Input-output modes and their relevance to noise reduction of shock-laden jet flows

Input-output analysis is used to describe the radiated noise of the shock-laden, supersonic exhaust generated by an axisymmetric bi-conical jet nozzle. Large-eddy simulations (LES) are used to predict the unsteady, turbulent jet at a fixed nozzle pressure ratio (NPR) of 4 and three total temperature ratios (TTR) of 1, 3, and 7. To understand the sound field generated by the shock-laden jet and to develop an approach for jet noise reduction, using input-output mode descriptions of the jet, the presence of the strong shock waves must be addressed. To this end, a method capable of computing input-output modes in shock laden base flows is developed and then used to perform a non-modal, input-output analysis about each time-averaged shock-laden jet base flow corresponding to the three TTRs. This provides the optimal linear forcing and corresponding response modes through the singular value decomposition of the input-output operator. The physical relevance of the resulting modes are evaluated through projection onto the unsteady data. Sensitivities of the gains to the TTR are measured and compared with analytical predictions.