An adjoint optimization method is utilized to design an inviscid outer wall
shape required for a turbulent flow field solution of the So-Mellor convex
curved wall experiment using the Navier-Stokes equations. The associated c
ost function is the desired pressure distribution on the inner wall. Using
this optimized wall shape with a Navier-Stokes method, the abilities of var
ious turbulence models to simulate the effects of curvature without the com
plicating factor of streamwise pressure gradient are evaluated. The one-equ
ation Spalart-Allmaras (SA) turbulence model overpredicts eddy viscosity, a
nd its boundary layer profiles are too full. A curvature-corrected version
of this model improves results, which are sensitive to the choice of a part
icular constant. An explicit algebraic stress model does a reasonable job p
redicting this flow field. However, results can be slightly improved by mod
ifying the assumption on anisotropy equilibrium in the model's derivation.
The resulting curvature-corrected explicit algebraic stress model (EASM) po
ssesses no heuristic functions or additional constants. It slightly lowers
the computed skin friction coefficient and the turbulent stress levels for
this case, in better agreement with experiment. The effect on computed velo
city profiles is minimal. (C) 2001 Elsevier Science Inc. All rights reserve
d.