Modelling hydrodynamics and turbulence in a bubble column using the Euler–Lagrange procedure

This paper describes an extension and validation of the Euler/Lagrange approach for time-dependent calculations of the flow evolving in a bubble column. The continuous phase velocity is obtained by solving the two-dimensional axisymmetric Reynolds-averaged Navier–Stokes equations augmented by the k–ε turbulence model. The coupling between the phases is considered through momentum source terms and source terms in the k- and ε-equations, which include the effect of wake-generated turbulence by means of consistent Lagrangian-like terms. Bubble motion is calculated by solving the equations of motion taking into account drag force, liquid inertia, added mass, buoyancy and gravity, and the transverse lift force. In order to identify the relative importance of the different physical phenomena involved in the model, the radial variation of the corresponding constitutive terms that appear in the transport equations of the liquid variables is analyzed in an instantaneous as well as in the time-averaged configuration. As a conclusion, the bubble source terms are directly responsible for the production of fluctuating kinetic energy and dissipation rate in the liquid, which means that their modelling determines the topology of the liquid flow in the bubble column. For validation the numerical results are quantitatively compared with detailed measurements utilizing phase-Doppler anemometry.