Aviation industry is constantly striving for more efficient design processes in respect to optimal time, human and computational resources utilization. This implies a need for application of an approximation techniques enabling for fast responses generation with maintained level of results quality. This study focuses on an advancement of aerodynamic shape optimization process of a small aircraft engine intake system by introduction of a surrogate modelling step into the design loop. The multi-objective metamodel assisted optimization is carried out in order to reduce pressure losses along the engine intake duct and increase flow homogeneity at the engine compressor intake plane. Latin Hypercube Design method is utilized in order to sample the design space. A set of initial objective function evaluations is generated with application of Reynolds-averaged Navier–Stokes solver. The ensemble of samples is further used to train a Kriging-based surrogate model. The Efficient Global Optimization algorithm basing on the Expected Improvement function is employed to gradually increase the metamodel prediction quality by usage of sequential sampling technique. Finally, the optimal point predicted by the Kriging surrogate is validated against the high-fidelity model with usage of the Computational Fluid Dynamics code. The paper presents an application of the abovementioned methodology to the design process of the I-31T aircraft turboprop engine intake system. Proposed Kriging-based optimization workflow is utilized in order to reduce pressure losses and improve flow homogeneity in the engine air-intake duct.
WangGGShanS. Review of metamodeling techniques in support of engineering design optimization. J Mech Des2007; 129(4): 370–380.
2.
SimpsonTWPoplinskiJDKochPN, et al. Metamodels for computer-based engineering design: survey and recommendations. Eng Comput2001; 17(2): 129–150.
3.
HanZ-HZhangK-S. Surrogate-based optimization. In: RoevaO (ed) Real-World Applications of Genetic Algorithms. London, UK: InTech, 2012, pp. 343–362.
4.
PrzysowaKŁaniewski-WołłkŁRokickiJ. Shape optimisation method based on the surrogate models in the parallel asynchronous environment. Appl Soft Comput J2018; 71: 1189–1203.
FurlanFChiereghinNKipourosT, et al.Computational design of S-Duct intakes for distributed propulsion. Aircr Eng Aerosp Tech2014; 86: 473–477.
8.
D’AmbrosAKipourosTZachosP, et al.Computational Design Optimization for S-Ducts. Designs2018; 2(4): 36.
9.
ImmonenE. Shape optimization of annular S-ducts by CFD and high-order polynomial response surfaces. Eng Comput2018; 35(2): 932–954.
10.
ImmonenE. 2D shape optimization under proximity constraints by CFD and response surface methodology. Appl Math Model2017; 41: 508–529.
11.
LuHZhengXLiQ. A combinatorial optimization design method applied to S-shaped compressor transition duct design. Proc Inst Mech Eng G J Aerosp Eng2014; 228(10): 1749–1758.
12.
DonghaiJXiwuLWeiguangZ, et al.Optimization of endwall contouring in axial compressor S-shaped ducts. Chin J Aeronaut2015; 28(4): 1076–1086.
13.
GanWZhangX. Design optimization of a three-dimensional diffusing S-duct using a modified SST turbulent model. Aerosp Sci Technol2017; 63: 63–72.
14.
KooG-WLeeS-MKimK-Y. Shape optimization of inlet part of a printed circuit heat exchanger using surrogate modeling. Appl Therm Eng2014; 72(1): 90–96.
15.
ZerbinatiADésidériJADuvigneauR. Application of Metamodel-Assisted Multiple-Gradient Descent Algorithm (MGDA) to Air-Cooling Duct Shape Optimization. ECCOMAS 2012 - Eur Congr Comput Methods Appl Sci Eng E-b Full Pap, 2012, pp. 3964–3973.
16.
StornRPriceK. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim1997; 11(4): 341–359.
17.
VerstraeteTLiJ. Multi-objective optimization of a U-bend for minimal pressure loss and maximal heat transfer performance in internal cooling channels. In: Heat Transfer, Vol. 3A. San Antonio: American Society of Mechanical Engineers (ASME); 2013, pp. 1–12.
18.
JonesDRSchonlauMWelchWJ. Efficient global optimization of expensive black-box functions. J Glob Optim1998; 13(4): 455–492.
19.
DehghaniMAjamHFarahatS. Automated diffuser shape optimization based on CFD simulations and surrogate modeling. J Appl Fluid Mech2016; 9(7): 2527–2535.
20.
BaeHParkSKwonJ. Efficient global optimization for S-duct diffuser shape design. Proc Inst Mech Eng Part G J Aerosp Eng2013; 227(9): 1516–1532.
21.
BiancoliniMECostaECellaU, et al.Glider fuselage-wing junction optimization using CFD and RBF mesh morphing. Aircr Eng Aerosp Technol2016; 88(6): 740–752.
22.
KapsoulisDAsoutiVGiannakoglouK, et al.Evolutionary aerodynamic shape optimization through the RBF4AERO platform. In: Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016). Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece; 2016, pp. 4146–4155.
23.
SavastanoWPranzitelliAAndrewsGE, et al. Goal Driven Shape Optimisation for Conjugate Heat Transfer in an Effusion Cooling Plate. Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. Volume 5A: Heat Transfer. Montreal, Quebec, Canada. 15–19 June 2015. V05AT10A003. Volume 5A: Heat Transfer. American Society of Mechanical Engineers (ASME), 2015, pp. 1–11.
24.
MastrippolitoFAubertSDucrosF, et al.RBF-based mesh morphing improvement using Schur complement applied to rib shape optimization. Int J Number Methods Heat Fluid Flow2019; 30(9): 4241–4257.
25.
MarchlewskiKŁaniewski-WołłkŁKubackiS. Aerodynamic shape optimization of a gas turbine engine air-delivery duct. J Aerosp Eng2020; 33(4): 04020042.
26.
AlessiGKoloszarLVerstraeteTet al. Node-based adjoint surface optimization of U-bend duct for pressure loss reduction. Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems. Cham: Springer, 2019, pp. 61–75.
27.
AissaMHMaffulliRMuellerL, et al.Optimisation of a turbine inlet guide vane by gradient-based and metamodel-assisted methods. Int J Comut Fluid Dyn2019; 33(6–7): 302–316.
StalewskiWŻółtakJ. The preliminary design of the air-intake system and the nacelle in the small aircraft-engine integration process. Aircr Eng Aerosp Tech2014; 86(3): 250–258.
30.
NikulinYMiettinenKMäkeläMM. A new achievement scalarizing function based on parameterization in multiobjective optimization. OR Spectr2012; 34(1): 69–87.
31.
MiettinenK. Nonlinear Multiobjective Optimization. Boston, MA: Springer US; 1998. (International Series in Operations Research & Management Science; Vol. 12).
32.
SiegerDMenzelSBotschM. High quality mesh morphing using triharmonic radial basis functions. In: Proceedings of the 21st International Meshing Roundtable, San Jose,California, USA, October 2012
33.
de BoerAvan der SchootMSBijlH. Mesh deformation based on radial basis function interpolation. Comput Struct2007; 85(11–14): 784–795.
BarthTJespersenD. The design and application of upwind schemes on unstructured meshes. In: 27th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics; 1989.
AzzolaJHumphreyJACIacovidesH, et al. Developing turbulent flow in a U-bend of circular cross-section: measurement and computation. J Fluids Eng1986; 108(2): 214–221.
39.
AzzolaJHumphreyJAC. Developing Turbulent Flow in a 180° Curved Pipe and its Downstream Tangent. Second Int Symp Appl Laser Anemometry to Fluid Mech1984; (July): 35–43.
40.
LiuHOngY-SCaiJ. A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design. Struct Multidiscip Optim2018; 57(1): 393–416.
41.
SacksJWelchWJMitchellTJ, et al.Design and analysis of computer experiments]: Rejoinder. Stat Sci1989; 4(4): 433–435.
42.
MuschCCremannsKHeckerS, et al. Combined optimisation of the last stage and diffuser in a steam turbine using meta-models. In: 12th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics,Stockholm, Sweden, April 2017, pp. 1–12.
43.
WansaseubKPholdeeNBureeratS. Optimal U-shaped baffle square-duct heat exchanger through surrogate-assisted self-adaptive differential evolution with neighbourhood search and weighted exploitation-exploration. Appl Therm Eng2017; 118: 455–463.
44.
DemirelGAcarECelebiogluK, et al.CFD-driven surrogate-based multi-objective shape optimization of an elbow type draft tube. Int J Hydrogen Energy2017; 42(28): 17601–17610.
45.
SamadALeeK-DKimK-Y. Shape optimization of a dimpled channel to enhance heat transfer using a weighted-average surrogate model. Heat Transf Eng2010; 31(13): 1114–1124.
46.
CarnellR. lhs: Latin hypercube samples. R Package Version 0.162019.
47.
KrigeDG. Journal of the Chemical Metallurgical & mining society of South Africa. J Chem Metall Soc South Min Africa1951; 52(6): 119–139.
48.
MatheronG. Principles of geostatistics. Econ Geol1963; 58(8): 1246–1266.
49.
RoustantOGinsbourgerDDevilleY. DiceKriging, DiceOptim : Two R Packages for the analysis of computer experiments by Kriging-Based metamodeling and optimization. J Stat Softw2012; 51(1): 1–55.
50.
ScruccaLGA. A package for genetic algorithms in R. J Stat Softw2013; 53(4): 1–37.
