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.

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number (${Re}_{cr}$ ), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The ${Re}_{cr}$ is also calculated at every retardation ratio ($\beta$ ) and elongational viscosity. The results revealed a significant impact of viscoelasticity on ${Re}_{cr}$ so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, ${Re}_{cr}$ decreases linearly with $\beta$ according to ${Re}_{cr}=-34.5\beta +46.525$ and increases with extensional viscosity. It is also found that $\beta$ plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient ($\overline{C_D}$ ) and the amplitude of lift coefficient ($C_{\mathit{Lmax}}$ ) do not have similar behaviors for low and high $\beta$ . Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of $C_{\mathit{Lmax}}$ with El are also similar to $\overline{C_D}$ , but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

In this study, a new vortex-based fluidic oscillator was designed whose performance was numerically evaluated by solving the URANS equations. The oscillator consists of a primary chamber and secondary chamber, separated by a mid-throat and connected by two feedback channels. The jet passing through these chambers forms two pairs of vortices inside the primary and secondary chambers. These vortices roll onto the jet shear layer, and gradually disturbs the jet symmetry. As a result, the vortices grow and shrink asymmetrically, activating the feedback flow to make a harmonic oscillation. The collision of the oscillating jet with the mid-throat traps a part of the jet shear layer in the primary chamber, which forms a strong vortex, returning the jet toward the other side of the mid-throat. The vortex inside the secondary chamber causes the jet to attach to one side of the secondary chamber, deviating the outlet jet to the other side. To compare the performance of the new oscillator with the original one, URANS equations were solved for two-dimensional models of both oscillators with the same grid generation and boundary conditions. The new oscillator had a higher oscillation frequency, a lower pressure drop, and a higher output momentum flux.