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.