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On the disturbance evolution downstream of a cylindrical roughness element

Published online by Cambridge University Press:  08 October 2014

B. Plogmann ,
W. Würz  and
E. Krämer
B. Plogmann*
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
W. Würz
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
E. Krämer
Affiliation:
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Roughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

JFM classification

Boundary Layers: Boundary layer stability Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 238 - 286
Copyright
© 2014 Cambridge University Press 

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