Predictions of developing flow with buoyancy-assisted flow separation in a vertical rectangular duct: Parabolic model versus elliptic model

The relative performance and validity of the parabolic-equation model coupled with a modified FLARE procedure for analyzing three-dimensional buoyancy-assisted flow separation in a vertical duct are verified by the full elliptic Navier ? Stokes model. Numerical solutions for the flow and thermal fields are presented, and a comparison between the two models under various heating conditions and over wide ranges of values of Prandtl number (Pr), aspect ratio of the cross section of the duct (B), and buoyancy parameter (Gr/Re) has been made. Results show that the solutions yielded by the parabolic model agree closely with the elliptic-model solutions within the considered parameter ranges. Computation time required in the full elliptic model is approximately 15,000 CPU seconds on a CRAY XMP EA/116se computer to complete a case, whereas the parabolic-model analysis takes only about 2000 CPU seconds or less.