09_gen_boundary

# 09_gen_boundary - The Generalized Boundary Layer Equations...

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The Generalized Boundary Layer Equations Gareth H. McKinley (MIT-HML), November 2004 We have seen that, in general, high Reynolds number flow past a slender body such as an airfoil can be considered as an irrotational “outer” flow (that can be determined in principle at least from potential flow theory) and a thin “inner” flow regime in which viscous effects are important and lead to the generation of vorticity. This thin inner region is often referred to as a viscous boundary layer and denoted generically ! ( x ) . Here we shall consider the “inner flow” region in detail and wish to see what simplifications to the equations of motion are possible due to the thinness of the boundary layer. We consider a 2D boundary layer next to a solid wall on which the no-slip boundary condition is to be applied. We shall use a “boundary layer” coordinate system in which x is along the surface and y is normal to the surface. A similar analysis can be performed in three-dimensions but requires an explicit assumption of the lateral scale of the three-dimensional flow. The following analysis is also applicable to boundary layers on axisymmetric objects provided that the boundary layer is thin enough that local curvature terms are always negligible (i.e.

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09_gen_boundary - The Generalized Boundary Layer Equations...

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