A new numerical model for stratified two-phase flows with wavy interface is derived in this study. Assuming an equilibrium condition between turbulent kinetic energy, potential energy, and surface energy, the turbulent length scale in the inner region of a two-layer turbulence approach can be described by a statistical model to account for the influence of the waves. The average wave number, which is an input parameter to this model, is taken from wave spectra. They can be predicted from a Boltzmann statistic of turbulent kinetic energy. The new turbulence model is compared with the two-phase k–ϵ turbulence model. Time-averaged flow properties calculated by the new approach, such as velocity, turbulence, and void profiles, are shown to be in good agreement with experimental data.

References

1.
White
,
F. M.
,
1999
,
Fluid Mechanics
, 4th ed.,
McGraw-Hill
,
Boston, MA
.
2.
Rashidi
,
M.
,
Hetsroni
,
G.
, and
Banerjee
,
S.
,
1991
, “
Mechanisms of Heat and Mass Transport at Gas–Liquid Interfaces
,”
Int. J. Heat Mass Transfer
,
34
(
7
), pp.
1799
1810
.
3.
Komori
,
S.
,
Ueda
,
H.
,
Ogino
,
F.
, and
Mizushina
,
T.
,
1982
, “
Turbulence Structure and Transport Mechanism at the Free Surface in an Open Channel Flow
,”
Int. J. Heat Mass Transfer
,
25
(
4
), pp.
513
521
.
4.
Rashidi
,
M.
, and
Banerjee
,
S.
,
1988
, “
Turbulence Structure in Free-Surface Channel Flows
,”
Phys. Fluids
,
31
(
9
), pp.
2491
2503
.
5.
Rashidi
,
M.
,
Hetsroni
,
G.
, and
Banerjee
,
S.
,
1992
, “
Wave-Turbulence Interaction in Free-Surface Channel Flows
,”
Phys. Fluids A
,
4
(
12
), pp.
2727
2738
.
6.
Lorencez
,
C.
,
Nasr-Esfahany
,
M.
,
Kawaji
,
M.
, and
Ojha
,
M.
,
1997
, “
Liquid Turbulence Structure at a Sheared and Wavy Gas–Liquid Interface
,”
Int. J. Multiphase Flow
,
23
(
2
), pp.
205
226
.
7.
Stäbler
,
T. D.
,
2007
, “
Experimentelle Untersuchung und physikalische Beschreibung der Schichtenströmung in horizontalen Kanälen
,” Ph.D. dissertation, Forschungszentrum Karlsruhe GmbH, Karlsruhe, Germany, Sc. Report No. FZKA 7296.
8.
Stäbler
,
T. D.
,
Meyer
,
L.
,
Schulenberg
,
T.
, and
Laurien
,
E.
,
2009
, “
Turbulence and Void Distribution in Horizontal Counter-Current Stratified Flow
,”
Int. J. Transp. Phenom.
,
11
, pp.
209
218
.
9.
Gabriel
,
S. G.
,
2014
, “
Experimentelle Untersuchung der Tropfenabscheidung einer horizontalen, entgegengerichteten Wasser/Luft-Schichtenströmung
,” Ph.D. dissertation, Karlsruher Institut für Technologie, Karlsruhe, Germany, KIT Sc. Report No. 7683.
10.
Daly
,
B. T.
, and
Harlow
,
F. H.
,
1981
, “
A Model of Countercurrent Steam–Water Flow in Large Horizontal Pipes
,”
Nucl. Sci. Eng.
,
77
, pp.
273
284
.
11.
Akai
,
M.
,
Inoue
,
A.
, and
Aoki
,
S.
,
1981
, “
The Prediction of Stratified Two-Phase Flow With a Two-Equation Model of Turbulence
,”
Int. J. Multiphase Flow
,
7
(
1
), pp.
21
39
.
12.
Wintterle
,
T.
,
Laurien
,
E.
,
Stäbler
,
T.
,
Meyer
,
L.
, and
Schulenberg
,
T.
,
2008
, “
Experimental and Numerical Investigation of Counter-Current Stratified Flows in Horizontal Channels
,”
Nucl. Eng. Des.
,
238
(
3
), pp.
627
636
.
13.
Höhne
,
T.
, and
Mehlhoop
,
J.-P.
,
2014
, “
Validation of Closure Models for Interfacial Drag and Turbulence in Numerical Simulations of Horizontal Stratified Gas–Liquid Flows
,”
Int. J. Multiphase Flow
,
62
, pp.
1
16
.
14.
Berthelsen
,
P. A.
, and
Ytrehus
,
T.
,
2005
, “
Calculations of Stratified Wavy Two-Phase Flow in Pipes
,”
Int. J. Multiphase Flow
,
31
(
5
), pp.
571
592
.
15.
Chen
,
H. C.
, and
Patel
, V
. C.
,
1988
, “
Near-Wall Turbulence Models for Complex Flows Including Separation
,”
AIAA J.
,
26
(
6
), pp.
641
648
.
16.
Benz
,
M.
,
2016
, “
Statistische Modellierung einer geschichteten Zweiphasenströmung
,” Ph.D. dissertation, Karlsruher Institut für Technologie, Karlsruhe, Germany, KIT Sc. Report No. 7705.
17.
Belt
,
R. J.
,
Van‘t Westende
,
J. M. C.
,
Prasser
,
H. M.
, and
Portela
,
L. M.
,
2010
, “
Time and Spatially Resolved Measurements of Interfacial Waves in Vertical Annular Flow
,”
Int. J. Multiphase Flow
,
36
(
7
), pp.
570
587
.
18.
Rusche
,
H.
,
2002
, “
Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions
,”
Ph.D. dissertation
, Imperial College of Science, Technology and Medicine, London, UK.
19.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
,
1992
, “
A Continuum Method for Modelling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.
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