Sensitivity Analysis Using Adjoint Parabolized Stability Equations for Compressible Flows

Authors: Pralits, J. O., Airiau, C., Hanifi, A., Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: Flow, Turbulence and Combustion, Kluwer
Volume: 65 3/4   321-346
Year: 2001


The sensitivity of two- and three dimensional disturbances in a compressible boundary layer is investigated for changes in initial condition, wall- and momentum forcing. This is done by using the nonlocal adjoint equations for quasi three-dimensional compressible flow with curvilinear coordinates derived from the parabolized stability equations, PSE. Sensitivity coefficients are given by the adjoint field. Analysis of two-dimensional boundary layers for Mach numbers between 0 and 2.5 show that wall- and momentum forcing close to branch I of the neutral stability curve give the largest amplification at a position downstream of branch II. Forcing at the wall with the wall normal velocity gives the largest amplification. In case of incompressible flow, the two-dimensional disturbances are the most sensitive ones to wall inhomogeneity. For compressible flow, the three-dimensional disturbances are the most sensitive ones. Further, it is shown that momentum forcing is most effectively done in the vicinity of the critical layer.