The application of similarity theory for heat transfer investigation in rotational internal cooling channel

Full-scale test for turbine blade internal cooling is difficult for laboratory researches. The original turbine blade channel is always proportionally scaled up to laboratory-scale channel, as well as its hydraulic diameter and rotating radius. But the proportion scale of radius is too large for any rotating rig to operate the test, and thus the insufficient rotating radius causes incomplete similarity application. Because of the dissimilar radius induced incomplete similarity, heat transfer results obtained in laboratory-scale channel cannot be directly used by actual turbine blade design process. Therefore, this paper deals with this problem and numerically studies the influence of incomplete similarity through a rotating square channel with smooth walls and radially outward flow. Dimensionless parameters analysis demonstrates that the radius ratio (R/D) only shows influence on the buoyancy number (Buo) which causes much smaller buoyancy number for dissimilar model. Thus, three models with various scales and rotating radius are built. Model 1 is the original channel simplified from actual turbine blade internal cooling channel; Model 2 (similar model) and Model 3 (experimental model) are the corresponding scaled-up channels from Model 1 with complete similar radius and insufficient radius respectively. And two correction methods (variable radius and variable wall temperature) are developed to revise the influence caused by incomplete similarity of Model 3. Variable radius is used to vary rotating radius and variable wall temperature is used to vary wall temperature. The simulation is completed using commercial CFD solver and k-ω turbulent model. Result shows that the conventional application of similarity theory can predict heat transfer well for complete similar model (Model 2), but with a large deviation for dissimilar model (Mode 3). Given the same Re and Ro, the smaller Buo in Model 3 causes over 17% deviation heat transfer result. Then, the two revised methods concerning the effect of rotational radius ratio and wall temperature ratio are detailedly discussed, and both of them show less than 3% deviation in heat transfer distribution results. The detailed revised steps are also provided for both methods.