Modal analysis of the liquid sheet breakup with and without acoustic forcing

Abstract

• The coupling between the acoustic field and the liquid sheet atomization process is studied. • Modal decomposition techniques like Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are employed. • Frequency response of the liquid sheet is found to be dependent on the laminar or turbulent nature of the impacting jets. • Liquid sheet breakup gets coupled with the external forcing when the acoustic energy goes into low frequency modes. • Decoupling occurs when the acoustic energy goes into the dominant modes which are higher ones having a higher frequency. The objective of the present study is to understand the coupling between the acoustics and the sheet atomization process. The phenomenon is studied through modal decompositions of time-resolved images of acoustically perturbed liquid sheets by employing the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques. The injector operating conditions are selected in order to allow the transition of a smooth liquid sheet to a highly turbulent sheet or fully developed spray. The sheet is destabilized by the traveling acoustic waves of known frequency and sound pressure level. POD modes of the smooth sheets and DMD modes of the turbulent sheets clearly highlight distinct effects of the acoustic perturbations on the liquid sheets. The frequency response of the liquid sheet is found to be dependent on the laminar or turbulent nature of the impacting jets. When the impinging jets are laminar, interestingly the dominant POD mode frequencies are either equal to or harmonics of the external acoustic excitation frequency which confirms the coupling of the atomization process with the acoustic perturbations. Below the lower cutoff frequency, the POD mode having frequency equal to the forcing frequency always dominates other modes. Also, for laminar jets, the DMD growth rate is maximum for the mode having frequency equal to the external forcing. However, for the turbulent impinging jets, the first DMD mode frequency is not always equal to the external forcing frequency but one of the mode in the DMD frequency spectrum show the frequency which is either close to the forcing frequency or close to its integer multiple.