Turbulent flows are characterized by the presence of "scales of fluctuations", or "structures" of varying magnitudes, the effects in which the mixing, transfer and dissipation of energy are preponderant. Most importantly, dissipation determines the depth profile of the flow. This contribution aims to implement a model able to predict unsteady turbulent flows generated by the presence of obstacles in a channel with complex geometry and to report, where the complexity of the phenomena are observed, such as: the separation of the boundary layer, the succession of vortices, local heat transfers, and the recirculation zones in the wake of obstacles and the oscillatory regime of the hydraulic jump for which this research is of exclusive interest. The current work therefore, presents the numerical simulation in unsteady turbulent regime based on the resolution of balance equations, using the RANS (Reynolds-Averaged Navier–Stokes) approach with an RNG k−ε closure model. To solve the incompressible Navier–Stokes equations governing these flows, we appealed to the motivated finite volume method, and its ability to process complex geometries. The simulation software FLUENT we used is based on the finite volume method. It allows to explore, the velocity and pressure fields in the digital channel of the studied flows.

The Reynolds–averaged Navier–Stokes (RANS) equations were solved along with Reynolds stress model (RSM), to study the fully-developed unsteady and anisotropic single-phase turbulent flow in 90° bend pipe with circular cross-section. Two flow configurations are considered the first is without ribs and the second is with ribs attached to solid walls. The number of ribs is 14 ribs regularly placed along the straight pipe. The pitch ratios is 40 and the rib height e (mm) is 10% of the pipe diameter. Both bends have a curvature radius ratio, of 2.0. The solutions of these flows were obtained using the commercial CFD software Fluent at a Dean number range from 5000 to 40000. In order to validate the turbulence model, numerical simulations were compared with the existing experimental data. The results are found in good agreement with the literature data. After validation of the numerical strategy, the axial velocity distribution and the anisotropy of the Reynolds stresses at several downstream longitudinal locations were obtained in order to investigate the hydrodynamic developments of the analyzed flow. The results show that in the ribbed bend pipe, the maximum velocity value is approximately 47% higher than the corresponding upstream value but it is 9% higher in the case of the bend pipe without ribs. It was also found for both cases that the distribution of the mean axial velocity depends faintly on the Dean number. Finally, it can be seen that the analyzed flow in the bend pipe without ribs appears more anisotropic than in bend pipe with ribs.