Correlation between Linear Stability Theory and Transition of Compressible Jet Shear Layer

Abstract

A correlation between spatial linear stability calculations and the onset of transition in compressible jet shear layer was investigated. In the present study, an attempt was made to apply the conventional e^N method to a transition prediction of the free shear layer flow in a compressible jet. The mean velocity profiles for a compressible circular jet were experimentally obtained at different downstream locations, which were used as an input to the linear stability calculation code. The growth rates of disturbances from the stability calculation were integrated to obtain an envelope curve. On the other hand, the transition was detected experimentally by the use of three techniques: (1) oil flow visualization, (2) microphone measurements for pressure fluctuations, (3) hot wire anemometer measurements for velocity fluctuations. The results from both the microphone and the hot wire anemometer measurements showed that the transition starts at about 1.333D from the nozzle exit, where D is the nozzle diameter, which is near the “apparent origin” in the fully developed jet flow. It was found that the value of factor N in the e^N method is about 3.5 for axisymmetric (n=0) and 2.8 for asymmetric (n=1) disturbance modes in the present compressible jet.