Study of Supersonic Twin Jet Coupling Using Higher Order Spectral Analysis

Abstract

The purpose of this paper is to understand non-linear processes occurring during the coupling of twin jet plumes using higher order spectral methods. To the best of our knowledge, most previous studies have used linear spectral analysis to document coupling and have focused on identifying configurations and conditions that produce coupling, without much knowledge of the ‘why’ and ‘how.’ Our work demonstrates the inadequacies of linear spectral analysis when closely spaced multiple screech sources exist in complex configurations. We use the cross-bicoherence for identifying the non-linear interactions. In order to evaluate the efficacy of the tool in identifying non-linear coupling we chose rectangular nozzles with spanwise oblique exit geometries. Jets from such nozzles are known to be rich in closely spaced complex screech source structures. In addition, they can produce multiple screech tones with the simultaneous presence of multiple feedback loops. The twin jets could be placed in two configurations, one that produced a ‘V’ shape in the inter-nozzle region and another that produced an ‘arrow head’ shape. The following significant findings emerged from our study: (i) some configurations that were apparently uncoupled by linear spectral analysis metrics were found to be nonlinearly coupled. (ii) two types of non-linear coupling were observed – one dominated by the fundamental and its interaction with higher modes, and another that displayed clusters of interactions between a frequency component and its sidebands. (iii) a new interaction density metric was developed to quantify non-linear coupling. (iv) a second metric known as the average interaction density was shown to increase sharply during coupling mode transition. Our results indicate that nonlinear spectral analysis has the potential to uncover twin jet coupling mysteries that have eluded researchers for many years.