Understand the underlying physics in a perturbed or controled environment of a jet flow is one of the key to reduce noise emission in an aircraft turbofan engine. A sensitivity analysis of the pressure instability wave has been performed in a single and double-stream supersonic jet flow. The mean flow is obtained from accurate LES simulation performed at CERFACS (Toulouse) and contains some shock cells and two shear layers which are producing large noise emission. As it has been previously demonstrated, the noise source originates from some instabilities which are amplified through inviscid and viscous mechanisms. The instability are studied in this work using the linear nonlocal stability equations (PSE) under an inviscid formulation. To investigate sensitivity, their adjoint counterpart called ’APSE’ have been developed following the previous Airiau’s works on the laminar boundary layer control(2003). Sensitivities of the energy or acoustic energy of the perturbation are solved with any local forcing (mass, momentum, energy). The maximun of sensitivities are found in a very narrow band of the flow, close to the shear layers, and are related to two Kelvin-Helmholtz modes. Sensitivities of the acoustic wave will be emphasized and regions of high sensitivities will be analyzed through several criteria, as for instance, the location of the critical layer, the inflexion point line, the potential cone limit and others. Conclusions will be drawn to give some possible paths toward noise control of a double-stream jet.
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