Numerical study of bubbly upflows in a vertical channel using the Euler–Lagrange two-way model

Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles.