Abstract

Numerical simulations were carried out to study the evaporation of a drop that is released into a parallel stream of fluid at a higher temperature. A coupled level-set and volume-of-fluid (CLSVOF) interface capturing method was deployed to capture the dynamic interface between the drop liquid and the surrounding fluid. Modified forms of mass, momentum, and energy equations were solved together with the species concentration equation. The pressure jump at the interface was handled by accurate estimation of the continuum surface force. The jumps in mass and energy at the interface were carefully resolved by considering appropriate source terms in the continuity and energy equations. At the interface, the procedure of velocity computation was incorporated by extending the liquid-phase velocity onto the entire domain and by calculating the Stefan flow to predict the interface velocity accurately. The calculation of the velocity using this step leads to the exact estimation of mass transfer through the interface. The model was validated against both temperature gradient-based and vapor mass concentration gradient-based evaporation test cases. Temporal histories of the average Nusselt number and Sherwood number during the lifetime of an evaporating drop were predicted in terms of the pertinent input parameters, namely, Reynolds number, Prandtl number, and Schmidt number.

References

1.
Hirt
,
C.
, and
Nichols
,
B.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
(
1
), pp.
201
225
.10.1016/0021-9991(81)90145-5
2.
Nichols
,
B. D.
,
Hirt
,
C. W.
, and
Hotchkiss
,
R. S.
,
1980
, “
SOLA-VOF: A Solution Algorithm for Transient Fluid Flow With Multiple Free Boundaries
,”
Los Alamos National Laboratory
Report, Los Alamos, NM, Report No. LA-8355.
3.
Wohak
,
M. G.
, and
Beer
,
H.
,
1998
, “
Numerical Simulation of Direct-Contact Evaporation of a Drop Rising in a Hot, Less Volatile Immiscible Liquid of Higher Density—Possibilities and Limits of the SOLA-VOF/CSF Algorithm
,”
Numer. Heat Transfer, Part A
,
33
(
6
), pp.
561
582
.10.1080/10407789808913955
4.
Osher
,
S.
, and
Sethian
,
J. A.
,
1988
, “
Fronts Propagating With Curvature Dependent Speed: Algorithms Based on Hamilton–Jacobi Formulations
,”
J. Comput. Phys.
,
79
(
1
), pp.
12
49
.10.1016/0021-9991(88)90002-2
5.
Unverdi
,
S. O.
, and
Tryggvason
,
G.
,
1992
, “
A Front-Tracking Method for Viscous, Incompressible, Multi Fluid Flows
,”
J. Comput. Phys.
,
100
(
1
), pp.
25
37
.10.1016/0021-9991(92)90307-K
6.
Son
,
G.
, and
Dhir
,
V. K.
,
1998
, “
Numerical Simulation of Film Boiling Near Critical Pressures With a Level Set Method
,”
ASME J. Heat Transfer-Trans. ASME
,
120
(
1
), pp.
183
192
.10.1115/1.2830042
7.
Son
,
G.
, and
Dhir
,
V. K.
,
2008
, “
Numerical Simulation of Nucleate Boiling on a Horizontal Surface at High Heat Fluxes
,”
Int. J. Heat Mass Transfer
,
51
(
9–10
), pp.
2566
2582
.10.1016/j.ijheatmasstransfer.2007.07.046
8.
Welch
,
S. W.
, and
Wilson
,
J.
,
2000
, “
A Volume of Fluid-Based Method for Fluid Flows With Phase Change
,”
J. Comput. Phys.
,
160
(
2
), pp.
662
682
.10.1006/jcph.2000.6481
9.
Agarwal
,
D.
,
Welch
,
S.
,
Biswas
,
G.
, and
Durst
,
F.
,
2004
, “
Planar Simulation of Bubble Growth in Film Boiling in Near-Critical Water Using a Variant of the VOF Method
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
126
(
3
), pp.
329
338
.10.1115/1.1737779
10.
Huang
,
L. J.
, and
Ayyaswamy
,
P. S.
,
1990
, “
Evaporation of a Moving Liquid Drop: Solutions for Intermediate Reynolds Numbers
,”
Int. Commun. Heat Mass Transfer
,
17
(
1
), pp.
27
38
.10.1016/0735-1933(90)90076-V
11.
Jog
,
M. A.
,
Ayyaswamy
,
P. S.
, and
Cohen
,
I. M.
,
1996
, “
Evaporation and Combustion of a Slowly Moving Liquid Fuel Droplet: Higher Order Theory
,”
J. Fluid Mech.
,
307
, pp.
135
165
.10.1017/S0022112096000079
12.
Sadhal
,
S. S.
,
Ayyaswamy
,
P. S.
, and
Chung
,
J. N.
,
1997
,
Transport Phenomena With Drops and Bubbles
,
Springer Verlag
,
New York
.
13.
Sirignano
,
W. A.
,
2010
,
Fluid Dynamics and Transport of Droplets and Sprays
,
Cambridge University Press
,
New York
.
14.
Tanguy
,
S.
,
Menard
,
T.
, and
Berlemont
,
A.
,
2007
, “
A Level Set Method for Vaporizing Two-Phase Flows
,”
J. Comput. Phys.
,
221
(
2
), pp.
837
853
.10.1016/j.jcp.2006.07.003
15.
Schlottke
,
J.
, and
Weigand
,
B.
,
2008
, “
Direct Numerical Simulations of Evaporating Droplets
,”
J. Comput. Phys.
,
227
(
10
), pp.
5215
5237
.10.1016/j.jcp.2008.01.042
16.
Sussman
,
M.
,
2003
, “
A Second Order Coupled Level Set and Volume-of-Fluid Method for Computing Growth and Collapse of Vapor Bubbles
,”
J. Comput. Phys.
,
187
(
1
), pp.
110
136
.10.1016/S0021-9991(03)00087-1
17.
Irfan
,
M.
, and
Muradoglu
,
M.
,
2017
, “
A Front Tracking Method for Direct Numerical Simulation of Evaporation Process in a Multiphase System
,”
J. Comput. Phys.
,
337
, pp.
132
153
.10.1016/j.jcp.2017.02.036
18.
Scapin
,
N.
,
Costa
,
P.
, and
Brandt
,
L.
,
2020
, “
A Volume-of-Fluid Method for Interface-Resolved Simulations of Phase Changing Two-Fluid Flows
,”
J. Comput. Phys.
,
407
, p.
109251
.10.1016/j.jcp.2020.109251
19.
Zhao
,
S.
,
Zhang
,
J.
, and
Ming
,
J. N.
,
2022
, “
Boiling and Evaporation Model for Liquid-Gas Flows: A Sharp and Conservative Method Based on the Geometrical VOF Approach
,”
J. Comput. Phys.
,
452
, p.
110908
.10.1016/j.jcp.2021.110908
20.
Popinet
,
S.
,
2015
, “
A Quadtree-Adaptive Multigrid Solver for the Serre–Green–Naghdi Equations
,”
J. Comput. Phys.
,
302
, pp.
336
358
.10.1016/j.jcp.2015.09.009
21.
Reutzsch
,
J.
, Kieffer-
Roth
,
C.
, and
Weigand
,
B.
,
2020
, “
A Consistent Method for Direct Numerical Simulation of Droplet Evaporation
,”
J. Comput. Phys.
,
413
, p.
109455
.10.1016/j.jcp.2020.109455
22.
Tomar
,
G.
,
Biswas
,
G.
,
Sharma
,
A.
, and
Agrawal
,
A.
,
2005
, “
Numerical Simulation of Bubble Growth in Film Boiling Using a Coupled Level-Set and Volume-of-Fluid Method
,”
Phys. Fluids
,
17
(
11
), p.
112103
.10.1063/1.2136357
23.
Gerlach
,
D.
,
Tomar
,
G.
,
Biswas
,
G.
, and
Durst
,
F.
,
2006
, “
Comparison of Volume-of-Fluid Methods for Computing Surface Tension-Dominant Two-Phase Flows
,”
Int. J. Heat Mass Transfer
,
49
(
3–4
), pp.
740
754
.10.1016/j.ijheatmasstransfer.2005.07.045
24.
Pandey
,
V.
,
Deka
,
H.
,
Biswas
,
G.
, and
Dalal
,
A.
,
2020
, “
Dynamics of Growth and Breakup of an Evaporating Pendant Drop
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
142
(
2
), p.
021601
.10.1115/1.4045414
25.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
,
1992
, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.10.1016/0021-9991(92)90240-Y
26.
Clift
,
R.
,
Grace
,
J. R.
, and
Weber
,
M. E.
,
1978
,
Bubbles, Drops, and Particles
,
Academic Press
,
New York
.
27.
Ranz
,
W. E.
, and
Marshall
,
W. R.
,
1952
, “
Evaporation From Drops Part II
,”
Chem. Eng. Prog.
,
48
, pp.
173
180
.
28.
Kulmala
,
M.
,
Vesala
,
T.
,
Schwarz
,
J.
, and
Smolik
,
J.
,
1995
, “
Mass Transfer From a Drop—II. Theoretical Analysis of Temperature Dependent Mass Flux Correlation
,”
Int. J. Heat Mass Transfer
,
38
(
9
), pp.
1705
1708
.10.1016/0017-9310(94)00302-C
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