported theoretical determination and

experimental investigations of viscosity and thermal conductivity of nanofluid. They measured viscosity and thermal conductivity of nanofluid at different

volume concentrations. It was found out that thermal conductivity increase was


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substantially lower than the increase in viscosity. They proposed models to predict

viscosity and thermal conductivity which showed good agreement with the experimental

results.

Yu et al. (2010) investigated the effect of addition Aluminium nitride nanoparticles

in the thermal conductivity of conventional heat exchange fluids. They carried out the

study for two types of base fluids, for ethylene glycol and propylene glycol. The

enhancement in thermal conductivity was found out to be slightly more for propylene

glycol. The temperature had a negligible effect on the conductivity enhancement ratio.

The two nanofluids behaved as Newtonian fluid at lower volume concentrations. While

the nanofluids exhibited shear-shinning behaviour at higher volume concentrations.

Suresh et al. (2010) investigated friction factor and convective heat transfer

characteristics of CuO/water nanofluid in a dimpled tube. They determined the effect of

nanofluids and dimples on the Reynolds number and Nusselt number. They investigated

effect of nanoparticles inclusion on viscosity, thermal conductivity, heat transfer

enhancement and pressure loss. Though the use of nanoparticles increased the heat

transfer, there was negligible increase in friction factor. Also the pressure drop was found

to be slightly increased with the addition of nanoparticles. This implied the nanofluid

may be suitable for practical application. The viscosity of the nanofluid increased with

increase in particle concentration.

Suresh et al. (2012) in another paper investigated the friction factor and convective

heat transfer characteristics of nanofluid in circular tube under turbulentflow. The circular tube had spiraled rod inserts. They encountered enhancement in heat

transfer increases with the increase in particle volume fraction. The pressure drop was

found to be more with spiralled rod insert.

2.2. NANOFLUIDS BASED NATURAL CIRCULATION LOOP:

Nayak et al.(2008) investigated the natural circulation behaviour in a rectangular

loop experimentally with water and different concentration of nanofluids. They


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found out that flow rates increased and flow instabilities decreased in the case of

nanofluids as compared with water. These two activities were found to depend upon the

nanoparticles volume fraction. They measured flow rate at different power. The initial

conditions of the loop and the rate of power rise were similar in all the cases. In the case

of nanofluids the flow rates were found to be higher than that in the case of water.

Nayak et al. (2011) studied the stability and transient behaviour of a boiling two-

phase natural circulation loop with water based nanofluid and water. The naturalcirculation flow behaviour with rise in power is similar with nanofluid and waterin single-phase condition. However, for same operating conditions nanofluid had higher

buoyancy induced flow rates than with water alone. In addition, with nanofluid, the

boiling induced type 1 flow instabilities are found to be at much lower level. It was found

out that the operating pressure has very little effect on single-phase natural circulation,

both for nanofluid and water.

Namburu et al. (2007) investigated experimentally rheological properties of copper

oxide nanoparticles suspended in water and ethylene glycol and mixture. It was revealed

that as the fluid temperature increases the viscosity diminishes exponentially. Also the

viscosity was found to be increasing with the increase in concentrations of nanofluids

possess. The change in relative viscosity over temperature is minimal at lower volume

fractions of nanofluid. Xuan el al. (2003) found that a nanofluid at low volume fractions

had higher the heat transfer coefficient even though there was not much pressure loss.

Misale et al. (2012) presented an experimental study focused on the macroscopic

effects on the thermal performance of a mini-loop. They carried out the experiments for

two fluids:

and distilled water. The difference between hot heat

exchanger and cold heat exchanger was similar for water and nanofluid. Overall heat

transfer coefficient and the average fluid temperature also similar for both the fluids.

They compared their results of experimental data with Vijayans correlation, developed

for large scale loops. It was similar for water. It showed good agreement even in the case

of nanofluid.


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3.

MODELS FOR TURBULENCE ANALYSIS-

TRANSPORT EQUATIONS

3.1.TRANSPORTATION EQUATIONS FOR STANDARD K- MODEL:

For turbulent kinetic energy k

[ ] (3.1.1)For dissipation

,

[ ] (3.1.2)3.2. MODELLING TURBULENT VISCOSITY:

Turbulent viscosity is modelled as:

Production of k

Where S is the modulus of the mean rate-of-strain tensor, defined as:

Efficiency of buoyancy


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Where Prt is the turbulent Prandtl number for energy and gi is the component of

the gravitational vector in the ith

direction. For the standard and realizable models, the

default value if Prt is 0.85.The coefficient of thermal expansion B, is given as

Model constants

C1c=1.44, C2c=1.92, C3c=-0.33, C=0.99, k=1.0, c=1.

Strengths

Robust

Economical

reasonably accurate;

long accumulated performance data.

Weaknesses

Mediocre results for complex flows with severe pressure gradients,

Strong streamline curvature, swirl and rotation.

Predicts that round jets spread 15% faster than planar jets whereas in actualitythey spread 15% slower

3.3. RNG k- EQUATIONS:

The RNG model was developed using Re-Normalisation Group (RNG) methods

by to renormalize the Navier-Stokes equations, to account for the effects of smaller

scales of motion. In the standard k-epsilon model the eddy viscosity is determined from a

single turbulence length scale, so the calculated turbulent diffusion is that which occurs

only at the specified scale, whereas in reality all scales of motion will contribute to the


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turbulent diffusion. The RNG approach, which is a mathematical technique that can be

used to derive a turbulence model similar to the k-epsilon, results in a modified form of

the epsilon equation which attempts to account for the different scales of motion through

changes to the production term.

There are a number of ways to write the transport equations for k and epsilon, a

simple interpretation where buoyancy is also included.

[ ] (3.2.1) [ ] (3.2.2)

Where With the turbulent viscosity being calculated in the same manner as with the

standard k- model.

Pkis the production of kinetic energy

Constants:

It is interesting to note that the values of all of the constants (except ) are derived

explicitly in the RNG procedure. They are given below with the commonly used values

in the standard k-epsilon equation in brackets for comparison:

Cu = 0.0845(0.09) , k = 0.7194(1.0) , c = 0.7194(1.30) , Ce1 = 1.42(1.44) , Ce2 =

1.68(1.92) ,0= 4.38 and = 0.012 (derived from experiment).


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3.4. k- MIXTURE TURBULENCE MODELS

The mixture turbulence model is the default multiphase turbulence model. It

represents the first extension of the k- model, and it is applicable when phases separate,

for stratified (or nearly stratified) multiphase flows, and when the density ratio between is

close to 1.

The k and equations describing this model are as follows:

(3.2.4)And

Where the mixture density and velocity, and are computed from

And

The turbulent viscosity, , is computed from

And the production of turbulence kinetic energy, Gk,m is computed from


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3.5.k- DISPERSED TURBULENCE MODELS

The model is applicable when there is clearly one primary continuous phase and the

rest are dispersed dilute secondary phases. Time and length scales that characterize the

motion are used to evaluate dispersion coefficient, correlation functions, and the turbulent

kinetic energy of each dispersed model.

The characteristic particle relaxation time connected with inertial effects acting on a

dispersed phase p is defined as

The Lagrangian integral time scale calculated along particle trajectories, mainly affected

by the crossing trajectory effect is defined as

( )Where

|| And

Where is the angle between the mean particle velocity and the mean relative

velocity.

The ratio between these two characteristic times is written as


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Strengths

Good for moderately complex behaviour like jet impingement

separating flows

swirling flows

secondary flow

Weakness

Subjected to limitations due to isotropic eddy viscosity assumption.

3.6. STANDARD k- MODEL:

Kinematic Eddy Viscosity

Turbulence Kinetic Energy

Specific Dissipation Rate

Closure Coefficient and Auxiliary Relations

=5/9, =3/40, *=9/100, =1/2, *=1/2, = *k

Strength

Behaviour of k-omega model in the logarithmic region is superior than k-epsilon

in equillibrium adverse pressure gradient flows.


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Weaknesses

Away from the wall k-w model depicts strong sensitivity to the free stream values

K-w model does not accurately represent k and epsilon distribution in agreement

with DNS data.

3.7.Transport Equations for the SST k- Model

The SST k- model has a similar form to the standard k- model:

And

() In these equations,

represents the generation of turbulence kinetic energy due

to mean velocity gradients, calculated from Gkand defined in Eq.1 under Modelling the

Turbulent Production, Gkrepresents the generation of , calculated as described for the

standard k- model in Modelling the Turbulence Production. kand represents the

effective diffusivity for k and due to turbulence, YkandYrepresent the dissipation of

k and due to turbulence, calculated as described in Modelling the Turbulence

Dissipation. Drepresents the cross-diffusion term, calculated as described below, Skand

Sare user-defined source terms.

Strength

Functions as k-omega near the wall and k-epsilon away from the wall

Weakness

Fails to predict velocity profiles in severe adverse pressure gradient flow.


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3.8.TRANSPORT EQUATIONS FOR THE k-kl- MODEL:

The k-kl- model is considered to be the three-equation eddy-viscosity type, which

includes transport equations for turbulent kinetic energy (kT), laminar kinetic energy (kL),

and the inverse turbulent scale ()

The inclusion of the turbulent and laminar fluctuations on the mean flow and

energy equations via the eddy viscosity and thermal diffusivity is as follows:

Strength

Able to predict laminar to turbulent transition

Weakness

Grid dependency and over-prediction of turbulence in transition zones if not

correctly handled.


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4.

DESCRIPTION OF MULTIPHASE MODELS

4.1.THE MIXTURE MODEL

The mixture model is designed for two or more phases (fluid or particulate). As in

the Eulerian model, the phases are treated as interpenetrating continua. The mixture

model solves for the mixture momentum equation and prescribes relative velocities to

describe the dispersed phases. Applications of the mixture model include particle-laden

flows with low loading, bubbly flows, sedimentation, and cyclone separators. The

mixture model can also be used without relative velocities for the dispersed phases to

model homogeneous multiphase flow.

4.1.1 OVERVIEW

The mixture model is a simplified multiphase model that can be used in different

ways. It can be used to model multiphase flows where the phases move at different

velocities, but assume local equilibrium over short spatial length scales. It can be used to

model homogeneous multiphase flows with very strong coupling and phases moving at

the same velocity and lastly, the mixture models are used to calculate non-Newtonian

viscosity.

The mixture model can model n phases (fluid or particulate) by solving the

momentum, continuity, and energy equations for the mixture, the volume fraction

equations for the secondary phases, and algebraic expressions for the relative velocities.

Typical applications include sedimentation, cyclone separators, particle-laden flows with

low loading, and bubbly flows where the gas volume fraction remains low.

The mixture model is a good substitute for the full Eulerian multiphase model in

several cases. A full multiphase model may not be feasible when there is a wide

distribution of the particulate phase or when the interphase laws are unknown or their

reliability can be questioned. A simpler model like the mixture model can perform as


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well as a full multiphase model while solving a smaller number of variables than the full

multiphase model.

The mixture model allows you to select granular phases and calculates all

properties of the granular phases. This is applicable for liquid-solid flows.

4.1.2. LIMITATIONS

The following limitations apply to the mixture model in ANSYS FLUENT:

Pressure-based solver is to be used. The mixture model is not available with the

density-based solver.

Only one of the phases can be defined as a compressible ideal gas. There is no

limitation on using compressible liquids using user-defined functions.

When the mixture model is used, stream wise periodic flow is not to be modelled

with specified mass flow rate.

Solidification and melting are not to be modelled in conjunction with the mixture

model.

The Singhal et al. cavitation model (available with the mixture model) is not

compatible with the LES turbulence model.

The relative formulations in combination with the MRF and mixture model are

not to be used. The mixture model does not allow for inviscid flows.

The shell conduction model for walls is not allowed with the mixture model.

When tracking particles in parallel, do not use the DPM model with the mixture

model if the shared memory option is enabled.


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The mixture model, like the VOF model, uses a single-fluid approach. It differs from

the VOF model in two respects:

The mixture model allows the phases to be interpenetrating. The volume fractionsand for a control volume can therefore be equal to any value between 0 and1, depending on the space occupied by phase q and phase p.

The mixture model allows the phases to move at different velocities, using the

concept of slip velocities.

The mixture model solves the continuity equation for the mixture, the momentum

equation for the mixture, the energy equation for the mixture, and the volume fraction

equation for the secondary phases, as well as algebraic expressions for the relative

velocities (if the phases are moving at different velocities).

4.1.3. CONTINUITY EQUATION

The continuity equation for the mixture is

where is the mass-averaged velocity:

and is the mixture density: where is the volume fraction of k.


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4.1.4. MOMENTUM EQUATION

The momentum equation for the mixture can be obtained by summing the

individual momentum equations for all phases. It can be expressed as

Where n is the number of phases, F is a body force, and is the viscosity of themixture:

is the drift velocity for secondary phase k :

4.1.5. ENERGY EQUATION

The energy equation for the mixture takes the following form:

where is the effective conductivity, where is the turbulent thermal conductivitydefined according to the turbulence model being used. The first term on the right-hand


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side represents energy transfer due to conduction includes any other volumetric heatsources.

4.1.6. RELATIVE SLIP VELOCITY AND THE DRIFT VELOCITY

The relative velocity (also referred to as the slip velocity) is defined as the velocity of

a secondary phase (p) relative to the velocity of the primary phase (q): The mass fraction for any phase (k) is defined as:

The drift velocity and the relative velocity () are connected by the followingexpression:

While solving a mixture multiphase calculation with slip velocity, the following

formulations are available for the drag function:

Schiller-Naumann (the default formulation)

Morsi-Alexander

Symmetric

Constant

User-defined


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4.1.7. GRANULAR PROPERTIES

Since the concentration of particles is an important factor in the calculation of the

effective viscosity for the mixture, we may use the granular viscosity to get a value for

the viscosity of the suspension. The volume weighted averaged for the viscosity would

now contain shear viscosity arising from particle momentum exchange due to translation

and collision.

The collisional and kinetic parts, and the optional frictional part, are added to give

the solids shear viscosity: 4.1.8. KINETIC VISCOSITY

ANSYS FLUENT provides two expressions for the kinetic viscosity:

Syamlal et al. (default)

Gidaspow et al.

4.1.9.

GRANULAR TEMPERATURE

The viscosities need the specification of the granular temperature for the solids phase. Here we use an algebraic equation from the granular temperaturetransport

equation. This is only applicable for dense fluidized beds where the convection and the

diffusion term can be neglected under the premise that production and dissipation of

granular energy are in equilibrium.

: where , :=the generation of energy by the solid stress tensor


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the collisional dissipation energy

the energy exchange between the fluid or solid phase and the solidphase.The collisional dissipation of energy, , represents the rate of energy dissipation

within the solids phase due to collisions between particles. This term is representedby the expression derived by Lun et al.

The granular temperature can be solved with the following options in ANSYS:

Algebraic formulation (the default)

Constant granular temperature-This is useful in very dense situations where the

random fluctuations are small.

UDF for granular temperature

4.1.10.INTERFACIAL AREA CONCENTRATION

Interfacial area concentration is defined as the interfacial area between two phases

per unit mixture volume. This is an important parameter for predicting mass, momentum

and energy transfers through the interface between the phases. In two-fluid flow systems,

one discrete (particles) and one continuous, the size and its distribution of the discrete

phase or particles can change rapidly due to growth (mass transfer between phases),

expansion due to pressure changes, coalescence, breakage and/or nucleation mechanisms.

The Population Balance model (see the Population Balance Module Manual)

ideally captures this phenomenon, but is computationally expensive since several

transport equations need to be solved using moment methods, or more if the discretemethod is used. The interfacial area concentration model uses a single transport equation

per secondary phase and is specific to bubbly flows in liquid at this stage.


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The transport equation for the interfacial area concentration can be written as

Where is the interfacial area concentration ), and is the gas volume

fraction.

The first two terms on the right hand side are of gas bubble expansion due to

compressibility and mass transfer (phase change).

Where, is the mass transfer rate into the gas phase per unit mixture volume. and are the coalescence sink terms due to random collision and wakeentrainment, respectively. is the breakage source term due to turbulent impact.

Two sets of models, the Hibiki-Ishii model and the Ishii-Kim model, exist for those,

source and sink terms for the interfacial area concentration, which are based on the worksof Ishii et al. According to their study, the mechanisms of interactions can be summarized

in five categories:

Coalescence due to random collision driven by turbulence.

Breakage due to the impact of turbulent eddies.

Coalescence due to wake entrainment.

Shearing-off of small bubbles from large cap bubbles.

Breakage of large cap bubbles due to flow instability on the bubble surface.


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4.2. EULERIAN MODEL

The Eulerian multiphase model in ANSYS FLUENT allows for the modeling of

multiple separate, yet interacting phases. The phases can be liquids, gases, or solids in

nearly any combination. An Eulerian treatment is used for each phase, in contrast to the

Eulerian-Lagrangian treatment that is used for the discrete phase model.

With the Eulerian multiphase model, the number of secondary phases is limited

only by memory requirements and convergence behaviour. Any number of secondary

phases can be modeled, provided that sufficient memory is available. For complex

multiphase flows, however, you may find that your solution is limited by convergence

behaviour.

ANSYS FLUENTs Eulerian multiphase model does not distinguish between fluid-

fluid and fluid-solid (granular) multiphase flows. A granular flow is simply one that

involves at least one phase that has been designated as a granular phase.

The ANSYS FLUENT solution is based on the following:

A single pressure is shared by all phases.

Momentum and continuity equations are solved for each phase.

The following parameters are available for granular phases:

Granular temperature (solids fluctuating energy) can be calculated for

each solid phase. You can select either an algebraic formulation, a

constant, a user-defined function, or a partial differential equation.

Solid-phase shear and bulk viscosities are obtained by applying kinetic

theory to granular flows. Frictional viscosity for modeling granular flow

is also available.

Several interphase drag coefficient functions are available, which are appropriate

for various types of multiphase regimes. All of the k- and k-w turbulence models are available, and may apply to all

phases or to the mixture.


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4.2.1. LIMITATION OF EULERIAN MODEL

All other features available in ANSYS FLUENT can be used in conjunction with

the Eulerian multiphase model, except for the following limitations:

The Reynolds Stress turbulence model is not available on a per phase basis.

Particle tracking (using the Lagrangian dispersed phase model) interacts only with theprimary phase.

Streamwise periodic flow with specified mass flow rate cannot be modeled when theEulerian model is used (the user is allowed to specify a pressure drop).

Inviscid flow is not allowed.

Melting and solidification are not allowed.

When tracking particles in parallel, the DPM model cannot be used with the Eulerianmultiphase model if the shared memory option is enabled.

To change from a single-phase model to a multiphase model, you will have to do

this in a series of steps. You will have to set up a mixture solution and then a multiphase

solution. However, since multiphase problems are strongly linked, it is better to start

directly solving a multiphase problem with an initial conservative set of parameters (first

order in time and space). This is of course problem dependent. The modifications

involve, among other things, the introduction of the volume fractions 1, 2, n for the

multiple phases, as well as mechanisms for the exchange of momentum, heat, and mass

between the phases.

4.2.2.

VOLUME OF FRACTION EQUATION

The description of multiphase flow as interpenetrating continua incorporates the

concept of phasic volume fractions, denoted here by q. Volume fractions represent the

space occupied by each phase, and the laws of conservation of mass and momentum are

satisfied by each phase individually. The derivation of the conservation equations can be


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done by ensemble averaging the local instantaneous balance for each of the phases or by

using the mixture theory approach.

The volume of phase q, Vqis defined by

Where

The effective density of phase q is Where is the physical density of phase q.

4.2.3. EQUATIONS IN GENERAL FORM

Conservation of Mass

The continuity of phase q is

() ( )

Where

is the velocity of phase q and

characterises the mass transfer from

the pthand q

thphase and characterises the mass transfer from phase q to phase p.


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Conservation of Momentum

The momentum balance for phase q yields ( ) ( ) ( )

Where,

is the qthphase stess-strain tensor

( ) Here, and are the shear and bulk viscosity of phase q, is an external

force, is a lift force, is the virtual mass force, is an interaction forcebetween phases, and p is the pressure shared by all phases.

is the interphase velocity, defined as follows. If > 0 (i.e.; phase p mass isbeing transferred to phase q), = ; . If < 0 (i.e.; phase q mass is being transferredto phase p), = ; Likewise, if > 0 then = , if < 0 then = .

Continuity Equation

The volume fraction of each phase is calculated from a continuity equation:

(

) (

) (

)

Where is the phase reference density, or the volume averaged density of the q thphasein the solution domain.


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Fluid-Solid Momentum Equations

The conservation of momentum for the sth

solid phase is ( )

Where ps is the sth solid pressure, Kis =Ksi is the momentum exchange coefficient

between fluid or solid phase I and solid phase phase s, N is the total number of phases,

and .Maximum Packing Limit in Binary Mixtures

The packing limit is not a fixed quantity and may change according to the number

of particles present within a given volume and the diameter of the particles. Small

particles accumulate in between larger particles increasing the packing limit.

For a binary mixture with different diameters, the mixture composition is defined as:

Where,

As this is a condition for application of the maximum packing limit for the binary

mixtures.


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The maximum packing limit of the mixture is the minimum of the twoexpressions.

( ) ( ( ))

( ) The packing limit is used for the calculation of the radial distribution function.

Granular Temperature

The granular temperature for the sth

solid phase is proportional to the kinetic

energy of the random motion of the particles. The transport equation derived from the

kinetic theory takes the form

( ) () (5.13)Where,

( ) =the generation of energy by the solid stress tensor the diffusion energy (is the diffusion coefficient)= the collisional dissipation of energy= the energy exchange between the ith fluid or solid phase and the s th solid

phase


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4.3.VOLUME OF FLUID (VOF) MODEL THEORY

4.3.1. OVERVIEW OF THE VOF MODEL:

The VOF model can model two or more immiscible fluids by solving a single set of

momentum equations and tracking the volume fraction of each of the fluids throughout

the domain. Typical applications include the prediction of jet breakup, the motion of

large bubbles in a liquid, the motion of liquid after a dam break, and the steady or

transient tracking of any liquid-gas interface.

4.3.2. LIMITATIONS OF THE VOF MODEL:

The VOF model is not available with the density-based solver.

The VOF model does not allow for void regions where no fluid of any type is

present.

Only one of the phases can be defined as a compressible ideal gas. There is no

limitation on using compressible liquids using user-defined functions.

Stream wise periodic flow (either specified mass flow rate or specified pressure

drop) cannot be modeled when the VOF model is used.

The second-order implicit time-stepping formulation cannot be used with the

VOF explicit scheme.

4.3.3. STEADY-STATE AND TRANSIENT VOF CALCULATIONS:

A steady-state VOF calculation is sensible only when your solution is

independent of the initial conditions and there are distinct inflow boundaries for the

individual phases. The VOF formulation relies on the fact that two or more fluids (or

phases) are not interpenetrating. For each additional phase that you add to your model, a

variable is introduced: the volume fraction of the phase in the computational cell. In each

control volume, the volume fractions of all phases sum to unity. The fields for all

variables and properties are shared by the phases and represent volume-averaged values,

as long as the volume fraction of each of the phases is known at each location. Thus the

variables and properties in any given cell are either purely representative of one of the

phases, or representative of a mixture of the phases, depending upon the volume fraction


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values. In other words, if the fluids volume fraction in the cell is denoted as thenthe following three conditions are possible:

; The cell is empty (of the fluid) ; The cell is full (of the fluid) ; The cell contains the interface between the fluid and one or more

other fluids. Based on the local value of the appropriate properties andvariables will be assigned to each control volume within the domain.

Volume Fraction Equation:

The tracking of the interface(s) between the phases is accomplished by the

solution of a continuity equation for the volume fraction of one (or more) of the phases.

For the phase, this equation has the following form: () ( ) ( ) (6.1)

Where

is the mass transfer from phase q to phase p and

is the mass

transfer from phase p to phase q.

The volume fraction equation will not be solved for the primary phase; the

primary-phase volume fraction will be computed based on the following constraint: The implicit scheme:

When the implicit scheme is used for time discretization, standard finite-difference interpolation schemes, QUICK, Second Order Upwind and First Order

Upwind, and the Modified HRIC schemes, are used to obtain the face fluxes for all cells,

including those near the interface.

() ( ) (6.2)


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Since this equation requires the volume fraction values at the current time step

(rather than at the previous step, as for the explicit scheme), a standard scalar transport

equation is solved iteratively for each of the secondary-phase volume fractions at each

time step. The implicit scheme can be used for both time-dependent and steady-state

calculations.

The explicit scheme:

In the explicit approach, standard finite-difference interpolation schemes are

applied to the volume fraction values that were computed at the previous time step.

( ) ( ) (6.3)Where,

n+1=index for new (current) time step

n=index for previous time step

=face value of the

volume fraction, computed from the first- or second-

order upwind, QUICK, modified HRIC, compressive, or CICSAM scheme

V=volume of the cell

=volume flux through the face, based on normal velocityThis formulation does not require iterative solution of the transport equation

during each time step, as is needed for the implicit scheme. When the explicit scheme is

used, a time-dependent solution must be computed. When the explicit scheme is used for

time discretization, the face fluxes can be interpolated either using interface

reconstruction or using a finite volume discretization scheme.


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Material Properties

The properties appearing in the transport equations are determined by the

presence of the component phases in each control volume. In a two-phase system, for

example, if the phases are represented by the subscripts 1 and 2, and if the volume

fraction of the second of these is being tracked, the density in each cell is given by

(6.4)All other properties (e.g., viscosity) are computed in this manner.

Momentum Equation

A single momentum equation is solved throughout the domain, and the resulting

velocity field is shared among the phases. The momentum equation, shown below, is

dependent on the volume fractions of all phases through the properties and . (6.5)One limitation of the shared-fields approximation is that in cases where large

velocity differences exist between the phases, the accuracy of the velocities computed

near the interface can be adversely affected.

Energy Equation

The energy equation, also shared among the phases, is shown below.

(6.6)

The VOF model treats energy,, and temperature, , as mass-averaged variables.The properties and (effective thermal conductivity) are shared by the phases. Thesource term, , contains contributions from radiation, as well as any other volumetricheat sources.


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As with the velocity field, the accuracy of the temperature near the interface is

limited in cases where large temperature differences exist between the phases. Such

problems also arise in cases where the properties vary by several orders of magnitude.

For example, if a model includes liquid metal in combination with air, the conductivities

of the materials can differ by as much as four orders of magnitude. Such large

discrepancies in properties lead to equation sets with anisotropic coefficients, which in

turn can lead to convergence and precision limitations.

4.4.HOW TO CHOOSE A RIGHT MODEL?

Fig 3:Choosing the right Model

Note:

The Stokes number is defined as a ratio of the particle response time to the

characteristic time of the flow. (7.1) (7.2)

The St gives a measure of temporal correlation between particle velocity and the fluid

velocity

If St


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If St = 1, the particle tend to substantially modify the bulk macroscopic flow.

If St>>1, the particle motion is weakly affected by the motion.

To choose between the mixture model and the Eulerian model, you should

consider the following guidelines:

- If there is a wide distribution of the dispersed phases (i.e., if the particles vary in

size and the largest particles do not separate from the primary flow field), the mixture

model may be preferable (i.e., less computationally expensive). If the dispersed phases

are concentrated just in portions of the domain, you should use the Eulerian model

instead.- If interphase drag laws that are applicable to your system are available (either

within ANSYS FLUENT or through a user-defined function), the Eulerian model can

usually provide more accurate results than the mixture model. Even though you can apply

the same drag laws to the mixture model, as you can for a non-granular Eulerian

simulation, if the interphase drag laws are unknown or their applicability to your system

is questionable, the mixture model may be a better choice. For most cases with spherical

particles, the Schiller-Naumann law is more than adequate. For cases with non-spherical

particles, a user-defined function can be used.

- If you want to solve a simpler problem, which requires less computational effort,

the mixture model may be a better option, since it solves a smaller number of equations

than the Eulerian model. If accuracy is more important than computational effort, the

Eulerian model is a better choice. Keep in mind, however, that the complexity of the

Eulerian model can make it less computationally stable than the mixture model.


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5.

PHYSICAL MODEL OF NCL

5.1.PHYSICAL MODEL

Figure 8.1. shows the schematic of a 3-D rectangular NCL which consists of an

isothermal sink, an isothermal source, left and right insulated pipes. The loop fluid is

heated sensibly in the isothermal heat source (TH) and is cooled sensibly in the

isothermal heat sink (TC). Circulation of the loop fluid is maintained due to the buoyancy

effect caused by heating at the bottom and cooling at the top.

The following simplifying assumptions are made in the analysis:

i. The loop fluids, CO2 and water, are in single-phase throughout the loop.

ii. The system is operating at steady-state.

iii. All external walls except the heat source and sink are perfectly insulated.

iv. Wall material is isotropic with constant thermal conductivity.

Fig.4: Schematic of the Natural Circulation Loop employed in the model

5.2.GEOMETRIC AND MATERIAL SPECIFICATIONS FOR THE MODE

Internal diameter of the loop (d) = 15 mm

Length of isothermal sink or source (L) = 120 cm

Total width of the loop () = 146 cm


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Total height of the loop () = 124.5 cmTotal length of the loop (

) = 545 cm

Insulated pipe length in horizontal pipe (2) = 26 cmRadius of curvature for bend (R) = 30 mmTube wall thickness = 2 mm

Material of the loop = copper

5.3.

GRID GENERATION

Meshing of a three dimensional geometry has been carried out in Gambit 2.4.6.

Figure 8.2 shows the meshing (fluid part only) of a cross section of the loop which has a

minimum grid size of 0.2 mm in radial direction near the wall and increases to the

maximum grid size of 1.5 mm away from the wall. Coarse meshing is adopted in the

axial direction (5 mm grid size in horizontal pipes including bends and 10 mm for

vertical pipes). Mesh generation yielded a total of 235,552 nodes. The values of Y+ and

Y* have been checked for all the cases of turbulent flow to ensure optimal choice of

fineness of grid. Maximum Y+ and Y* values in the present study are 54.5 and 54.4,

respectively, which ensure that the grid is suitable for the assumption of standard wall

function near the wall (Launder and Spalding, 1974).

Where, u is the friction velocity, defined as (w/). w is the

wall shear stress.

Fig5 : Mesh generation

Where, k=turbulent kinetic energy, y= distance from the wall, C=0.0845.


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6.

RESULTS

6.1. COMPARITIVE STUDY OF DIFFERENT TURBULENT MODELS

All the turbulence models are compared for various outputs such as heat transfer

rate in the heat exchangers, mass flow rate of CO2 in the loop, Turbulence intensity,

turbulent kinetic energy, turbulent dissipation rate for various values of average

temperature of cold & hot heat exchanger. Also velocity contours at various cross

sections of the loop for different models are obtained. The plots obtained are shown

below:

310 315 320 325 330 335

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

TotalHeat

TransferRate,Q

(W)

Temperature (K)

ke RNG

ke STD

kw STD

kw SST

k-kl w

Total heat transfer rate vs Temperature

Fig6: Variation of heat transfer rate w.r.t temperature ()The total heat transfer showed a increasing trend upto certain temperature and

then decreases at higher temperatures. This can be explained due to the pseudo critical

point of carbon-di-oxide which is located at around 318K. Also the heat transfer rate

plots for all the models showed that the values are in good agreement except for the k-kl

w model.


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310 315 320 325 330 335

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

MassflowRate(kg/s)

Temperature (K)

ke RNG

ke STD

kw STDkw SST

k-kl w

Mass Flow rate Vs Temperature

Fig7: Variation of mass flow rate w.r.t temperature ()

310 315 320 325 330 335

4

5

6

7

8

9

TurbulentIntensity(%)

Temperature (K)

ke RNG

ke STD

kw STD

kw SST

k-kl w

Turbulent Intensity vs. Temperature

Fig8: Variation of Turbulent intensity rate w.r.t temperature ()


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310 315 320 325 330 335

0.002

0.004

0.006

0.008

0.010

0.012

F1

Temperature (K)

ke RNG

ke STD

kw STD

kw SST

k-kl w

Turbulent kinetic energy vs. temperature

Fig 9: Variation of turbulent kinetic energy transfer rate w.r.t temperature ()

310 315 320 325 330 335

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

TurbulentDissipationRate(Epsilon)(m2/s3)

Temperature (K)

ke RNG

ke STD

kw STD

kw SST

k-kl w

Turbulent dessipation rate vs Temperature

Fig 10 : Variation of Turbulent dissipation rate w.r.t temperature (

)

Other parameters of turbulent modelling i.e turbulent intensity and turbulent

kinetic energy and turbulent dissipation rate also increases with the increase in average

loop temperature. And the mass flow rate in the loop decreases.


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6.1.1. VALIDATION

1.60E+0161.80E+0162.00E+0162.20E+0162.40E+0162.60E+0162.80E+0163.00E+0163.20E+0163.40E+016

180000

190000

200000

210000

220000

230000

240000

250000

260000

Re

Grm*d/l

Vijayan_turb

ReRe vs Grm*d/l (ke RNG)

6.00E+0136.50E+0137.00E+0137.50E+0138.00E+0138.50E+0139.00E+0139.50E+013200000

205000

210000

215000

220000

225000

230000

235000

240000

245000

250000

255000

Re

Grm*d/l

Vijayan_turb

ReRe vs Grm*d/l (ke STD)

5. 00E+013 6.00E+013 7.00E+013 8.00E+013 9.00E+013 1.00E+014

190000

200000

210000

220000

230000

240000

250000

260000

Re

Grm*d/l

Vijayan_turb

ReRe vs Grm*d/l (kw STD)

5.00E+013 6.00E+013 7.00E+013 8.00E+013 9.00E+013 1.00E+014

190000

200000

210000

220000

230000

240000

250000

260000

Re

Grm*d/l

Vijayan_turb

ReRe vs Grm*d/l (kw SST)


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1.36E+0141.38E+0141.40E+0141.42E+0141.44E+0141.46E+0141.48E+0141.50E+014

260000

270000

280000

290000

300000

310000

320000

Re

Grm*d/l

Vijayan_turb

ReRe vs Grm*d/l (k-kl w)

Fig11 : Reynolds number v\s for various turbulence modelsThe results were plotted on Re v/s Gr*d/l and found that the results were in good

agreement with the Vijayans correlation.

Vijayans correlation:

Proposed correlation:


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6.1.2. INFERENCES

In this study, water is employed as the external fluid in both CHX and HHX. Inlet

temperature of water in CHX is kept constant at 305 K and that in HHX is varied from

313 K to 353 K in steps of 10 K. Results are obtained for operating pressure of 90 bar.

Operating pressure of the system is defined at the centre of HHX.

The total heat transfer rate reaches a maximum at temperature of around 315K

which is because of unique property of carbon dioxide, whose specific heat

reaches a maximum value at temperature of 315K (Pseudo critical region) as

shown below in the graph, which increases the heat transfer rate at that operating

temperature

Fig 12: Specific heat variation of Co2 with Temperature

The transition k-kl- turbulence model is seen deviating from the othermodels. This is because the transition from laminar to turbulence is over-predicted by the model, i.e, the transitional term is overestimated.

The Turbulence Intensity, Turbulence kinetic energy increases with

increase in temperature.


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6.2. SIMULATIONS OF WATER BASED NANOFLUIDS (Results)

6.2.1. ENHANCEMENT OF THERMAL CONDUCTIVITY AND HEAT

TRANSFER RATE.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.00

2

4

6

8

10

12

14

16

18

20

22

ThermalConducti

vity

Volume Fraction

Cu

TiO2

Al2O3

CuO

Fig13 :Variation of Thermal conductivity of Various nanofluids with volume

fraction

It is found after simulation of water based nanofluids with different nanoparticles

that the thermal conductivity as well as the heat transfer rate of the base fluid is enhanced

considerably. Further more the thermal conductivity increases linearly with the increase

in volume fraction of the nanoparticles in the base fluid. However there Heat transfer rate

in the CHX and HHX wall will increase upto a certain point after which it shows an

opposite trend which may be explained because of the settling and coagulation of

nanoparticles at higher volume fractions, the nanofluid tending to become a pure fluid.

And this Maximum point varies for different nanofluids which depends on the density of

the nanoparticles present.


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6.2.2. VISCOSITY

Viscosity is found to increase with the increases in Volume fraction (Vf) of the

nanoparticles present in the nanofluid.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

0.0024

0.0026

viscosity

vf

Cu

TiO2

Al2O3

CuO

Fig13 : Variation of Viscosity of Various nanofluids with Volume fraction

6.2.3. MASS FLOW RATE VARIATION

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.00.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0.019

0.020

Massflow

rate

Volume fraction

Cu

TiO2

Al2O3

CuO

Fig14 :Variation of the mass flow rate with Volume fraction


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Mass flow rate increases with increase in volume fraction Increase in mass flow

rate increases heat transfer rate. The trend followed is very much similar to heat transfer

rate. So, heat transfer rate is highly influenced by the mass flow rate.

6.2.4. VALIDATION

In order to validate the results obtained from the CFD simulation, an additional

comparison was carried out employing the experimental data reported earlier by Vijayan

(2002), which was obtained on a water based NCL with an electrical heater (with

constant wall heat flux) and a heat exchanger in place of a constant temperature heating

pipe and cooling pipe respectively. In view of the dissimilarity between two physical

configurations, the comparison was made in terms of non-dimensional parameters

Reynolds number (Re) and modified Grashof number (Grm) which are calculated at the

bulk mean temperature (Tm) of the loop. Figure shows that the data trends agree

reasonably well with the previously reported measured dataas shown in Fig 15-17.

Vijayans correlation

Proposed correlation


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0 6000000 12000000 180000002400000030000000200

300

400

500

600

700

800

900

1000

1100

1200

ReynoldsNumber

Gr(d/L)

Re

Re(Vijayan)Re(old)

Fig15 : Validation of Simulation results with Vijayans correlation (CuO)

3000000 6000000 9000000 12000000 15000000

400

600

800

1000

1200

1400

Re

Gr d/L

Re Al2O3

old prposed

vijayan

Fig16 : Validation of Simulation results with Vijayans correlation(Al2O3)


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6000000 7200000 8400000 9600000 10800000 12000000

200

400

600

800

1000

1200

Re

Gr d/L

Re TiO2Old proposed

Vijayan

Fig16 : Validation of Simulation results with Vijayans correlation (TiO2)


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7.

CONCLUSION

The addition of metal oxide nanoparticles considerably increases the heat transferrate in condenser and evaporator

High thermal conductivity of the solid nanoparticles than that of the base fluid

water increases the overall heat transfer rate .

The heat transfer rate is more for nanofluid containing pure Cu nanoparticles than

containing metal-oxide nanoparticles

The heat transfer rate increases with increase in volume fraction of nanoparticlesin the base fluid upto a certain point after which it decreases due to coagulation

and settling of particles.

Viscosity of the nanofluid increases with increase in the volume fraction of

nanoparticle.

Mass flow rate inside the natural circulation loop increases upto a certain amount

of volume fraction after which it decreases due to settling of particles

The peak of heat transfer rate reached shifts towards left as the density of the

particle increases


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8.

FUTURE WORKS

Further studies in the opted field on the basis of the carried out work can be extended to:

The study of behaviour of other nanoparticles like Carbon Nano Tubes(CNT),

Silver, Graphene Nanoflex and composites.

An experimental approach to further validate the results and suggest appropriate

correlations.

Other base fluid and particle combinations like Ethylene Glycol and PropyleneGlycol with the above suggested nano particles can be studied.

The geometrical properties of the loop can also be varied for a given nanofluid.

Effect of different operating conditions on the behaviour of nanofluid can be

studied.


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