Laminar to turbulent transition is the process in which a smooth orderly laminar flow becomes turbulent, chaotic and unpredictable. A laminar boundary layer (BL) may become turbulent due to growing disturbances in the flow. If a disturbance is small its behavior is governed by linear stability theory (LST). Early works on LST were focussed on the growth of normal modes in incompressible or ideal gas compressible boundary layers, with the more recent inclusion of high-temperature and/or dense gas effects. Consideration for growth of perturbations other than modal started in 1970s, and while it has received considerable attention in ideal gas boundary layers, the study of non-modal growth in heavily stratified boundary layers remains limited.
In recent years, research in supercritical fluids and their applications has risen substantially, where supercritical CO2 (SCO2) stands out. It has been proposed as a working fluid for power generation turbines, a heat carrier fluid in geothermal, etc. A supercritical fluid near its pseudo-boiling temperature exhibits extremely large variations of physicochemical properties, leading to strongly stratified transcritical boundary layer flows, which may heavily influence its stability. Recently, transcritical boundary layers have been shown to be unstable to a novel mode, not found in ideal gas boundary layers, further motivating the study of the hydrodynamic behaviour of supercritical fluids.
This study investigates the linear stability of SCO2 boundary layers in the region of the Widom line in the phase diagram. Both heating and cooling are considered, in the sub-, super- and transcritical regimes. Regarding the amplification of normal modes, a special focus is given to 3D perturbations and the conditions for which a 3D perturbation is more amplified than a 2D perturbation. A moderate Mach number is found to be necessary in the further destabilization of 3D waves when compared to 2D waves. As indicated by previous works, the Tollmien-Schlichting (TS) mode is found to be preferentially 3D for moderate Mach number in the sub- and supercritical regimes. However, in the transcritical regime, the TS mode is found to be most amplified for stream-wise propagating waves. The novel mode II, found solely in transcritical flows, is preferentially 3D at sufficiently high Mach number, both in the viscous and inviscid regimes. Regarding non-modal stability, the energy growth of sub- and supercritical boundary layers is comparable to that of an ideal gas compressible boundary layer, with optimal energy growth driven by the lift-up mechanism. In the transcritical regimes, the lift-up mechanism also dominates, but energy growth is considerably larger due to the presence of strong thermodynamic gradients within the flow. This results in substantial energy growth associated with density and temperature streaks in the perturbations. When considering purely kinetic effects, the cooled wall case shows higher growth when compared to an ideal gas boundary layer, whereas the heated wall case shows a reduction of the kinetic energy growth. The cooled wall condition results in high mean vorticity far from the wall, leading to high energy growth, while the heated wall condition results in low mean vorticity far from the wall, leading to a reduced energy growth.