Experimental and Computational Study of Two-Dimensional Roughness Effects on the Instability of the Flat Plate Boundary Layer.

Abstract

Experimental and computational study on the linear instability region downstream of a two-dimensional roughness element(a square rod)placed in a laminar boundary layer on a flat plate is described. The numerical solutions of the two-dimensional N-S equations were obtained by the MAC(marker-and-cell)method. Hot wire measurements were conducted in the boundary layer on a flat plate in a low-turbulence wind tunnel. A sinusoidal fluctuation, which grows exponentially, is observed behind the roughness element. The characteristics of sinusoidal fluctuation(linear region)depend on κ / δ*κ, where κ is the height of the roughness element and δ*κ is the displacement thickness at the roughness element. At κ / δ*κ=1.0, the predominant frequency of naturally excited sinusoidal fluctuation lies in the unstable zone, which is predicted using the theoretical calculation based on the Orr-Sommerfeld equation applied for Lin's profile. The response characteristics of the linear instability region to artificial external excitation were investigated in detail using sound as an exciting agent. Also, flow fields with forced time-dependent disturbances are studied by the numerical method. The effects of the artificial external excitation become maximum when the frequency of disturbance coincides with the natural frequency. The numerical results for the linear instability region(frequency, phase velocity and amplification rates)agree with the experimental measurements