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Multiphase Science and Technology
SJR: 0.124 SNIP: 0.222 CiteScore™: 0.26

ISSN Imprimer: 0276-1459
ISSN En ligne: 1943-6181

Multiphase Science and Technology

DOI: 10.1615/MultScienTechn.v17.i4.10
pages 293-320

ANALYSIS OF VOID WAVE PROPAGATION AND SONIC VELOCITY USING A TWO-FLUID MODEL

Richard T. Lahey, Jr.
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
J. Yin
Center for Multiphase Flow, Rensselaer Polytechnic Institute, Troy, NY, USA
P. Tiwari
Center for Multiphase Flow, Rensselaer Polytechnic Institute, Troy, NY, USA

RÉSUMÉ

In this study, a state-of-the-art, ensemble-averaged, two-fluid model, which is an extension of the model proposed by Park et al. [1998], was used for the analysis of void wave propagation. Ensemble-averaging is the most fundamentally rigorous form of averaging [Buyevich, 1971], [Batchelor, 1970], since, in the ensemble averaging process, the ensemble is a set of flows that can occur at a specified position and time. Thus, the ensemble-average may include all the phasic interactions without specifying the time and length scales, in contrast to space/time averaging techniques [Drew and Passman, 1998].
Since the properties of void waves have been found to be sensitive to the two-fluid model's closure relations [Boure, 1982], [Pauchon and Banerjee, 1988], [Park et al., 1990a], [Biesheuvel and Gorrisen, 1990], [Lahey, 1991], the well-posedness of the incompressible two-fluid model was studied by considering the mathematical system's void wave characteristics. The model was found to be well-posed within a range of void fractions which depends on an interfacial pressure parameter, Cp. When Cp has physically realistic values, the incompressible two-fluid model is well-posed over the whole range of void fractions.
Void wave propagation phenomenon was also analyzed by performing a dispersion analysis of the linearized incompressible two-fluid model. The celerity, stability and damping of the frequency dependent void waves were obtained and regions of instability for the incompressible two-fluid model were identified. Finally, the two-phase sonic velocity implied by the compressible two-fluid model was evaluated and shown to agree with bubbly flow data.