# What is the relation between the boundary layer and lift of an aerofoil?

Why do we try to reduce the thickness of the boundary layer over an aerofoil as much as possible if the boundary layer is responsible for creating lift?

I wouldn't say that the boundary layer is responsible for creating lift, even if the real world friction enables the creation of circulation and therefore lift. It is mainly responsible for the drag.

Why? Take a look at airfoils in potential flow: they have lift but neither drag nor a boundary layer. Lift is created due to a pressure difference between the upper and lower side of an airfoil and you don't need any boundary layer to explain this pressure difference.

However, you do need a boundary layer to explain drag. The no-slip condition on the airfoil surface creates a layer with a high velocity gradient (from zero on the surface to $V_\infty$- the freestream velocity). Its thickness depends mainly on the viscosity the fluid around the airfoil:

• No viscosity at all means no energy loss and therefore no drag.The velocity gradient can be infinite and the layer thickness is zero.
• With higher viscosity the particles won't be able to follow such high velocity gradients and the distance between the no-slip surface to the freestream flow around the airfoil will be bigger: the boundary layer will be thicker. The drag will be higher too.

I think the better way of putting it would "viscosity" is essential for lift rather than boundary layer is essential. If it were not for viscosity, the fluid wouldn't want to follow a curvature, leading to acceleration and decelerate and consequently decrease or increase the pressure. The pressure difference creates a net force in different directions. The force normal to free stream direction is lift (or could be negative lift depending on direction). The one parallel to the free stream is thrust or pressure drag (depending on direction). The layer of fluid closest to the surface sticks to the surface and an average momentum exchange with molecules above it leads to deceleration of flow and consequently the growth of the boundary layer. The boundary layer is essentially our concept of how far this effect is significant above the surface. And this is what causes skin friction drag. From point of view of the surface moving through the stationary fluid medium, the fluid molecules are trying to stop it from moving through the fluid and that force is the skin friction drag.

Also regarding the relation between lift and boundary layer, the boundary layer alters the apparent shape of the aerofoil surface, which can change the expected lift production.

• Upvoted only for the last sentence. Apr 22 '21 at 8:14

You're right--the boundary layer is related to lift production since, in a subsonic example, "guides" the air relative to the airfoil shape and enables the necessary flow accelerations that create the pressure differential and downwash. However, a thick boundary layer is not necessarily a good deal, especially on an airplane wing.

I think that this answer makes a good reference here. The thicker than a boundary layer is, the greater the velocity and pressure gradient across it. Therefore, the chance of flow separation (think of stall, when flow is no longer following the airfoil contour and is creating a ton of drag and not much lift) is also higher.

This consideration is further outlined here, in a master's thesis from TU Delft (a major technical university in the Netherlands). If the boundary layer is allowed to grow and is allowed to remain laminar, separation occurs relatively early, leading to dramatically increased drag and a similar reduction in lift. Artificial "tripping" (i.e., the introduction of turbulence) of the boundary layer prior to laminar separation re-energizes the boundary layer and allows it to remain attached for longer. It can also decrease your drag by some amount, but that's another story unto itself. This (or some more active sort of boundary layer control) is what I'm guessing you're referring to when you talk about keeping the boundary layer thin. It is, with the exception of circulation control and insofar as I'm familiar with it, related to energizing the boundary layer to delay flow separation as long as possible.

• Artificial "tripping" of the boundary layer from laminar flow to turbulent-attached flow is in fact the principle behind vortex generators which are often used to improve the low-speed/high-angle-of-attack performance of STOL aircraft. Jun 27 '16 at 19:09
• The thicker the boundary layer is the smaller will the velocity gradient become: $Gradient=\frac{\Delta V}{h}$. For constant $\Delta V=Free\_Airflow\_Speed-Airflow\_Speed\_on\_Surface$ a bigger thickness $h$ makes a smaller gradient. Jun 27 '16 at 19:30

The boundary layer is related to lift production, but indirectly. The incoming flow not only sees the shape of the airfoil but also the slow-moving air adjacent to the geometry. This effect is captured by the displacement thickness, as illustrated in the image below:

Image source

The formula of the displacement thickness is given by:

$$\delta^*= \int_0^{\delta} {\left(1-{u(x,y)\over u_e(x)}\right) \,\mathrm{d}y}$$

This is the equivalent thickness that when added to the airfoil captures the effect of the boundary layer on the external flow.

As you can see, the airfoil + boundary layer is thicker, and also has lost part of the curvature that is present in the airfoil. The airflow leaving at the right of the image will not be pointed downwards as would be the case without a boundary layer. The amount of downward turning that is experienced by the airflow is directly proportional to the amount of lift being generated.

In summary, we can say that the boundary layer acts as an intermediate layer, that reduces the curvature of the airfoil, and thereby reduces the amount of lift created. By reducing the thickness of the boundary layer, this effect is minimized, and more lift is created.

It is not the boundary layer per se that creates lift. It is the circulation around the airfoil. For that to get started, a starting vortex that is left behind on the runway, has to be produced. And that is created through boundary layer separation near the trailing edge of the wing.

Without boundary layers we would have a circulation-free flow around the airfoil with very high flowspeed where the flow rounds the trailing edge to a stagnation point near the trailing edge on the upside of the wing. With an absolutely sharp trailing edge, flowspeed would go towards infinity, and we would need exactly zero viscosity to avoid the production of a boundarly layer that would separate to create a starting vortex.