Measurements on the effect of steps on the transition of laminar boundary layers

Abstract

Abstract The effects of steps on the transition of laminar boundary layers were measured on a flat plate for low Reynolds numbers with critical and subcritical step heights. The transition position was measured by determining the intermittency distribution in streamwise direction, including the characteristic length of the transitional region. The results are compared with formulations of a critical step Reynolds number $${\textrm{Re}_\textrm{h}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Re</mml:mtext> <mml:mtext>h</mml:mtext> </mml:msub> </mml:math> , i.e., the step height that will instantly trigger transition at the step position, and—for subcritical step heights—with $${{\Delta N}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> -formulations from the literature. For backward-facing steps, the concept of a step Reynolds number can be used to distinguish between subcritical and critical step heights, whereas for forward-facing steps there seems not to be one unique $${\textrm{Re}_\textrm{h}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Re</mml:mtext> <mml:mtext>h</mml:mtext> </mml:msub> </mml:math> . Furthermore, for subcritical backward-facing steps the concept of a $${{\Delta N}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> -approximation gives a reasonable description of the experimental observations. Again in contrast, for forward-facing steps a $${{\Delta N}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> -approach scattered a lot and no clear dependency was found between the reduction in the critical N-factor of transition and the relative step height.

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