Sensitized Reynolds stress modeling of a bubbly jet emerging into a water cross-flow

The present work is concerned with the computational study of an air–water mixture stream emanating from a nozzle submerged in a water cross-flow inside a rectangular open channel to form a curved, intensively dispersed, bubbly jet. The work focuses on evaluating the predictive performance of an eddy-resolving turbulence model applied to the described case of a multiphase gas–liquid flow system characterized by a variety of closely coupled phenomena, including: turbulence anisotropy-induced secondary motion, free surface flow, bubbly jet propagation, and the varying interaction dynamics of the carrier water flow with the air bubble dispersion. Correspondingly, an appropriately extended differential near-wall Reynolds stress model, which describes the dynamics of unresolved subscale structures within the Sensitized Reynolds-Averaged Navier–Stokes (RANS) computational framework, is currently used in conjunction with a two-way coupled Euler–Lagrange approach to simulate this gas-water bubbly flow, with the operating and boundary conditions following the experimental reference of Zhang and Zhu (2013). Accordingly, the conditions at the free surface are adequately derived for all components of the residual turbulence stress tensor and the corresponding length scale determining variable. It is shown that the statistics of the bubble phase can be accurately captured, and the proper-orthogonal-decomposition analysis of the dynamic properties of the flow reveals at least two large-scale transient effects associated with the bubbly jet. Furthermore, in the preliminary part of this work it is shown that the currently applied turbulence model can be successfully used to correctly capture the effects of Reynolds stress anisotropy in the single-phase open-channel configuration, representing the incoming flow field of the main two-phase flow configuration. • A Sensitized Reynolds-stress model is applied to a bubbly jet emerging in an open channel water flow within an Eulerian-Lagrange approach. • Focus is on the predictive performance of this eddy-resolving differential near wall Reynolds stress model. • Free-surface conditions are derived for all components of the residual turbulence stress tensor and the corresponding length scale determining variable. • Mean flow and turbulence statistics of the carrier and bubble phases are captured in good agreement with LES and experimental reference. • Proper-orthogonal-decomposition analysis reveals at least two large-scale transient effects associated with the bubbly jet.