## 4 Numerical Simulation of Mixed Convection  
To understand the mechanism of this particular heat transfer behavior at low mass flux, a three-dimensional (3D) axisymmetric physical model was built. In order to obtain the fully developed flow upstream, the tested heated section with a length of 1000 mm was arranged after the adiabatic section along the length of 200 mm. Besides, the hydraulic pressure drop in this study was negligible compared with the system pressure. In order to significantly reduce the computational cost, the axisymmetric mesh was used. Finer mesh near the wall was built to ensure that the gradient in physical property could be properly resolved. The resolution of the boundary layer (mesh spacing near walls) plays a significant role in the accuracy of the determination of the wall's shear-stress and heat-transfer coefficients; therefore, it should be carefully adjusted. To fulfill the requirement of near-wall models, the non-dimensional  
Figure 12: Mixed convection in supercritical carbon dioxide. distance (y\({}^{+}\)) values at the wall-adjacent nodes should always be less than unity. Therefore, the position of the first near-wall node was adjusted for different fluids, as seen in Figure 13. At the inlet of the test section, the mass flux, temperature, turbulence intensity, and hydraulic diameter were specified, as seen in Table 1.  
The outlet pressure was specified as the condition of the outlet boundary for the calculation domain, and the wall face was set as the heat-flux boundary. A finite-volume method [41] was employed, and the equations of momentum and continuity were integrated over each computational cell. The computations of the heat transfer deterioration phenomenon were performed using the well-validated commercial CFD code Fluent. The coupling between the pressure and velocity was implemented using the SIMPLEC algorithm. A quick upwind scheme was used to discretize the equations in this work, while the discretization equations were then linearized and solved in a segregated manner. Considering the fast and steep variation in the supercritical fluid's thermo-physical properties in the pseudocritical region, precise thermo-physical properties should be given using a proper equation. Therefore, in this paper, a standard reference database derived from NIST RefProp [42] (National Institute of Standards and Technology) was called upon in the simulations. Firstly, the mesh dependence was analyzed, as shown in Figure 14. It was found that when the grid mesh number was 6.43 million, the wall temperature was similar to the experimental data. Further increase in the grid number did not improve the solution's accuracy. It is worth noticing that the accuracy of the numerical simulation of the heat transfer of supercritical carbon dioxide may strongly depend on the turbulence models employed in the numerical calculations. A previous study [36] pointed out that the SST _k-w_ turbulent model can obtain a better result than that of other turbulent models for supercritical vertical flow. Therefore, in the present paper, the numerical simulation was implemented based on this model, whereas the verification of the model is shown in Figure 15. A series of temperature profiles for different mass fluxes are shown in Figure 15. The calculated inner-wall temperatures for all of the mass fluxes were found to be in very good agreement with the experimental data, especially for the cases with low mass fluxes. After validation, the mechanism of heat transfer at low mass flux was further discussed. The case in which the pressure, mass flux, and heat flux were 7.5 MPa, 100 kg/m\({}^{2}\)s, and 30 kW/m\({}^{2}\), respectively, was chosen as an example to describe the distribution of various parameters along the cross-section. Figure 16 shows the distributions of density gradient, shear stress, and specific heat in the near-wall region at different cross-sections (\(H\) is the bulk enthalpy).