Computations of transonic flow with the v2–f turbulence model

Abstract

Abstract The v2–f (or k–e– v ′2 ) model of Durbin, which has shown very good performance in several test cases with separated flows at low speeds, has been applied to transonic flows over the Delery bump and the RAE 2822 airfoil. In both cases, shock-induced separation occurs. The elliptic relaxation equation of the model is used in the entire computational domain, i.e., it is computed in both the subsonic and supersonic regimes. The predicted size of the separation zone, surface pressures and mean velocities by two model variants agree reasonably well with the experimental data. Consistent with our earlier investigation, in which the v2–f model was applied to a subsonic high-lift airfoil at a high incidence angle, the level of turbulent shear–stress within the separation zone is underestimated. A `code-friendly' variant of the model is proposed to enhance numerical stability. It has proven to be advantageous if an implicit segregated equation-by-equation approach is used. This modification alleviates the `stiffness problem' associated with the original model caused by the boundary conditions at walls. This is particularly true when the Reynolds number is high and the near-wall grid spacing is extremely small.