Theoretical derivation of the interaction effects with expansion effects to bubbly two-phase flows

This paper was concerned with a theoretical closure relationships derivation to describe the hydrodynamic interaction in a dilute dispersion of gas bubbles in a continuos liquid phase with bubble radius variation due to expansion effects. The starting point in the present study was the three-dimensional transient averaged transport equations. The closure relationships were formulated as an associated problem for the deviation around averaging values of the local variables. The derivations were based on the concentric cell approach and taking in account compressibility of the gas phase. The closure relationships for the dyad product of velocity spatial deviations, virtual mass and the difference between the intrinsic and interface averages of the pressure on the continuous phase side were developed. In this work a new term, which is a function of the squared radial velocity, into the closure for the dyad product of velocity spatial deviation was founded.