Turbulence anisotropy and near-wall modeling in predicting three-dimensional shear-flows

Three-dimensional turbulent flow in a circular-to-rectangular transition duct is studied to assess the role of near-wall modeling and turbulence anisotropy in predicting the origin and growth of longitudinal vorticity and the secondary motion with which it is associated. Calculations are carried out using the standard k-e model and the Reynolds stress transport closure of Gibson and Launder (GL), both of which use wall functions. The computed solutions are compared with experimental data and with calculations previously reported by the authors which employed the near-wall version of the GL model proposed by Launder and Shima (LSH). These comparisons lead to the conclusion that accurate description of most three-dimensional turbulent flows, regardless of their origin, would require turbulence models that 1) resolve the near-wall flow and 2) account for anisotropy of the Reynolds stresses. Further evidence to support the latter conclusion is provided by employing the LSH solution to evaluate the various terms in the mean longitudinal-vorticity equation. It is shown that, vortex stretching, vortex skewing, and generation and destruction of vorticity by Reynolds stresses are all dominant in one region or another.