A Study on Time-Scales Ratio and Turbulent Prandtl Number in Ducts of Industrial Applications

This investigation concerns numerical time-scales ratio and turbulent Prandtl number in fully developed turbulent flows in ducts of various cross-sections. The low Reynolds number version of a non-linear eddy viscosity model is proposed to predict the Reynolds stresses and the temperature field is solved using a two-equation heat flux model.

The computed results compare satisfactory with the available experimental data. The time-scale ratio R is defined as the ratio between the dynamic time-scale (k/ε) and the scalar time-scale(0.5θθ/εθ). Based on existing DNS data and calculations in this work the ratio between the time-scales is found to be approximately 0.7.

In light of this assumption an expression for the turbulent diffusivity is considered and the turbulent Prandtl number variation across the duct is studied. This study can also be regarded as engineering calculation methodic for ducts of heat exchangers for various applications area.