Analysis and modeling of bubble-induced agitation from direct numerical simulation of homogeneous bubbly flows
Résumé
In this study based on direct numerical simulations (DNS) of homogeneous bubbly flows, an analysis of velocity fluctuations is performed and a methodology for the development of a bubble-induced agitation (or pseudoturbulence) model is described. This process is based on the separation of two phenomena causing velocity fluctuations in the liquid: the agitation resulting from wakes and their collective interactions [wake-induced agitation (WIA)], which is our main focus, and the nonturbulent fluctuations resulting from averaged wakes and potential flows around bubbles [potential flow and averaged wake fluctuations (PWFs)]. We run DNS of fixed bubbles, with random spatial distribution, and compare the results to free-bubble simulations in order to build a model for those phenomena. The simulation of motionless bubbles allow the decomposition of the Reynolds stress transport equation to study WIA and PWFs separately. Then the main characteristics of bubbly flows are analyzed. The signature of an energy conversion from wake kinetic energy (PWFs) to turbulent kinetic energy (WIA) is observed, revealing the importance of nonlinear interactions and transfers between PWFs and WIA. A first proposal of model is made, which gives satisfactory results on our database for a wide range of bubble Reynolds numbers and is consistent with experimental observations. It is operational and can be implemented and assessed in an averaged code.