Abstract
Inducing spanwise motions in the vicinity of solid boundaries alters the energy, mass and/or momentum transfer. Under some conditions, these motions are such that drag is reduced and/or transition to turbulence is delayed. There are several possibilities to induce those spanwise motions, be it through active imposition a predefined velocity distribution at the walls or by careful design of the wall shape, which corresponds to passive control.In this contribution, we investigate the effect that wavy walls might have on delaying transition to turbulence. Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes are conducted. A pseudo laminar regime that remains stable until a Reynolds number 20% higher that the critical is found for the wavy-walled simulations. Dynamic Mode Decomposition applied to the simulation data reveals that in these configurations, modes with wavelength and frequency compatible with the surface undulation pattern appear. We explain and visualize the appearance of these modes. At higher Reynolds numbers we show that these modes remain present but are not dominant anymore. This work is an initial demonstration that flow control strategies that trigger underlying stable modes can keep or conduct the flow to new configurations more stable than the original one.
Highlights
To shed some light about the physical reasons, in this contribution, we investigate the effect of wavy walls in delaying the transition to turbulence
We have investigated the effect that wavy walls have on delaying transition to turbulence
Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes has been conducted, using our in-house solver based on Discontinuous Galerkin Spectral Element Method
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The drag reducing effect of spanwise/streamwise periodic velocity enforced at the wall had been already investigated using Direct Numerical Simulation (DNS): [9,10,11] showed how the spatial Stokes layer disrupts the turbulent production cycle, resulting into a positive shift of the logarithm layer (much as riblets do, [12]) They went further as to identify combinations of forcing amplitudes, wavelengths and frequencies for the wall velocity leading to net-energy savings of up to 23%. As noted in [13], well-designed perturbations introduced in a boundary layer can potentially inhibit the growth of the most unstable disturbances This has been recently confirmed by [14], who experimentally described how spanwise perturbation introduced by a 3D wavy-walled roughness is more effective in delaying transition than its 2D counterpart (transition Re = 120,000 vs 50,000). (a) Generic flow configuration (b) Computational setup A (c) Computational setup B
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