Modal and non-modal stability for Hagen-Poiseuille flow with non-ideal fluid

Modal and non-modal stability analyses are applied to Hagen-Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor-liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO₂ near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen-Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.