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Purpose This paper aims to conduct, a detailed investigation of various Reynolds averaged Navier–Stokes (RANS) models to study their performance in attached and separated flows. The turbulent flow over two airfoils, namely, National Advisory Committee for Aeronautics (NACA)-0012 and National Aeronautics and Space Administration (NASA) MS(1)-0317 with a static stall setup at a Reynolds number of 6 million, is chosen to investigate these models. The pre-stall and post-stall regions, which are in the range of angles of attack 0°–20°, are simulated. Design/methodology/approach RANS turbulence models with the Boussinesq approximation are the most commonly used cost-effective models for engineering flows. Four RANS models are considered to predict the static stall of two airfoils: Spalart–Allmaras (SA), Menter’s k – ω shear stress transport (SST), k – kL and SA-Bas Cakmakcioglu modified (BCM) transition model. All the simulations are performed on an in-house unstructured-grid compressible flow solver. Findings All the turbulence models considered predicted the lift and drag coefficients in good agreement with experimental data for both airfoils in the attached pre-stall region. For the NACA-0012 airfoil, all models except the SA-BCM over-predicted the stall angle by 2°, whereas SA-BCM failed to predict stall. For the NASA MS(1)-0317 airfoil, all models predicted the lift and drag coefficients accurately for attached flow. But the first three models showed even further delayed stall, whereas SA-BCM again did not predict stall. Originality/value The numerical results at high Re obtained from this work, especially that of the NASA MS(1)-0317, are new to the literature in the knowledge of the authors. This paper highlights the inability of RANS models to predict the stall phenomenon and suggests a need for improvement in modeling flow physics in near- and post-stall flows.

To achieve consistent second-order spatial accuracy in cell-centered finite volume methods using the divergence theorem, the gradient computation at the cell-centers should at least be first-order accurate, which is not assured by the Traditional Green-Gauss (TGG) method on irregular meshes. The Circle Green-Gauss (CGG) method, however, achieves this by constructing a new auxiliary volume (AV) around the cell of interest using a circle and then employs linear interpolation to obtain estimates of the solution at the face centers of this AV, which are then used to compute the cell-center gradients. We propose a modified method, which we call the mid-point Green-Gauss method (mpGG), that alleviates the complexity in the implementation while maintaining the same accuracy as the CGG method. We offer detailed construction of the three-dimensional AV for the most commonly used multi-hydral elements in unstructured meshes, that is, hexahedral, pyramidal, prism, and tetrahedral cells, using an in-house finite volume solver that reads and writes data based on the computational fluid dynamics (CFD) General Notation System (CGNS).Accuracy analysis of the proposed method is carried out in comparison with the TGG, CGG, and weighted least squares methods. The proposed method is further validated using the case of laminar flow over a sphere at a Reynolds number of 100. An inviscid vortex dissipation study is performed to compare the level of numerical dissipation produced by these methods. Further, we study the performance of these methods in a problem that involves turbulent shock-wave boundary layer interaction.

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