Mathematical Model of Two-layer in Pipe

The problem of stationary turbulent flow in an inclined pipe of two immiscible liquids is solving. The formulation and method of solving the problem are close to our previous works, but the flow is turbulent. At the phase surface (y = h, h is the depth of the lower layer of the liquid) axial velocity w, frictional stress and turbulent viscosity v(t) are assumed to be continuous, the densities rho(i) and molecular viscosities v(i) are different for i = 1 (y <= h) and for i = 2 (y >= h). The equations of momentum in each layer and the equation for turbulent viscosity are numerically solved. At moderate Reynolds numbers, the regimes were observed in the calculations when in a layer with a small volume fraction the flow became laminar with turbulent flow in the second layer.