Introduction to Fluid Mechanics

Boundary Layers

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Combined Couette / Poiseuille flow is the steady flow between two flat plates, a fixed distance apart, in which the plates move relative to each other and there is a pressure gradient parallel to the plates. When the pressure gradient pushes the fluid in the opposite direction to the plate's motion, the flow can move in the opposite direction to the plate. It is useful to bear this flow in mind when considering boundary layers next.

This worked example examies combined Couette/Poiseuille flow and calculates the pressure gradient at which the flow will reverse.

A boundary layer is the region of a fluid next to a boundary that has been affected by the boundary. Viscous forces are non-negligible in a boundary layer.

Whenever a solid moves through a fluid, boundary layers form along the edge of the solid. This clip explains the velocity profile in these boundary layers.

In a horizontal boundary layer, horizontal momentum diffuses predominantly in the vertical direction. This is a one-dimensional diffusion problem and therefore, in 2D, boundary layers grow either (i) with the square root of time in an impulsively-started flow or (ii) with the square root of distance from the leading edge when a plate is places in a steady flow.

Bernoulli cannot be applied inside a boundary layer because viscous forces are non-negligible.

In a boundary layer, if a pressure gradient forces the flow in the direction of the free stream, then the boundary layer becomes thinner and steeper. On the other hand, if a pressure gradient forces the flow in the opposite direction to the free stream, then the flow in the boundary layer can reverse.

If the flow in a boundary layer reverses, then the boundary layer must separate from the body. The streamlines of the flow are then completely different from those obtained for an inviscid flow.

This clip explains why boundary layers separate and compares boundary layers with the Couette and Poiseuille flow studied in chapter 3. It then explains some of the consequences for flow around wings and other objects. lecture_5_neat_1

There is a competition between momentum diffusion from the free stream, which hinders separation, and an adverse pressure gradient, which promotes separation. In a given adverse pressure gradient, separation can be prevented by increasing momentum transfer from the free stream, e.g. by increasing the fluid's viscosity, or by injecting high momentum fluid directly into the boundary layer.

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