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 express analytically the void fraction profile as a function of the liquid velocity and pressure profiles. This relation is valid independently of the Reynolds stress model in the liquid phase -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. It presents a peak near the wall for upward flows, whereas its maximum is reached in the center of the pipe for downward flows. This is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code.
-In a recent paper, we derived an analytical expression for the void fraction profile in low Reynolds number bubbly pipe flows, based on a balance of hydrodynamic forces on bubbles. The objective of the present work is to perform a comparison of this analytical Bubble Force Balance Formula (BFBF) with an experiment from the literature. We begin by simulating this experiment with the NEPTUNE_CFD code. In particular we show that using an R ij -e model to account for the liquid velocity fluctuations yields reasonable results. In order to compare our analytical profile with experimental measurements, we restrict ourselves to the near-wall region. In this region, the void fraction profile results from a balance between dispersion and wall forces, and the dispersion coefficient can be considered as uniform. The analytical BFBF profile is seen to be in good agreement with the measurements. We are also capable to estimate the dispersion coefficient in this near-wall region.Résumé -Profil analytique de taux de vide en proche paroi dans les écoulements en conduite à bulles à faible nombre de Reynolds : comparaison expérimentale et estimation du coefficient de dispersion -Dans une publication récente, nous avons obtenu une expression analytique pour le profil de taux de vide dans un écoulement en conduite à bulles à bas nombre de Reynolds, basée sur un bilan des forces hydrodynamiques sur les bulles. L'objectif du travail est d'effectuer une comparaison de cette Formule de Bilan des Forces sur les Bulles (FBFB) avec une expérience de la littérature. Nous commençons par simuler cette expérience avec le code NEPTUNE_CFD. En particulier, nous montrons qu'en utilisant un modèle R ij -e, nous obtenons des résultats acceptables pour les fluctuations de vitesse liquide. Ensuite, afin de comparer notre profil analytique avec les mesures expérimentales, nous nous restreignons à la zone de proche paroi. Dans cette région, le profil de taux de vide résulte de l'équilibre entre forces de dispersion et de paroi, et le coefficient de dispersion peut être considéré comme uniforme. Le profil analytique FBFB est en bon accord avec les mesures et nous sommes capables d'estimer le coefficient de dispersion dans la zone de proche paroi. 2017 DOI: 10.2516 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Oil & GasScience and Technology -Rev. IFP Energies nouvelles (2017) 72, 4 Ó O. Marfaing et al., published by IFP Energies nouvelles,NOTATIONS BFBF Bubble Force Balance Formula B Constant in Equation (16), determined from the knowledge of the average void fraction over a cross-section
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