Numerical investigation of the fully developed turbulent flow over a moving wavy wall using k-ε turbulence model

The subject matter of this research is that of improving and enhancing the results of the mathematical models of the classical turbulent flows with increasing Reynolds numbers over the surfaces of complex configurations to improve its applicability in diverse realistic disciplines. As the sinusoidal solid surface with the wavy boundary in the mainstream direction develops periodic pressure gradient in the fluid flow, successive acceleration and deceleration associated with multiple fluid flow separations and reattachments, leads to enrich the analysis and the consequent results. Also, as this issue represents the focal point of many researchers over the previous three decades and consequently the numerical and experimental results available in the literature are enough for conducting its investigation. Therefore, turbulent flow over a sinusoidal solid surface is investigated using two versions of the standard k-ε turbulence model. In this regard, the present investigation is performed within the framework of the 2D modeling to simplify the involved rigorous mathematical processing and to introduce a reliable physical interpretation of the numerical results, which validated against the available results of the Direct Numerical Simulations (DNSs) and experimental works at moderate Reynolds numbers with the recirculation zones captured well. Also, the influences of alternating pressure gradients induced by the fluctuating surface curvatures, the sequential fluid flow separations and reattachments, the higher wave steepness ratios 2α/λ and the higher Reynolds number of order 106 are clarified. This comparative analysis has proved - with no doubt - that the fluid flow in the recirculation zones is so sensitive to the refinement of the modeling grid in the near-wall region of the flow channel, which leads to improving the results of the classical turbulence models through improving both the skin friction and the flow recirculation zones, and also leads to clarifying the shortcomings of the available published results.