Experimental Data-Driven Flow Field Prediction for Compressor Cascade based on Deep Learning and ℓ1 Regularization

LIU Tantao; GAO Limin; LI Ruiyu

doi:10.1007/s11630-024-2035-8

Journal of Thermal Science >

2024 , Vol. 33 >Issue 5: 1867 - 1882

DOI: https://doi.org/10.1007/s11630-024-2035-8

Experimental Data-Driven Flow Field Prediction for Compressor Cascade based on Deep Learning and ℓ₁ Regularization

LIU Tantao ,
GAO Limin ,
LI Ruiyu

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1. School of Power and Energy, Northwestern Polytechnical University, Xi’an 710012, China
2. School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Online published: 2024-09-09

Supported by

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (No. 52106053, No. 92152301)

Copyright

Science Press, Institute of Engineering Thermophysics, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2024

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Abstract

For complex flows in compressors containing flow separations and adverse pressure gradients, the numerical simulation results based on Reynolds-averaged Navier-Stokes (RANS) models often deviate from experimental measurements more or less. To improve the prediction accuracy and reduce the difference between the RANS prediction results and experimental measurements, an experimental data-driven flow field prediction method based on deep learning and ℓ₁ regularization is proposed and applied to a compressor cascade flow field. The inlet boundary conditions and turbulence model parameters are calibrated to obtain the high-fidelity flow fields. The Saplart-Allmaras and SST turbulence models are used independently for mutual validation. The contributions of key modified parameters are also analyzed via sensitivity analysis. The results show that the prediction error can be reduced by nearly 70% based on the proposed algorithm. The flow fields predicted by the two calibrated turbulence models are almost the same and nearly independent of the turbulence models. The corrections of the inlet boundary conditions reduce the error in the first half of the chord. The turbulence model calibrations fix the overprediction of flow separation on the suction surface near the tail edge.

Key words： experimental data-driven; compressor cascade; deep learning; ?₁ regularization

Cite this article

LIU Tantao , GAO Limin , LI Ruiyu . Experimental Data-Driven Flow Field Prediction for Compressor Cascade based on Deep Learning and ℓ₁ Regularization[J]. Journal of Thermal Science, 2024 , 33(5) : 1867 -1882 . DOI: 10.1007/s11630-024-2035-8

References

[1] Ewald B., Wind tunnel wall correction. AGARD-AG-336, Neuilly-SurSeine, France, 1998.
[2] Xue X., Zhou X., Liu X., et al., Investigation on pitch-wise non-uniform and inflecting inlet flow of low-speed plane cascade. ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, South Korea, 2016, Paper No: GT2016-56934.
[3] Cai M., Gao L., Li H., et al., Flow quality improvement of the wind tunnel testing for a highly-loaded compressor cascade at high incidence. International Journal of Turbo & Jet-Engines, 2023, 40(s1): s87–s99. DOI: 10.1515/tjj-2021-0028
[4] Corriveau D., Sjolander S.A., Impact of flow quality in transonic cascade wind tunnels: measurements in an HP turbine cascade. 23rd Congress of International Council of the Aeronautical Sciences, Toronto, Canada, 2002, Paper: ICAS 2002-5.11.4.
[5] Wilcox D.C., Turbulence modeling for CFD, third ed., DCW Industries, 2006.
[6] Parish E.J., Duraisamy K., A paradigm for data-driven predictive modeling using field inversion and machine learning. Journal of Computational Physics, 2016, 305: 758–774.
[7] Li Z., Zhang H., Bailey S.C.C., et al., A data-driven adaptive Reynolds-averaged Navier-Stokes k-ω model for turbulent flow. Journal of Computational Physics, 2017, 345: 111–131.
[8] Duraisamy K., Iaccarino G., Xia H., Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 2019, 51(1): 357–377.
[9] Foures D.P.G., Dovetta N., Sipp D., et al., A data-assimilation method for Reynolds-averaged Navier-Stokes-driven mean flow reconstruction. Journal of Fluid Mechanics, 2014, 759: 404–431.
[10] Symon S., Dovetta N., McKeon B.J., et al., Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil. Experiments in Fluids, 2017, 58(5): 61.
[11] He C., Wang P, Liu Y., Data assimilation for turbulent mean flow and scalar fields with anisotropic formulation. Experiments in Fluids, 2021, 62(5): 117.
[12] Kato H., Obayashi S., Data assimilation for turbulent flows. 16th AIAA Non-Deterministic Approaches Conference, Maryland, USA, 2014, AIAA 2014-1177.
[13] Singh A.P., Medida S., Duraisamy K., Machine-learning- augmented predictive modeling of turbulent separated flows over air-foils. AIAA Journal, 2017, 55(7): 2215– 2227.
[14] He C., Liu Y., Gan L., A data assimilation model for turbulent flows using continuous adjoint formulation. Physics of Fluids, 2018, 30(10): 105108.
[15] Kato H., Ishiko K., Yoshizawa A., Optimization of parameter values in the turbulence model aided by data assimilation. AIAA Journal, 2016, 54(5): 1512–1523.
[16] Deng Z., He C., Liu Y., Deep neural network-based strategy for optimal sensor placement in data assimilation of turbulent flow. Physics of Fluids, 2021, 33(2): 025119.
[17] Deng Z., He C., Wen X., et al., Recovering turbulent flow field from local quantity measurement: Turbulence modeling using Ensemble-Kalman-filter-based data assimilation. Journal of Visualization, 2018, 21(6): 1043– 1063.
[18] Matsui K., Perez E., Kelly T.R., et al., Calibration of modified Spalart-Allmaras model parameters for linear compressor cascade corner flow. Journal of Thermal Science, 2022, 31(1): 163–172.
[19] Matsui K., Perez E., Kelly R.T., et al., Calibration of Spalart-Allmaras model for simulation of corner flow separation in linear compressor cascade. Journal of the Global Power and Propulsion Society, 2021, Special Issue: Data Driven Modelling and High-Fidelity Simulations, pp: 1–16. DOI: 10.33737/jgpps/135174
[20] Zhang K., Zhao Y., Wang Q., et al., Uncertainty analysis and calibration of SST turbulence model for free shear layer in cavity-ramp flow. Acta Astronautica, 2022, 192(3): 168–181.
[21] He X., Zhao F., Vahdati M., A turbo-oriented data-driven modification to the Spalart-Allmaras turbulence model. Journal of Turbomachinery, 2022, 144(12): 121007.
[22] Liu Y., Tang Y., Scillitoe A.D., et al., Modification of shear stress transport turbulence model using helicity for predicting corner separation flow in a linear compressor cascade. Journal of Turbomachinery, 2020, 142(2): 021004.
[23] Brunton S.L., Noack B.R., Koumoutsakos P., Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 2020, 52(1): 477–508.
[24] Zhou H.M., Yu K.T., Luo Q., et al., Design methods and strategies for forward and inverse problems of turbine blades based on machine learning. Journal of Thermal Science, 2022, 31(1): 82–95.
[25] Schmidt M., Lipson H., Distilling free-form natural laws from experimental data. Science, 2009, 324(5923): 81–85.
[26] Duraisamy K., Iaccarino G., Xiao H., Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 2019, 51(1): 357–377.
[27] Ling J., Kurzawski A., Templeton J., Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. Journal of Fluid Mechanics, 2016, 807: 155–166.
[28] Zhao Y., Akolekar H.D., Weatheritt J., et al., RANS turbulence model development using CFD-driven machine learning. Journal of Computational Physics, 2020, 411: 109413.
[29] Mckay M.D., Beckman R.J., Conover W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 2000, 42(1): 55–61.
[30] Loh W.L., On Latin hypercube sampling. The Annals of Statistics, 1996, 24(5): 2058–2080.
[31] Herbrich R., Graepel T., Sparse modeling theory, algorithm, and applications. CRC Press, New York, 2015.
[32] Tibshirani R., Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B, 1996, 58(1): 267–288.
[33] Zou H., The adaptive LASSO and its oracle properties. Journal of the American Statistical Association, 2006, 101(476): 1418–1429.
[34] Kingma D.P., Ba J., Adam: A method for stochastic optimization. 3rd International Conference for Learning Representations, San Diego, USA, 2015. DOI: 10.48550/arXiv.1412.6980
[35] Steinert W., Eisenberg B., Starken H., Design and testing of a controlled diffusion airfoil cascade for industrial axial flow com-pressor application. Journal of Turbomachinery, 1991, 113(4): 583–590.
[36] Dixon S.L., Hall C.A., Fluid mechanics and thermodynamics of turbomachinery, 7th ed. Butterworth-Heinemann, Oxford, 2014.
[37] Shi H., Liu B., Yu X., Polynomial-based continuous- curvature leading edge design method and its application. Journal of Aerospace Power, 2020, 35(2): 397–409.
[38] Kong Q., Du X., Qiang X., et al., Compressor airfoil optimization based on camber curvature control. Journal of Propulsion Technology, 2020, 41(8): 1710–1747.
[39] Wang Y., Wu Y., Zong H., et al., A parametric study on control authority and vorticity transport in a compressor airfoil with plasma actuation at low Reynolds number. Physics of Fluids, 2023, 35(3): 036117.
[40] Wang Y., Zhang H., Wu Y., et al., Compressor airfoil separation control using nanosecond plasma actuation at low Reynolds number. AIAA Journal, 2022, 60(2): 1171–1185.
[41] Fei T., Ji L., Application of new empirical models based on mathematical statistics in the through-flow analysis. Journal of Thermal Science, 2021, 30(6): 2087–2098.
[42] Belligoli Z., Dwight R.P., Eitelberg G., Nonlinear wind-tunnel wall-interference corrections using data assimilation. AIAA Journal, 2021, 59(2): 596–606.
[43] Tyler W.D., Review of transonic wall interference corrections and considerations for development. AIAA Aviation 2019 Forum, Dallas, USA, 2019, AIAA 2019-3094.

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