Direct numerical simulation of complete transition to turbulence with a fluid at supercritical pressure

TL;DR

This study uses direct numerical simulations to explore the laminar-to-turbulent transition of a heated boundary layer at supercritical pressure, revealing unique instability mechanisms and transition scenarios influenced by pseudo-critical phenomena.

Contribution

It is the first detailed numerical investigation of boundary layer transition at supercritical pressures, highlighting the effects of pseudo-boiling and variable properties on flow instabilities and turbulence.

Findings

Billow-like structures form around the Widom line resembling Kelvin-Helmholtz instability.

Transition can be triggered early with a single 2D wave amplifying background noise.

Variable-property scaling accurately predicts turbulent skin friction and heat transfer.

Abstract

The objective of this work is to investigate the unexplored laminar-to-turbulent transition of a heated flat-plate boundary layer with a fluid at supercritical pressure. Two temperature ranges are considered: a subcritical case, where the fluid remains entirely in the liquid-like regime, and a transcritical case, where the pseudo-critical (Widom) line is crossed and pseudo-boiling occurs. Fully compressible direct numerical simulations are used to study (i) the linear and nonlinear instabilities, (ii) the breakdown to turbulence, and (iii) the fully developed turbulent boundary layer. In the transcritical regime, two-dimensional forcing generates not only a train of billow-like structures around the Widom line, resembling Kelvin-Helmholtz instability, but also near-wall travelling regions of flow reversal. These spanwise-oriented billows dominate the early nonlinear stage. When high subharmonic three-dimensional forcing is applied, staggered $\Lambda$-vortices emerge more abruptly than in the subcritical case. However, unlike the classic H-type breakdown under zero pressure gradient observed in ideal-gas and subcritical regimes, the H-type breakdown is triggered by strong shear layers caused by flow reversals -- similar to that observed in adverse-pressure-gradient boundary layers. Without oblique wave forcing, transition is only slightly delayed and follows a naturally selected fundamental breakdown (K-type) scenario. Hence, in the transcritical regime, it is possible to trigger nonlinearities and achieve transition to turbulence relatively early using only a single two-dimensional wave that strongly amplifies background noise. In the fully turbulent region, we demonstrate that variable-property scaling accurately predicts turbulent skin-friction and heat-transfer coefficients.