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MSs Thesisi Presentation about two-phase nanofluid modelling
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
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Need for Improved Thermal Management
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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?
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TEM image of nanoparticles, source: M.H. Kayhania et al.
Al2O3 water nanofluid, source: http://www.xtremesyste ms.org/f
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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.
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Nanofluid Modeling
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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
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Experimental Studies on Nanofluids
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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.
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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
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Mathematical Models
Single-phase models
Two-phase models
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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.
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Introduction to Single-phase Models
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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):
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= 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.
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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.
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Dispersion and Brownian Viscosities
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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)
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Two phase models
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Continuity Equation: m = 0
= + 1
= 1 +
Momentum Equation:
= + + + +
(,, ,,)
Mixture Model
Drift Velocity: Particle phase: , = Base fluid phase: , =
Mixture Viscosity: =
+ + + =
= +
Energy Equation:
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For incompressible nanofluid at steady state:
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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:
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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;
=
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Eulerian-Eulerian Model
Kalteh et al. (2011) showed that and are negligible. Therefore both forces are neglected in our model.
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Base fluid Phase:
, +
,
=
,
+
(,
) ( )
Particle Phase:
, +
,
=
,
+
,
+ ( )
Steady State Energy Equation:
Eulerian-Eulerian Model
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)
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Numeric Methods and Problem Description
Problem domain
Numeric methods
Boundary conditions
Model validation
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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
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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.
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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
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Results
Friction factor prediction of models
Convective heat transfer prediction of models
Computational efficiency of models
hBN-water nanofluid results
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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).
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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.
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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.
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Recommendations for Future Work
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Acknowledgments
Boazii University Department of Mechanical Engineering
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.
Questions
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