Recently, an inverse design algorithm called ball–spine algorithm (BSA) was introduced for the design of 2D ducts. In this approach, the walls are considered as a set of virtual balls that can move freely along the straight directions called spines. In the present work, the method is developed for quasi-three-dimensional (quasi-3D) design of S-shaped ducts with a predefined width. To do so, the upper and lower lines of the S-duct symmetric section are modified under the BSA and then, the 3D S-duct geometry is obtained based on elliptic cross-sectional profiles. The target pressure distributions (TPDs) along the upper and lower lines are prescribed so that separation does not occur. Finally, the flow through the designed S-duct is numerically analyzed using a viscous flow solver with the SST turbulence model to validate the designed S-duct performance. The performance of the designed S-duct is compared to original and optimized versions of a benchmark S-duct diffuser. Results show that the present S-duct has a better performance.

In this paper, the viscous and inviscid flow fields of a gas turbine blade cascade are investigated. A two-dimensional CFD solver is developed to simulate the flow field through VKI blade cascade. A high resolution flux difference splitting scheme of Roe is applied to discretize the convective part of Navier–Stokes equations. Baldwin Lomax (BL) model is used to account for turbulent effects on the viscous flow field of the blade cascade. For validation of the code, the flow field was solved by Ansys Fluent commercial software. The flow solution was done by third order flux difference splitting scheme of Roe and k–ω turbulence model. The findings show that the high turbulent and the shock creation in the flow field, lead to the same results in viscous and inviscid flows. Also, the results show that the grid and solver’s focus must be on the precise prediction of the shock effects, when the shock is occurred in the domain