Flow dynamics in longitudinally grooved duct

Abstract

Flow in a finite-width rectangular duct with a corrugated top-bottom wall has been studied. The primary goal is to establish geometries that allow early flow destabilization at a possibly low drag increase. The flow is assumed periodic in the streamwise direction and bounded by the duct sidewalls in the spanwise direction; the top and bottom wall corrugations have a form of sinusoidal waves oriented transversely to the flow and form longitudinal grooves; i.e., the lines of constant elevation (or phase) are parallel to the direction of the flow. The analysis is performed up to the Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is focused on the properties of the two-dimensional base flow. Mainly, the dependence of hydraulic losses and drag reducing properties on duct’s geometry is characterized. The second part of the analysis discusses the onset of the three-dimensional travelling wave instability over a wide spectrum of geometric configurations. Linear stability is investigated by means of the direct numerical simulation of the Navier-Stokes equations. Critical conditions for the onset of instabilities at a range of geometric parameters are determined. Finally, the nonlinear saturation of unstable modes and the resulting secondary flows are examined. We have shown that in the state resulting from the nonlinear saturation of the disturbance, the flow becomes more complex while the drag reducing properties of the base flow can be maintained.

On the use of transpiration patterns for reduction of pressure losses

“…If the smooth surface is viewed as the reference case, all its alterations increase the wetted area and, thus, the reduction of the wall shear must be large enough to overcome the increase of this area. It is known that short wavelength longitudinal grooves (riblets) can reduce drag by forcing the stream to lift above the grooves (Walsh 1980, 1983). It is also known that long wavelength longitudinal grooves can lead to drag reduction through changes in the distribution of the bulk flow (Szumbarski, Blonski & Kowalewski 2011, Moradi & Floryan 2013; Mohammadi & Floryan 2013 a , 2014, 2015; Mohammadi, Moradi & Floryan 2015, Chen et al.…”

Slowing down convective instabilities in corrugated Couette–Poiseuille flow

“…Results of this verification are outlined in the Appendix. We also note that the approach used here has already been established for similar flows (Gepner & Floryan 2016;Yadav et al 2017Yadav et al , 2018Hossain, Cantwell & Sherwin 2021;Yadav, Gepner & Szumbarski 2021) and both spatial and temporal resolutions used in this work are more than sufficient to recover both hydrodynamic stability and nonlinear saturation states, as outlined in Yadav et al (2017).…”

“…For the pressure-driven flow, presence of longitudinal grooves has been shown to cause onset of nonlinear flow solutions (Yadav et al 2017(Yadav et al , 2018Moradi & Tavoularis 2019), to which the flow transitions via a supercritical Hopf bifurcation ) already at very low values of the Reynolds number (critical conditions occur below Re = 60 using the Poiseuille, centreline velocity scale). Those non-stationary solutions remain connected to the laminar state in the linear sense and are linked to the travelling wave mode instability that develops due to the corrugation-induced variations in the streamwise velocity.…”

Use of Surface Corrugations for Energy-Efficient Chaotic Stirring in Low Reynolds Number Flows

“…The Fourier expansion was truncated after M modes with M selected to make ratio of kinetic energies of this mode and mode zero small enough (10 −20 was used in the computations). The spectral element mesh as well as the local expansions were selected based on the convergence studies carried out previously in the context of stability and nonlinear saturation studies 19,26,33 . Sufficient temporal accuracy and resolution were achieved with the step size of ∆ = t 2e-2 26,33 , which translates to approximately 1000 timesteps per period of the oscillatory flow.…”

“…The spectral element mesh as well as the local expansions were selected based on the convergence studies carried out previously in the context of stability and nonlinear saturation studies 19,26,33 . Sufficient temporal accuracy and resolution were achieved with the step size of ∆ = t 2e-2 26,33 , which translates to approximately 1000 timesteps per period of the oscillatory flow. The computational box extended over two groove wavelengths in the spanwise direction and over a single wavelength of the travelling wave in the streamwise directions to account for possible x-and z-subharmonics, but none were found.…”