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978-3-8439-1599-1, Reihe Ingenieurwissenschaften

Oliver Schmidt Numerical investigations of instability and transition in streamwise corner-flows

130 Seiten, Dissertation Universität Stuttgart (2014), Softcover, A5

In the present thesis, the stability of the boundary-layer in a streamwise corner formed by two perpendicular semi-infinite flat plates is investigated numerically. Here, the main focus is on the discrepancy between the findings of linear stability theory, and experimental results that suggest a critical Reynolds number lower by one order of magnitude. As the general validity of the commonly accepted theoretical self-similar corner-flow base-state is questionable, selected stability calculations within this work utilize a modified base-state. It mimics a particular deformation of the laminar mean-flow in the near-corner region, consistently observed in experiment.

Within the framework of local linear stability theory, the effects of compressibility up to Mach numbers of 1.5, and wave obliqueness are considered. The local linear analysis is complemented by a local non-modal analysis that addresses the sensitivity of the discretized linear stability operator to random perturbations. For both the classical linear and the non-modal local approach, the connection between temporal and spatial theory is discussed.

The global stability is investigated by means of direct numerical simulation. First, the laminar base-state is perturbed by a broadband of low-amplitude oscillations near the wall for comparison with linear theory. Second, the non-linear behavior is examined through an expansion in the perturbation amplitude based on three simulations of different perturbation levels. The quadratic and cubic parts of the expansion are identified as mean-flow deformation and higher-harmonic wave in the spanwise directions, respectively. The global non-modal stability is considered in terms of optimal perturbations, artificially localized in the streamwise direction. In the final part of the thesis, the laminar-turbulent transition process is triggered in direct numerical simulations by high-amplitude mono-frequency forcing. A turbulent wedge originating from the corner is observed, and analyzed by means of spectral decomposition.