Starting Flow by Pitch Acceleration of Flat-Plate Foil

Abstract

This paper presents the investigation of the starting flow in association with pitch acceleration using transient laminar-flow computation and an unsteady inviscid-flow theory. A thin flat-plate foil pitched at the leading edge is modeled in a two-dimensional incompressible fluid at chord Reynolds numbers of the order of 10 3 . Several acceleration amplitudes (1.1 ≤ α 00 m t 2 c ≤ 17.0) and acceleration durations (0.0693 ≤ β Δα∕α m Δt∕t p ≤ 0.5) are maneuvered using a modified canonical kinematic equation at reduced pitch rates from 0.196 to 0.763. Comparisons between computational and theoretical data reveal that the formation of the starting vortex is determined by the acceleration amplitude scaled by the square of the convective time. The corresponding starting force coefficient that scales with the dimensionless acceleration amplitude is proportional to the acceleration angle Δα, which decreases with increasing reduced pitch rate. The starting vortex, once formed at the trailing edge, is shed at the end of the acceleration period. The quasi-steady theory that includes only pitch motion as the strength of the dipolar sheet for apparent-mass flow can also yield an acceptable approximation to capture the apparent-mass force coefficient spike in acceleration.