Adjoint Parabolized Stability Equations for Receptivity Prediction
نویسندگان
چکیده
This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier–Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document the nonparallel receptivity characteristics of both Blasius and Falkner–Skan boundary layers for two-dimensional and oblique Tollmein–Schlichting (TS) instabilities. These results are compared to receptivity predictions based on local parallel theory in order to establish the effects of mean boundary layer growth on receptivity. In general, the inclusion of nonparallel effects for the receptivity prediction of TS instabilities is found to be small under all conditions. Comparing results from Blasius and Falkner–Skan base flows shows that adverse pressure gradients tend to reduce receptivity while favorable pressure gradients lead to an increase in receptivity. This is in contrast to the well known effects of pressure gradient on TS instability growth rates. Likewise, our investigations for three-dimensional disturbances also show that oblique modes have greater receptivity than two dimensional waves, again in contrast to the effects of obliquity on instability growth rates. In general there is a trade-off between receptivity and instability – the stronger the instability the weaker the receptivity.
منابع مشابه
Evaluation of Adjoint Based Methods for the Prediction of Receptivity
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 a...
متن کاملAdjoint Methods for Receptivity Prediction in Nonparallel Flows
The Adjoint Parabolized Stability Equations (APSE) are used to predict the receptivity of boundary layers to a variety of disturbances. The method is validated through comparisons to direct solutions of the linearized Navier–Stokes (LNS) and adjoint Navier–Stokes (ANS) equations and APSE is found to accurately predict receptivity with significant gains in efficiency compared to Navier–Stokes ba...
متن کاملRice University Adjoint Analysis for Receptivity Prediction
Adjoint Analysis for Receptivity Prediction
متن کاملAsymptotic receptivity analysis and the Parabolized Stability Equation : a combined approach to boundary layer transition
We consider the interaction of free-stream disturbances with the leading edge of a body and its effect on the transition point. We present a method which combines an asymptotic receptivity approach, and a numerical method which marches through the Orr-Sommerfeld region. The asymptotic receptivity analysis produces a three deck eigensolution which in its far downstream limiting form, produces an...
متن کامل