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- Title
The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration.
- Authors
Klettner, C. A.; Smith, F. T.
- Abstract
The Poiseuille flow (centreline velocity Uc) of a fluid (kinematic viscosity ν) past a circular cylinder (radius R) in a Hele-Shaw cell (height 2h) is traditionally characterised by a Stokes flow (Λ = (UcR/ν)(h/R)² ≪ 1) through a thin gap (≮ = h/R ≪ 1). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space Λ-≮ when these conditions are not met. Starting with the Navier-Stokes equations and increasing Λ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the 'inner' region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For ≮ = 0.01, the limiting condition for a steady flow as Λ is increased is the instability of the Poiseuille flow. However, for larger ≮, this limit is at a much higher Λ, resulting in a laminar separation bubble, of size O(h), forming for a certain range of ≮ at the back of the cylinder, where the azimuthal location was dependent on ≮. As ≮ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space Λ-≮.
- Subjects
POISEUILLE flow; STOKES flow; BOUNDARY layer (Aerodynamics); KINEMATIC viscosity; FLOW instability
- Publication
Journal of Fluid Mechanics, 2022, Vol 934, pA8-1
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2021.1128