Global Instability Analysis of Laminar Boundary Layer Flow Over a Bump at Transonic Conditions

AbstractModal three-dimensional BiGlobal linear instability analysis is performed in steady, spanwise-homogeneous two-dimensional laminar compressible boundary-layer flow past a millimeter-tall hemispherical bump at transonic conditions. Starting with subsonic inlet flow, at the flow conditions considered a stationary shock is formed near the downstream end of the bump. The interplay of shock and adverse-pressure-gradient results in a steady spanwise homogeneous laminar two-dimensional laminar separation bubble being formed at the downstream end of the bump.The objective of the present analysis is to interrogate this basic flow with respect to its potential to sustain low-frequency unsteadiness arising from linear amplification of unstable traveling global flow eigenmodes. Such unsteadiness, coupled to eigen- frequencies of the structure, can lead to resonance phenomena that are detrimental for the performance and adversely affect the efficiency of systems on which the bump configuration is employed. Only damped global eigenmodes have been identified at the parameters examined, pointing to the possibility of the above mentioned unsteadiness being the result of algebraic instability

Los elementos finitos de alto orden (hp-FEM) como método de cálculo en problemas de estabilidad fluidodinámica

En los problemas de estabilidad BiGlobal en un contexto fluidodinámico se han encontrado un cierto tipo de condicionantes que todo buen método numérico debe ser capaz de satisfacer. Por un lado y como condición más indispensable, se encuentra la libertad geométrica, es decir, el método debe ser capaz de discretizar cualquier dominio espacial de forma que no quede sujeto a formas simples o fácilmente transformables a estas. En segundo lugar se desea que las condiciones de contorno necesarias en los clásicos problemas de Mecánica de Fluidos sean fácilmente implementables. Por último que el orden del método elegido en la resolución del problema sea fácilmente variable en función de la precisión exigida. En este contexto se conoce que la precisión necesaria crece a través de un parámetro que no es otro que el número de Reynolds del problema, y por tanto es muy ventajoso que no se sea el tamaño de la malla el único grado de libertad para mejorar la precisión del cálculo, ver [2] G.E.Karniadakis, S. Sherwin, Spectral/hp Element Methods for Computational Fluid Dynamics, Oxford Science Publications,2005 y [3] Ch. Schwab. p and hp-Finite Element Methods. Theory and Applications in Solid and Fluid Mechanics. Oxford Science Publications, 2004 Con todos estos condicionantes se ha construido un código basado el elementos finitos de alto orden (hp-FEM) que ha sido aplicado al cálculo de los valores propios y los modos propios de algunos problemas clásicos de la Mecánica de Fluidos como son el movimiento de fluidos en un conductos. En los casos aquí presentados, hemos aplicado el método de Arnoldi para el cálculo del espectro y los modos propios en los problemas de autovalores generalizados que aparecen. Como resultados del trabajo se muestran el cálculo del flujo base de una tubería rectangular y el posterior análisis de estabilidad BiGlobal de dicho flujo base. Los resultados han sido coherentes y en buena consonancia con los obtenidos mediante otros métodos en la literatura clásica, ver [1] L.González, V.Theofilis, Rafael Gómez Blanco. Finite-element numerical methods for viscous incompressible BiGlobal linear instability analysis on unstructured meshes. AIAA Journal 2007, vol.45 no.4 (840-854). Eliminar seleccionado

Global Instability on Laminar Separation Bubbles-Revisited

In the last 3 years, global linear instability of LSB has been revisited, using state-of-the-art hardware and algorithms. Eigenspectra of LSB flows have been understood and classified in branches of known and newly-discovered eigenmodes. Major achievements: World-largest numerical solutions of global eigenvalue problems are routinely performed. Key aerodynamic phenomena have been explained via critical point theory, applied to our global mode results. Theoretical foundation for control of LSB flows has been laid. Global mode of LSB at the origin of observable phenomena. U-separation on semi-infinite plate. Stall cells on (stalled) airfoil. Receptivity/Sensitivity/AFC feasible (practical?) via: Adjoint EVP solution. Direct/adjoint coupling (the Crete connection). Minor effect of compressibility on global instability in the subsonic compressible regime. Global instability analysis of LSB in realistic supersonic flows apparently quite some way down the horizon

Susceptibility of shock-transitional-boundary-layer interaction to shock oscillations in hypersonic flow

The present study shows results from Direct Numerical Simulations (DNS) of a shock-transitional-boundary-layer interaction with imposed shock oscillations in a Mach 5 flow. The shock oscillation frequency matches the frequency pre- dicted by a previous Direct Simulation Monte Carlo (DSMC) study for the inner thermal nonequilibrium of the shock and the resulting induced shock oscillations, for the same Mach number. The transition process is induced in the upstream region by imposed disturbance waves at the wall representative of the most unstable modes, as predicted by a Linear Stability Theory (LST) study. An oblique shock corresponding to a 8-deg wedge angle is generated at the top boundary, which impinges on the boundary layer within the region of nonlinear breakdown. Simulations have been carried out both with and without oscillations imposed on the oblique shock, and for different amplitudes of the shock oscillations. It is found that the shock-boundary-layer interaction (SBLI) produces an acceleration of the transition process to a turbulent state downstream of the impingement point, and that the shock oscillations produce a quasi-2D wave-pattern mode modulation of the downstream turbulent boundary layer, which represents the footprint of the post-shock waves generated by the shock oscillations. Increasing amplitudes of the shock oscillations show a progres- sively enhanced modulation of the turbulent boundary layer, with higher amplitude wall pressure fluctuations. These, in turn, have a relevant effect on the time-averaged wall pres- sure profiles, with an increasing mean wall pressure in the downstream turbulent boundary layer at increasing shock oscillation amplitudes. The wall pressure fluctuation amplitudes are found to scale linearly with the shock oscillation amplitudes in the higher amplitude range, however at lower amplitudes a higher sensitivity of the wall response to a change in amplitude of the shock oscillations is observed, suggesting that the correlated effects on the flow features may be relevant also for relatively small amplitudes of the shock oscillations