**home**
Above certain conditions of temperature and pressure, fluids reach a supercritical state, in which the distinction between liquid and gas phases no longer exists. The hydrodynamics of supercritical fluids — the way they flow under the action of forces, is an active topic of research.
Numerous industrial applications require a fundamental understanding of these phenomena. Supercritical power cycles in nuclear or solar power plants, supercritical geothermal energy, cooling and mixing in rocket engines, all involve supercritical fluids flowing in pipes, jets or turbines. Being able to predict their behaviour has a practical importance for the design of these applications: heat transfer lies at the centre of these designs and dramatically depends on the laminar or turbulent nature of the flow. A lot of recent research efforts have been directed towards the description of supercritical fluids in the turbulent regime. But fewer works have focused on the manner in which these fluids evolve from the smooth laminar regime to the chaotic turbulent one.
Supercritical region in a pressure-temperature phase diagram. The dashed line is the Widom line, across which all fluid properties greatly vary. In particular, the kinematic viscosity is minimum here.
This ‘transition to turbulence’ problem in supercritical fluids is of great practical interest and involves exciting fundamental questions. We note that because supercritical fluids exhibit large property variations, such as density and viscosity, they belong to a more general set of flows that can be referred to as strongly stratified, and that can be studied in a general theoretical framework.
Future work will tackle the subsequent (non-linear) developments of this instability using Direct Numerical Simulation (DNS). Resolvent analysis, which I used in past projects and which I present in the next section, will also be used analyse to the non-modal growth mechanisms. In particular, the behaviour of streaks in supercritical fluids, which lose their streamwise invariance as shown in our recent preprint, will be further analysed.
Resolvent analysis is an increasingly popular theoretical and numerical approach to model flow systems and gain insights into their physics. It is based on an input-output formalism, in which a forcing is linearly associated to a response through the resolvent operator. This versatile framework can be used to tackle different problems, from non-modal stability analysis to the identification of coherent structures in turbulent flows.
A NCL is a system in which a flow circulated in a closed pipe (thereby forming a loop) under the effect of buoyancy. This is achieved by heating the loop at the bottom and cooling it down at the top.
Marko Draškić, who is doing his PhD at TU Delft, designed and built an experimental set-up of a NCL for supercritical fluids. This system may undergo different instabilities: the steady flow generated at low heating rate, which we study in this paper, becomes unsteady at some threshold value. Other bifurcations are expected as the heating rate is further increases.
We now aim to develop a 1D numerical model of the system based on DNS, linear stability analysis and continuation methods in order to predict the bifurcation diagram for the different hydrodynamic and thermodynamic parameters.