Global instability of laminar separation bubbles
- Autores: Dani Rodríguez Álvarez
- Directores de la Tesis: Vassilios Theofilis (dir. tes.)
- Lectura: En la Universidad Politécnica de Madrid ( España ) en 2010
- Idioma: español
- Tribunal Calificador de la Tesis: Francisco Javier Jiménez Sendín (presid.), Leo Miguel González Gutiérrez (secret.), Odayarkoil Natarajan Ramesh (voc.), Michael Gaster (voc.), Hermann Fasel (voc.)
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- Resumen
Flow separation is intimately related with intrinsic topological changes in a variety of flows over or through configurations of engineering signincance. Invariably, adverse effects on the performance of lifting surfaces are associated with flow separation, which has provided motivation for research efforts into both incompressible and compressible separated flows, spanning over half a century. However, and despite the continuous research, many questions related to the appearance, structure and behaviour of separation bubbles remain open. While predominance of the Kelvin-Helmholtz instability associated with the shear-layer formed on account of flow separation has been confirmed in a multitude of experimental and numerical investigations, it does not suffice to explain neither the occurrence of breathing or flapping bubble behavior, i.e. oscillations of the separation bubble región at frequencies substantially lower than those predicted for the Kelvin-Helmholtz instability, ñor the effectiveness of such frequencies in controlling the size of separation bubbles, ñor the time-persisting breakdown of bubbles into fully three-dimensional patterns. On the other hand, global instability analysis considering the essentially non-parallel, non-local nature of separation bubbles, are able to predict global instability mechanisms diíferent from the Kelvin-Helmholtz instability.
The BiGlobal instability analysis has been used in this thesis to investígate the global instability of laminar separation bubbles. This approach has been historically confined to simple geometries and low resolutions because of the large computational resources required for the direct solution of the associated partial-derivative-based eigenvalue problems. Recent developments achieved in the course of the present work have resulted into the parallelization of the algorithms used in the solution of the problem, significantly relaxing the constrains related to the serial solution, up to the possibilities of state-of-art distributed memory supercomputers.
Two kinds of configurations comprising separation bubbles have been considered herein: a series of model laminar separation bubbles on a fíat píate, and the flow around a stalled NACA 0015 airfoil. The first part of the present investigation is concerned with the BiGlobal instability analysis of the laminar separation bubble models. The many parameters involved in the description of possible separated states, and their potentially decisive effect on the instability properties suggests the search for adequate models of laminar separation bubbles in which the influence of the parameters could be analyzed independently. Comparisons with well-established results of both temporal and spatial local stability theories, based on the solution of the Orr-Sommerfeld equation, are used as a basis for the identification and classification of the modal instability mechanisms recovered by BiGlobal analysis. In particular, an unstable, stationary and three-dimensional global mode is found both in the flat píate and the stalled airfoil; its properties have been analyzed in detail.
In the second part of the thesis, critical-point concepts have been employed in order to unveil the diíferent topological bifurcations resulting from the linear superposition of the two-dimensional basic states and the three-dimensional global mode. Special attention has been paid to the surface streamlines or skin-friction lines, in order to make direct comparisons between the present reconstructions and the experimental oil-streak topologies. In addition, three-dimensional field streamline topologies associated with laminar separation have been analyzed. The topological de-scription of the resulting flows, besides been in agreement with the theoretical U-shaped separation topology, is qualitatively equivalent to the stall cells recovered experimentally: spanwise periodic structures in which the separated flow regions are organized around two counter-rotating vórtices, separated by fully attached bands. In addition, the periodicity length predicted by the instability analysis is in good agreement with the characteristic length observed in experiments. Comparison of the present results and experiments in the literature shows that the amplification of the global mode of laminar separation bubbles is a plausible origin of the stall cells.
The main conclusión of this thesis is that the classic picture of laminar separation bubbles, as dominated by the inflectional instability of disturbance waves, is neither necessarily representative of all the possible separation bubbles, ñor sufficient to explain the complete dynamics of the separated flow. The presence of the self-excited, temporally amplified global mode not only explains the origin of three-dimensionality in nominally two-dimensional bubbles, but may also serve as the triggering instability mechanism leading to unsteady three-dimensional states, in those cases in which the classic (inflectional) Rayleigh scenario alone would predict stable two-dimensional flow.
