Explain the effect of pressure gradient on boundary layer separation

(5 Marks) May-2018

Subject Fluid Mechanics 2

Topic Boundary layer theory

Difficulty Medium

The effect of pressure gradient (dp/dx) on boundary layer separation can be explained by considering the flow over a curved surface ABCSD as shown in Fig.

1. In the region ABC of the curved surface,
2. The area of flow decreases and hence the velocity increases. This means that flow gets accelerated in this region.
3. Due to the increase of the velocity, the pressure decrease in the direction of the flow and hence the pressure gradient (dp/dx) is negative in this region.

4. As long as (dp/dx) < zero, the entire boundary layer moves forward as shown in fig.

5. In the region CSD of the curved surface,

6. The pressure is minimum at the point C.
7. Along the region CSD of the curved surface, the area of a flow increases and hence the velocity of flow along the direction of fluid decreases.

8. Due to the decrease of velocity, the pressure increases and hence dp/dx is positive i.e dp/dx>0.

9. The velocity of the layer adjacent to the solid surface along the length of the solid surface goes on decreasing as the kinetic energy of the layer is used to overcome the frictional resistance of the surface.

10. Thus the combined effect of positive pressure gradient and of surface resistance reduce the momentum of the fluid is unable to the surface.

11. A stage comes, when the momentum of the fluid unable to overcome the surface resistance and the boundary layer starts separating from the surface at the point S. Downstream the point S, the flow is taking place in the reverse direction and the velocity gradient becomes negative.