An analytical relation for the void fraction distribution in a fully developed bubbly flow in a vertical pipe

Abstract : The problem of a steady, axisymmetric, fully developed adiabatic bubbly flow in a vertical pipe is studied analytically with the two-fluid model. The exchange of momentum between the phases is described as the sum of drag, lift, wall and dispersion contributions, with constant coefficients. Under these conditions, we are able to derive an analytical relation between the void fraction, the liquid velocity, and the pressure profiles. This relation is valid independently of the turbulence model in the liquid phase-here, a k-ε model is used-and can serve as a verification case for multiphase flow codes. The analytical void fraction profile vanishes at the wall, as a result of the balance between dispersion and wall forces. This profile is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code.
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O. Marfaing, M. Guingo, J. Laviéville, G. Bois, N. Mechitoua, et al.. An analytical relation for the void fraction distribution in a fully developed bubbly flow in a vertical pipe. Chemical Engineering Science, Elsevier, 2016, 152, pp.579-585. ⟨10.1016/j.ces.2016.06.041⟩. ⟨cea-02388704⟩

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