Boundary Layer

Boundary layers are a phenomenon associated with real flows. It is the effect of viscosity through the no slip condition. In real flows near a surface (or an object) the flow at the surface will have the velocity of the surface. Therefore if the surface is at rest (see flow over a flat plate below), flow at the surface must be zero. Flow away from the surface will have a velocity distribution, called a profile. Because of this

Close to the surface the momentum of the fluid is reduced - fluid is slowed down - has less energy

At the surface a velocity gradient is developed (can be related to the shear)

Consider uniform flow over a flat plate

Assumptions of the Boundary Layer Theory

Boundary layer over an airfoil and boundary layer coordinates (curvilinear)

The boundary layer coordinates are curvilinear. The flow over the airfoil can be expressed as flow over the flat plate as the curvature can be geometrically ignored. Note that the curvature of the airfoil surface is responsible for creating a pressure gradient on the surface (for a true flat plate there will be no pressure gradient).

Here is a flow visualization picture showing the developing of the boundary layer over a cylinder (Hydrogen bubbles in water). On the right is a physical/mathematical model/representation of the same flow

(C. B. Millikan - Aerodynamics of an Airplane)

Things to observe

• boundary layer starts at the stagnation point and is on both the top and bottom surface (on the model)
• unlike a flat plate where the velocity at the edge of the boundary layer is constant - here it increases on the way to the top and then starts decreasing
• boundary layer thickness increases the flow goes over the cylinder
• on the trailing side the flow separates
• beyond separation, there is reverse flow close to the surface - suggesting a vortex or swirling flow
• by Bernoulli's eqn. as the speed increase over the top the pressure decreases - and vice versa.
• after minimum pressure, the pressure opposes the flow on the rear - called adverse pressure gradient
• when the momentum of the fluid near the surface is insufficient to overcome the adverse pressure the flow separates

Separation

Separation, in real flows implies that the flow is no longer attached to the surface. The separated flow is also called the wake or the wake region. The wake region is not very useful in creating lift. Flows will usually separate in the adverse pressure gradient region.

Separation is accompanied by

• loss of lift
• increase in drag

Separation with time (Prandtl-Tietjens) Flow past cylinder (ONERA France)

Separation will usually take place at the rear of the object. It implies loss/lack of streamlining. For good aerodynamics you need to keep the flow attached to the surface (particularly airfoils) as long as possible. If the flow separates, then the pressure stops changing (increasing) after the separation point. Since at the front of the object there is flow stagnation (highest pressure) and on the rear a lower pressure, there is a large force in the direction of the flow - this is called drag. or more specifically pressure drag. The drag due to the viscosity is called the skin friction drag.

For flows

• with no (or little) separation, the skin friction drag is higher than pressure drag
• for flow with separation, the pressure drag is greater than skin friction drag
• Separation can take place in laminar and turbulent flows.
• A turbulent flow will sometimes reattach itself to the surface.