Blades in gas turbines have cross sections at the root that are larger than those at the tip so that internal cooling passages in blades are tapered. In this study, a reduced-order model (ROM) — based on the integral continuity, momentum, and energy equations for a thermally and calorically perfect gas was developed to enable rapid assessments of radially outward flow in a tapered duct subjected to constant heat flux with and without rotation. The following parameters were investigated by using the ROM developed: taper angle (α = 0°, 1.5°, 3.0°), ratio of mean radius to hydraulic diameter (Rm/Dh = 45, 150), rotation number (Ro = 0, 0.025, 0.25), Reynolds number (Re = 37,000, 154,000), and thermal loading (q” = 5 × 104, 105 W/m2). Results obtained show the density and pressure variation along the duct to be most affected by rotation number; velocity to be more affected by duct’s taper angle; and temperature by rotation number and taper angle. Results obtained also show the temperature along the duct could decrease if the taper is sufficiently large even with high heat flux into the duct because taper increases velocity, which converts thermal energy to mechanical energy. Within the range of parameters studied, the mass flow of the cooling flow could be reduced by as much as 44% for a tapered duct to achieve bulk temperature variation similar to that of a duct without a taper. The ROM developed was validated by comparing its predictions with grid-converged CFD results obtained by steady RANS with the SST turbulence model. The maximum relative errors for density, velocity, temperature, and pressure distributions along the duct were found to be 0.6%, 3.3%, 0.4%, 0.3% for the smooth section of the duct and 3.2%, 5.6%, 0.9%, 3.0% for the ribbed section of the duct. Thus, the ROM developed performs nearly as well as CFD based on RANS but orders of magnitude more efficient computationally.
No takes yet. Share an insight, caveat, or question.
Kim et al. (2024) studied this question.