Instability in a channel with grooves parallel to the flow

Abstract

Flow in a channel with corrugated walls has been studied, with the primary goal of establishing channel geometries that enhance achievable mixing at possibly low drag increase. The wall corrugation has the form of a sinusoidal wave oriented transversely, 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 the drag on the channel’s geometry is characterized. The second part of the analysis discusses the onset of the three-dimensional traveling wave instability. Linear stability is investigated by 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, nonlinear saturation of the unstable modes and the resulting secondary flows is examined. It is shown that the drag reduction property of the base flow can be maintained in the state resulting from non-linear saturation of the disturbance.

On the use of transpiration patterns for reduction of pressure losses

“…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. 2016; DeGroot, Wang & Floryan 2016; Raayai-Ardakani & McKinley 2017; Yadav, Gepner & Szumbarski 2017, 2018). Such grooves can be optimized (Mohammadi & Floryan 2013 b ) with their most effective forms changing with the imposed constraints.…”

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

“…The first step towards flow evolution to a chaotic state is the onset of the recently discovered inviscid 24 instability modes with the critical Re being as low as O(10 2 ) [24][25][26] . We illustrate in Fig.…”

“…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.…”

Time‐dependent flows in grooved non‐isothermal channels

“…The correct approach is to determine the flow for the actual wall geometry. The first possible approach is to use grid-based methods-their use to quantify mixing intensification in longitudinally grooved channel can be found in References 21,22. Grids are computed numerically to map the geometry, but this process is labor intensive and prohibitively expensive if many geometries need to be investigated. Most of the existing grid generators are only second-order accurate 23, 24 which raises questions regarding the accuracy of the results.…”