Does skin friction change with AoA?

Does skin friction change with AoA or stay constant during change in angle of attack?

I think that local airflow velocity change with AoA so this must affect skin friction .. But what definiton tells?

• I think the skin friction increases due to more surface area when angle of attack increases or decreases. – Auberron Sep 8 '20 at 3:16

Let's start by skin friction drag formula: $$F_s=\overline{C_f}\frac{\rho V^2}{2}A$$ where $$\overline{C_f}$$ is the average skin friction coefficient, $$\rho$$ is the density, $$V$$ is the True Airspeed and $$A$$ is the surface area of the wing.

By varying the Angle of attack, the term $$\frac{\rho}{2}A$$ stays constant assuming incompressible flow. As the Angle of attack increases, the velocity of the fluid increases over the top surface of the airfoil due to the lower static pressure being created. Therefore, as the Angle of attack increases, the skin friction drag also increases.

As the Angle of attack increases, the skin friction coefficient will also change. Let's assume two scenarios, one in which the angle of attack is close to zero, and one in which the angle of attack is very high, but the airfoil is not stalled, for instance, $$12^{\circ}$$. In the first scenario where $$\alpha\approx0$$, the flow over the airfoil is mostly laminar, that is, the velocity gradient inside the boundary layer is smaller close to the surface $$\left(\nabla V=\frac{\partial{V}}{\partial{y}}|_{y=0}\right)$$ which exhibits lower skin friction coefficient. Therefore, in scenario #$$1$$, the drag due to skin friction would be lower.

If the angle of attack is suddenly increased to $$12^{\circ}$$, scenario #$$2$$, the transition point on the upper surface would move upstream thus increasing the portion of the turbulent layer over the airfoil. And since the turbulent boundary layer has a higher skin friction coefficient, as a result, the skin friction drag would increase. On the lower surface, things are reversed. On the lower surface, the transition point would move downstream, increasing the laminar portion and lowering the skin friction coefficient. Since the fluid becomes more turbulent around the airfoil with an increasing angle of attack, the net change would be an increase in the skin friction coefficient resulting in the higher skin friction drag.

If we were to account for the compressibility effect on the skin friction coefficient, the skin friction coefficient would decrease. That is, the skin friction coefficient in the compressible flow would be smaller compared to the skin friction coefficient determined by incompressible flow:

$$\overline{C_f}^\prime=\frac{\overline{C_f}}{(1+0.144Ma^2)^{0.65}}$$ where $$\overline{C_f}^\prime$$ is the skin friction coefficient of the compressible flow, and $$Ma$$ the Mach number.

To summarize, with an increase in the angle of attack there would be an increase in the skin friction coefficient due to the presence of turbulent flow along with an increase in the fluid velocity over the airfoil, which would result in higher skin friction drag.

• Good answer! I think this answer would benefit from a description of skin friction in the case of separated flow. – ROIMaison Sep 29 '20 at 9:33