Secondary instability analysis of 3D laminar separation bubbles based on cross-plane WKB approximation
Elmer Mateus Gennaro1; Daniel Rodríguez2; Leandro Franco de Souza3
1 Universidade Estadual Paulista; 2 Pontifícia Universidade Católica do Rio de Janeiro; 3 ICMC/USP
doi:10.20906/CPS/COB-2015-0672
Resumo
Laminar flow separation and the formation of closed separation bubbles is a problem of primary technological significance due to its strong relation with the aerodynamic properties of lifting surfaces operating at high angles-of-attack. The behavior of these laminar separation bubbles (LSB) is believed to be dominated by hydrodynamic instability processes. The present research builds upon the idea put forward by U. Dallmann in the late 80s, that a global instability mechanism may exist acting on two-dimensional recirculating flows, that under an infinitesimally weak perturbation originates a fully three-dimensional flow. In our previous research, we demonstrated that this instability is recovered as a 3D eigenmode of the linearized Navier-Stokes equations, and proposed a weakly nonlinear expansion of the center manifold to study the nature of the bifurcation associated with the primary 3D eigenmode. In this paper, we study the secondary instability of the fully 3D bifurcated flow by means of a novel technique that applies the weakly non-parallel (WKB) approximation to cross-stream planes. The results obtained show that the self-excited 3D global instability of LSB also has the potential of triggering a secondary instability mechanism that originates the flow unsteadiness.
Palavras-chave: boundary layer; separated flow; global instability