Boundary Layer Two-Phase Bubbly Flow Equation

Experimental data indicate that bubbly, turbulent, boundary layer has the same structure as its single-phase counterpart. The modified logarithmic law of the wall for the bubbly turbulent log layer is obtained. Eddy viscosity concept is used to obtain boundary layer equation. Total turbulent stress in the inner layer is assumed to be the sum of the local stress caused by bubbles in the log layer and the stress taking into account the inherent liquid turbulence and bubble-liquid interaction in the outer layer. The proposed two-phase law of the wall can be used as a boundary condition in multidimensional models of two-phase turbulent flows. It is applicable to the upward and downward flows with the value of void fractions in the log layer not more than 10%.