Heat Transfer Predictions With Extended k–ε Turbulence Model in Radial Cooling Ducts Rotating in Orthogonal Mode

Abstract

Standard and extended k–ε turbulence closure models have been employed for three-dimensional heat transfer calculations for radially outward flow in rectangular and square cooling passages rotating in orthogonal mode. The objective of this modeling effort is to validate the numerical model in an attempt to fill the gap between model predictions and the experimental data for heat transfer in rotating systems. While the trend of heat transfer predictions by the standard k–ε turbulence model is satisfactory, the differences between the data and the predictions are approximately 30 percent or so in the case of high rotation number flow. The extended k–ε turbulence model takes an approach where an extra “source” term based on a second time scale of the turbulent kinetic energy production rate is added to the equation for the dissipation rate of turbulent kinetic energy. This yields a more effective calculation of turbulent kinetic energy as compared to the standard k–ε turbulence model in the case of high rotation number and high density ratio flow. As a result, comparison with the experimental data available in the literature shows that an improvement of up to a significant 15 percent (with respect to data) in the heat transfer coefficient predictions is achieved over the standard k–ε model in the case of high rotation number flow. Comparisons between the results of the standard k–ε model and the extended formulation are made at different rotation numbers, different Reynolds numbers, and varying temperature ratio. The results of the extended k–ε turbulence model are either as good or better than those of the standard k–ε model in all these cases of parametric study. Thus, the extended k–ε turbulence model proves to be more general and reduces the discrepancy between the model predictions and the experimental data for heat transfer in rotating systems.