Analysis and modeling of Reynolds stressesin turbulent bubbly up-flows from directnumerical simulations
Résumé
Two-phase bubbly flows are found in many industrial applications. These flows involvecomplex local phenomena that are still poorly understood. For instance, two-phaseturbulence modeling is still commonly based on single-phase flow analyses. A directnumerical simulation (DNS) database is described here to improve the understandingof two-phase turbulent channel flow at Re et964; = 127. Based on DNS results, a physicalinterpretation of Reynolds stresses and momentum budgets is proposed. First, surfacetension is found to be the strongest force in the direction of migration so that budgets ofthe momentum equations suggest a significant impact of surface tension in the migrationprocess, whereas most modeling used in industrial application do 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 theReynolds stresses transport equation computed from DNS reveal an interaction betweenSPT and BIF, revealing weaknesses in the classical way in which pseudoturbulence andperturbations to standard single-phase turbulence are modeled. An SPT reduction isshown due to changes in the diffusion because of the presence of bubbles. An increaseof the redistribution leading to a more isotropic SPT has been observed as well. BIF iscomprised of a turbulent (Wake Induced Turbulence, WIT) and a non-turbulent (WakeInduced Fluctuations, WIF) part which are statistically independent. WIF is related toaveraged wake and potential flow, whereas WIT appears when wakes become unstable orinteract with each other for high-velocity bubbles. In the present low gravity conditions,BIF is reduced to WIF only. A thorough analysis of Reynolds stresses transport equationsis performed in order to propose an algebraic closure for the WIF towards an innovativetwo-phase turbulence model.