Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel

• Own data sets from DNS of bubbles in turbulent channel flow are analysed.
• Budget of the turbulent kinetic energy for bubbly flows evaluated.
• New data constitute a reference for model evaluation and development.
• Dedicated flow visualizations address the local contribution to the TKE budget.
• Existing closures for interfacial term assessed and an improved variant proposed.

This paper analyses the turbulent kinetic energy budget for bubble swarms in a turbulent channel flow configuration with realistic density difference. The data employed result from Euler–Lagrange Direct Numerical Simulations of vertical turbulent channel flow laden with finite-size bubbles and enable the individual evaluation of each term of the budget equation. Two monodisperse swarms are addressed with the same bubble diameter but with different total void fraction. For the parameter range investigated bubbles enhance the liquid turbulence, and this is quantified in the terms of the budget. The turbulence enhancement is generated by the interfacial term which is balanced by the dissipation term in the core region. In the near-wall region, also the production term and the transport term contribute to the budget in a significant manner. Furthermore, the local turbulence modification induced by the bubbles is investigated by means of the transport equation of the local instantaneous kinetic energy and its contributions. Finally, existing closures for the modelling of the interfacial term are assessed and an improvement of these closures is proposed. The data provided may constitute a reference for model development in the framework of Euler–Euler approaches to bubbly flows.