Mechanisms and models of the turbulent boundary layers at transcritical conditions

Computational models for high-pressure transcritical turbulence in wall-modeled large-eddy simulations typically rely on wall-function models to overcome the need for resolving the boundary layer structures. However, the mechanisms and models of a turbulent boundary layer at transcritical conditions remain poorly understood since the near-wall flow and heat transfer are significantly affected by the enhanced fluctuations and steep gradients in thermodynamic properties. To address this issue, we study the mechanisms of transcritical turbulent boundary layers and wall-attached models at transcritical conditions. It is shown that the real-fluid variable-property effects are associated with the coupling between the near-wall cycle and the wall-normal coherent motions in the outer layer, resulting in the amplification of turbulent energy in the outer layer and noticeable energy transfer between the logarithmic layer and the outer layer; hence, turbulence in the logarithmic layer is modulated by the outer layer. Based on this underlying physical principle, we propose the characteristic velocity and length scales for the attached eddy at transcritical conditions, and extend the attached eddy model to transcritical turbulent boundary layers by introducing a mixed scaling that incorporates both inner and outer scalings. We show that the characteristic scales and extended attached eddy model perform well in characterizing the structures in transcritical turbulent boundary layers.