Abstract
This study presents a numerical procedure to optimize the cooling passage structure of turbine blade to enhance aerodynamic and heat transfer. Surrogate model based optimization technique is used with Navier-Stokes analysis of fluid flow and heat transfer with RNG k-epsilon transport turbulence model. The objective function is defined as a nonlinear combination of heat transfer and pressure loss with K-S function. Optimal Latin Hypercube Sampling is used to determine the training points as a mean of design of experiment. Two Loops Dynamic Optimization System (TLDOS) is performed to implement the cooling blade optimization. Blade performance improves obviously, especially the kriging model based system. Result shows a significant impact of rib positions for blade heat transfer but slightly for total pressure loss. Numerical simulation proves the feasibility and validity of the TLDOS methods.
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Abbreviations
- \(x_1^{\it rib}, x_2^{\it rib}\) :
-
Rib relative positions
- X:
-
Vector of design variable
- Xlow :
-
Lower bounds on design variables
- Xup :
-
Upper bounds on design variables
- \(\hat{y}({\bf X})\) :
-
Approximation value of the target function
- r(x):
-
Vector of correlation
- β, θ:
-
Unknown parameters of kriging
- l(θ):
-
Maximum likelihood estimation of θ
- \(\textbf{\textit{R}}\) :
-
n × n correlation matrix
- a i :
-
Constant coefficients of polynomial function
- T i :
-
Inlet total temperature
- P i :
-
Inlet total pressure
- M :
-
Mass flow rate of coolant air
- \(T_{\emph{AVER}}\) :
-
Facet average temperature of blade external wall
- \(T_{\emph{MAX}}\) :
-
Maximum temperature of blade
- \(P_{\emph{LOSS}}\) :
-
Total pressure loss
- f max :
-
Maximum value of vector f(x)
- \(f_{\emph{KS}}(X)\) :
-
KS function
- d:
-
Blade maximal displacement
- σ max :
-
Blade maximal Von Mises stress
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Acknowledgments
The work was supported by Doctoral Research Fund of Henan University of Science and Technology, the fund of the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University (SKLSP201008) and China National High-tech Research and Development Program (No. 2009AA04Z418).
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Yu, K., Yang, X. & Yue, Z. Aerodynamic and heat transfer design optimization of internally cooling turbine blade based different surrogate models. Struct Multidisc Optim 44, 75–83 (2011). https://doi.org/10.1007/s00158-010-0583-x
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DOI: https://doi.org/10.1007/s00158-010-0583-x