Modeling evaporation in a Flat Evaporator Loop Heat Pipe with a Modified VOF Approach

1. Bharat B. Sharma
(Doctoral Student)
Guide:
Dr. Sudip K. Samanta, Prof. Gautam Biswas, Prof. Himadri Chattopadhyay,
Bharat B. Sharma1, Sudip K. Samanta1 , Gautam Biswas1,2, Balewgize A. Zeru1,3
Himadri Chattopadhyay4
1CSIR-CMERI, M.G. Avenue, Durgapur-713209, India, 2Indian Institute of Technology, Kanpur,
India , 3Jimma University, Jimma, Ethiopia , 4Jadavpur University, Kolkata, India
1

2.  Introduction to Flat Plate LHP(FPLHP)
 Available Literature and Gaps
 Problem Formulation
 Model Equations
 Numerical Scheme: Summary
 Interface Tracking using modified VOF method
 Validation of Mass Transfer Model
◦ Validation Problem
◦ Results
 Results for FPLHP
 Conclusions
 References
2

3.  Used for cooling electronic devices
 Suitable for widely found flat heating surfaces (no need of saddle as are used for
cylindrical evaporator)
 Passive(Works on application of heat load)
 Maintains Isothermality at contact surface
 High Capillary Pumping
 Coupled Phenomena of Capillary
Pumping, Evaporation, Convection and
Conduction
 Principal Element is Porous Wick
3

4. Author’s Wick Confg. Liquid Feeding
Direction
Wick
Condition
Heat
Load/Flux
Heat
Transfer
Coeff.
Dime
nsion
Cao and Faghri
(1994)
Flat Wick
without
Grooves
Bottom Fed Saturated 1.5 W/cm2 N.A Mixed
2D +
3D
Khrustalev and
Faghri(1995)
Inverted
Grooved Wick
Fed from Top
Surface
Unsaturated 13 to 260
W/cm2
50×103 to
175×103
W/m2 K
1D
Zhao and
Liao(2000)
Flat Wick
without
Grooves
Bottom Fed Unsaturated 7.5 to 22.5
W/cm2
6×103
to 11×103
W/m2 K
1D
Ren et al
(2007)
Flat Wick
without
Groove
Bottom Fed Unsaturated 0.02 to 2
W/cm2
5×103 to
15×103
W/m2 K
2D
Li and
Peterson(2011)
Flat Grooved
Wick
Fed from Top
Surface
Saturated 5 to 30 W/cm2 N.A 3D
Chernysheva
and
Maydanik(2012,
2013)
Flat Grooved
Wick
Side Feeding Unsaturated 20 to 900 W N.A 3D
4

5.  Assumed a vapor film to be present at wick-wall
interface following[1] in accordance with Solov`ev
and Kovalev[2]
 Implemented Modified VOF [3] model in ANSYS-
FLUENT for capturing interface dynamics
 Used extended Navier-Stokes Equations having Darcy
Viscous Drag Term for two-phase flow in porous wick
along with energy equation
 Used Kelvin Equation along with Clausius-Clapeyron
for modeling Capillary Pressure at L-V interface
following Ren et al[4]
5
Substance k,
W/mK
Cp, J/kgK µ, Pas ρ, kg/m3
Liquid
Ammonia
0.5003 4743.34 0.000138 610.44
Ammonia
Vapor
0.02563 3048.03 9.704×10-06 6.8919
Sintered
Nickel Wick
9.0 488.46 N.A 3854
Thermophysical Properties

6.  Assumptions:
◦ Homogeneous, Isotropic, and Rigid Porous Media
◦ Constant Solid and Fluid Properties
◦ Incompressible Fluid
◦ Energy Viscous Dissipation neglected
◦ Local Thermal Equilibrium between solid and Fluid phases
◦ Inertia drag term due to porous media in momentum equation is neglected
 Main features
◦ 2D Unsaturated Wick Modeling
◦ Evaporation at Liquid-Vapor interface
◦ Phase Change Mass Transfer Rate(Evaporation/Condensation)
6

7. 7
)
(
0
),
(
0
,
,
:
)
(
2
0
,
2
),
(
2
,
2
;
0
;
0
;
0
;
0
,
;
DE
x
u
x
v
and
CD
y
u
y
v
with
along
T
T
P
P
DE
for
H
y
and
B
x
at
and
CD
for
B
y
B
and
H
y
at
x
T
x
v
x
at
q
q
y
at
T
T
P
P
H
y
at
out
out
load
in
in

































8.  
 
 
    h
e
v
lv
e
T
sat
sat
v
l
g
l
v
c
v
l
l
v
v
l
l
v
v
v
v
l
vl
lv
v
v
v
v
S
h
k
h
U
t
h
T
T
R
h
P
P
T
P
P
v
T
R
P
P
pressure
Capillary
P
Term
Force
Capillary
Volumetric
F
F
U
K
g
p
UU
t
U
vapor
liquid
v
l
m
m
U
t
l

































































































.
.
1
1
exp
)
(
ln
.
,
,
;
1
.
)
(
2
.
.
Evaporative
Mass
Transfer
=
lv
h
q
.
Kelvin Equation
Clausius-Clapeyron Equation
Continuity Equation
Extended Navier-Stokes Equation
Energy Equation
8

9.  SOLVER : ANSYS-FLUENT13.0
 Pressure-Velocity Coupling :SIMPLE
 Pressure Interpolation :PRESTO
 Unsteady Terms :1st Order Accurate
 Momentum and Energy Equations :QUICK
 Volume fraction Equation :Geo-Reconstruct
 Gradients :Least-Squares Cell Based Scheme
 Interface Capturing :LVIRA algorithm following procedure specified by
Welch and Wilson[5]
 Interface Advection :Rudman’s Direction-split approach[6]
9

10.  Interface(orientation) is captured using modified VOF model following Agarwal[3]
in which LVIRA(Least Square Volume-of-Fluid Interface Reconstruction Algorithm)
algorithm of Puckett[7] was used for estimating correct normal vector to the
interface.
 Interface was advected using Flux Corrected Transport(FCT) method of Rudman[6].
 Interface Boundary Conditions:
 Jump in Mass Conservation Equation
 This contribution is used to estimate evaporating mass transport rate at L-V
interface using User Defined Subroutines
10

11. k,
W/mK
Cp,
J/kgK
µ, Pas ρ, kg/m3
Liquid
Water
0.5454 21800
0
4.67×10-
05
402.4
Water
Vapor
0.5383 35200
0
3.23×10-
05
242.7
 Problem Solved is Film Boiling at Near Critical Water conditions[3] assuming
bubbles to be present on the hot wall separated by Taylors fastest growing
wavelength given by Berenson[8] as
 g
v
l 






3
2
0
Thermophysical Properties
11

12.  Growth of Vapor Bubble
 Area Averaged Vapor Fraction
a) Agarwal et al[3]
b) Present Work(Constant Thermal
Properties)
a b
12

13. 10 W/cm2 40 W/cm2
Temperature Field
13

14. Velocity Field
14

15.  Mean Wall Temperature Vs Outlet Temperature
15

16.  Heat Transfer Coefficient
out
wall T
T
q
U


16

17.  We are able to predict startup characteristics of FPLHP.
 Model considers evaporation at the interface and is suitable for studying the
dynamics of evaporating front.
 H.T.C predicted results available in literature.
 Grooved Wick is better than wick without groove due to increased area of
evaporation
17

18. 1. Khrustalev, D., and Faghri, A.,1995. “Heat transfer in the inverted meniscus type evaporator at high
heat fluxes,” International Journal of Heat and Mass Transfer, 38(16),Nov, pp. 3091–3101.
2. Solov'ev, S.L., and Kovalev, S.A.,1987. "Heat transfer and hydrodynamics in the inverted meniscus
evaporator of a heat pipe", Proceedings of the Sixth International Heat Pipe Conference, Grenoble,
France, Vol. I, pp. 116-120
3. Agarwal, D.K., Welch, S.W.J., Biswas, G., and Durst, F., 2004. "Planer Simulation of Bubble Growth in
Film Boiling in Near-Critical Water Using a Variant of the VOF Method", J. Heat Transfer, 126, pp. 1-
11
4. Ren, C., Wu, Q.S., and Hu, M.B., 2007. “Heat transfer with flow and evaporation in loop heat pipe’s
wick at low or moderate heat fluxes,” International Journal of Heat and Mass Transfer, 50(11–12),
Jun., pp. 2296–2308.
5. Welch, S.W.J., and Wilson, J., A Volume of Fluid Based Method for Fluid Flows with Phase Change,
Journal of Computational Physics, Vol. 106, pp. 662-682 (2000).
6. Rudman, M., 1997, ‘‘Volume-Tracking Methods for Interfacial Flow Calculations,’’ Int. J. Numer.
Methods Fluids, 24, pp. 671– 691.
7. Puckett, E. G., Almgren, A. S., Bell, J. B., Marcus, D. L., and Rider, W. J., 1997, ‘‘High-Order
Projection Method for Tracking Fluid Interface in Variable Density Incompressible Flows,’’ J.
Comput. Phys., 130, pp. 269–282.
8. Berenson, P. J., 1961, ‘‘Film-Boiling Heat Transfer from a Horizontal Surface,’’ ASME J. Heat
Transfer,83, pp. 351–358
18

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