The effect of slip on the development of flow separation due to a bump in a channel

Abstract

A numerical study on the effect of surface slip on the flow in a constricted channel is presented, with the aim of exploring the use of surface slip to control flow separation. Our focus is on two-dimensional flow in a channel over a bump, with a fixed aspect ratio, upon which a Robin-type slip boundary condition is imposed. When the channel walls are fully no-slip, such a flow is known to develop a region of separation behind the bump, at sufficiently large Reynolds numbers. The effect of slip on the separation bubble dynamics occurring behind the bump is investigated, for Reynolds numbers $2000$ and $4000$ . It is shown that surface slip (i) attenuates the intensity of separation as it diminishes the minimum of the streamwise velocity within the recirculation region; (ii) delays the onset of flow separation, shifting it downstream, along the bump, and (iii) reduces the dimensions of the separation bubble behind the bump, allowing the flow to reattach sooner. Ultimately, slip inhibits separation, with both the points of separation and reattachment coalescing, for a slip length $\lambda$ of approximately $0.2$ .

Two-dimensional flow over a smooth depression in a channelwith a slip wall

“…Indeed, this was achieved for slip lengths 𝜆 = 0.15 and 𝜆 = 0.1 for the respective wide and narrow gap deformations. Thus, similar to Ceccacci et al (2022a) for two-dimensional bumps in a channel, slip provides an effective control mechanism for flow separation in a dilated channel. Moreover, the slip length, 𝜆, required here to achieve flow separation control is less than that needed for the bump configuration.…”

“…The main qualitative conclusion drawn from this analysis is that slip provides a mechanism for flow control in a dilated channel as it reduces the intensity and dimensions of the separation bubble that forms within the gap region. Moreover, comparing the observations for the gap geometry with those similar-sized bump configurations modelled by Ceccacci et al (2022a), a smaller slip length, 𝜆, is required to suppress the formation of separated flow in gap concavities than along the rear side of bump deformations. In their investigation, Ceccacci and co-workers showed that 𝜆 ≈ 0.2 was necessary to inhibit reversed flow forming downstream of the two-dimensional Gaussian-shaped bump when the Reynolds number Re = 4000.…”

“…In the present study, we extend the numerical investigation of Ceccacci et al (2022a) to the flow through a two-dimensional channel with a gap deformation and slippery channel walls. The surface deformation is imposed along the lower channel wall, and surface slip is achieved by implementing slip boundary conditions along the length of the gap deformity.…”

“…In addition, slip surfaces have proven to be effective in delaying laminar-turbulent transition in channel flows (Lauga and Cossu, 2005;Min and Kim, 2004;Ceccacci et al, 2022b) and favourably control flow separation and reduce drag (Daniello et al, 2009;Fairhall et al, 2019;Mollicone et al, 2022). Ceccacci et al (2022a) recently undertook a numerical study of the two-dimensional flow through a channel with a bump along the lower wall and used a slippery surface to inhibit flow separation.…”

“…Nektar++ has been extensively used to perform high-fidelity direct numerical simulations (DNS) on a variety of flows and geometries, including transient flow past a wind turbine aerofoil to investigate flow structures and aerodynamic performance (Nakhchi et al, 2021), the flow past a transversely oscillating cylinder for dynamic mode decomposition analysis (Ping et al, 2021), the boundary layer on an unswept wing to characterise tip effects on three-dimensional separated flows (Zhang et al, 2020), convective heat transfer in turbulent flow in porous media (Chu et al, 2019), and turbulent separated flow in a channel with streamwise periodic hill-shaped constrictions (Wang et al, 2021). The latter work considered a geometry similar to that modelled by Ceccacci et al (2022a), while the current study considers a smooth depression along the lower channel wall. Flow over a curved surface is a complicated phenomenon and has been, and continues to be, extensively investigated due to its industrial and academic significance (Park, 2017;Razi et al, 2017).…”