Application of fractal theory in the arrangement of truncated ribs in a rectangular cooling channel (4:1) of a turbine blade

Ribs are widely employed in internal cooling passages of turbine blades and other heat transfer equipment to enhance heat transfer by making cooling air flow through internal ribbed passages. From mathematics, a fractal is an abstract object used to simulate naturally occurring objects, which exhibits similar patterns and properties also at smaller scales. The evolving fractal structures of the continuous ribbed channels contains two sides truncated ribs, three sides truncated ribs, five sides truncated ribs and nine sides truncated ribs. The thermal performance of the ribbed channels is compared by taking both heat transfer and pressure drop into consideration. Steady Liquid Crystal Thermography (LCT) is employed to measure surface temperature and derive heat transfer coefficients over the ribbed surfaces in the tested channels. Turbulent flow details are presented by numerical calculations with an established turbulence model, i.e. the k-ω SST model. From the experimental results, it is found that fractal truncated ribs with smaller length scales have larger heat transfer at the low Reynolds numbers. On the other hand, the difference of Nusselt numbers for different cases can be negligible at the high Reynolds numbers. Generally, fractal truncated ribs with smaller length scales have a more uniform heat transfer distribution. The correlation between Nusselt number and Reynolds number are respectively Re0.69, Re0.64 and Re0.61 for case 2 (Two Sides Truncated ribs), case 3 (Three Sides Truncated Ribs) and case 4 (Five Sides Truncated Ribs). The distribution of the high Nusselt number regions is kept identical during the fractal truncated ribs evolving process, which is also valid for the flow field.