Global linear stability analysis framework for supercritical fluid flows

Supercritical fluid flows exhibit complex dynamics and stability characteristics because of drastic thermophysical property variations across the pseudo-boiling line. Conventional stability analysis methods, primarily developed for ideal gases at low pressures, cannot be directly applied to supercritical flows. The present study establishes a unified framework of global linear stability analysis (GLSA) suitable for supercritical fluid flows for the first time. The framework incorporates real-fluid effects in terms of a cubic equation of state and detailed treatment of thermodynamic and transport properties, and integrates both energy and species transport equations into the linearised governing equations. For demonstration, the developed GLSA framework is implemented to examine the stability characteristics of jets in crossflow at different supercritical pressures and momentum flux ratios ( upper J J J ). Global linear stability analysis provides quantitative assessments of growth rates of dynamical events by recognising large eigenvalues and associated eigenmodes. The results show that the real-fluid modification is critical to accurately capture the growth rate magnitude of unstable modes. At low supercritical pressure, the position of the dominant GLSA eigenmode shifts from near the nozzle exit to farther downstream, accompanied by a significant reduction in growth rate magnitude. This shift is in alignment with the transition from global to convective instability in the jet upstream shear layer, where the Rayleigh–Taylor instability is enhanced owing to a pronounced density gradient. Furthermore, the GLSA eigenvalue spectrum quantifies the distinction in stability characteristics induced by the real-fluid effect even under identical upper J J J . The novel real-fluid algorithm can be extended to the stability analysis of many other supercritical fluid flows.