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 $0.2$ .
A linear stability investigation is undertaken on the two-dimensional flow that develops in a channel whose walls are coated with a superhydrophobic material. The surfaces are modeled as classical slip surfaces, exploiting a linear Navier slip condition imposed on the channel walls. Both symmetric and asymmetric slip walls are considered, whereby the linearized stability of the flow is determined via an OrrโSommerfeld normal-mode approach. In both instances, the application of slip establishes a significant stabilizing effect and increases the critical Reynolds number associated with the onset of linearly unstable behavior. Indeed, for sufficiently large slip lengths, the upper and lower branches of the neutral stability curve coalesce. Consequently, the flow becomes linearly stable to all disturbances for all wavelengths and Reynolds numbers.
The effect of slip along a Gaussian-shaped gap deformity, located about a fixed position on the lower wall of a two-dimensional channel, is numerically investigated. Two gap deformations are modelled, with dimensions sufficient to generate localised pockets of reversed flow when the channel walls are fully no-slip. The Reynolds number of the flow, based on the channel half-width, is 4000 for this investigation. The two gap deformations have the same depth, ๐, but different widths, ๐, leading to a wide gap with an aspect ratio ๐ = ๐/๐ = 0.4 and a narrow gap with an aspect ratio ๐ = 0.8. The wide gap establishes a higher intensity region of separated flow within the deformation than the narrow gap. Surface slip with slip length, ๐, is modelled via a Robin-type slip boundary condition. Applying the slip condition to the gap concavity reduces the intensity and thickness of the separation bubble within the deformation. Eventually, slip eliminates flow separation altogether for slip lengths ๐ = 0.15 and ๐ = 0.1 for the wide and narrow gaps, respectively.
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