On the absolute instability in a boundary-layer flow with compliant coatings |
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| Institution: | 1. Laboratoire de Mécanique de Lille, Université de Lille 1, Bd. P. Langevin, 59655 Villeneuve d''Ascq cedex, France;2. Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice cedex 2, France;1. University of Manchester, Manchester, UK;2. Department of Neurosurgery, Salford Royal NHS Foundation Trust, Salford, UK;1. Département de Mathématique et Statistique, Université d''Ottawa, 585 King Edward, Ottawa, ON, K1N6N5, Canada;2. WPI Advanced Institute for Materials Research, Tohoku University, Mathematics Unit, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan;3. CNRS, Institut Camille Jordan, Université Lyon 1, France;4. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland;5. Dept. of Math. and Stat. Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada;6. Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland;7. Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland;1. Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS, Delft, The Netherlands;2. Aeronautics and Aerospace Department, Von Kármán Institute for Fluid Dynamics, Chausseé de Waterloo 72, 1640, Rhode-St.-Genése, Belgium |
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| Abstract: | The question of absolute instabilities occuring in a boundary-layer flow with compliant coatings is reassessed. Compliant coatings of the Kramer's type are considered. Performing a local, linear absolute/convective stability analysis, a family of spring-backed elastic plates with damping is shown to be absolutely unstable for sufficiently thin plates. The absolute instability arises from the coalescence between an upstream propagating evanescent mode and the Tollmien–Schlichting wave. To reinforce the local, linear stability results the global stability behaviour of the system is investigated, integrating numerically the full nonparallel and nonlinear two-dimensional Navier–Stokes system coupled to the dynamical model. Injecting Gaussian-type, spatially localized flow disturbances as initial conditions, the spatio-temporal evolution of wave packets is computed. The absolute stability behaviour is retrieved in the global system, for a compliant panel of finite length. It is demonstrated numerically that the global stability behaviour of the wall, triggered by finite-end-effects, may be independent of the disturbance propagation in the flow. |
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