The present paper illustrates a new method for solving the two-dimensional turbulent fluid flow, for an incompressible fluid, near solid walls. Equations of energy conservation and momentum for thin layers have been used and solved with a slip velocity implemented in the Navier-Stokes equations. As a first step, a pseudo-laminar analysis was made. In parallel, some other models for turbulence were analyzed, to estimate the most appropriate model in conformity with the obtained experimental results. The numerical simulation was performed to investigate the effects of the Reynolds number on the flow characteristics, over a two-dimensional rectangular body and a curved shape surface. It was used the CFD, near the solid surfaces with a strong adverse pressure gradient. The viscous layer is expressed as an integral solution, imposing the wall shear stress as a boundary condition on solid surfaces. The velocity and shear stress are deduced from the Navier-Stokes equations as long as the convergence is reached. Numerical modeling was tested for Reynolds numbers ranging from 2040 to 13000. Firstly, the theoretical model for the flow equations and velocity distribution is described. Some details are presented for estimating as better as possible the wall velocity and the shear stresses. Numerical modeling, with the FEM model, is based on the Galerkin formulation. Some aspects referring to the boundary conditions, for the analyzed cases are also mentioned. The flow is restricted at a central vortex, considered the primary vortex. In turbulent boundary layer, for the analyzed applications were not considered the axial vortices. Some aspects referring to the flow domain and the grid generation are mentioned in a dedicated paragraph. For numerical modeling, firstly was adopted the non-viscous solution, as the initial condition. It depends on the available information concerning the shapes geometry, the curvature radius, and the flow conditions for the considered problems. For the first approximation, was used the integral boundary-layer method, which can provide a proper solution. The advantage consists of reducing the number of iteration to reach the numerically final settlement. If it will be used the integral method, will be provided only an approximate distribution for the edge velocity. Variation of the reattachment length of vortices over the analyzed solid bodies is correlated with the experimental results from the literature. Exclusive analysis of the selected data shows that the turbulent values correlated directly to the body length-b are more accurate than those referring to the dimensionless rapport δ/b. From the analyzed models, the K-ε model presents better agreement with experimental data, also for the negative values of the Reynolds shear stress in the re-attachment point. Finally, some conclusions and references are mentioned.

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