MSc Thesis Document

SINGLE AND TWO PHASE CONTINUUM MODELING OF

LAMINAR NANOFLUID FORCED CONVECTION

by

Sinan Gktepe

June, 2013

Supervisor: Dr. Kunt Atalk Co-supervisor: Dr. Hakan Ertrk

Boazii University

Department of Mechanical Engineering

Outline

Introduction to Nanofluids

Literature

Mathematical Models

Single-phase Approach

Two-phase Approach

Problem Domain and Numerical Methods

Results

Conclusion

03.07.2013 Sinan GKTEPE 2

Boazii University Department of Mechanical Engineering

Need for Improved Thermal Management



Increasing cooling demand for data centers, power electronics, etc. Focus:

High efficiency, smaller form factors. Rapid battery charging and prolonged battery life of EVs.

Increase in power density: need for improved thermal management. Engineered fluids are key to improve thermal performance.

What is and Why Nanofluids?


TEM image of nanoparticles, source: M.H. Kayhania et al.

Al2O3 water nanofluid, source: http://www.xtremesyste ms.org/f


Nanofluids:

Colloidal suspensions of nanoparticles (Al203, Ti02, Fe304, hBN, etc.).

Production methods: One-step, two-step

Improved thermal management:

Enhanced thermal conductivity and convection heat transfer.

Tunable physical properties:

- Particle size, concentration, type, etc.

- Magnetic field

Application areas:

Automotive industry, cooling of electronics, bio medical, solar water heating, nuclear reactors.

Thermal and hydrodynamic characterization and robust modeling is needed for system and equipment design.


Nanofluid Modeling


Micro Models Essential for property characterization Molecular dynamics Lattice Boltzmann Brownian dynamics

Macro Models Essential for design of engineering systems Single-phase: Nanofluid is a single continuum

Homogeneous model non-Homogeneous model

Two-phase: Particle and fluid phases are considered separately Eulerian- Volume of Fluid Model Eulerian - Mixture Model Eulerian - Eulerian Model

Heat Transfer Studies on Macro Models Researcher Flow Regime Flow B.C. Prop. Model Geo.

Maiga et al. (2004) Laminar/ Turbulent FD CHF Const. SP Tube

Ozerinc et al. (2012) Laminar FD CHF/CWT Temp. Dep.

SP-D Tube

Fard et al. (2009) Laminar FD CWT Const. SP/TP Tube

Akbari et al. (2011) Laminar Entry CHF Temp. Dep.

SP/EE/M/VOF

Tube

Kalteh et al. (2011) Laminar Entry CHF Const. EE Micro

Ch.

Bianco et al. (2009) Laminar Entry CHF Temp. Dep.

SP/EE Tube

Lotfi et al. (2010) Laminar Entry CHF Const. SP/EE/M Tube

Mokmeli et al. (2009) Laminar Entry CHF Const. SP-D Tube

Moraveji et al.(2011) Laminar Entry CHF Const. SP Tube

There is no complete study comparing, state-of-the art and recently proposed models

No comparison of computational efficiency of models and coupling algorithms

14.11.2012 6 6


Experimental Studies on Nanofluids

14.11.2012 7


Annop et al., 2009 Effect of electro viscous forces on nanofluids viscosity is investigated, data is unusable.

Hwang et al., 2009 Laminar nanofluid flow in a circular tube is investigated .

C.T. Nguyen et al. Hysteresis in Al2O3 nanofluids viscosity above 60

oC is reported.

Wen et al., 2004 Forced convection of nanofluid in a circular pipe with constant heat flux boundary condition.

Heris et al., 2006 Forced convection of nanofluid in a circular pipe with constant wall temperature boundary condition.

Li et al., 2011 Thermal conductivity of Boron Nitride ethylene glycol nanofluid.

Sinan GKTEPE



Current status

Over 2000 publications since 1995

Over 100 patents since 2001

Used in high-end automotive applications (tunable dampers)

Commercialization stage

Challenges

Production cost of nanoparticles.

Long term instability and reliability issues.

Environmental and health impact.

Lack of agreement between reported results:

Heat transport mechanism and rheological behavior

Experimental data

Lack of agreement in modeling approaches.

Current Status and Challenges

Objective of this study is: To compare accuracies and computational efficiencies of recent

state-of-the-art nanofluid models.

To introduce a new viscosity model to increase accuracy of single-phase models.

Compare two-different coupling algorithms for Eulerian-Eulerian two-phase model.

Provide data for forced convection of hBN nanofluid.

Objective




Mathematical Models

Single-phase models

Two-phase models


For all single phase models, nanofluid is a single continuum, nanoparticles and base fluid share same temperature and velocity field.

Homogeneous Models:

Nanofluid is represented by its effective properties.

Effect of particle-fluid, and particle-particle interactions are neglected.

non-Homogeneous Models:

Nanofluid is represented by its effective properties.

Effect of particle-fluid, and particle-particle interactions are included in the effective properties.

Calibration of models with respect to experimental data is required.

Can be regarded as advanced homogeneous models.

03.07.2013 Sinan GKTEPE 11 Boazii University Department of Mechanical Engineering

Introduction to Single-phase Models



Single-phase Model Equations

Continuity Eq. = 0

Momentum Eq. nf = + 2

Energy Eq. nf , = ()

Effective density and specific heat:

= +

, = , + ,

Effective thermal conductivity and viscosity:

Homogeneous model:

= and =

non-Homogeneous models: Dispersion models: = + and = +

Brownian model: = + and = +

For incompressible nanofluid, at steady state:

Nanofluid Properties Nanofluid Thermal Conductivity

Hamilton and Crosser, (1962) (no Temp. Depend.):

= + 1 1

+ 1 +

Chon et al. (2005) (Temperature dependent):

= 1 + 64.7 0.7460

0.3690

0.7476

Pr0.99551.2321

Pr =

Re =

=

32 bf

= 10/()

Nanofluid Viscosity:

Einstein equation (1906):

14.11.2012 13

= 1 + 2.5

To account for the effect of Brownian motion of particles on energy transport. Two thermal dispersion models and one Brownian conductivity model are proposed.

1. Single-phase dispersion model 1, (Xuan and Roetzel, 2000) (SPD1)

is = 1

2. Single-phase dispersion model 2, (Mokmeli and Saffar-Avval , 2009) (SPD2)

isp = 2 p

3. Single-phase Brownian thermal conductivity model (Koo and Kleinstreuer, 2004) (SPBM):

br = 5 104,

Nanofluid viscosity is estimated by Einstein Equation.

Nanofluid thermal conductivity is estimated by temperature dependent model.



Dispersion and Brownian Thermal Conductivities

To account for the effect of Brownian motion of particles on momentum transport. Dispersion and Brownian viscosity models are considered.

1. Brownian viscosity model (BVM) (Raisee, M. and M. Moghaddami, 2008) :

Brownian Prandtl () number assumed to be equal to unity so;

=,

br = 5 104 ,

,

2. Dispersion viscosity model (DVM):

Brownian Prandtl number assumed to be equal to nanofluid Prandtl number so;

=,

= 2 p

Nanofluid viscosity for DVM, and BVM is estimated by Einstein Equation.



Dispersion and Brownian Viscosities



Summary of Single Phase Models

Model Name Thermal Conductivity Model(s) Viscosity Model(s)

HSPM Hamilton et al. 0 Einstein 0

HSPM-TD Chon et al. 0 Einstein 0

SPD1 Chon et al. Xuan et al. Einstein 0

SPD2 Chon et al. Mokmeli et al. Einstein 0

DVM Chon et al. Mokmeli et al. Einstein From Mokmeli Prbr=Prnf = 6.97

SPBM Hamilton et al. Koo et al. Einstein 0

BVM Hamilton et al. Koo et al. Einstein From Koo et al.

Prbr=1

Summary of mathematical models that are used to build up single-phase models

DVM: Dispersion viscosity model. BVM: Brownian viscosity model. SPD1 and SPD2: Single phase dispersion models 1 and 2.

SPBM: Single-phase Brownian conductivity model. HSPM: Homogeneous single-phase model. HSPM-TD: Homogeneous single-phase model with temperature dependent properties.

Base fluid and nanoparticles can have different velocity and temperature fields.

Two phase models are suggested for applications where interaction between phases are not well defined

Two common two-phase models:

Eulerian Eulerian Each phase is considered as different continuum, and phase equations are coupled using interphase equations

Eulerian Mixture Equations are solved for mixture phase , and phase velocities are related by empirical correlations.

Coupling schemes:

Phase Coupled Semi Implicit Method for Pressure Linked Equations (PC-SIMPLE)

Full Multiphase Coupled (FMC)



Two phase models

14.11.2012 18

Continuity Equation: m = 0

= + 1

= 1 +

Momentum Equation:

= + + + +

(,, ,,)

Mixture Model

Drift Velocity: Particle phase: , = Base fluid phase: , =

Mixture Viscosity: =

+ + + =

= +

Energy Equation:


For incompressible nanofluid at steady state:



Eulerian-Eulerian Model

Continuity Equation:

Liquid phase:

+

= 0

Particle phase:

+

= 0

x Momentum Equation:

+

=

+

+

+ +

+

=

+

+

+

For incompressible nanofluid at steady state:

Particle phase:

Base fluid phase:


Fd (Drag force): = ( )

For dilute solutions is defined accordingly to Syamlal and Gidaspow (1985) as;

=3

4

1

2.65

Cd is the drag coefficient and it is given as;

=

24

1 + 0.150.697 1000

0.44 > 1000

Rep is particle Reynolds number and defined as;

=



Kalteh et al. (2011) showed that and are negligible. Therefore both forces are neglected in our model.

14.11.2012 21

Base fluid Phase:

, +

,

=

,

+

(,

) ( )

Particle Phase:

, +

,

=

,

+

,

+ ( )

Steady State Energy Equation:


Volumetric heat transfer coefficient ():

=6 1

hp is defined by Wakao and Kagei (1982) as;

=

= 2 + 1.10.61/3

, , are the effective thermal conductivity determined by Kuipers et al. (1992)


Sinan GKTEPE


Numeric Methods and Problem Description

Problem domain

Numeric methods

Boundary conditions

Model validation




Numerical Methods and Definition of Problem

Boundary conditions: Uniform inlet velocity no-slip boundary condition at walls Constant heat flux at wall

Domain discretization Quadrilateral elements Uniform structured grid 15 x 2000 elements

Actual problem domain:

Part of the grid used in discretization: R

x=0



Grid Independency/Validation Study

Figure: Grid independency study

Fluid: Water Re: 1050 Shah Eq. Used in this study is;

+ 1

= 1 +

115.2

0.53 5

5 3 3 10

= 5.364 1 + 220 10 9 3 10

= 1 + ( 0.0207) 2 3

= 1 + 220 10 9

Nusselt Number is defined as;

=

=

"

( )

=

0 50 100 150 200 250 3000

5

10

15

20

25

30

x/D

Nu

x

G1 - 6 x 1000

G2 - 10 x 1000

G3 - 15 x 2000

Exp.

Shah Eq.



Grid Independency Study

G3 has 0.7% error from theoretical value of Darcy friction factor

=82

Darcy friction factor used here;

: wall shear stress : mean velocity

Fluid: Water Re: 1050

0 50 100 150 200 250 3000.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

x/D

Fri

cti

on

fac

tor

(

f x )

G1 - 6 x 1000

G2 - 10 x 1000

G3 - 15 x 2000

Theoretical - Water

Theoretical pure water


Results

Friction factor prediction of models

Convective heat transfer prediction of models

Computational efficiency of models

hBN-water nanofluid results




Friction Factor Predictions

EEM is the most accurate model. Single-phase model fails to predict

friction factor.

BVM:

br = 5 104,

=,

Prbr Prbr = 1

DVM:

is = 2

=,

Prbr Prbr= 6.97

Calibration point: = 178

Calibration data: Wen and Ding.

DVM Prbr=6.97 is the most accurate single-phase model.

400 450 500 550 600 6500.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

Reynolds Number

Ap

pare

nt

Fri

cti

on

Facto

r

HSPM

DVM Prbr

=1

DVM Prbr

=6.97

BVM

EEM

EMM

Water

Exp. Hw ang et al.

2 3



Friction Factor Predictions

The most accurate model is EEM.

DVM model is the most accurate single-phase model.

Brownian effects can be represented as an additional diffusion mechanism.

= 8

2

Re = 501

Nanofluid: 0.3%Al2O3-water

0 50 100 150 200 250 3000.12

0.14

0.16

0.18

0.2

0.22

0.24

x/D

Fri

cti

on

Fac

tor

(

f x )

EEM

EMM

BVM

DVM Prbr

=6.97

DVM Prbr

=1

Water



Predicted Heat Transfer Coefficient

EEM and EMM are the most accurate models. SPD2 is the most accurate single-phase model. SPBM and HSPM-TD have same accuracies.

SPD 1:

= 1

SPD2:

= 2

SPBM:

br = 5 104,

Calibration point: = 178

Re = 1050

Nanofluid: 1.6% Al2O3-water 0 50 100 150 200 250 300

500

1000

1500

2000

2500

3000

x/D

hx

[W

/m2 K

]

EMM

Exp. Wen and Ding

EMM by Akbari et al.

EEM

HSPM

HSPM-TD

SPD2

SPD1

SPBM



Accuracy of Models

20 40 60 80 100 120 140 160 180-50

-40

-30

-20

-10

0

10

20

30

x/D

Erro

r i

n P

red

icti

ng

hx (

x )

[%

]

EEM 1.6%

EEM 0.6%

SPD2 1.6%

SPD2 0.6%

SPBM 1.6%

SPBM 0.6%

HSPM 1.6%

HSPM 0.6%

2 3

Only EEM is considered, since it has same accuracy as EMM.

Error decreases as volume faction decreases

The most accurate single phase model is SPD2

EEM model is the most accurate model in entry region

SPD1:

= 1

SPD2:

= 2



Effect of Volume Fraction

0 50 100 150 200 250 300600

800

1000

1200

1400

1600

1800

2000

x/D

hx [

W/m

2 K]

1.6% Exp.

1% Exp.

0.6% Exp.

Water

1.6%, EEM

1%, EEM

0.6%, EEM

2 3

0 50 100 150 200 250 300600

800

1000

1200

1400

1600

1800

2000

x/D

hx

[W/m

2 K]

1.6% Exp.

1% Exp.

0.6% Exp.

Water

1.6% SPD2

1% SPD2

0.6% SPD2

Eulerian-Eulerian model over predicts heat transfer as flow develops.

Error in Eulerian-Eulerian model increases as volume fraction increases.

Same calibration constant is also valid for 0.6% and 1.6% volume concentrations.

SPD2 under predicts heat transfer coefficient.

2 3

Calibration point



Nusselt Number Predictions

Nusselt Number:

=

For all models, by Hamilton and Crosser.

SPD2 is most accurate at specified axial distance.

SPD2 can predict change in Reynolds number accurately compared to other models.

SPBM model is the least accurate non-homogeneous model.

600 800 1000 1200 1400 1600 1800 20005

6

7

8

9

10

11

12

Reynolds Number

Nu

x

1.6%, Exp.

1.6%, SPD1

1.6%, SPD2

1.6%, EMM

1.6%, EEM

1.6% BVM

2 3



PC-SIMPLE vs. Full Multiphase Coupled

For low volume concentrations, computational cost can be reduced up to 50%

EEM model is the most efficient two-phase model.

Nanofluid: 1.6% Al2O3-water Reynolds Number: 1050

0 50 100 150 200 250 3001000

2000

3000

4000

5000

6000

x/D

hx [

W/m

2K

]

PC - SIMPLE

FCM

E.Eulerian E.Mixture S.Phase

[%] PC-

SIMPLE FMC SIMPLE

0.6 157.14 82.19 552.80 77.64

1 158.62 89.81 572.71 78.05

1.6 163.79 111.69 566.50 81.68

CPU Time [s]

Processor: Intel XEON 2.4 GHz



Hexagonal Boron Nitride

Graphite like layered atomic structure.

Orthotropic properties

High conductive in direction parallel to its basal plane.

Poor conductive in direction perpendicular to its basal plane.

Di-electric

Only one study in literature that considers hBN-EG nanofluids.

Density Specific heat Thermal conductivity

Al2O3 3984 kg/m3 755 J/Kg K 33 W/mK

hBN 2300 kg/m3 800 J/Kg K 600 , 30 , 33.47 W/mK (D.A)

Atomic structure of hexagonal Boron Nitride

Covalent bonds Van der Waals Forces

Basal plane



hBN-water Results

Comparison with experimental data is required.

Comparison of effective conductivity models for hBN is required.

0 50 100 150 200 250 300500

600

700

800

900

1000

1100

1200

1300

1400

1500

x/D

hx(x

) [

W/m

2K

]

Water

1.6% hBN-water

1% hBN-water

0.6% hBN-water

0 50 100 150 200 250 3000

500

1000

1500

2000

2500

3000

3500

4000

x/D

hx(x

) [W

/m2K

]

Water

1.6% hBN-water

1% hBN-water

0.6% hBN-water

There is %50 difference between two model.



hBN-water vs. Al2O3-water

600 700 800 900 1000 11001090

1095

1100

1105

1110

1115

1120

1125

1130

P

hx(x

) [

W/m

2K

]

1.6% Al2O

3-w ater

1.6% hBN-w ater

Even for the worst case scenario, use of hBN particles yields higher heat transfer coefficient.

Re=1050

Single Phase Models:

Fails to represent change in friction coefficient at fully developed region.

With thermal dispersion, single phase model can be used as an effective method at entry region if experimental data is available for calibration.

Dispersion model with new formulation (SPD2) is more accurate than the older formulation (SPD1) at entry region.

Dispersion viscosity model is the most accurate single-phase model in prediction of friction factor.

Calibration constant is independent of Reynolds number and particle volume fraction (SPD2).



Conclusion

Two Phase Models:

Eulerian-Eulerian model is effective in predicting friction and convective heat transfer coefficients at entry region.

Eulerian-Eulerian model is suggested if there are no experimental data.

For Eulerian-Eulerian model, computational time can be reduced up to 50% by implementation of Full Multiphase Coupled Scheme.

hBN:

Assessment of effective thermal conductivity models is required.

Experimental results are needed to compare numeric models.

For fixed pressure drop, hx enhancement is higher than that of Al2O3.



Cont. Conclusion

Unsteady comparison of single and two phase models.

Extensive study that covers calibrations constants of single-phase models for different nanoparticles and base fluids

Experimental studies of Hexagonal Boron Nitride nanofluids.

Numerical studies on anisotropic nanoparticles.

Theoretical studies on two-phase mode parameters for better modeling of nanofluids.



Recommendations for Future Work


Acknowledgments


I would like to thank to my supervisors Dr. Atalk and Dr. Ertrk for their guidance during my academic study.

This study is supported by TBTAK Under the grant 111M1777 of the 1001 Program.

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