BiGlobal Stability Analysis: Laminar Shock-Wave/Boundary-Layer Interactions

Abstract

The Shock-Wave/Boundary-Layer Interaction (SWBLI) occurs in the inlet of high-speed engines and on transonic wings, and can exhibit unsteadiness. Large scale unsteadiness may cause the premature fatigue of aerodynamic structures and the instabilities of the air intakes, while small scales cause laminar-turbulent transition, leading to higher friction and thermal load. The latter small scales are studied in this work with stability theory.

The linearised Navier-Stokes equations for stability analyses are used to identify the linear eigenmode growth present in a broad range of flow applications. They present a pertinent approach to identify the origin of the unsteadiness and of the laminar-turbulent transition occurring in the SWBLI. The compressible BiGlobal stability equations are implemented and the validation of the solver with well-known Blasius flows shows excellent agreements with the literature.

The convective instability represented by the Tollmien-Schlichting waves in developing boundary layers is thoroughly analysed. A moving reference frame is used to represent the most unstable instability by one unique eigenfunction, aiming to improve the effectiveness of the BiGlobal approach drastically. Finally, the convective instabilities associated with the Kelvin-Helmholtz waves and the underlying characteristics of steady modes existent in the SWBLI are detailed through the Reynolds-Orr energy equation.