Pressure wave speeds from the characteristics
of two ¯uids, two-phase hyperbolic
, Keun-Shik Chang
*, Kyungdoo Kim
Korea Atomic Energy Research Institute, Thermo-hydraulic Research Team, Yusung-ku, Taejon 305-353, Korea
Korea Advanced Institute of Science and Technology, Aerospace Engineering Department, 373-1 Kusong-Dong,
Yusung-Ku, Taejon 305-701, Korea
Received 7 June 1997; received in revised form 25 November 1997
Considerable eort has been made in the past, without much success, to determine the
pressure wave propagation speed for two ¯uids, two-phase ¯ow. Delhaye et al. (1981) and Ishii
(1975) have showed systematic derivation of the governing equations for two-phase ¯ows.
However, this governing equation system has complex characteristics, making the two-phase
¯ow formulation mathematically ill-posed, see Ramshaw and Trapp (1978); Stewart (1979).
Various modi®cations of the governing equations has therefore been followed to render the
characteristic roots real.
The single-pressure models in the classical two ¯uids, two-phase formulation assume that the
pressure is continuous across the interface boundary. Unfortunately, these models lead to the
afore-mentioned complex eigenvalues for the practical problems under review. In contrast, the
two-pressure models assume that the gas and the liquid pressures are not necessarily
continuous across the interface. These models have, as a matter of fact, produced real
eigenvalues, see Ransom and Hicks (1984); Holm and Kupershmidt (1986); Ramshaw and
Trapp (1978). However, most of the two-pressure models are either de®cient of the constraint
binding the two phasic pressures, producing nonphysical behavior in the solution, or based on
the pressure constraints true only for a particular type of two-phase ¯ows.
To construct new two ¯uids and two-phase ¯ow formulation, we consider one-dimensional
mass and momentum conservation equations
International Journal of Multiphase Flow 24 (1998) 855±866
0301-9322/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved.
PII: S030 1 - 932 2 ( 97) 0 0 089 - X
* To whom correspondence should be addressed.