## onsdag 13 mars 2019

### The Illusion of a Wing with Laminar Boundary Layer

Aerodynamicists have long and still carry a dream of a laminar wing as a wing of special shape like the P-51 Mustang with special flow characteristics, including less drag as compared to that of a traditional wing as pictured below:

Our New Theory of Flight revealing the true Secret of Flight shows that this dream is built on misconceptions going back to the boundary layer theory of Prandtl/Schlichting based on the idea of a no-slip boundary condition with fluid particles sticking to the surface of the wing with zero velocity thus creating a thin boundary layer, which can be laminar or turbulent, connecting to the free stream flow.

The dream of a laminar wing would then be a wing with a laminar boundary layer on the upper surface of the wing with small skin friction, which hopefully would be the case for a wing with special shape, like that of P-51. The New Theory shows that this can only be a dream or illusion, because flow with a laminar boundary layer separates on the crest of a wing and generates little lift.

The New Theory of Flight builds on the observation that for the high Reynolds number relevant for a wing, the boundary layer is always turbulent with an effect of small skin friction on the main flow, which can be modeled by Navier-Stokes equations with a slip (small friction) boundary condition instead of the dictate of Prandtl to use a no-slip condition.

The New Theory shows that it is the slip boundary condition modeling the action of a turbulent boundary layer, which prevents the flow from separating on the crest and delays separation until the trailing edge (before stall). You can see this in the video below showing computational solution of Navier-Stokes with a slip boundary condition which agrees very well with experiments, as documented in the references in Solution of the Clay Navier-Stokes Problem.

Summary:
1. With a slip boundary condition there is no boundary layer and the flow can stay non-turbulent attached until turbulent separation at the trailing edge and thus give large lift.
2. With a no-slip boundary condition and laminar boundary layer the flow separates on the crest and gives little lift.
3. With a no-slip boundary condition the boundary layer is in fact always turbulent with an action on the main flow like a slip boundary condition.
4. The dream of drag reduction of a laminar wing is already cashed in by a slip/small friction boundary condition.
5. It is a turbulent boundary layer which can be modeled with slip, and not a laminar boundary layer even though its skin friction is small.
A laminar wing in the sense of having laminar boundary layer, does not work.

A laminar wing in the sense of a flow with a slip boundary condition without layer and turbulence until the trailing edge, works fine. In this sense a standard wing thus already has made the dream come true, but that is not what aerodynamicists call a laminar wing.