**3. Validations of the new boundary layer theories**

In order to validate the new laws of boundary layer without and with suction, we studied the 2D, laminar, and incompressible flow around the flat plate by means of CFD using the software package Fluent.

permeable plate, because of the mesh refinement above the suction zone to account for the velocity gradient. The Navier-Stokes equations for 2D, laminar, and incompressible flow were resolved by using the finite volume method (FVM). We used

*Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions…*

In the case without suction, we studied the flow with free-steam velocity *U* = 5 m/s around the flat plate to compare their boundary layers with Blasius profiles. **Figure 3** shows the effect of the trailing edge flap angle on the position of the stagnation point. For *β* = 40°, the stagnation point is displaced to the upper surface of plate resulting in the reduction of the separation flow at the leading edge compared to the case of *β* = 0°. This result is compared to those obtained in the

In **Figure 4**, we compared the Blasius profiles with the results from the CFD of the flow boundary layer on the upper side of the impermeable flat plate for *β* = 40°. It is shown that the boundary layer of the flat plate at different positions favorably follows the Blasius profile. Thus, the shapes of the leading edge and the deflected trailing edge have an effect to neglect the pressure gradient in the flow of the upper side of the plate which greatly influences the formation of the boundary layer. In the continuation of this work, we select the case of the trailing edge deflected to 40°.

Many solutions were found based on the Prandtl equations such as Blasius and Schlichting [9] profiles. The differential equations of Blasius have no solutions for

*)0,5/U ): (a) trailing edge flap angle*

the algorithm "SIMPLE" for the pressure-velocity coupling.

*DOI: http://dx.doi.org/10.5772/intechopen.88637*

*Streamline velocity colored by dimensionless velocity magnitude ((u<sup>2</sup> + v<sup>2</sup>*

*Comparison between Blasius and CFD profiles for impermeable flat plate for β = 40°.*

literature [26].

**Figure 3.**

**Figure 4.**

**127**

**3.2 Validation and discussion**

*β = 0°; (b) trailing edge flap angle β = 40°.*
