Three-Dimensional Integral Boundary Layer Formulation for General Configurations

A three-dimensional integral boundary layer formulation IBL3 is developed to enable rapid viscous analyses of 3D aerodynamic flows via strongly-coupled viscous/inviscid solution methods. It employs four equations which allow representation of separated flow and crossover profiles, with two additional equations included to model Reynolds stress transport and thus capture turbulence lag effects. In laminar regions the stress-transport equations revert to a form which represents unstable-wave envelope growth, thus making transition prediction an inherent part of the overall formulation. All six equations have a proper rotation-invariant form which allows solution on arbitrary surface meshes via a finite-element method constructed in a local cartesian basis for each residual stencil. This eliminates the traditional 3D boundary layer curvilinear surface coordinates, and thus sidesteps their inconvenient requirements on geometry smoothness. The presentation includes the derivation of the integral equations, the formulation of the finite-element solution scheme, and computation of test cases to demonstrate the correctness and accuracy of the overall method. Also presented is the methodology for strong coupling of the integral boundary layer formulation to a number of inviscid-flow solvers.