We examine wave characteristics of a liquid-vapor mixture in order to investigate certain features of the homogeneous relaxation model. The model is described by one-dimensional averaged mass, momentum, energy equations, and a rate equation. Since the homogeneous relaxation model delivers a qualitative incompatibility of numerical and experiment results of large wave propagation, it is extended so as to take into account the heat conduction in the liquid surrounding vapor bubbles. With this extension, the effects of spreading and damping of the waves in the numerical solutions are similar to those observed in the experiment. Thus, a new model is created, the homogeneous relaxation-diffusion model which contains two physical quantities—the relaxation time and macroscopic heat conduction coefficient. Both quantities are determined based on experimental data. It seems that the results obtained from the new model agree well qualitatively with the experiments.

1.
Ardron
K. H.
, and
Duffey
R. D.
,
1978
, “
Acoustic Wave Propagation in a Flowing Liquid-Vapor Mixture
,”
International Journal of Multiphase Flow
, Vol.
4
, pp.
303
322
.
2.
Batchelor, G. K., 1969, “Compression Waves in a Suspension of Gas Bubbles in Liquid,” Fluid Dynamics Transactions, W. Fiszdon, P. Kucharczyk and W. J. Prosnak, eds., PWN Warszawa, Vol. 4, pp. 415–424.
3.
Bilicki
Z.
, and
Kestin
J.
,
1990
, “
Physical Aspects of the Relaxation Model in Two-Phase Flow
,”
Proceedings of Royal Society, London
, Series A
0428
, pp.
379
397
.
4.
Bilicki
Z.
,
Kestin
J.
, and
Pratt
M. M.
,
1990
, “
A Reinterpretation of the Results of the Moby Dick Experiments in Terms of the Nonequilibrium Model
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
112
, pp.
212
217
.
5.
Bilicki
Z.
, and
Kardas
D.
,
1993
, “
Numerical Solution of Transient and Non-equilibrium Two-Phase Liquid-Vapour Flow
,”
Transactions of Institute of Fluid-Flow Machinery
, Vol.
95
, pp.
105
129
.
6.
Bilicki, Z., 1994, “Concept of Internal Variables in the Light of Contemporary Thermodynamics of Irreversible Processes and its Application in Two-Phase Flow” (in Polish), Zeszyty Naukowe IMP PAN, Vol. 421/94.
7.
Bilicki
Z.
,
Kwidzinski
R.
, and
Mohammadein
S. A.
,
1996
, “
Evaluation of the Relaxation Time of Heat and Mass Exchange in the Liquid-Vapour Bubble Flow
,”
International Journal of Heat and Mass Transfer
, Vol.
39
, pp.
753
759
.
8.
Bilicki
Z.
, and
Michaelides
E. E.
,
1997
, “
Thermodynamic Nonequilibrium in Liquid-Vapour Flow
,”
Journal of Nonequilibrium Thermodynamics
, Vol.
22
,
99
109
.
9.
Campbell, I. J. and Pitcher, A. S., 1954, “Flow of Air-Water Mixtures,” Symposium at Admiralty Research Laboratory, Middlesex.
10.
Downar-Zapolski, P., 1992, “An Influence of the Thermodynamic Disequilibrium on the Pseudo-Critical Flow of One-Component Two-Phase Mixture” (in Polish), Ph.D. thesis, Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdansk.
11.
Downar-Zapolski
P.
,
Bilicki
Z.
,
Bolle
L.
, and
Franco
J.
,
1996
, “
The Nonequilibrium Relaxation Model for One-Dimensional Flashing Liquid Flow
,”
International Journal of Multiphase Flow
, Vol.
22
, pp.
473
483
.
12.
Guha, A., and Young, J. B., 1990, “Stationary and Moving Normal Shock Waves in Wet Steam,” Adiabatic Waves in Liquid-Vapor Systems G. E. A. Meier and P. A. Thompson, eds., Springer-Verlag, 159–170.
13.
Ishii, M., 1975, Thermo-Fluid Dynamics Theory of Two-Phase Flow, Eyrolle, Paris.
14.
Kardas, D., 1994, “Effect of the Dissipation Terms on Numerical Solutions of Non-Steady-State Two-Phase Flow” (in Polish), Ph.D. thesis. Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdansk.
15.
Kardas, D., and Bilicki, Z., 1995, “Approximation of the Thermodynamic Properties of Superheated Water and Subcooled Steam” (in Polish), Zeszyty Naukowe IMP PAN, Vol. 454/95.
16.
Kestin, J., 1979, A Course in Thermodynamics, Vol. I and Vol. II, Hemisphere Publishing Corporation, New York.
17.
Kestin, J., 1993, “Thermodynamics” (An essay), Zagadnienia Maszyn Przeplywowych, Gdansk, pp. 319–334.
18.
Konorski
A.
,
1971
, “
Shock Waves in Wet Steam Flows
,”
Transactions of Institute of Fluid-Flow Machinery
, Vol.
57
, pp.
101
110
.
19.
Lebon
G.
,
Jou
D.
, and
Casas-Vazquez
J.
,
1992
, “
Questions and Answers About a Thermodynamic Theory of Third Type
,”
Contemporary Physics
, Vol.
33
, pp.
41
51
.
20.
Lemonnier
H.
, and
Selmer-Olsen
S.
,
1992
, “
Experimental Investigations and Physical Modelling of Two-Phase Two Component Critical Flow in a Convergent Nozzle
,”
International Journal of Multiphase Flow
, Vol.
18
, pp.
1
20
.
21.
Michaelides
E. E.
, and
Feng
Z. G.
,
1994
, “
Heat Transfer from a Rigid Sphere in a Nonuniform Flow and Temperature Field
,”
International Journal of Heat and Mass Transfer
, Vol.
37
, pp.
2069
2076
.
22.
Nakoryakov
V. E.
,
Pokusaev
G. B.
,
Shreiber
I. R.
, and
Pribaturin
N. A.
,
1988
, “
The Wave Dynamics of Vapour-Liquid Medium
,”
International Journal of Multiphase Flow
Vol.
14
, pp.
655
677
.
23.
Nakoryakov, V. E., Pokusaev, G. B., and Shreiber, I. R., 1993, Wave Propagation in Gas-Liquid Media, CRC Press.
24.
Nigmatulin, R. I., 1991, Dynamics of Multiphase Media, Vol. 1 and Vol. 2, Hemisphere Publishing Corporation.
25.
Puzyrewski, R., 1980, “Gasdynamics Effects due to Homogeneous Condensation of Vapours,” Heat and Mass Transfer in Multicomponent Gas-Liquid System, Ossolineum.
26.
Ransom, V. H., Wagner, R. J., and Trapp, J. A., 1983, “The RELAP 5 Two-Phase Fluid Model and Numerical Scheme for Economic LWR System Simulation,” Transient Two-Phase Flow, M. S. Plesett, N. Zuber, and I. Catton, eds., Hemisphere Publishing Corporation, pp. 513–531.
27.
Szaniawski
A.
,
1957
, “
Propagation of Small Disturbances in the Mixture of Liquid and Gas Bubbles” (in Polish)
,
Rozprawy Inzynierskie
, Vol.
LXXI
, p.
5
5
.
This content is only available via PDF.
You do not currently have access to this content.