On Mechanics of Turbulent Gas-Liquid Flows

A sequential spatial-temporal averaging procedure taking into account fluctuations of concentration and their correlation with the kinematic characteristics of the gas-liquid mixture is employed to derive governing and constitutive equations for description of two-phase systems. The momentum balance provides the basis for the turbulent viscosity and bubble diffusion models, and an additional impulse due to virtual mass force as a result of bubble pulsations is considered. Closed-form theoretical expressions have been obtained for mixtures of bubble sizes predicting the bubble concentration profiles for each size fraction as well as the total concentration profile in the pipe cross-section exhibiting experimentally found non-uniform multi-peaked bubble concentration profiles. The local homogeneous approximation enables the concept of turbulent boundary layer with vanishing viscosity to be employed. In the limiting case of high Reynolds number, analytical solutions for the wall shear stress, velocity and void fraction distributions, and the basic average parameters of the gas-liquid flow are obtained from a relative friction law with a single additional empirical constant only.