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A study of two-fluid model equations. (English) Zbl 1241.76389
Summary: A theoretical study of the interaction term in the two-fluid model equations is presented. The relevant Navier-Stokes equation is volume-integrated in a control volume fixed in a field of dispersed two-phase flow; then it is time-integrated. An expression for the interaction term is obtained in the limit of infinitesimal control volume, which rigorously fits to the two-fluid model equation based on time averaging. The interaction term is then analysed for dispersed two-phase flow with homogeneous particle size. The mathematical expression of the resulting interaction term clearly shows its property, which has been overlooked for more than 40 years. It can be decomposed into the conventional interaction term and an additional ‘virtual force’ term. The virtual force term is evaluated approximately for two types of dispersed multiphase flow in order to demonstrate its effectiveness. The first is solid-liquid dispersed two-phase flow with spherical solid particles undergoing creeping flow, and the second is gas-liquid dispersed two-phase flow with large bubbles in a highly turbulent flow field. For solid spherical particles in a homogeneous creeping flow, the term vanishes, as was found numerically by A. Ten Cate and S. Sundaresan [Int. J. Multiphase Flow 32, No. 1, 106–131 (2006; Zbl 1135.76555)], although the term could be significant for a flow field with velocity gradient. For large bubbles in bubble columns in a recirculating turbulent flow regime, the term is significant. The two-fluid model equations are corrected by the introduction of these virtual force terms, which in some circumstances are important in simulating the macroscopic properties of dispersed two-phase flow with spatial variations.

MSC:
76T10 Liquid-gas two-phase flows, bubbly flows
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