Investigation of viscous fluid flow in T-shaped channel with no slip/slip boundary conditions on the solid wall

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three models of fluid interaction with solid walls are considered:
(a) Traditional no-slip boundary condition implying the vanishing velocity vector on the solid walls.
(b) Navier slip boundary condition according to which the tangential velocity on the solid wall is linearly proportional to the shear stress and the normal velocity is equal to zero.
(c) Slip boundary condition with ultimate shear stress supposes that the tangential velocity on the solid wall is equal to zero when the shear stress does not exceed a certain ultimate shear stress; if the shear stress is more than the ultimate shear stress, the behavior of the fluid is similar to the Navier model.
The fluid flow is provided by uniform pressure profiles in boundary sections of the channel. The problem is numerically solved using the finite difference method based on the SIMPLE procedure.
As a result, the characteristic flow regimes have been found for described models of fluid interaction with a solid wall. The effect of Reynolds number, pressure of boundary sections, and parameters of the models on the flow pattern was performed. The criterion dependences describing the main flow characteristics under mathematical conditions of the present work have been plotted.