Abstract:

A simple, fast and adequate approach to the turbulent boundary layer calculation on the surface of a rotating permeable cylinder has been elaborated for the case of a strong suction through the cylinder surface. Firstly, the rotational gap flow between two concentric cylinders was analyzed theoretically; the outer cylinder is stationary, and the inner porous cylinder is rotating with suction condition. Based on the fact that the stationary outer cylinder does not influence the flow near the rotating inner one, it can be treated as a boundary layer on the surface of rotating permeable cylinder, and an analytical expression for the circumferential velocity distribution is obtained. Secondly, the Cebeci-Smith two-layer algebraic turbulence model has been adjusted to account for centrifugal force field (streamlines curvature), wall suction, and low-Reynolds-number effects. Analytical corrections and empirical coefficients are used to tune the model for the specific conditions of coupled influence of the factors mentioned above. The calibration database was used which has been obtained by detailed numerical simulation based on the Reynolds stress turbulent model. The numerical simulation approach has been comprehensively verified in the known study for the specific flow conditions under consideration. Finally, the solution algorithm based on generalized Cebeci-Smith two-layer algebraic turbulence model was offered to solve the boundary layer flow over the rotating porous cylinder surface. The algorithm is suited for the situation of flow uniformity in the azimuthal and axial directions that required a special iterative procedure to be elaborated. The results of the algebraic turbulence model with different combinations of the rotational speed and the suction velocity agree well with the simulation results of the Reynolds stress turbulent model. It is demonstrated that the method developed reproduces also the laminar boundary layer at the same initial conditions when the detailed numerical simulation predicts the stable laminar flow in the inner cylinder boundary layer.

Key words: turbulent boundary layer, concentric rotating cylinders, wall suction, Cebeci-Smith algebraic turbulence model