Absolute instability in hot jets

Abstract

The linear inviscid stability of heated compressible axisymmetric jets is re-examined, focusing on the impulse response of the flow. The case is of particular interest in which a transient grows exponentially in place, i.e., at the location at which it was generated. Such a situation is commonly termed absolutely unstable as opposed to correctively unstable. Limiting the analysis to locally parallel mean velocity and density profiles, infinite Froude number, and zero Eckert number, the absolute instability boundaries, i.e., the boundaries between absolute and convective instability, are explored in the mean flow parameter space. The influence of mean flow profiles, exit Mach number, exit temperature ratio, and exit velocity ratio are considered and discussed separately. It is shown that heated jets, i.e, jets with lower than ambient density, can, depending on operating conditions, develop a region of local absolute instability in the potential core region if the jet density is less than 0.72 times the ambient density. The results suggest that a self-excited global resonance may dominate the heated jet response in situations of practical interest.