Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions

Abstract

Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.

Three-dimensional organisation of primary and secondary crossflow instability

“…For larger diameters, increasing the height of the roughness elements did not have an effect on the transition onset. Additionally, they showed relative insensitivity of the transition process to strong and broadband acoustic forcing in agreement with the work of Deyhle & Bippes (1996). Tempelmann et al (2012) studied the boundary layer receptivity to surface roughness by means of parabolised stability equations (PSE) and adjoint PSE together with DNS.…”

“…Experimental investigations on three-dimensional boundary layers were mainly carried in Germany (Deutsches Zentrum für Luft-und Raumfahrt (DLR) Göttingen) by Bippes and coworkers (Bippes 1999;Deyhle & Bippes 1996) and in United States by William Saric and his group (Arizona State University (ASU) first and Texas A&M University (TAMU) up to date) (Saric et al 2003;White & Saric 2005). These campaigns made use of very quiet wind tunnels, exhibiting a free stream turbulence level typically lower than 0.1% of the free stream velocity.…”

“…Hotwire anemometry (HWA) boundary layer measurements were performed using precision sensor traversing systems (e.g. Reibert et al (1996); Deyhle & Bippes (1996); Kawakami et al (1999); White & Saric (2005)). Glauser et al (2014) reported the use of hot-film surface sensors.…”

“…Deyhle & Bippes (1996)), making use of different models placed in several facilities in order to see the effect of model geometry and tunnel free stream turbulence on the instability development. It was found that the model leading edge radius influences the attachment line instability while the curvature of the surface has a stabilising effect when convex and a destabilising effect when concave due to the generation of Görtler vortices.…”

“…Floquet analysis was used by Fischer & Dallmann (1991) and Janke & Balakumar (2000) to inspect the secondary stability of the CF vortices of the DLR experiment (Deyhle & Bippes 1996) (in the second study, the secondary instability of a Hiemenz flow boundary layer was also considered). One of the main outcomes from these studies is the investigation of the low-frequency type-III mode.…”