<b>FLOW AND HEAT TRANSFER IN A TAPERED U-DUCT UNDER ROTATING AND NON-ROTATING CONDITIONS</b>
Creators: name: Kim, Wanjae
Publisher: name: Purdue University Graduate School
Year: 2024
Subjects: classificationCode: 401204
subject: Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)

description: The thermal efficiency of gas turbines improves with higher turbine inlet temperatures (TIT) or compressor outlet pressure. Nowadays, gas turbines achieve TITs up to 1600 °C for power generation and 2000 °C for aircraft. These temperatures far exceed the limits where structural integrity can be maintained. For Ni-based superalloys with thermal barrier coatings, that limit is about 1200 °C. Gas turbines can operate at these high temperatures because all parts of the turbine component that contact the hot gases are cooled so that material temperatures never exceed those limits. Gas-turbine vanes and blades are cooled by internal and film cooling with the cooling air extracted from the compressor. Since the extracted air could be used to generate power or thrust, the amount of cooling air used must be minimized. Thus, numerous researchers have investigated fluid flow and heat transfer in internal and film cooling to enable effective cooling with less cooling flow. For internal cooling, significant knowledge gaps persist, notably in ducts with varying cross sections. Reviews of existing literature indicate a lack of studies on flow and heat transfer in cooling ducts that account for the taper in the blade geometry from root to tip for both power-generation and aircraft gas turbines.This study investigates the flow and heat transfer in ribbed and smooth tapered U-ducts, under conditions relevant to turbine cooling by using computational fluid dynamics (CFD) and a reduced-order model (ROM) developed in this study. The CFD analysis was based on steady Reynolds-Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport (SST) turbulence model. The CFD analysis examined the effects of rotation number (Ro = 0, 0.0219, 0.0336, 0.0731), Reynolds number (Re = 46,000, 100,000, 154,000), and taper angle (α = 0°, 1.41°) under conditions that are relevant to electric-power-generation gas turbines. CFD results obtained showed increasing the taper angle significantly increases both the friction coefficient and the Nusselt number, regardless of rotation. With rotation at Ro = 0.0336 and Re = 100,000, the maximum increase in the average friction coefficient and Nusselt number due to taper was found to be 41.7% and 36.6% respectively. Without rotation at Re = 46,000, those increases were 11.5% and 14.7% respectively. The ROM was derived from the integral continuity, momentum, and energy equations for a thermally and calorically perfect gas to provide rapid assessments of radially outward flow in tapered ducts subjected to constant heat flux. The ROM was used to study the effects of 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 loadings (q" = 5×104, 105 W/m2) on the mean density, velocity, temperature, and pressure along the duct. The parameters studied are relevant to both electric-power-generation and aircraft gas turbines. Results obtained show density and pressure variations to be most affected by the rotation number, while velocity along the duct is most affected by the duct’s taper angle. Additionally, it was found that if the taper angle is sufficiently large (α = 3°), then the temperature could reduce along the duct despite being heated because the thermal energy is converted to mechanical energy. When compared to a duct without taper, the mass flow rate of the cooling air could be reduced by up to 44% to achieve the same temperature distribution of the cooling flow along the duct.The ROM developed was assessed by comparing against grid-converged CFD results for both ribbed and smooth sections of the duct. The validation study showed the maximum relative errors for density, velocity, temperature, and pressure distributions to be 0.6%, 3.3%, 0.4%, and 0.3% for smooth sections, and 3.2%, 5.6%, 0.9%, and 3.0% for ribbed sections, respectively. Thus, the ROM developed has accuracy comparable to CFD based on steady RANS but is order of magnitude more efficient computationally, making it a valuable tool for preliminary design. <br>