Experimental study on the stability of laminar flow in a channel with streamwise and oblique riblets

Abstract

The influence of riblets on the streamwise growth of Tollmien-Schlichting (T-S) waves was examined experimentally in a channel flow. Riblets having triangular ridges and trapezoidal valleys, with a height-to-width ratio of 0.5, were glued on the upper channel wall. The ridge spacing was 11% of the channel half-depth which gave a non-dimensional wavenumber of 57. In addition to the effects of streamwise riblets, the effects of oblique riblets whose direction was inclined to the streamwise direction were examined to see how the instability characteristics depended on the riblet alignment. The result showed that the critical Reynolds number for the linear instability Recr was reduced to about 4200 by the streamwise riblets, while the wavenumber of the T-S wave was little influenced by the presence of riblets. For the present small riblets, the parabolic velocity profile was modified only in the vicinity of the ribbed surface, with the virtual wall position located inside the riblets. Such a local and small change in the velocity profile enhanced the instability of the plane Poiseuille flow appreciably. When the riblets were inclined to the streamwise direction, Recr increased as the oblique angle of riblets ϕ was increased. For ϕ ≥ 45°, the riblets had no noticeable influence on the structure of the T-S wave and the growth rates were the same as those in the smooth-wall case.