ON THE STABILITY OF ATTACHMENT-LINE BOUNDARY-LAYERS .2. THE EFFECT OFLEADING-EDGE CURVATURE

The stability of the incompressible attachment-line boundary layer has been studied by Hall, Malik & Poll (1984) and more recently by Lin & Malik (1996). These studies, however, ignored the effect of leading-ed ge curvature. In this paper, we investigate this effect. The second-or der boundary-layer theory is used to account for the curvature effects on the mean flow and then a two-dimensional eigenvalue approach is ap plied to solve the linear stability equations which fully account for the effects of non-parallelism and leading-edge curvature. The results show that the leading-edge curvature has a stabilizing influence on t he attachment-line boundary layer and that the inclusion of curvature in both the mean-flow and stability equations contributes to this stab ilizing effect. The effect of curvature can be characterized by the Re ynolds number R(a) (based on the leading-edge radius). For R(a) = 10(4 ), the critical Reynolds number (R) over bar (based on the attachment- line boundary-layer length scale, see 2.2) for the onset of instabilit y is about 637; however, when R(a) increases to about 10(6) the critic al Reynolds number approaches the value obtained earlier without curva ture effect.