On stability and receptivity of boundary-layer flows

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations, both twoand threedimensional boundary layers, are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and di↵erent means of transition control of such flows which are of great interest in aeronautical applications. In the first flow case, acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coe cient defined as the relative amplitude of acoustic disturbances in the freestream and generated Tollmien-Schlichting (TS) wave inside the boundary layer. The existing results in the literature for this flow case plot a scattered image and are inconclusive. Moreover, our review of previous numerical and experimental works has identified contradictory trends in the results of those works. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods and independent methods of computing TS wave amplitude. Our results have shown that the generally-accepted level of acoustic receptivity coe cient for this flow case is one order of magnitude too high. In continuation of this work, biorthogonal eigenfunction system of linear stability equations is employed to extract TS waves amplitudes. The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. In the second flow configuration, a swept flat plate of Falkner-Skan-Cooke type boundary layer with a cylindrical surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent at vicinity of it and find its relation to the global stability characteristics of the flow generated by that roughness. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed. The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed micron-sized roughness elements in the presence of acoustic waves