Linear stability analysis of wall-bounded high-pressure transcritical fluids

TL;DR

This paper uses linear stability theory to analyze the destabilization mechanisms in wall-bounded high-pressure transcritical flows, revealing how pseudo-boiling region thermodynamics promote laminar-to-turbulent transition.

Contribution

It provides a detailed linear stability analysis of transcritical flow instabilities, highlighting the roles of thermodynamics, Brinkman number, and non-isothermal conditions in flow transition.

Findings

Pseudo-boiling region enhances flow destabilization.

Non-isothermal conditions accelerate turbulence transition.

Larger kinetic energy budgets due to increased production rates.

Abstract

Mixing and heat transfer rates are typically enhanced when operating at high-pressure transcritical turbulent flow regimes. The rapid variation of thermophysical properties in the vicinity of the pseudo-boiling region can be leveraged to significantly increase the Reynolds numbers and destabilize the flow. The underlying physical mechanism responsible for this destabilization is the presence of a baroclinic torque mainly driven by large localized density gradients across the pseudo-boiling line. As a result, the enstrophy levels are enhanced compared to equivalent low-pressure cases, and the flow physics behavior deviates from standard wall turbulence characteristics. In this work, the nature of this instability is carefully analyzed and characterized by means of linear stability theory. It is found that, at isothermal wall-bounded transcritical conditions, the non-linear thermodynamics exhibited near the pseudo-boiling region propitiates the laminar-to-turbulent transition with respect to sub- and super-critical thermodynamic states. This transition is further exacerbated for non-isothermal flows even at low Brinkman numbers. Particularly, neutral curve sensitivity to Brinkman numbers and perturbation profiles of dynamic and thermodynamic unstable modes based on modal and non-modal analysis, which trigger the early flow destabilization, confirm this phenomenon. Nonetheless, a non-isothermal setup is a necessary condition for transition when operating at low-Mach/Reynolds-number regimes. In detail, on equal Brinkman number, turbulence transition is accelerated and algebraic growth enhanced in comparison to isothermal cases. Consequently, high-pressure transcritical setups result in larger kinetic energy budgets due to larger production rates and lower viscous dissipation.