Predictive behaviors by the extended k-${varepsilon}$ turbulence model and the standard k-${varepsilon}$ turbulence model are compared. Grid dependency is tested with the H-type grid as well as the O-type grid. Computations have been performed on a circular-to-rectangular transition duct. The Reynolds number is 390,000 based on the bulk velocity at the inlet. The computed axial velocity contours, transverse velocity profiles, static pressure contours, peripheral skin friction coefficient, peripheral wall static pressure distributions and turbulence kinetic energy have been compared with experimental results. The computed results than those obtained with the standard k-${varepsilon}$ turbulence model. Comparing to the computed results obtained with the H-type grid and O-type grid, those with H-type grid seem to agree well with experimental results.