1 Copyright © 2018 by ASME Proceedings of ASME Turbo Expo 2018: Turbomachinery Technical Conference & Exposition GT2018 June 11-15, 2018, Oslo, Norway GT2018-75530 STEADY RANS OF FLOW AND HEAT TRANSFER IN A SMOOTH AND PIN-FINNED U-DUCT WITH A TRAPEZOIDAL CROSS SECTION Kenny S., Hu, Xingkai Chi, and Tom I-P. Shih, School of Aeronautics and Astronautics, Purdue University West Lafayette, IN 47907, USA Minking Chyu Swanson School of Engineering University of Pittsburgh Pittsburgh, PA 15261, USA Michael Crawford Siemens Energy, Inc. Orlando, FL 32817, USA ABSTRACT Steady RANS were performed to examine four turbulence models’ ability to predict the turbulent flow and heat transfer in a U-duct that has a trapezoidal cross section with and without a staggered array of pin fins at Reynolds number of 20,000 based on the duct’s hydraulic diameter . The four turbulence models examined are the realizable k-ε model (k-ε), the two-equation shear-stress transport (SST) model, the seven-equation Reynolds stress model with linear pressure strain (RSM-LPS), and the stress-omega full Reynolds stress model (RSM-τω). For the k-ε and RSM-LPS models, the Chen and Patel’s one- equation model was used in the near-wall region. Results generated for the heat-transfer coefficient (HTC) were compared with experimentally measured values. Results obtained for the smooth U-duct show all models to yield similar HTCs in the up-leg part. The predicted regionally-averaged HTCs matched well with measurements. The maximum relative error is 2.5% for k-ε, SST, and RSM-τω and 9% for RSM-LPS model. In the turn region, RSM-τω provided the best predictions of the HTC. The maximum relative error is 14.5% for RSM-τω, 29% for SST, and 50% for k-ε model and RSM-LPS. In the down-leg part after the turn region, SST gave the best predictions and RSM-τω being a close second with maximum relative error less than 10%. The ability to correctly predict the secondary flow in the turn region and the separated flow downstream of the turn region dominate how well the models predict the HTC. Results obtained for the U-duct with pin fins show k-ε to predict the lowest and the least accurate HTCs, and SST and RSM-τω to predict the best. For k-ε, the relative error in the averaged HTC is about 10% in the up-leg, 25% in the turn region, and 20% in the down-leg. For SST and RSM-τω, the relative error in the averaged HTC is less than 10% in the up- leg, less than 15% in the turn region, and less than 15% in the down-leg. SST performed slightly better than RSM-τω on total heat transfer and heat flux. Though all models predicted a separated region after each pin fin with reduced HTC in the wake, the experimental measurement did not. In the turn region, the staggered array of pin fins was found to behave like guide vanes in turning the flow. The pin fins also greatly reduced the size of the separated regions in the corners and around the bend of the U-duct. INTRODUCTION To improve thermal efficiency of advanced gas turbines, designs must enable further increases in the temperature of the hot gas entering the turbine component and/or enable further reductions in the amount of cooling flow needed to ensure that the turbine material’s temperature never exceed the maximum permitted for strength and service life. Both could be achieved by improving the effectiveness of cooling. To improve cooling requires increased understanding on how geometry and operating conditions affect internal and film cooling. Physics- based design and analysis tools, rooted in first principles, could generate the understanding needed. Computational fluid dynamics (CFD) with and without conjugate analysis has reached considerable maturity during the past decades [1-3] and offers promise as the physics-based tool that could deliver on the needs in the design and analysis of turbine cooling. CFD based on RANS is widely used to design and analyze internal cooling of turbine blades and vanes. The most commonly used RANS models invoke the eddy-viscosity analogy to relate the Reynolds stresses to the mean strain-rate tensor. The simplicity of the eddy-viscosity models comes with a number of assumptions, which limit its range of applicability [4-10].