Viscous flow normal to a flat plate at moderate Reynolds numbers

Abstract

An experimental and numerical investigation of the two-dimensional flow normal to a flat plate is described. In the experiments, the plate is started impulsively from rest in a channel for Reynolds numbers, based on the breadth of the plate, in the range 5 ≤ Re ≤ 20. Over this range of Re the flow remains symmetrical and stable and tends to a steady state but is shown to depend strongly on the ratio λ of the plate to channel breadth. The evolution of the experimental flow with time and Reynolds number is studied and the variation with λ in the range 0.05 ≤ λ ≤ 0.2 is investigated sufficiently to enable an estimate of properties of the flow as λ → 0 to be obtained for the steady-state flow. The numerical results are obtained for steady flow normal to a flat plate in an unbounded fluid for Reynolds numbers up to Re = 100. They supplement and extend results for this flow obtained for values of Re up to 20 by Hudson & Dennis (1985). The present solutions have been found using a vorticity-stream function formulation rather than the primitive-variable approach of Hudson & Dennis and provide an independent check on these results. A comparison of the theoretical results for Re ≤ 20 with the limit λ → 0 of the experimental results is, generally speaking, extremely satisfactory.

Numerical simulation of viscous flow interaction with an elastic membrane

“…The no-slip condition is imposed on the mesh edges coincident with the plate. Figure 5 shows the variation of non-dimensionalized eddy length with Reynolds number, in comparison with published data; the results demonstrate a clear agreement, particularly with the work of Hudson and Dennis [27] and Dennis et al [28], who use a finite difference approach on a polar grid, in a primitive variable and stream function-vorticity formulation, respectively. The variation of drag coefficient with Reynolds number is shown in Figure 6, also demonstrating good agreement with published data.…”

Laminar forced convection heat transfer from a two-dimensional transverse plate in Bingham plastic fluids

“…Similarly, In et al [22] solved the Navier-Stokes equations (vorticity-stream function formulation) numerically using the finite difference method by treating the singularity at the tip analytically to improve the solution accuracy over the range of Reynolds number, 0.1 6 Re 6 30. Subsequently, Dennis et al [23] and Stack and Bravo [24] revisited this problem. Dennis et al [23] have experimentally studied the effect of confinement (5% to 20%) on the flow characteristics of a [24] approached the flow normal to a two-dimensional surface by considering the case of a very slender elliptical cylinder.…”

“…Subsequently, Dennis et al [23] and Stack and Bravo [24] revisited this problem. Dennis et al [23] have experimentally studied the effect of confinement (5% to 20%) on the flow characteristics of a [24] approached the flow normal to a two-dimensional surface by considering the case of a very slender elliptical cylinder. However, the major thrust of their studies was to delineate the critical values of the Reynolds number as a function of the aspect ratio for the onset of flow separation.…”

Flow around a flexible plate in a free stream

“…Taneda and Honji [16] used the aluminum dust method to provide experimental visualizations of the flow around a flat plate. Dennis et al [17] presented experimental and numerical results of flow around a plate normal to a free stream. They also presented results on the early time development of the wake and the effects of the blockage ratio.…”