Flow dynamics and enhanced mixing in a converging–diverging channel

Abstract

An analysis of flows in converging–diverging channels has been carried out with the primary goal of identifying geometries which result in increased mixing. The model geometry consists of a channel whose walls are fitted with spanwise grooves of moderate amplitudes (up to 10 % of the mean channel opening) and of sinusoidal shape. The groove systems on each wall are shifted by half of a wavelength with respect to each other, resulting in the formation of a converging–diverging conduit. The analysis is carried out up to Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is based on a two-dimensional model and demonstrates that increasing the corrugation wavelength results in the appearance of an unsteady separation whose onset correlates with the onset of the travelling wave instability. The second part of the analysis is based on a three-dimensional model and demonstrates that the flow dynamics is dominated by the centrifugal instability over a large range of geometric parameters, resulting in the formation of streamwise vortices. It is shown that the onset of the vortices may lead to the elimination of the unsteady separation. The critical Reynolds number for the vortex onset initially decreases as the corrugation amplitude increases but an excessive increase leads to the stream lift up, reduction of the centrifugal forces and flow stabilization. The flow dynamics under such conditions is again dominated by the travelling wave instability. Conditions leading to the formation of streamwise vortices without interference from the travelling wave instability have been identified. The structure and the mixing properties of the saturated states are discussed.

Active chaotic mixing in a channel with rotating arc-walls

“…Active stirring Converging-diverging channel [3,25] Hydrodynamics [8,47] Rigid or flexible structures [2,38] Rigid or flexible structures [18,28,36,45] Staggered herringbone channel [56] Acoustics [14,33] Partitioned pipe mixer [35] Electro-hydrodynamics [13] Twisted pipes [7,12,34] Magneto-hydrodynamics [27] Focusing channels [37] Acoustically driven bubbles [49] Elastic turbulence [9,10,29] Dielectrophoresis [40] Corrugated channel [26] Electrokinetics [46] TABLE I: Examples of configurations for passive stirring, and types of forcing for active stirring, for open flow mixing (not exhaustive list).…”

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).…”

“…While numerical investigations characterizing effects of longitudinal corrugation on hydrodynamic stability (Szumbarski 2007;Szumbarski & Błoński 2011;, and analysis of consequent nonlinear states (Yadav et al 2017;Pushenko & Gepner 2021) have been performed, to date there seem to be no experimental results reported to support existing numerical findings. The lack of experimental results is somewhat surprising, considering that the alternative, transverse groove configuration received much attention, both from experimental as well as computational perspectives (Sobey 1980;Nishimura, Ohori & Kawamura 1984;Nishimura et al 1985Nishimura et al , 1990aGschwind, Regele & Kottke 1995;Blancher, Creff & Quere 1998;Cabal, Szumbarski & Floryan 2002;Floryan & Floryan 2010;Mitsudharmadi, Jamaludin & Winoto 2012;Rivera-Alvarez & Ordonez 2013;Gepner & Floryan 2016). On the other hand, it seems that, at least in the qualitative sense, the destabilization mechanism caused by the presence of longitudinal grooves and consequent variation in the streamwise velocity, is similar to the gap instability (Moradi & Tavoularis 2019;Lamarche-Gagnon & Tavoularis 2021) that exists in the eccentric annular flow configuration and has been experimentally investigated (Piot & Tavoularis 2011).…”

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

“…Active methods employ external body forces 17 , actuated particles 18 and various stirrers 9 with all of them requiring an external energy input. Three-dimensionality and unsteadiness do not guarantee chaos 19,20 , and not every chaotic state guarantees good stirring; either Poincaré maps or Lyapunov exponents must be used to verify whether the resulting flow is both chaos-and stirring-capable.…”

“…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.…”