Large-Eddy Simulation and Rans Studies of the Flow And Heat Transfer in a U-Duct with Trapezoidal Cross Section

Kenny S Hu, Purdue University

Abstract

The thermal efficiency of gas turbines increases with the temperature of the gas entering its turbine component. To enable high inlet temperatures, even those that far exceed the melting point of the turbine materials, the turbine must be cooled. One way is by internal cooling, where cooler air passes through U-ducts embedded inside turbine vanes and blades. Since the flow and heat transfer in these ducts are highly complicated, computational fluid dynamics (CFD) based on RANS have been used extensively to explore and assess design concepts. However, RANS have been found to be unreliable – giving accurate results for some designs but not for others. In this study, large-eddy simulations (LES) were performed for a U-duct with a trapezoidal cross section to assess four widely used RANS turbulence models: realizable k-ε (k-ε), shear-stress transport (SST), Reynolds stress model with linear pressure strain (RSM-LPS), and the sevenequation stress-omega full Reynolds stress model (RSM). When examining the capability of steady RANS, two versions of the U-duct were examined, one with a staggered array of pin fins and one without pin fins. Results obtained for the heat-transfer coefficient (HTC) were compared with experimental measurements. The maximum relative error in the predicted “averaged” HTC was found to be 50% for k-ε and RSMLPS, 20% for SST, and 30% for RSM-τω when there are no pin fins and 25% for k-ε, 12% for the SST and RSM-τω when there are pin fins. When there are no pin fins, all RANS models predicted a large separated flow region downstream of the turn, which the experiment does show to exist. Thus, all models predicted local distributions poorly. When there were pin fins, they behaved like guide vanes in turning the flow and confined the separation around the turn. For this configuration, all RANS models predicted reasonably well. To understand why RANS cannot predict the HTC in the U-duct after the turn when there are no pin fins, LES were performed. To ensure that the LES is benchmark quality, verification and validation were performed via LES of a straight duct with square cross section where data from experiments and direct numerical simulation (DNS) are available. To ensure correct inflow boundary condition is provided for the U-duct, a concurrent LES is performed of a straight duct with the same trapezoidal cross section and flow conditions as the U-duct. Results obtained for the U-duct show RANS models to be inadequate in predicting the separation due to their inability to predict the unsteady separation about the tip of the turn. To investigate the limitations of the RANS models, LES results were generated for the turbulent kinetic energy, Reynolds-stresses, pressure-strain rate, turbulent diffusion, pressure diffusion, turbulent transport, and velocity-temperature correlations with focus on understanding their behavior induced by the turn region of the U-duct. As expected, the Boussinesq assumption was found to be incorrect, which led to incorrect predictions of Reynolds stresses. For RSM-τω, the modeling of the pressure-strain rate was found to match LES data well, but huge error was found on modeling the turbulent diffusion. This huge error indicates that the two terms in the turbulent diffusion – pressure diffusion and turbulent transport – should be modeled separately. Since the turbulent transport was found to be ignorable, the focus should be on modeling the pressure diffusion. On the velocity-temperature correlations, the existing eddy-diffusivity model was found to be over simplified if there is unsteady separation with shedding. The generated LES data could be used to provide the guidance for a better model.

Degree

Ph.D.

Advisors

I-P Shih, Purdue University.

Subject Area

Energy|Fluid mechanics|Hydraulic engineering|Mechanics|Thermodynamics

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