Stability of co-axial jets with temperature non-uniformity

In this study, the Kelvin-Helmholtz (KH) instability in co-axial jets with non-uniform mean velocity and temperature profiles is analysed. Linear stability analysis and spectral proper orthogonal decomposition were used to investigate existing particle-image velocimetry (PIV) and time-resolved Doppler global velocimetry (TR-DGV) data. Comparisons between predicted mode shapes and decomposed experimental data reveal several similarities. Parameters such as azimuthal wave number m, Mach number M, velocity ratio h, and temperature ratio S₂ are investigated through a parametric analysis, isolating their influence on the growth rate, axial wave-number, and phase velocity of KH instability waves. An analysis of an isothermal co-axial jet with an inverted velocity profile confirms the existence of two KH modes (inner and outer) arising from the two shear layers, with the outer mode generally exhibiting a much larger growth rate than the inner mode. Varying the Mach number minimally affects the inner mode, while significantly increasing the growth rate of the outer mode. Increasing the velocity ratio drastically decreases the frequency range in which the outer mode is active but increases the frequency range of the inner mode. Finally, introducing thermal non-uniformity in the form of heating the bypass increases the growth rate of the outer mode while also decreasing the frequency range in which it is growing.