Analysis of the homogeneous turbulence structure in uniformly sheared bubbly flow

Separating “shear induced turbulence” and “bubble induced turbulence” contributions in gas-liquid bubbly flows is still experimentally difficult to characterize. Numerical simulations were investigated in order to isolate the turbulence produced by the mean velocity gradient of the continuous phase which comprises the turbulence generated in bubbles wakes, from the pseudo-turbulence induced by the bubbles' displacements. Simulations of the uniformly sheared flow over an isolated sphere are carried out to superimpose the homogeneous turbulence with constant shear at equilibrium conditions with the turbulence produced in the bubble wake. The analyses of the turbulence statistics computed on a control volume whose size is set based on void fractions, for different shear rates, are carried out in order to assess the modelling of the transport equation of the “shear induced turbulence”. Simulation results show that for low void fractions, the hypothesis of turbulence equilibrium in the bubble wake is verified in a wide range of shear rate. Numerical results are in satisfactory agreement with the formulations resulting from the reduction of second order turbulence closures in bubbly flow. These formulations are based on a dimensionless number expressed in terms of two time scales which characterizes the bubbles' effects on turbulence structure in sheared flow.