On the new unstable mode in the boundary layer flow of supercritical fluids

Abstract

Ren et al. (2019) recently studied the stability of the boundary layer flow over a flat plate for supercritical CO2. While only one unstable mode usually exists for boundary layer flows, the authors found an additional unstable mode, whose origin has so far not been identified. In the present work, we carry out a stability analysis in the general case of a fluid following the Van der Waals equation of state and flowing over a heated flat plate in the limit of zero Eckert number. In this framework, the second unstable mode is also recovered, ruling out an acoustic origin. From the Rayleigh equation derived in the presence of density gradients, a generalised inflection point (GIP) criterion of instability exists, similar to that of fully compressible flows. Inviscid stability calculations confirm the existence of an unstable mode in the presence of a GIP, which is linked to the additional second mode found at finite Reynolds numbers. A theoretical analysis is then carried out by approximating the momentum equation for a base flow exhibiting strong gradients of dynamic viscosity. It is shown that the origin of the GIP, and hence the additional unstable mode, is associated with a minimum of kinematic viscosity at the Widom line. The universality of this result beyond supercritical fluids is eventually discussed.