The first step of the sensitivy analysis of some quadratic quantity related to acoustic waves with respect to any flow or wall disturbance is proposed in the configuration of audlow and large Reynolds number jet flow. The generation of noise has been demonstrated to originate from convective instabilities amplifying in the jet stream. Several authorsudhave investigated them throught the Parabolized Stability Equations approach(PSE). The present work aims to developp the adjoint of the PSE to extract from a mathematicallyudwell posed problem the sensitivity coefficients which can be understood as gradient. The final aim is to propose some path of possible actuations in order to decrease noise emission in some jet flows. Event is it is too early to produce some final conclusions, some trend can be given. The shape and the location of the maximun of sensitivity are strongly related to the radial and streamwise variation of the base flow. In particuler the maximun of sensitivyudis located along the border of the potential cone and seems to be well correlated with the location of the sound generation. In addition the sensitivity to radial momentum forcing is much higher than to a streamwise momentum forcing. Finally the sensitivity increases when the streamwise coordinate decreases.
展开▼
