Evaluation of Adjoint Based Methods for the Prediction of Receptivity

Abstract

This paper explores the use of nonparallel adjoint methods to predict the receptivity of two and three-dimensional boundary layers. Solutions obtained from both adjoint Navier—Stokes (ANS) and adjoint parabolized stability equations (APSE) have been validated against linearized Navier—Stokes (LNS) solutions that provide a full description of the linear receptivity process. The adjoint methods are used to document the nonparallel receptivity characteristics of both Blasius and Falkner-Skan boundary layers and these results are compared to local parallel theory. To evaluate the ability of adjoint methods, especially the APSE, to predict receptivity for strongly nonparallel flows, we also investigate the receptivity of the three-dimensional boundary layer on a swept parabolic cylinder. In all cases, our results indicate that adjoint methods accurately predict receptivity with significant gains in efficiency compared to LNS.