Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer—Part I: Model Formulations

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity, and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent states. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from Durbin et al. (2001, “Rough Wall Modification of Two Layer k-ε ,” ASME J. Fluids Eng., 123, pp. 16–21), which builds upon a two-layer $k-ε$-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer $k-ε$-turbulence model by the present authors. The discrete-element model will be formulated in a new way, suitable for randomly rough topographies. Part I of the paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high-pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors as well as new experimental data from a low-pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.