Fundamentals of Aerodynamics 2024, 52: Boundary Layers

Flow over flat planes contains viscous effects within a thin layer adjacent to the surface. By all the continuity equations, we gain the no-slip condition and continuity of temperature gradients. We consider the velocity boundary layer thickness δ with the variation across it as the velocity profile. The thermal boundary layer is considered analogously. The displacement thickness δ* is proportional to the missing mass flow due to the boundary layer. It shows up as a partial obstruction to the freestream, so it could be read as part of an "effective body", thus allowing for a simplified model, if the effects in the boundary layer aren't of particular interest. The momentum thickness θ is an index proportional to the momentum flow decrement due to the boundary layer.

Usually, the boundary layer thickness is assumed to be very thin in comparison to the scale of the body, and the Reynolds number is large. The fundamental boundary layer equations are the usual suspects

which requires sensible boundary conditions at the walls and boundary-layer edges.