Linear stability of rotating pipe flow with non-ideal fluid

A linear stability analysis is performed on rotating pipe flow with a non-ideal fluid. The study focuses on supercritical CO${}_2$ near its vapor–liquid critical point, where thermodynamic properties deviate significantly from ideal gas. Different wall temperatures are considered, ensuring centerline temperatures span subcritical, transcritical, and supercritical conditions. The modal analysis reveals that at low rotation speeds, unstable mode only exists at rotational speed $\Omega <0$. Also multiple unstable modes emerge, introducing a more complex instability mechanism compared to non-rotating pipe flow. As rotation speed increases, viscous dissipation plays a key role in flow stabilization, while thermodynamic effects remain secondary. The non-modal analysis further demonstrates that optimal system response under fixed-frequency forcing shifts due to rotation, with stronger deviations from incompressible behavior at high compressibility. In rotating pipe flow, the dependence of transient energy growth on the azimuthal wavenumber ($n$) is inherently nonlinear, which stands in stark contrast to the approximately linear relationship typically observed in non-rotating pipe flow. This nonlinearity arises primarily due to the influence of azimuthal velocity components introduced by rotation. These findings highlight the intricate coupling between rotation, compressibility, and thermodynamics, providing new insights into instability mechanisms in non-ideal fluid systems.