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Wedge flow boundary layer

Physics Asked on May 23, 2021

Why does the velocity of free stream outside the boundary layer in wedge flow changes in direction of flow ($x$)?

Why thickness of boundary layer on the wedge is less than thickness of boundary layer on the flat plate?

One Answer

For a laminar flow with a Reynolds number of 100-500 and for three wedges with an angle of $alpha =0, pi/6,pi/4$, there is a difference in the thickness of the boundary layer noticeable by eye (under certain boundary conditions). For modeling, I used the complete system of Navier-Stokes equations and the finite element method. Code published on https://community.wolfram.com/groups/-/m/t/1433064

Figure 1 shows the distribution of the velocity modulus in the boundary layer for three wedges

Figure 1 If we compare these three flows in detail, then we can see in Fig. 2 that on a flat plate, a jet is formed at the leading edge, and then damps, and on the wedge this jet is amplified.This is due to the rotation of the flow (angle $alpha$). In contrast with the external jet, it seems that the boundary layer on the wedge is thinner. If we determine the thickness of the boundary layer from condition $u=1$, then on the plate the boundary layer grows in thickness (in Blasius theory too), and on the wedge the boundary layer growing very slowly and it seems it remains constant in thickness. Figure 2

Answered by Alex Trounev on May 23, 2021

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