Non-Modal Growth Induced by Discrete Roughness Elements in a Swept Wing Boundary Layer

Abstract

Laminar-to-turbulent boundary layer transition on the wings and stabilizers of aircraft leads to a large increase in the skin-friction drag they experience during flight. This has motivated prolific research into understanding and delaying the transition process, in an effort to improve the economic and ecological impact of air travel. The swept wing poses a particular challenge to this, as the transition scenario in flight is typically governed by the growth and breakdown of stationary crossflow instabilities (CFI). These are destabilized by flow conditions that would suppress instabilities on straight wings, such as Tollmien–Schlichting waves, complicating the use of laminar flow control techniques. Previous research has shown stationary CFI to be highly receptive to surface roughness, with the use of discrete roughness elements (DRE) having emerged as a forcing/control strategy. However, the mechanisms behind which DRE condition the onset of CFI in a swept wing boundary layer are still a topic of ongoing investigations.

The research presented in this Master thesis aims to further characterize the relation between the DRE forcing configuration and the onset of swept wing boundary layer instabilities, through an investigation of its wake flowfield. The DRE wake has previously been observed to be highly non-modal in nature, limiting the use of modal linear stability theory in predicting stationary disturbance evolution in the element vicinity. To address this, a linear, non-modal, parabolized stability framework is derived, capable of simulating transient growth within the DRE wake region. The numerical framework is initialized with experimental DRE wake data from a previous study, for a DRE array of critical forcing height. The predicted stability characteristics qualitatively agree with experiment, with the numerical solver successfully evolving the stationary DRE wake structure into stationary CFI downstream of the array. However, a quantitative match with experiment could not be attained. The results were also noted to be sensitive to the choice of initial conditions, as well as to the numerical discretization.

In addition to the stationary numerical simulations, hot-wire anemometry measurements are conducted at the TU Delft low turbulence wind tunnel, providing a first-time experimental characterization of the evolution of unsteady disturbances in the DRE wake for a swept wing boundary layer. Regions of high fluctuation intensity are observed to be localized around the top and sides of each element in the DRE array, with their spectral characteristics associated to circular cylinder shedding. For a critical DRE forcing, the evolution of the wake flow is largely governed by the stationary structures, although unsteady disturbance energy is observed to undergo a brief period of transient energy amplification. A super-critical DRE forcing introduces strongly tonal fluctuations into the DRE wake, whose amplification is enhanced by interaction between the stationary structures. The high fluctuation levels are sustained and grow to non-linear amplitudes, inhibiting the relaxation of steady disturbance energy. This leads to rapid, local turbulent breakdown in the vicinity of the elements.