The study of turbulent Prandtl number is important for turbulent flows with heat transfer. Despite its importance, no universal model exists that is able to capture its behavior for a range of molecular Prandtl numbers. In this study, new turbulent Prandtl number models were developed using multi-gene gene expression programming (MGGEP) based on direct numerical simulation (DNS) data for heated periodic channel flows. DNS datasets covering both medium- and low-Prandtl-number fluids were employed to construct more universal closures suitable for Reynolds-averaged Navier–Stokes (RANS) simulations. Two case studies were conducted. In the first case study, turbulent Prandtl number models optimized for air (Pr = 0.71) were obtained using the friction Reynolds number and normalized wall distance as the physical inputs. In the second case study, generalized models applicable to both medium- and low-Prandtl-number fluids (down to Pr = 0.025) were developed. A novel Galilean-invariant local Reynolds number parameter was introduced to accurately capture the near-wall behavior and spatial variations in turbulent heat transfer. The resulting models demonstrated mean percent relative errors below 3% for the turbulent Prandtl number compared with the DNS data, while existing models in the literature show errors of up to 26.7%. In terms of root mean square error for the periodic channel flow, medium Prandtl number studies showed root mean square error reduction from 0.0596 to 0.0302, and low-Prandtl-number studies exhibited root mean square error reduction from 0.3128 to 0.0256 when MGGEP models and models from the literature are compared with respect to turbulent Prandtl number. The models were also validated using the turbulent periodic pipe flow problem, where the mean percent relative error for the turbulent Prandtl number decreased from 31.0% to 5.8%. The developed models were subsequently implemented in RANS simulations, showing that the proposed turbulent Prandtl number models lead to highly accurate temperature predictions for the periodic channel flow problem.
Pehlivan et al. (Mon,) studied this question.