Collective Interaction in a Linear Array of Supersonic Rectangular Jets: A Linear Spatial Instability Study

Abstract

A linear spatial instability model for multiple spatially periodic supersonic rectangular jets is solved using Floquet-Bloch theory. It is assumed that in the region of interest a coherent wave can propagate. For the case studied large spatial growth rates are found. This work is motivated by an increase in mixing found in experimental measurements of spatially periodic supersonic rectangular jets with phase-locked screech and edge tone feedback locked subsonic jets. The results obtained in this paper suggests that phase-locked screech or edge tones may produce correlated spatially periodic jet flow downstream of the nozzles which creates a large span wise multi-nozzle region where a coherent wave can propagate. The large spatial growth rates for eddies obtained by model calculation herein are related to the increased mixing since eddies are the primary mechanism that transfer energy from the mean flow to the large turbulent structures. Calculations of spacial growth rates will be presented for a set of relative Mach numbers and spacings for which experimental measurements have been made. Calculations of spatial growth rates are presented for relative Mach numbers from 1.25 to 1.75 with ratios of nozzle spacing to nozzle width ratios from s/w(sub N) = 4 to s/w(sub N) = 13.7. The model may be of significant scientific and engineering value in the quest to understand and construct supersonic mixer-ejector nozzles which provide increased mixing and reduced noise.