Mean Flow Perturbation Analysis of an Underexpanded Jet

Here, we illustrate a novel method to predict sound generated by imperfectly expanded jets where the resulting shock-cells can yield significant broadband noise in the far-field. We describe continued development of mean flow perturbation method to analyze the response of an underexpanded jet to small perturbations. This method originates from the work of Touber \& Sandham (Theor. Comput. Fluid. Dyn., 2009) for nominally 2D shock-wave turbulent-boundary layer interactions. This method is an initial boundary value problem and is equally applicable to flows with sharp gradients. It degenerates into the LST, global and PSE analysis under suitable conditions. We use this method to study finer details of the noise generation mechanisms of an under-expanded round jet at $M=1.0$. Preliminary results on time-averaged mean turbulent flow-field perturbed by an annular multi-periodic excitation close to the nozzle-exit plane show interaction of downstream propagating disturbances with the feet of the shock-cells. This causes significant amplification of disturbances resulting in the formation of toroidal vortical structures. This further destabilize the shock-cells, finally resulting in acoustic wave propagation in two distinct downstream and upstream directions.