written 6.9 years ago by | modified 2.7 years ago by |
Subject: Fluid Mechanics 2
Topic: Boundary layer theory
Difficulty: Low
written 6.9 years ago by | modified 2.7 years ago by |
Subject: Fluid Mechanics 2
Topic: Boundary layer theory
Difficulty: Low
written 2.7 years ago by |
Consider the flow of fluid past a solid surface. let P represent the static pressure at any point and x denote the distance measured along the flow direction, then$\frac{dp}{dx}$ is called the pressure gradient
For the flow of a fluid over a smooth thin plate which is flat and placed parallel to the direction for free stream of fluid, $\frac{dp}{dx}$ is zero.
If the pressure gradient is zero, the boundary layer thickness increases continuously with increase in distance from the leading edge of the plate along the flow.
In the region ABC of the curved surface, the flow area decreases and therefore the velocity increases. This means that the flow is accelerated. Due to increase in velocity, the pressure decreases in the direction of flow.
Therefore the pressure gradient $\frac{dp}{dx}$ is negative in the region of ABC.
In this case the pressure force acts in the direction of flow, against the frictional resistance. That gives the fluid an additional push in the direction of flow.
Along the path CSD of the curved surface, the area of flow increases and hence the velocity decreases and the pressure increases in the direction of flow. Therefore the pressure gradient $\frac{dp}{dx}$ is positive in the region of CSD.
Here the pressure force acts opposite to the direction of flow. The positive pressure gradient is called adverse pressure gradient.
This positive pressure gradient is unfavourable because some kinetic energy of fluid particles is utilized to increase the pressure. Also some part of kinetic energy is used to overcome the surface friction of the solid body.
At Separation point S,
$$ \left(\frac{d u}{d y}\right)_{y=0}=0 $$
If $\left(\frac{d u}{d y}\right)_{y=0}$ is negative, the flow is separated
If $\left(\frac{d u}{d y}\right)_{y=0}$ the flow is on the verge of separation
If $\left(\frac{d u}{d y}\right)_{y=0}$is positive, the flow will not separate
Following are the methods for preventing separation of boundary layer
a. Suction of slow moving fluid by a suction slot
b. Supplying additional energy from a blower
c. Providing a bypass in the slotted wing
d. Providing rotating cylinder near leading edge
e. Providing small divergence in a diffuser
f. Providing guide blades in a bend
g. Providing a trip-wire in the laminar region for the flow over a sphere