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].