Surface step effects on boundary-layer transition dominated by tollmien–schlichting instability

Abstract

Surface step effects on boundary-layer transition are modeled using a variable N-factor method for transition dominated by Tollmien–Schlichting instabilities. Experimental correlations provide a bounding expression for the change in the critical N-factor for transition onset, which provides a predictive means to account for surface steps. An investigation is conducted to assess the applicability of this approach for more general step arrangements. The approach is applied to capturing the superposition of a forward-facing and a backward-facing step in the form of a rectangular protrusion or a wide gap. Results show that a rectangular protrusion is well modeled by a linear combination of steps. However, a wide gap is best represented by a backward-facing step, without regard for the following forward-facing step. The sensitivity to streamwise step position is also investigated. Results show that the method is effective at capturing step effects for step positions in the neighborhood of the instability neutral point, and extending downstream close to the smooth-surface transition location. The effects of steps placed well upstream of the instability neutral point are overpredicted by the step model, likely the result of nonparallel effects on the upstream decay or as a result of the underlying receptivity occurring in the neighborhood of the neutral point.