Over the past decades, engineers have focused on a common goal - to reduce emissions by making industrial processes more efficient and by utilizing renewable energy sources. One possibility to reach this goal can be achieved by employing processes with non-ideal fluids, such as fluids at supercritical conditions in refrigeration, heat pump cycles and power cycles.
Most of the flows in industry are turbulent and hence the need to study turbulence in non-ideal fluids arose. Turbulence in non-ideal fluids is extremely challenging since there are many complex effects at play. One such effect is caused by variations in properties, which also occurs in compressible flows, flows with high concentration gradients, or flows in heat exchangers.

This thesis presents a review of the existing theory on semi-local scaling for variable property flows with the aim to take it one step further and apply it to turbulent heat flux modeling. Two types of variable property cases are analysed in this thesis; (1) low-Mach number flows with uniform pseudo-heating sources, (2) high-Mach number flows with non-uniform viscous heating. For the former, a Direct Numerical Simulation (DNS) data-base, already available at TU Delft, has been post-processed with the main goal to investigate if the semi-local theory can also be applied to thermal turbulence and its modeling. For the latter, additional DNS simulations of high-Mach number channel flows have been performed to investigate how the viscous heating and its correlations can be accounted for in the semi-local scaling framework.

Using a 2-equation heat flux model, we find that modeling thermal turbulence in semi-local scales considerably improves the results for low-Mach number flows. However, for high-Mach number flows, additional unknown (closure) terms arise due to fluctuations in the viscous heating source. A model for the source term in the enthalpy variance equation is successfully proposed. In addition, the DNS study of two high-Mach number flows with constant semi-local Reynolds number profiles shed light on the importance of a newly defined parameter (modified Eckert number) and also unveils one of the most important conditions in which semi-local theory can be compromised, e.g. extreme density gradients.