Interaction dynamics of longitudinal corrugations in Taylor-Couette flows

Abstract

In this paper, numerical simulations are performed on the interaction of vortices with a longitudinal corrugated wall in a Taylor-Couette (TC) setting with the inner smooth surface cylinder rotating and the outer corrugated surface cylinder stationary. The motivation of the study is to shed light on how such an interaction affects the drag/torque with respect to two geometric parameters of the corrugations, namely, the wavelength λc* and amplitude A*, where * indicates a normalization by the gap width d. Results show that in the circular Couette flow regime, the secondary vortices induced by the corrugations cause the torque to increase. When λc*<1, there is a linear relationship between torque and λc*, and when λc*>1, there is a steeper increase of torque due to the interaction of the growing secondary vortices and the opposite wall. In the Taylor-vortex flow regime, the interaction between the Taylor vortices and the corrugations produces three distinct behaviors characterized by λc*. As the wavelength increases, our results show that the stronger modulation effects can override the inherent TC flow dynamics, which in turn leads to a wide range of flow structures that can have a significant impact on the resulting drag/torque characteristics. Generally, a torque reduction is achieved when λc*≤1, while forcing the Taylor vortices to stay on the crests of the corrugations can lead to significant improvement in torque reduction. Finally, the geometrical shape of the corrugations mainly alters the wall shear stress distribution on the corrugated wall, with a negligible effect on the flow dynamics when compared to λc*.

Numerical study on wide gap Taylor Couette flow with flow transition

“…Most of the previous numerical studies on TCF were conducted using a single wavelength ( two gap widths or aspect ratio 2) fluid column as the axial height with periodic boundary condition at the both ends of cylinder (Marcus, 1984;Fazel & Booz, 1984;Liao, Jane & Young, 1999;Bilson & Bremhorst, 2006;Dong, 2007;Abshagen et al, 2008;Pirrò & Quadrio, 2008;Heise et al, 2008;Jeng & Zhu, 2010;Kristiawan, Jirout & Sobolík, 2011;Sobolik et al, 2011;López et al, 2015;Ng, Jaiman & Lim, 2018; Dessup et al, 2018). In this study, DNS has been carried out for two different heights of fluid column, namely single wavelength fluid column (Height = 2 times the annular gap size) and four wavelengths fluid column (Height = 8 times the annular gap size).…”

Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

“…Additional numerical tests were made with . In the second situation, following several authors (Razzak et al. 2019; Ng, Jaiman & Lim 2018; Teng et al. 2015; Fasel & Booz 1984), we have assumed axial periodic boundary conditions at the upper and lower endwalls, i.e.…”

“…100. Additional numerical tests were made with L 1 = L/200.-In the second situation, following several authors,Razzak et al (2019),Ng et al (2018),Teng et al (2015),Fasel & Booz (1984), we have assumed axial periodic boundary conditions at the upper and lower endwalls, i.e.f (r, 0, t) = f (r, L, t) ,(2.12)where f represents any of the dependent variables. Note that the height L of the domain is an integer multiple of the expected wavelength.…”

Slowing down convective instabilities in corrugated Couette–Poiseuille flow

“…Such an unstable mode, if amplified, develops downstream at a relatively slow pace, while all the time being advected with the speed that is comparable with the bulk flow velocity. This, in turn, requires any prospective experimental set-up to imitate periodicity conditions, so easily enforced numerically, either by resorting to the corrugated Taylor-Couette configuration (see Ng et al (2018), for numerical analysis of such configuration) or by application of impractically long arrangements with very long test sections, such as to allow for the development of the unstable mode long enough for it to become detectable. Preferably, the measurement section should be long enough to the point where nonlinear interactions cause nonlinear saturation and onset of secondary flows, before the bulk of the flow flushes the investigated phenomenon out of the measurement domain.…”

“…This type of grooves has been investigated as a means to manipulate flow dynamics in a doubly periodic grooved channel (Szumbarski 2007; Mohammadi & Floryan 2014; Mohammadi, Moradi & Floryan 2015; Yadav, Gepner & Szumbarski 2017; Gepner & Floryan 2020; Gepner, Yadav & Szumbarski 2020), singly periodic corrugated duct (Yadav, Gepner & Szumbarski 2018; Pushenko & Gepner 2021) and grooved, annular (Moradi & Floryan 2019; Moradi & Tavoularis 2019) configurations. It has been shown that properly shaped longitudinal grooves lead to a reduction of hydraulic drag (Szumbarski & Błoński 2011; Szumbarski, Blonski & Kowalewski 2011; Mohammadi & Floryan 2015; Ng, Jaiman & Lim 2018; Moradi & Floryan 2019). Interestingly, there are indications, both experimental (Kim & Hidrovo 2012; Bolognesi, Cottin-Bizonne & Pirat 2014) and theoretical (Crowdy 2017), that drag reduction, attributed to the superhydrophobic effect, could, at least in some cases, be related to drag reduction reported for flows through longitudinally patterned geometries, such as those considered here.…”