Effect of surface waviness on boundary-layer transition in two-dimensional flow

Abstract

In this paper, the effect of surface waviness on boundary-layer transition in two-dimensional subsonic flow is investigated. The mean flow is calculated using an interacting boundary-layer procedure, thereby accounting for viscous–inviscid interaction. Then, the linear parabolized stability equations are used to compute Tollmien–Schlichting (TS) wave amplification. As expected, wall waviness is found to destabilize TS waves. This effect is quantified by examining parameters such as wave height, wave length, wave number, wave location, unit Reynolds number, compressibility and pressure gradient and then comparing the results against those obtained in the absence of waviness. From these results, an empirical equation is extracted which correlate the waviness size with the increment in the N-factor due to waviness. The present correlation is compared with the empirical criteria derived from experiments by Fage (Aeronautical Research Council, R & M 2120, 1943) and Carmichael [Northrop Corp., Report No. NOR-59-438 (BLC-123), 1959]. In agreement with the experiments, the present results show that the effect of waviness scales as h 2/ λ where h is the wave height and λ is the wavelength. Computational results indicated that the critical size of waviness below which waviness has no influence does not exist provided the waviness is located in the unstable TS region. It is also shown that the centrifugal instability introduced by a wavy wall is relatively less significant and the dominant effect of waviness on boundary-layer transition is through its effect on TS wave amplification. It is likely, however, that streamwise vortices generated due to waviness will play a role in the nonlinear breakdown process.