A Direct Design Method of 2d Duct Based on the Compressible Navier-Stokes Equations

In this paper، a fully coupled formulation of the surface shape design problem، called the direct design approach، has been proposed. In this method both the target surface pressure and the unknown nodal coordinates appear explicitly in the formulations. The proposed method is based on the compressible Navier-Stokes equations، but in the past work it has only been applied in the context of inviscid fluid flows. A cell-centered finite volume method and AUSM+ scheme are used to discretize the Navier-Stokes equations. The details of linearization and imposition of the target pressure are discussed there. The validation test case is presented which show the robustness of the method in handling complex geometries and complex physical phenomena (such as shock waves). The importance role of viscosity dictates aerospace designers to consider this phenomenon especially in thick boundary layer regions (hypersonic nozzles)، diffusers with separation possibility and many other cases. Stability of this method in viscous flow decreased extensively in comparison with the last version the method based on the Euler equations. The significant results of this study، no single answer that is where the separation occurs.