Sensitivity Analysis Using Adjoint Parabolized Stability Equations for Compressible Flows

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作者：

JO Pralits，C Airiau，A Hanifi，DS Henningson

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摘要：

An input/output framework is used to analyze the sensitivity of two- and three-dimensional disturbances in a compressible boundary layer for changes in wall and momentum forcing. The sensitivity is defined as the gradient of the kinetic disturbance energy at a given downstream position with respect to the forcing. The gradients are derived using the parabolized stability equations (PSE) and their adjoint (APSE). The adjoint equations are derived in a consistent way for a quasi-two-dimensional compressible flow in an orthogonal curvilinear coordinate system. The input/output framework provides a basis for optimal control studies. Analysis of two-dimensional boundary layers for Mach numbers between 0 and 1.2 show that wall and momentum forcing close to branch I of the neutral stability curve give the maximum magnitude of the gradient. Forcing at the wall gives the largest magnitude using the wall normal velocity component. 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.

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关键词：

Theoretical or Mathematical/ boundary layers compressible flow flow control flow instability optimal control sensitivity analysis/ sensitivity analysis adjoint parabolized stability equations compressible flows input/output framework three-dimensional disturbances compressible boundary layer wall forcing momentum forcing kinetic disturbance energy downstream position quasi-two-dimensional compressible flow orthogonal curvilinear coordinate system optimal control two-dimensional boundary layers Mach numbers neutral stability curve wall normal velocity component incompressible flow two-dimensional disturbances compressible flow critical layer/ A4740 Compressible flows shock and detonation phenomena A4762 Flow control A4720 Hydrodynamic stability and instability C3120T Level, flow and volume control C1310 Control system analysis and synthesis methods C1330 Optimal control