A mathematical formulation is presented to describe the transient flow of homogeneous gas–liquid mixtures in deformable pipes. The mixture density is defined by an expression averaging the two-component densities where isothermal evolution of the gaseous phase is admitted. Instead of the void fraction, which varies with pressure, the gas–fluid mass ratio (or the quality), assumed to be constant, is used. By application of the conservation of mass and momentum laws, a nonlinear hyperbolic system of two differential equations is obtained for the two principal dependent variables, which are the fluid pressure and velocity. Consideration is given in this paper to the numerical solution of these equations by the method of characteristics and the finite difference conservative scheme. The finite difference scheme computes the pressure by using a Newton–Raphson iterative formula, where the pressure wave speed takes place explicitly. To verify the validity of the computed results, comparison has been made with those of the numeric-experimental example of Chaudry et al. “Analysis of Transient in Bubbly Homogeneous Gas–Liquid Mixtures,” 1990. ASME J. Fluids Eng., 112, pp. 225–231. [S0098-2202(00)00301-1]

1.
Campbell
,
I. J.
, and
Pitcher
,
A. S.
,
1958
, “
Shock Waves in Liquid Containing Gas Bubbles
,”
Proc. R. Soc. London
,
243
, pp.
534
545
.
2.
Padmanabhan
,
M.
, and
Martin
,
C. S.
,
1983
, “
Shock-Wave Formation in Moving Bubbly by Steepening of Compression Waves
,”
Int. J. Multiphase Flow
,
4
, pp.
81
88
.
3.
Martin
,
C. S.
, and
Padmanabhan
,
M.
,
1975
, “
The Effect of Free Gases on Pressure Transients
,”
L’Energia Elettrica
,
5
, pp.
262
267
.
4.
Martin, C. S., Padmanabhan, M., and Wiggert, D. C., 1976, “Pressure Wave Propagation in Two-Phase Bubbly Air-Water Mixtures,” Second International Conference on Pressure Surges, City University, London, England, paper C1, pp. 1–16.
5.
Martin
,
C. S.
, and
Padmanabhan
,
M.
,
1979
, “
Pressure Pulse Propagation in Two-Component-Slug Flow
,”
ASME J. Fluids Eng.
,
101
, pp.
44
52
.
6.
Chaudry
,
M. H.
,
Bhallamudi
,
S. M.
,
Martin
,
C. S.
, and
Naghash
,
M.
,
1990
, “
Analysis of Transient in Bubbly Homogeneous, Gas–Liquid Mixtures
,”
ASME J. Fluids Eng.
,
112
, pp.
225
231
.
7.
Pascal
,
H.
,
1983
, “
Compressibility Effect in Two-Phase Flow and its Application to Flow Metering with Orifice Plate and Convergent-Divergent Nozzle
,”
ASME J. Fluids Eng.
,
105
, pp.
394
399
.
8.
Streeter, V. L., and Wylie, E. B., 1982, Hydraulic Transients, F.E.B. Press, Ann Arbor.
9.
Stuckenbruck
,
S.
,
Wiggert
,
D. C.
, and
Otwell
,
R. S.
,
1985
, “
The Influence of Pipe Motion on Acoustic Wave Propagation
,”
ASME J. Fluids Eng.
,
107
, pp.
518
522
.
10.
Lerat
,
A.
, and
Peyret
,
R.
,
1973
, “
Sur le Choix des Sche´mas aux Diffe´rences du Second Ordre Fournissant des Profils de Choc Sans Oscillations
,”
C. R. Acad, Sci Paris
,
277
, pp.
363
366
.
11.
Stoer, J., and Burlisch, R., 1983, Introduction to Numerical Analysis, Springer Verlag, Berlin.
12.
Wiggert
,
D. C.
, and
Sundquist
,
M. J.
,
1979
, “
The Effect of Gaseous Cavitation on Fluid Transients
,”
ASME J. Fluids Eng.
,
101
, pp.
79
86
.
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