Abstract
This work shows the application of Gene Expression Programming to augment RANS turbulence closures for flows though complex geometries. Specifically, an optimized internal cooling channel of a turbine blade, designed for additive manufacturing. One of the challenges in internal cooling design is the heat transfer accuracy of the RANS formulation in comparison to higher fidelity methods, which are still not used in design on account of their computational cost. However, high fidelity data can be extremely valuable for improving current lower fidelity models and this work shows the application of data-driven approaches to develop turbulence closures for an internally ribbed duct. Different approaches are compared and the results of the improved model are illustrated; first on the same geometry, and then for an unseen predictive case.
The work shows the potential of using data-driven models for accurate heat transfer predictions even in non-conventional configurations and indicates the ability of closures learnt from complex flow cases to adapt successfully to unseen test cases.
References
1.
Chyu
, M. K.
, and Siw
, S. C.
, 2013
, “Recent Advances of Internal Cooling Techniques for Gas Turbine Airfoils
,” ASME J. Therm. Sci. Eng. Appl.
, 5
(2
), p. 021008
. 2.
Tang
, Y.
, and Zhao
, Y. F.
, 2016
, “A Survey of the Design Methods for Additive Manufacturing to Improve Functional Performance
,” Rapid. Prototyp. J.
, 22
(3
), pp. 569
–590
. 3.
Pietropaoli
, M.
, Montomoli
, F.
, and Gaymann
, A.
, 2018
, “Three-Dimensional Fluid Topology Optimization for Heat Transfer
,” Struct. Multidiscipl. Optim.
, 59
(3
), pp. 801
–812
. 4.
Kunz
, R. F.
, Hanson
, D. R.
, Mcclain
, S. T.
, Kinzel
, M. P.
, Reutzel
, E. W.
, Snyder
, J. C.
, and Thole
, K. A.
, 2018
, “Direct Numerical Simulation, Up-Scaled Measurement and RANS Analysis of Additively and Conventionally Manufactured Internal Turbine Cooling Passages
,” 71st Annual Meeting of the APS Division of Fluid Dynamics
, Atlanta, GA
.5.
Wilcox
, D. C.
, 2006
, Turbulence Modeling for CFD
, 3rd ed, DCW Industries
, La Canada, California
.6.
Slotnick
, J.
, Khodadoust
, A.
, Alonso
, J.
, and Darmofal
, D.
, 2014
, CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences. Technical Report, NASA Langley Research Center, Hampton.7.
Sandberg
, R. D.
, and Michelassi
, V.
, 2019
, The Current State of High-Fidelity Simulations for Main Gas Path Turbomachinery Components and Their Industrial Impact
, Vol. 102
. Flow, Turbulence and Combustion.8.
Durbin
, P. A.
, 2018
, “Some Recent Developments in Turbulence Closure Modeling
,” Annu. Rev. Fluid. Mech.
, 50
(1
), pp. 77
–103
. 9.
Duraisamy
, K.
, Iaccarino
, G.
, and Xiao
, H.
, 2019
, “Turbulence Modeling in the Age of Data
,” Annu. Rev. Fluid. Mech.
, 51
(1
), pp. 357
–377
. 10.
Wang
, J. X.
, Wu
, J. L.
, and Xiao
, H.
, 2017
, “Physics-Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data
,” Phys. Rev. Fluids
, 2
(3
), pp. 1
–22
.11.
Wu
, J. L.
, Xiao
, H.
, and Paterson
, E.
, 2018
, “Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework
,” Phys. Rev. Fluids
, 7
(3
), pp. 1
–28
.12.
Ling
, J.
, Kurzawski
, A.
, and Templeton
, J.
, 2016
, “Reynolds Averaged Turbulence Modelling Using Deep Neural Networks With Embedded Invariance
,” J. Fluid. Mech.
, 807
, pp. 155
–166
. 13.
Weatheritt
, J.
, and Sandberg
, R. D.
, 2016
, “A Novel Evolutionary Algorithm Applied to Algebraic Modifications of the RANS Stress-Strain Relationship
,” J. Comput. Phys.
, 325
, pp. 22
–37
. 14.
Akolekar
, H. D.
, Sandberg
, R. D.
, Hutchins
, N.
, Michelassi
, V.
, and Laskowski
, G.
, 2019
, “Machine-Learnt Turbulence Closures for Low-Pressure Turbines With Unsteady Inflow Conditions
,” J. Turbomach.
, 141
(10
), pp. 1
–11
.15.
Pichler
, R.
, Sandberg
, R. D.
, Michelassi
, V.
, and Bhaskaran
, R.
, 2016
, “Investigation of the Accuracy of RANS Models to Predict the Flow Through a Low-Pressure Turbine
,” ASME J. Turbomach.
, 138
(12
), p. 121009
. 16.
Schoepplein
, M.
, Weatheritt
, J.
, Sandberg
, R.
, Talei
, M.
, and Klein
, M.
, 2018
, “Application of An Evolutionary Algorithm to LES Modelling of Turbulent Transport in Premixed Flames
,” J. Comput. Phys.
, 374
, pp. 1166
–1179
. 17.
Weatheritt
, J.
, Pichler
, R.
, Sandberg
, R. D.
, Laskowski
, G.
, and Michelassi
, V.
, 2017
, “Machine Learning for Turbulence Model Development Using a High-Fidelity HPT Cascade Simulation
,” Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Volume 2B: Turbomachinery
, Charlotte, NC
, pp. 1
–12
.18.
Weatheritt
, J.
, and Sandberg
, R. D.
, Nov. 2017
, “The Development of Algebraic Stress Models Using a Novel Evolutionary Algorithm
,” Int. J. Heat Fluid Flow
, 68
, pp. 298
–318
. 19.
Weatheritt
, J.
, and Sandberg
, R. D.
, 2019
, “Improved Junction Body Flow Modeling Through Data-Driven Symbolic Regression
,” J. Ship Res.
, 63
(4
), pp. 283
–293
. 20.
Weatheritt
, J.
, Zhao
, Y.
, Sandberg
, R. D.
, Mizukami
, S.
, and Tanimoto
, K.
, 2019
, “Data-Driven Scalar-flux Model Development With Application to Jet in Cross Flow
,” Int. J. Heat. Mass. Transfer.
, 147
, p. 118931
.21.
Pietropaoli
, M.
, Gaymann
, A.
, and Montomoli
, F.
, 2020
, “Three-Dimensional Fluid Topology Optimization and Validation of a Heat Exchanger With Turbulent Flow
,” Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. Volume 7A: Heat Transfer
, Virtual, Online
, pp. 1
–11
.22.
Hossain
, J.
, Fernandez
, E.
, Garrett
, C.
, and Kapat
, J.
, 2017
, “Flow and Heat Transfer Analysis in a Single Row Narrow Impingement Channel: Comparison of PIV, LES, and RANS to Identify RANS Limitations
,” Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Volume 5A: Heat Transfer
, Charlotte, NC
, pp. 1
–12
.23.
Shams
, A.
, and De Santis
, A.
, 2019
, “Towards the Accurate Prediction of the Turbulent Flow and Heat Transfer in Low-Prandtl Fluids
,” Int. J. Heat Mass. Transfer.
, 130
, pp. 290
–303
. 24.
Dhopade
, P.
, Capone
, L.
, Mcgilvray
, M.
, Gillespie
, D.
, and Ireland
, P.
, 2015
, “Numerical Modelling Techniques for Turbine Blade Internal Cooling Passages
,” Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. Volume 5A: Heat Transfer
, Montreal, Quebec, Canada
, pp. 1
–13
.25.
Pope
, S. B.
, 1975
, “A More General Effective-Viscosity Hypothesis
,” J. Fluid. Mech.
, 72
(2
), pp. 331
–340
. 26.
Rodi
, W.
, 1976
, “A New Algebraic Relation for Calculating the Reynolds Stresses
,” Gesellschaft Angewandte Mathematik und Mechanik
, 56
(3
), p. 219
. 27.
Spencer
, A. J.
, and Rivlin
, R. S.
, 1958
, “The Theory of Matrix Polynomials and Its Application to the Mechanics of Isotropic Continua
,” Archive for Rational Mech. Anal.
, 2
(1
), pp. 309
–336
. 28.
Gatski
, T. B.
, and Jongen
, T.
, 2000
, “Nonlinear Eddy Viscosity and Algebraic Stress Models for Solving Complex Turbulent Flows
,” Prog. Aerosp. Sci.
, 36
(8
), pp. 655
–682
. 29.
Ferreira
, C.
, 2001
, “Gene Expression Programming: A New Adaptive Algorithm for Solving Problems
,” Complex Syst.
, 13
(2
), pp. 87
–129
.30.
Wissink
, J. G.
, Michelassi
, V.
, and Rodi
, W.
, 2004
, “Heat Transfer in a Laminar Separation Bubble Affected by Oscillating External Flow
,” Int. J. Heat Fluid Flow
, 25
(5
), pp. 729
–740
. 31.
Wallin
, S.
, and Johansson
, A. V.
, 2000
, “An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows
,” J. Fluid. Mech.
, 403
, pp. 89
–132
.32.
Parneix
, S.
, Laurence
, D.
, and Durbin
, P.
, 1996
, “Second Moment Closure Analysis of the Backstep Flow Database
,” Center for Turbulence Research Summer Program
, Stanford, CA
, pp. 47
–62
.33.
Le
, H.
, Moin
, P.
, and Kim
, J.
, 1997
, “Direct Numerical Simulation of Turbulent Flow Over a Backward-Facing Step
,” J. Fluid. Mech.
, 330
, pp. 349
–374
. Copyright © 2022 by ASME
You do not currently have access to this content.
