Biot Number Analogy for Design of Experiments in Turbine Cooling

Cooling of turbine components that come in contact with the hot gases strongly affects the turbine's efficiency and service life. Designing effective and efficient cooling configurations requires detailed understanding on how geometry and operating conditions affect the way coolant cools the turbine materials. Experimental measurements that can reveal such information are difficult and costly to obtain because gas turbines operate at high temperatures (up to 2000 K), high pressures (30+ bar), and the dimensions of many key features in the cooling configurations are small (millimeters or smaller). This paper presents a method that enables experiments to be conducted at near room temperatures, near atmospheric pressures, and using scaled-up geometries to reveal the temperature and heat-flux distributions within turbine materials as if the experiments were conducted under engine operating conditions. The method is demonstrated by performing conjugate computational fluid dynamics (CFD) analyses on two test problems. Both problems involve a thermal barrier coating (TBC)-coated flat plate exposed to a hot-gas environment on one side and coolant flow on the other. In one problem, the heat transfer on the coolant side is enhanced by inclined ribs. In the other, it is enhanced by an array of pin fins. This conjugate CFD study is based on 3D steady Reynolds-averaged Navier–Stokes (RANS) closed by the shear-stress-transport turbulence model for the fluid phase and the Fourier law for the solid phase. Results obtained show that, of the dimensionless parameters that are important to this problem, it is the Biot number that dominates. This study also shows that for two geometrically similar configurations, if the Biot number distributions on the corresponding hot-gas and coolant sides are nearly matched, then the magnitude and contours of the nondimensional temperature and heat-flux distributions in the material will be nearly the same for the two configurations—even though the operating temperatures and pressures differ considerably. Thus, experimental measurements of temperature and heat-flux distributions within turbine materials that are obtained under “laboratory” conditions could be scaled up to provide meaningful results under “engine” relevant conditions.