Secondary crossflow instability through global analysis of measured base flows

Abstract

A combined experimental and numerical approach to the analysis of the secondary stability of realistic swept-wing boundary layers is presented. Global linear stability theory is applied to experimentally measured base flows. These base flows are three-dimensional laminar boundary layers subject to spanwise distortion due to the presence of primary stationary crossflow vortices. A full three-dimensional description of these flows is accessed through the use of tomographic particle image velocimetry (PIV). The stability analysis solves for the secondary high-frequency modes of type I and type II, ultimately responsible for turbulent breakdown. Several pertinent parameters arising from the application of the proposed methodology are investigated, including the mean flow ensemble size and the measurement domain extent. Extensive use is made of the decomposition of the eigensolutions into the terms of the Reynolds–Orr equation, allowing insight into the production and/or destruction of perturbations from various base flow features. Stability results demonstrate satisfactory convergence with respect to the mean flow ensemble size and are independent of the handling of the exterior of the measurement domain. The Reynolds–Orr analysis reveals a close relationship between the type I and type II instability modes with spanwise and wall-normal gradients of the base flow, respectively. The structural role of the in-plane velocity components in the perturbation growth, topology and sensitivity is identified. Using the developed framework, further insight is gained into the linear growth mechanisms and later stages of transition via the primary and secondary crossflow instabilities. Furthermore, the proposed methodology enables the extension and enhancement of the experimental measurement data to the pertinent instability eigenmodes. The present work is the first demonstration of the use of a measured base flow for stability analysis applied to the swept-wing boundary layer, directly avoiding the modelling of the primary vortices receptivity processes.

Investigation of the structures in the unstable rotating-cone boundary layer

“…For increasing x (or Re) the disturbance amplitude saturates and the stationary vortices "collapse" leading to transition from a laminar to a turbulent boundary layer. These vortices are quite similar to those observed in swept-wing boundary layer [10,11]. In the recent work by Groot et al [11] a comprehensive collection of references to swept-wing boundary-layer stability and transition can be found.…”

Conditioning of unsteady cross-flow instability modes using dielectric barrier discharge plasma actuators

“…Later, dedicated measurements were performed by Kawakami et al [14], White and Saric [38], Glauser et al [11] and Serpieri and Kotsonis [32]. Theoretical studies using secondary linear instability theory were published by Koch et al [15], Malik et al [21,22], Bonfigli and Kloker [3] and Groot et al [12] while direct numerical simulations were performed by Högberg and Henningson [13] and Wassermann and Kloker [35,36]. The overall consensus of the aforementioned studies indicates that the convective secondary instability vortices abruptly grow over the strong shear regions caused by the primary waves and eventually lead to laminar-turbulent breakdown within a relatively confined streamwise region.…”

Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer

“…Denoting the wall-normal coordinate in the collocation grid by , the wall-normal coordinate in the physical space is obtained as where is the maximum wall-normal coordinate (location of the wall-normal far-field boundary) and denotes the coordinate at which the number of grid points is split into two halves. In the spanwise direction, a biquadratic mapping is considered (Esposito 2016; Groot et al 2018), given by where denotes the spanwise coordinate in the collocation grid, and are respectively the minimum and maximum spanwise coordinates of the physical domain (location of the spanwise far-field boundaries) and , are the spanwise locations which divide the domain into three different regions. This transformation is a generalization of (4.1) that concentrates one-third of the grid points in each of the three regions demarcated by .…”

“…where y max is the maximum wall-normal coordinate (location of the wall-normal far-field boundary) and y i denotes the coordinate at which the number of grid points is split into two halves. In the spanwise direction, a biquadratic mapping is considered (Esposito 2016;Groot et al 2018), given by…”