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Supercritical fluid has many applications due to its unique thermodynamic characteristics. When a material’s pressure and temperature exceed its critical point, the distinction between liquid and vapor (or gas) phases disappears. However, when the material crosses the critical point or a pseudocritical temperature at which the specific heat of the material at constant pressure is maximal, the thermal and hydraulic properties vary sharply (Fig. 1); the fluid does not undergo an actual phase transition but the pseudocritical temperature separates the fluid into liquid-like and gas-like states.

Fig.1. Normalized thermal and hydraulic properties (density, dynamic viscosity, specific heat, thermal conductivity) of CO2 at 7.5 MPa.
Because of the drastic variation of properties, heat transfer of a supercritical fluid for internal flows has unusual characteristics that are caused by buoyancy and bulk flow acceleration. In this research, the objectives are
- to investigate heat transfer characteristics with various parametric studies,
- to model heat transfer based on a theoretical approach with respect to experiments,
- to develop a turbulence model which improves prediction of heat transfer with respect to CFD.
All objectives are achieved by experimental and CFD analyses.
1. Heat transfer characteristics of sCO2 in horizontal channels

Flow acceleration and buoyancy induced by the density variation make a difference between a heat transfer behavior of sCO2 and that of normal fluids. In the case of the vertical flow, buoyancy causes the heat transfer deterioration for the upward flow and enhancement for the downward flow while flow acceleration always causes the heat transfer deterioration regardless of the flow direction. However, in the case of the horizontal flow, the heat transfer characteristics are more complex than that for the vertical flow because buoyancy occurs in a perpendicular direction of the flow. Whiles, flow acceleration still exerts its force in the flow direction. Eventually, buoyancy causes a non-uniform temperature distribution on a circumference. It results in different heat transfer behaviors at the top and bottom sides of the circular tube.
Heat flux and mass flux usually have the opposing effect on heat transfer (Figs. 3 and 4). Heat transfer is analyzed by using a reference heat transfer correlation, which is the Gnielinski correlation (NuGn). Heat transfer is less deteriorated as the mass flux increases at both walls. Heat transfer can be even enhanced (NuExp/NuGn>1) at a specific condition due to generation of a thin layer, which has a high specific heat. While, heat transfer is more deteriorated as the heat flux increases at both walls.
The different heat transfer behaviors are observed at each wall. This difference results from buoyancy. The hot and lighter fluid (gas-like fluid) flows upward and is stacked at the top wall. As a result, heat transfer at the bottom wall undergoes less deterioration than that at the top wall. Meanwhile, heat transfer is deteriorated as the flow goes downstream due to flow acceleration regardless of the buoyancy effect.

Fig. 2. Normalized Nusselt number along the axial location at different mass fluxes at (a) top wall and (b) bottom wall.
Fig. 3. Normalized Nusselt number along the axial location at different heat fluxes at (a) top wall and (b) bottom wall.
2. Heat transfer model for vertical flows

Heat transfer model for vertical flows was suggested in a semi-empirical form. The model based on thermal resistance of a turbulent boundary layer. The turbulent boundary layer is composed of viscous sublayer, buffer layer and fully turbulent layer. The thermal resistance in the fully turbulent layer is usually negligible since it has a smaller temperature difference than other two layers. Based on this, the model was derived considering buoyancy and flow acceleration as the following form,

Fig. 4 shows a comparison result between the model and experiments. The study on the heat transfer model for horizontal flows is ongoing by using similar theoretical approaches.

Fig. 4. Comparison between the vertical heat transfer model and experiments.

A gas Brayton power cycle using sCO2 as a working fluid is a promising power cycle (Fig. 5). It has high efficiency, compactness and simplicity of the layout compared to other types of the power cycle such as steam Rankine power cycle, Helium Brayton power cycle. In addition, the sCO2 power cycle is able to adopt various heat sources such as solar energy, geothermal energy, waste heat and nuclear energy. The big issue of sCO2 Brayton cycle is to develop compact heat exchangers, which are comparable to the size of turbines and compressors. Thus, it is important to understand the heat transfer characteristics of sCO2 to the HXs.

Fig. 5. Schematic of a simple sCO2 Brayton cycle layout.