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Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations

Published online by Cambridge University Press:  05 March 2019

A. du Cluzeau Open the ORCID record for A. du Cluzeau [Opens in a new window] ,
G. Bois Open the ORCID record for G. Bois [Opens in a new window]  and
A. Toutant Open the ORCID record for A. Toutant [Opens in a new window]
A. du Cluzeau*
Affiliation:
DEN-Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
G. Bois*
Affiliation:
DEN-Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
A. Toutant
Affiliation:
PROMES-CNRS (UPR 8521), Université de Perpignan Via Domitia, 66100 Perpignan, France
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Two-phase bubbly flows are found in many industrial applications. These flows involve complex local phenomena that are still poorly understood. For instance, two-phase turbulence modelling is still commonly based on single-phase flow analyses. A direct numerical simulation (DNS) database is described here to improve the understanding of two-phase turbulent channel flow at a parietal Reynolds number of 127. Based on DNS results, a physical interpretation of the Reynolds stress and momentum budgets is proposed. First, surface tension is found to be the strongest force in the direction of migration so that budgets of the momentum equations suggest a significant impact of surface tension in the migration process, whereas most modelling used in industrial application does not include it. Besides, the suitability of the design of our cases to study the interaction between bubble-induced fluctuations (BIF) and single-phase turbulence (SPT) is shown. Budgets of the Reynolds stress transport equation computed from DNS reveal an interaction between SPT and BIF, revealing weaknesses in the classical way in which pseudoturbulence and perturbations to standard single-phase turbulence are modelled. An SPT reduction is shown due to changes in the diffusion because of the presence of bubbles. An increase of the redistribution leading to a more isotropic SPT has been observed as well. BIF is comprised of a turbulent (wake-induced turbulence, WIT) and a non-turbulent (wake-induced fluctuations, WIF) part which are statistically independent. WIF is related to averaged wake and potential flow, whereas WIT appears when wakes become unstable or interact with each other for high-velocity bubbles. In the present low gravity conditions, BIF is reduced to WIF only. A thorough analysis of the transport equations of the Reynolds stresses is performed in order to propose an algebraic closure for the WIF towards an innovative two-phase turbulence model.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 132 - 168
Copyright
© 2019 Cambridge University Press 

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