A method for calculating turbulent boundary layers using a formulation of firstgradient type
Abstract
To develop a computer program for calculating a blown boundary layer at the hinge of a liftaugmenting flap, a calculation method was proposed which uses an equation governing the behavior of the Boussinesq coefficient, formulated by Nee and Kovasznay in the case of an incompressible boundary layer. It is shown that, in the inner turbulent zone, the expression for the local equilibrium, production = dissipation, is consistent with that of the logarithmic law for the velocity near the wall. This observation allows the production and dissipation terms to be deduced from the form taken by the logarithmic law in the case of compressible boundary layers, and the NeeKovasznay equation to be generalized to such flows. Similarly the persistence of the logarithmic law when the turbulent wall zone is the seat of mechanisms other than turbulent energy production and dissipation led to the adoption of a formulation conceived by Bradshaw and to a modification of the dissipation length in order to represent these supplementary mechanisms in an implicit manner. Knowing how to relate the value of this length to the value of the slope of the logarithmic law allows the wall jet and the blown boundary layer on deflected or undeflected flaps to be calculated. The numerical method is that of Spalding and Patankar, with modifications relating to the calculation of the entrainment rate and the velocity profiles in the viscous layer, and to the representation of the effect of wall curvature on the transverse variation of the static pressure.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1977
 Bibcode:
 1977STIN...7724439R
 Keywords:

 Boundary Layer Control;
 Gradients;
 TrailingEdge Flaps;
 Turbulent Boundary Layer;
 Compressible Boundary Layer;
 Computer Programming;
 Externally Blown Flaps;
 Hinges;
 Lift Augmentation;
 Wall Jets;
 Fluid Mechanics and Heat Transfer