Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

Abstract

We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans-or supercritical with respect to the pseudo-critical temperature, T pc . When transitioning from sub-to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub-and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to T pc and the higher the Eckert number. In the transcritical case, when the temperature profile crosses T pc , the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack's second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans-and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.

Dense-gas effects on compressible boundary-layer stability

“…Lees & Lin (1946) demonstrated that it gives a necessary condition for a compressible boundary-layer flow to be inviscidly unstable. Ren et al (2019b) showed that a similar criterion is applicable for non-ideal gases. The distributions of d(ρ du/dy)/dy with y/δ are plotted in figure 4.…”

Instabilities in non-ideal fluids

“…), that occur when the fluid evolves close to the critical point. Non-ideal fluids represent a research field of great importance for a wide range of applications; the work of Ren et al (2019b) aims to fill this gap.…”

“…The authors, however, point out that the Eckert number is better adapted than the Mach number to quantify the heat transfer dissipation due to friction and to the non-ideal gas effects. Ren et al (2019b) showed that the non-ideal behaviour of the gas stabilizes the boundary layer in the subcritical and supercritical regimes -i.e. when the temperature profile is fully below or above the pseudo-critical temperature T pc = 307.7 K, respectively.…”

“…The most interesting and original set of results obtained by Ren et al (2019b) is in the transcritical regime. Indeed, in this regime, where the temperature profile crosses the pseudo-critical line, Ren et al (2019b) showed that the flow is highly destabilized through a new unstable mode (Mode II) found in addition to the conventional mode (Mode I).…”

“…It seems essential, if we want to better predict the transition for non-ideal gases, to study in more detail the different linear and nonlinear stages. In conclusion, the work done by Ren et al (2019b) will help refine our understanding of the physical mechanisms at play for non-ideal fluids with strong property variations that can be used ultimately to improve the efficiency of many industrial processes.…”