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Effect of Pressure Gradient on the flow in a Boundary Layer. x. z. Boundary layer equation:. Pressure gradient is found from velocity field. Effect of Pressure Gradient on the flow in a Boundary Layer. x. z. At the wall, the boundary layer equation becomes:.
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Effect of Pressure Gradient on the flow in a Boundary Layer x z Boundary layer equation: Pressure gradient is found from velocity field
Effect of Pressure Gradient on the flow in a Boundary Layer x z At the wall, the boundary layer equation becomes: In the accelerating part of the stream,
Effect of Pressure Gradient on the flow in a Boundary Layer x z inflection point In the decelerating part of the stream,
Effect of Pressure Gradient on the flow in a Boundary Layer x z Velocity distribution suggests that a ∂p/∂x> 0 contributes to thicken the boundary layer, as seen from continuity: Deceleration adds viscous effects to make the boundary layer grow. w is directed away from the wall – increase in boundary layer thickness with x
Effect of Pressure Gradient on the flow in a Boundary Layer x z ∂p/∂x< 0 pressure gradient is “favorable” ∂p/∂x> 0 pressure gradient is “adverse” or “uphill” Rapid growth of boundary layer and large w field causes“flow separation”
from Kundu’s book u = 0 Separation point = boundary between forward flow and backward flow near wall Drag caused by adverse pressure gradient = form drag Boundary layer equations only valid as far as the point of separation
Analytical solutions of viscous flows can be found for Re << 1 Negligible inertial forces – Couette & Poiseuille flows
Analytical solutions of viscous flows can be found for Re >> 1 Negligible viscous forces, except near a surface -- match irrotational outer (freestream) flow with boundary layer near surface
For intermediate Re, more difficult analytical solutions – experiments and numerical solutions Low Re<< 1 1×103 < Re < 2×105 Re > 2×105
https://www.arl.psu.edu/capabilities/fsm.html Another example
von Karman Vortex Street http://upload.wikimedia.org/wikipedia/commons/b/b4/Vortex-street-animation.gif
Re= 50 Re= 75 Re= 120
Aleutian Islands http://www.designyourway.net/blog/inspiration/extraordinary-satellite-photos-of-earth/
