How to calculate lift and drag coefficients of an airfoil with slotted flaps?

Question

I am doing a project attempting to determine the increase in lift and drag coefficients of an airfoil as the angle of its flap increases. In my research, I have found the thin airfoil with flap approximation in Mechanics of Flight:

However, this is a plain flap and not one for a slotted flap. Similarly, I basically cannot find anything on formulas that determine the drag coefficient with a flap deflection.

Of course, I am aware of the DATCOM methods, but I will need something physics-based.

Any help will be appreciated.

Answer 1

Slotted flaps work quite like camber flaps, only that the slot allows to create a new, fresh boundary layer on the flap surface which delays flow separation. Therefore, for small deflection angles the approximations for camber flaps can be applied to slotted flaps, too. If the flap deflection also in involves an increase in wing area by a backward movement of the flap, correct the result by the relative increase in chord.

For a very coarse drag approximation you may add a drag coefficient increment for every degree of flap extension as shown in NASA Contractor Report 4746, which is the source for the picture below:

The detailed drag increase depends a lot on the size and shape of the slot and should be looked up in the literature of the particular airfoil.

For higher deflection angles you will need to employ formulas which include viscous effects. The simplest ones are already far more complex than your one-liner; here it is best to use a panel code like MSES by Mark Drela. This will give good values for both lift and drag.