A Review of Simulations and Machine Learning Approaches for Flow Separation Analysis
Abstract
:1. Introduction
2. Mechanisms and Impacts of Flow Separation
2.1. 2D Flow Separation
2.2. 3D Flow Separation
2.3. Discussion
3. Simulations for Flow Separation
3.1. RANS
Reference | Geometry | Key Parameters | Methods | Key Findings | Limitations |
---|---|---|---|---|---|
Langtry et al. [30] | S809 airfoil (21% thickness) | Re = , AoA = 1°– 20°. FSTI = 0.2% | SST with transition model | Improved prediction of separation bubbles and torque; good prediction of lift/drag at moderate AoA | Struggles with massively separated flows; requires empirical correlations |
Wolgemuth & Walters [31] | NACA0012 airfoil at varying AoA | Re = – , AoA = 0°– 20°, Tu = 0.01–2% | Transition-sensitive | Good prediction of separation bubbles | Overpredicts stall angles at low Re; requires unsteady solvers for convergence |
Furst et al. [32] | Flat plate; two NACA0012 airfoils in tandem; VKI turbine blade | Re = , Tu = 0.3–9.43% | Algebraic model () with intermittency vs. model | Both predict bypass/natural transition; is better for separated flows | Grid dependency near walls; algebraic model struggles with 3D effects |
Menter et al. [33] | Flat plates (T3 series); Pak-B turbine blader; T106 cascade; V103 compressor | Re = – , Tu = 0.03–8% | One equation intermittency () model coupled with SST | Galilean invariant; captures the separation bubbles and reattachment | Limited calibration for crossflow transition; requires fine grids for separation bubbles |
3.2. LES
3.3. DNS
3.4. Hybrid Modeling Techniques
3.4.1. Hybrid CFD Methods
3.4.2. Incorporated High-Order Methods in CFD Simulations
3.4.3. ROM
3.5. LBM
3.6. Further Discussion
4. ML for Flow Separation
4.1. ML Enhancement of Turbulent Modelling Closure
4.2. ML-Enhanced ROMs
4.3. CNNs
4.4. GNNs
4.5. PINNs
4.6. Data Assimilation Enhanced ML
5. Discussions and Future Trends
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Roshko, A. Perspectives on Bluff Body Aerodynamics. J. Wind. Eng. Ind. Aerodyn. 1992, 49, 79–100. [Google Scholar] [CrossRef]
- Rizzi, A.; Luckring, M.J. Historical Development and Use of CFD for Separated Flow Simulations Relevant to Military Aircraft. Aerosp. Sci. Technol. 2021, 117, 106940. [Google Scholar] [CrossRef]
- Gursul, I.; Wang, Z. Flow Control of Tip/Edge Vortices. AIAA J. 2018, 56, 1731–1749. [Google Scholar] [CrossRef]
- Li, Y.; Chang, J.; Kong, C.; Bao, W. Recent Progress of Machine Learning in Flow Modeling and Active Flow Control. Chin. J. Aeronaut. 2022, 35, 14–44. [Google Scholar] [CrossRef]
- Sun, X.; Xu, Y.; Huang, D. Numerical Simulation and Research on Improving Aerodynamic Performance of Vertical Axis Wind Turbine by Co-flow Jet. J. Renew. Sustain. Energy 2019, 11, 013303. [Google Scholar] [CrossRef]
- Heinz, S. The Potential of Machine Learning Methods for Separated Turbulent Flow Simulations: Classical Versus Dynamic Methods. Fluids 2024, 9, 278. [Google Scholar] [CrossRef]
- Mokhtarpoor, R.; Heinz, S.; Stoellinger, M. Dynamic Unified RANS-LES Simulations of High Re Separated Flows. Phys. Fluids 2016, 28, 095101. [Google Scholar] [CrossRef]
- Zhao, Z.; Wang, J.; Gong, Y.; Xu, H. Large Eddy Simulation of Flow and Separation Bubbles Around a Circular Cylinder from Sub-critical to Super-critical Reynolds Numbers. J. Mar. Sci. Appl. 2023, 22, 219–231. [Google Scholar] [CrossRef]
- Ohlsson, J.; Schlatter, P.; Fischer, F.P.; Henningson, S.D. Direct Numerical Simulation of Separated Flow in a Three-dimensional Diffuser. J. Fluid Mech. 2010, 650, 307–318. [Google Scholar] [CrossRef]
- Brunton, S.L.; Noack, B.R.; Koumoutsakos, P. Machine Learning for Fluid Mechanics. Annu. Rev. Fluid Mech. 2020, 52, 477–508. [Google Scholar] [CrossRef]
- Jin, X.; Cai, S.; Li, H.; Karniadakis, G.E. NSFnets (Navier-Stokes flow nets): Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations. J. Comput. Phys. 2021, 426, 109951. [Google Scholar] [CrossRef]
- Greenblatt, D.; Wygnanski, J.I. The Control of Fow Separation by Periodic Excitation. Prog. Aerosp. Sci. 2000, 36, 487–545. [Google Scholar] [CrossRef]
- Chang, P.K. Introduction to the Problems of Flow Separation. In Separation of Flow; Pergamon Press: Oxford, UK, 1970; pp. 3–35. [Google Scholar]
- Schlichting, H.; Gersten, K. Boundary Layer Theory. In Fundamentals of Boundary—Layer Theory; Springer: Berlin, Germany, 2017; pp. 29–49. [Google Scholar]
- Bezzola, A. Optimal Bass Reflex Loudspeaker Port Design. In Proceedings of the COMSOL Conference 2019, Boston, MA, USA, 2–4 October 2019. [Google Scholar]
- Van Dyke, M. An Album of Fluid Motion; The Parabolic Press: Stanford, CA, USA, 1982. [Google Scholar]
- Wikipedia Contributors. Flow Separation. Available online: https://en.wikipedia.org/wiki/Flow_separation (accessed on 3 March 2025).
- Pope, S.B. Wall Flows. In Turbulent Flows; Cambridge University Press: Cambridge, UK, 2000; pp. 264–332. [Google Scholar]
- Graham, M.; Li, J. Vortex Shedding and Induced Forces in Unsteady Flow. Aeronaut. J. 2024, 128, 2149–2190. [Google Scholar] [CrossRef]
- Leibovich, S.; Luckring, J.M. The Structure of Vortex Breakdown. Annu. Rev. Fluid Mech. 1978, 10, 221–246. [Google Scholar] [CrossRef]
- Wang, S.; He, G.; Liu, T. Estimating lift from wake velocity data in flapping flight. J. Fluid Mech. 2019, 868, 501–537. [Google Scholar] [CrossRef]
- Li, J.; Zhao, X.; Graham, M. Vortex force maps for three-dimensional unsteady flows with application to a delta wing. J. Fluid Mech. 2020, 900, A36. [Google Scholar] [CrossRef]
- Simpson, R.L. Junction Flows. Annu. Rev. Fluid Mech. 2001, 33, 415–443. [Google Scholar] [CrossRef]
- Délery, J. Separation in Three-Dimensional Flow: Critical Points, Separation Lines, and Vortices. Onera—The French Aerospace Lab. 2011. Available online: https://www.onera.fr/sites/default/files/ressources_documentaires/cours-exposes-conf/onera-3d-separation-jean-delery-2011-1a.pdf (accessed on 2 January 2025).
- Durbin, P.A. Some Recent Developments in Turbulence Closure Modeling. Annu. Rev. 2018, 50, 77–103. [Google Scholar] [CrossRef]
- Chaouat, B. The State of the Art of Hybrid RANS/LES Modeling for the Simulation of Turbulent Flows. Flow Turbul. Combust 2017, 99, 279–327. [Google Scholar] [CrossRef]
- Duraisamy, K.; Iaccarino, G.; Xiao, H. Turbulence Modeling in the Age of Data. Annu. Rev. Fluid Mech. 2019, 51, 357–377. [Google Scholar] [CrossRef]
- Peng, S.H.; Eliasson, P. Examination of the Shear Stress Transport Assumption with a Low-Reynolds Number k–ω Model for Aerodynamic Flows. In Proceedings of the 37th AIAA Fluid Dynamics Conference and Exhibit, Miami, FL, USA, 25–28 June 2007. AIAA 2007-3864. [Google Scholar]
- Liu, Y.; Li, P.; Jiang, K. Comparative Assessment of Transitional Turbulence Models for Airfoil Aerodynamics in the Low Reynolds Number Range. J. Wind. Eng. Ind. Aerodyn. 2021, 217, 104726. [Google Scholar] [CrossRef]
- Langtry, R.B.; Gola, J.; Menter, F.R. A One-Equation Local Correlation-Based Transition Model. In Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 9–12 January 2006. AIAA 2006-395. [Google Scholar]
- Wolgemuth, N.M.; Walters, D.K. CFD Prediction of Boundary Layer Transition And Separation on an Airfoil at Varying Angle of Attack. In Proceedings of the EDSM2007 5th Joint ASME/JSME Fluids Engineering Conference, San Diego, CA, USA, 30 July–2 August 2007. FEDSM2007-37111. [Google Scholar]
- Fürst, J.; Příhoda, J.; Straka, P. Numerical Simulation of Transitional Flows. Computing 2013, 95, S163–S182. [Google Scholar] [CrossRef]
- Menter, F.R.; Smirnov, P.E.; Liu, T.; Avancha, R. A One-Equation Local Correlation-Based Transition Model. Flow Turbul. Combust 2015, 95, 583–619. [Google Scholar] [CrossRef]
- Xia, X.; You, Z.; Wang, Z. The three types of turbulence models and stability numerical simulation studies for cylindrical flow. Hydro-Sci. Eng. 2024, 5, 84–94. [Google Scholar]
- Lysenko, D.A.; Ertesvåg, I.S.; Rian, K.E. Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 3900 Using the OpenFOAM Toolbox. Flow Turbul. Combust 2012, 89, 491–518. [Google Scholar] [CrossRef]
- Zhang, D.; Cadel, D.R.; Paterson, E.G.; Lowe, K.T. Hybrid RANS/LES Turbulence Model Applied to a Transitional Unsteady Boundary Layer on Wind Turbine Airfoil. Fluids 2019, 4, 128. [Google Scholar] [CrossRef]
- Li, J.; Wang, B.; Qiu, X.; Wu, J.; Zhou, Q.; Fu, S.; Liu, Y. Three-dimensional vortex dynamics and transitional flow induced by a circular cylinder placed near a plane wall with small gap ratios. J. Fluid Mech. 2022, 953, A2. [Google Scholar] [CrossRef]
- Guo, H.; Li, G.; Zou, Z. Numerical Simulation of the Flow around NACA0018 Airfoil at High Incidences by Using RANS and DES Methods. J. Mar. Sci. Eng. 2022, 10, 847. [Google Scholar] [CrossRef]
- Arias-Ramírez, W.; Oberoi, N.; Larsson, J. Multifidelity Approach to Sensitivity Estimation in Large-Eddy Simulation. AIAA J. 2023, 61, 3485–3495. [Google Scholar] [CrossRef]
- Sa, J.H.; Park, S.H.; Kim, C.J.; Park, J.K. Low-Reynolds number flow computation for eppler 387 wing using hybrid DES/transition model. J. Mech. Sci. Technol. 2015, 29, 1837–1847. [Google Scholar] [CrossRef]
- Beck, A.D.; Bolemann, T.; Flad, D.; Frank, H.; Gassner, G.J.; Hindenlang, F.; Munz, C. High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. J. Int. J. Numer. Meth. Fluids. 2014, 76, 522–548. [Google Scholar] [CrossRef]
- Zhao, M. A Review of Recent Studies on the Control of Vortex-induced Vibration of Circular Cylinders. Ocean. Eng. 2023, 285, 115389. [Google Scholar] [CrossRef]
- Liang, Z.; Wang, J.; Jiang, B.; Zhou, H.; Yang, W.; Ling, J. Large-Eddy Simulation of Flow Separation Control in Low-Speed Diffuser Cascade with Splitter Blades. Processes 2023, 11, 3249. [Google Scholar] [CrossRef]
- Piomelli, U.; Balaras, E. Wall-layer Models for Large-Eddy Simulations. Annu. Rev. Fluid Mech. 2002, 34, 349–374. [Google Scholar] [CrossRef]
- Meng, T.; Li, X.; Zhou, L.; Zhu, H.; Li, J.; Ji, L. Large Eddy Simulation and Combined Control of Corner Separation in a Compressor Cascade. Phys. Fluids 2022, 34, 075113. [Google Scholar] [CrossRef]
- Kawai, S.; Larsson, J. Wall-modeling in Large Eddy Simulation: Length Scales, Grid Resolution, and Accuracy. Phys. Fluids 2012, 24, 015105. [Google Scholar] [CrossRef]
- Malik, R.M.; Uzun, A. DNS of Accelerating and Decelerating Turbulent Flow. In Proceedings of the AIAA Aviation 2020 Forum, Virtual, 19 August 2020. [Google Scholar]
- Jones, L.E.; Sandberg, R.D.; Sandham, N.D. Direct Numerical Simulations of Forced and Unforced Separation Bubbles on an Airfoil at Incidence. J. Fluid Mech. 2008, 602, 175–207. [Google Scholar] [CrossRef]
- Shahab, M.F.; Omidyeganeh, M.; Pinelli, A. DNS of Separated Low-Re Flow Around a Cambered Aerofoil. In Direct and Large-Eddy Simulation XI; Springer: Berlin/Heidelberg, Germany, 2019; pp. 373–380. [Google Scholar]
- Spalart, R.P.; Watmuff, H.J. Experimental and Numerical Study of a Turbulent Boundary Layer with Pressure Gradients. J. Fluid Mech. 1993, 249, 337–371. [Google Scholar] [CrossRef]
- Wu, X.; Moin, P. Direct Numerical Simulation of Turbulence in A Nominally Zero-pressure-gradient Flat-plate Boundary Layer. J. Fluid Mech. 2009, 630, 5–41. [Google Scholar] [CrossRef]
- Coleman, G.N.; Sandberg, R.D. A Primer on Direct Numerical Simulation of Turbulence- Methods, Procedures and Guidelines; Technical Report AFM-09/01b; University of Southampton: Southampton, UK, 2010. [Google Scholar]
- Zhang, W.; Samtaney, R. Assessment of Spanwise Domain Size Effect on the Transitional Flow Past an Airfoil. Comput. Fluids 2016, 124, 39–53. [Google Scholar] [CrossRef]
- Cummings, M.R.; Squires, K.; Spalart, P. Multidisciplinary Applications of Detached-Eddy Simulation to Separated Flows at High Reynolds Numbers. In Proceedings of the 2004 Users Group Conference, Williamsburg, VA, USA, 7–11 June 2004; pp. 103–111. [Google Scholar]
- Spalart, P.R.; Deck, S.; Shur, M.L.; Squires, K.D.; Strelets, M.K.; Travin, A. A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities. Theor. Comput. Fluid Dyn. 2006, 20, 181–195. [Google Scholar] [CrossRef]
- Menter, F.R. Stress-Blended Eddy Simulation (SBES)—A New Paradigm in Hybrid RANS-LES Modeling. In Proceedings of the 6th Symposium on Hybrid RANS-LES Methods, Strasbourg, France, 20–21 November 2018; pp. 27–37. [Google Scholar]
- Menter, F.R.; Egorov, Y. The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description. Flow Turbul. Combust 2010, 85, 113–138. [Google Scholar] [CrossRef]
- Moller, F.M.; Tucker, P.G.; Wang, Z.; Morsbach, C.; Bergmann, M. On the Prediction of Separation-Induced Transition by Coupling Delayed Detached-Eddy Simulation with γ-Transition Model. In Proceedings of the 15th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics, Budapest, Hungary, 24–28 April 2023. [Google Scholar]
- Sandrin, S.; Mazzei, L.; Soghe, R.D.; Fontaneto, F. Computational Fluid Dynamics Prediction of External Thermal Loads on Film-Cooled Gas Turbine Vanes: A Validation of Reynolds-Averaged Navier–Stokes Transition Models and Scale-Resolving Simulations for the VKI LS-94 Test Case. Fluids 2024, 9, 91. [Google Scholar] [CrossRef]
- Rezaeiha, A.; Montazeri, H.; Blocken, B. CFD Analysis of Dynamic Stall on Vertical Axis Wind Turbines using Scale Adaptive Simulation (SAS): Comparison against URANS and Hybrid RANS/ LES. Energy Convers. Manag. 2019, 196, 1281–1298. [Google Scholar] [CrossRef]
- Weihing, P.; Letzgus, T.; Kramer, E. Development of Alternative Shielding Functions for Detached-Eddy Simulations. In Progress in Hybrid RANS-LES Modelling, Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Hoarau, Y., Peng, S.H., Schwamborn, D., Revell, A., Mockett, C., Eds.; Springer: Cham, Switzerland, 2019; pp. 109–118. [Google Scholar]
- Haering, W.S.; Oliver, A.T.; Moser, D.R. Active Model Split Hybrid RANS/LES. Phys. Rev. Fluids 2022, 7, 014603. [Google Scholar] [CrossRef]
- Wang, Z.J.; Fidkowski, K.; Abgrall, R.; Bassi, F.; Caraeni, D.; Cary, A.; Deconinck, H.; Hartmann, R.; Hillewaert, K.; Huynh, H.T.; et al. High-order CFD Methods: Current Status and Perspective. Int. J. Numer. Methods Fluids 2013, 72, 811–845. [Google Scholar] [CrossRef]
- Wang, S.; Dong, Y.; Deng, X. High-Order Simulation of Aeronautical Separated Flows with a Reynold Stress Model. J. Aircr. 2018, 55, 1177–1190. [Google Scholar] [CrossRef]
- Krank, B.; Kronbichler, M.; Wall, W.A. Wall Modeling via Function Enrichment Within a High-order DG Method for RANS Simulations of Incompressible flow. Int. J. Numer. Methods Fluids, 2024; accepted. [Google Scholar] [CrossRef]
- Ding, Q.; Zhao, M.; Xian, J.; Chen, Y.; Hao, S.; Cheng, C.; Li, X.; Liu, Z. Large Eddy Simulation Based on An Improved High-precision Interior Penalty Discontinuous Galerkin Method: Flow Past Cylinders and Airfoils. Acta Mech. 2024, 235, 6599–6623. [Google Scholar] [CrossRef]
- Brill, S.R.; Pal, P.; Ameen, M.; Xu, C.; Ihme, M. An Enrichment Wall Modeling Framework for Spectral Element Methods. Phys. Fluids 2024, 36, 125169. [Google Scholar] [CrossRef]
- Gassner, G.J.; Beck, A.D. On the Accuracy of High-order Discretizations for Underresolved Turbulence Simulations. Theor. Comput. Fluid Dyn. 2013, 27, 221–237. [Google Scholar] [CrossRef]
- Lucia, D.J.; Beran, P.S.; Silva, W.A. Reduced-order Modelling: New Approaches for Computational Physics. Prog. Aerosp. Sci. 2004, 40, 51–117. [Google Scholar] [CrossRef]
- Xu, Z.; Cao, N.Y.; Li, C.; Luo, Y.; Su, E.; Wang, W.; Tang, W.; Yao, Z.; Wang, Z.L.A. Digital Mapping of Surface Turbulence Status and Aerodynamic Stall on Wings of a Flying aircraft. Nat. Commun. 2023, 14, 2792. [Google Scholar] [CrossRef]
- Berkooz, G.; Holmes, P.; Lumley, J.L. The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows. Annu. Rev. Fluid Mech. 1993, 25, 539–575. [Google Scholar] [CrossRef]
- Sajadmanesh, S.M.; Mojaddam, M.; Mohseni, A.; Nikparto, A. Numerical Identification of Separation Bubble in an Ultra-high-lift Turbine Cascade Using URANS Simulation and Proper Orthogonal Decomposition. Aerosp. Sci. Technol. 2019, 93, 105329. [Google Scholar] [CrossRef]
- Tong, F.; Sun, D.; Li, X. Direct Numerical Simulation of Impinging Shock Wave and Turbulent Boundary Layer Interaction over a Wavy-wall. Chin. J. Aeronaut. 2021, 34, 350–363. [Google Scholar] [CrossRef]
- Zhao, M.; Zhao, Y.; Liu, Z. Dynamic Mode Decomposition Analysis of Flow Characteristics of an Airfoil with Leading Edge Protuberances. Aerosp. Sci. Technol. 2020, 98, 105684. [Google Scholar] [CrossRef]
- Taira, K.; Hemati, M.S.; Brunton, S.L.; Sun, Y.; Duraisamy, K.; Bagheri, S.; Dawson, S.T.M.; Yeh, C. Modal Analysis of Fluid Flows: Applications and Outlook. AIAA J. 2020, 58, 998–1022. [Google Scholar] [CrossRef]
- Chen, S.; Doolen, G.D. Lattice Boltzmann Method for Fluid Flows. Annu. Rev. 1998, 30, 329–364. [Google Scholar] [CrossRef]
- Ribeiro, R.L.; Dantas, C.; Wolf, W. Intermittency of a Transitional Airfoil Flow with Laminar Separation Bubble Solved by the Lattice-Boltzmann Method. Aerosp. Sci. Technol. 2025, 158, 109907. [Google Scholar] [CrossRef]
- Premnath, K.N.; Pattison, M.J.; Banerjee, S. An Investigation of the Lattice Boltzmann Method for Large Eddy Simulation of Complex Turbulent Separated Flow. J. Fluids Eng. 2013, 135, 051401. [Google Scholar] [CrossRef]
- Zhu, Y.; Zhao, S.; Zhou, Y.; Liang, H.; Bian, X. An unstructured adaptive mesh refinement for steady flows based on physics-informed neural networks. arXiv 2024, arXiv:2411.19200. [Google Scholar]
- Wan, Z.; Zhang, W. A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. Phys. Fluids 2023, 35, 025124. [Google Scholar]
- Xu, Z.; Maria, A.; Chelli, K.; Premare, T.D.; Bilbao, X.; Petit, C.; Zoumboulis-Airey, R.; Moulitsas, I.; Teschner, T.; Asif, S.; et al. Vortex and Core Detection using Computer Vision and Machine Learning Methods. Eur. J. Comput. Mech. 2023, 32, 467–494. [Google Scholar] [CrossRef]
- Hu, L.; Wang, W.; Xiang, Y.; Zhang, J. Flow Field Reconstructions with GANs Based on Radial Basis Functions. IEEE Trans. Aerosp. Electron. Syst. 2022, 58, 3460–3476. [Google Scholar] [CrossRef]
- Li, N.; Liu, Y.; Gong, G.; Zhao, L.; Yuan, H. A generative deep learning approach for real-time prediction of hypersonic vehicles in fluid-thermo-structural coupling fields. Aerosp. Sci. Technol. 2023, 139, 108398. [Google Scholar] [CrossRef]
- Guéniat, F.; Mathelin, L.; Hussaini, M.Y. A Statistical Learning Strategy for Closed-Loop Control of Fluid Flows. Theor. Comput. Fluid Dyn. 2016, 30, 497–510. [Google Scholar] [CrossRef]
- Zhu, L.; Zhang, W.; Kou, J.; Liu, Y. Machine Learning Methods for Turbulence Modeling in Subsonic Flows Around Airfoils. Phys. Fluids 2019, 31, 015105. [Google Scholar] [CrossRef]
- Vinuesa, R.; Brunton, S.L. Enhancing computational fluid dynamics with machine learning. Nat. Comput. Sci. 2022, 2, 358–366. [Google Scholar] [CrossRef]
- Areias, P.; Correia, R.; Melicio, R. Airfoil Analysis and Optimization Using a Petrov–Galerkin Finite Element and Machine Learning. Aerospace 2023, 10, 638. [Google Scholar] [CrossRef]
- Singh, A.P.; Medida, S.; Duraisamy, K. Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils. AIAA J. 2017, 55, 2215–2227. [Google Scholar] [CrossRef]
- Ling, J.; Kurzawski, A.; Templeton, J. Reynolds Averaged Turbulence Modelling Using Deep Neural Networks with Embedded Invariance. J. Fluid Mech. 2016, 807, 155–166. [Google Scholar] [CrossRef]
- Zhang, B. Airfoil-based Convolutional Autoencoder and Long Short-term Memory Neural Network for Predicting Coherent Structures Evolution Around an Airfoil. Comput. Fluids 2023, 258, 105883. [Google Scholar] [CrossRef]
- Liu, Z.; Han, R.; Zhang, M.; Zhang, Y.; Zhou, H.; Wang, G.; Chen, G. An Enhanced Hybrid Deep Neural Network Reduced-order Model for Transonic Buffet Flow Prediction. Aerosp. Sci. Technol. 2022, 126, 107636. [Google Scholar] [CrossRef]
- Jia, X.; Li, C.; Ji, W.; Gong, C. A Hybrid Reduced-order Model Combing Deep Learning for Unsteady Flow. Phys. Fluids 2022, 34, 097112. [Google Scholar] [CrossRef]
- Phung, V.H.; Rhee, E.J. A High-Accuracy Model Average Ensemble of Convolutional Neural Networks for Classification of Cloud Image Patches on Small Datasets. Appl. Sci. 2019, 34, 4500. [Google Scholar] [CrossRef]
- Bhatnagar, S.; Afshar, Y.; Pan, S.; Duraisamy, K.; Kaushik, S. Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks. Comput. Mech. 2019, 64, 525–545. [Google Scholar] [CrossRef]
- Chen, L.; Thuerey, N. Deep learning-based predictive modeling of transonic flow over an airfoil. Phys. Fluids 2024, 36, 127106. [Google Scholar] [CrossRef]
- Han, R.; Wang, Y.; Zhang, Y.; Chen, G. A novel spatial-temporal prediction method for unsteady wake flows based on hybrid deep neural network. Phys. Fluids 2019, 31, 127101. [Google Scholar] [CrossRef]
- Sekar, V.; Jiang, Q.; Shu, C.; Khoo, B.C. Fast Flow Field Prediction over Airfoils Using Deep Learning Approach. Phys. Fluids 2019, 31, 057103. [Google Scholar] [CrossRef]
- Duru, C.; Alemdar, H.; Baran, O.U. A Deep Learning Approach for the Transonic Flow Field Predictions Around Airfoils. Comput. Fluids 2022, 236, 105312. [Google Scholar] [CrossRef]
- Lee, S.; You, D. Data-Driven Prediction of Unsteady Flow Over a Circular Cylinder Using Deep Learning. J. Fluid Mech. 2019, 879, 217–254. [Google Scholar] [CrossRef]
- Ogoke, F.; Meidani, K.; Hashemi, A.; Farimani, B. Graph Convolutional Networks Applied to Unstructured Flow Field Data. Mach. Learn. Sci. Technol. 2021, 2, 045020. [Google Scholar] [CrossRef]
- He, X.; Wang, Y.; Li, J. Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information Using Graph Neural Networks. Phys. Fluids 2022, 34, 087114. [Google Scholar] [CrossRef]
- Massegur, D.; Da, R.A. Graph convolutional multi-mesh autoencoder for steady transonic aircraft aerodynamics. Mach. Learn. Sci. Technol. 2024, 5, 025006. [Google Scholar] [CrossRef]
- Hines, D.; Philipp, B. Graph neural networks for the prediction of aircraft surface pressure distributions. Aerosp. Sci. Technol. 2023, 137, 108268. [Google Scholar] [CrossRef]
- Yiren, S.; Alonso, J. Performance Evaluation of a Graph Neural Network-Augmented Multi-Fidelity Workflow for Predicting Aerodynamic Coefficients on Delta Wings at Low Speed. In Proceedings of the AIAA SCITECH 2025 Forum, Orlando, FL, USA, 6–10 January 2025; pp. 2025–2360. [Google Scholar]
- Raissi, M.; Wang, Z.; Triantafyllou, M.S.; Karniadakis, G.E. Deep learning of vortex-induced vibrations. J. Fluid Mech 2019, 861, 119–137. [Google Scholar] [CrossRef]
- Ren, Z.; Hu, P.; Su, H.; Zhang, F.; Yu, H. Physics-Informed Neural Networks for Transonic Flow Around a Cylinder with High Reynolds Number. Phys. Fluids 2024, 36, 036129. [Google Scholar] [CrossRef]
- Mons, V.; Chassaing, J.C.; Gomez, T.; Sagaut, P. Reconstruction of Unsteady Viscous Flows Using Data Assimilation Schemes. J. Comput. Phys. 2016, 316, 255–280. [Google Scholar] [CrossRef]
- Maulik, R.; Egele, R.; Raghavan, K.; Balaprakash, P. Quantifying Uncertainty for Deep Learning Based Forecasting and Flow-reconstruction Using Neural Architecture Search Ensembles. Phys. D 2023, 454, 133852. [Google Scholar] [CrossRef]
Category | Method | Key Parameters | Advantages | Limitations |
---|---|---|---|---|
Traditional | RANS | NACA0012, NACA4415 Airfoil , [29] | Significantly reduced computational cost. | Unable to accurately capture transient turbulent structures; limited predictive capability for separated flows. |
LES | NACA65-010, [43]; Blade NACA65 Airfoil, , [45] | Captures transient flow characteristics at high Re numbers, providing superior predictive capability for separated flows compared to RANS. | Significantly higher computational cost than RANS especially under conditions of high Re or complex geometries; requires high grid resolution near walls. | |
DNS | NACA0012, NACA65(12)10 , [48] | Resolves all scales of turbulent structures, offering the highest accuracy. | Requires extremely high grid resolution and fine time step; computational cost increases exponentially with Re. | |
Hybrid CFD | Circular cylinder, Airfoil, ; [55,59,60]; | Balances computational cost with accuracy, enabling simulations of high Re at complex geometries. | Low accuracy with strong interactions between turbulence scales; smooth transition between RANS and LES regions. | |
High-Order | NACA0012 , [63] | High fidelity in resolving
separation dynamics and complex flow features. | Heavy dependence on turbulence modelling; high computational cost and time. | |
ROM | Cascade, , [72]; NACA0012 Airfoil, , [74]; | Significant cost reduction due to essential flow physics preservation compared to traditional CFD methods. | Reliance on data quality and selected mode for accuracy. | |
LBM | NACA0012 Airfoil , [77] | Parallel efficiency; suitable for complex geometries and multiphase. | Challenges in handling high Re; compressibility constraints; associated computational costs. | |
Machine Learning | ML-Enhanced Turbulent Modelling | Airfoils, [87,88] [89] | Improved accuracy; limited training data; must deal with high Re. | Limited model generality; physical constraints and uncertainties; challenges in model interpretability; low adaptability. |
ML-Enhanced ROMs | Cylinder and airfoils [90,91,92] | Improved accuracy with low computational cost. | Error accumulation; limited universality; extended training time; limited performance for high-Re turbulent flows. | |
CNNs | Airfoils, Cylinder [94,95,96,97,98,99] | High accuracy; some generalization ability; reduce computational cost. | Limited by the quality and quantity of training data; difficulty in accurately predicting some complex flow phenomena such as small-scale vortical structures. | |
GNNs | Cylinder, airfoils, aircraft, delta wings [100,101,102,103,104], , | Handle
unstructured data; improve accuracy; good generalization ability. | Low adaptability to complex geometries and flow conditions; greatly rely on data quality and quantity. | |
PINNs | Cylinder [101,105,106] | High efficiency with low costs; integrate physical laws; efficient data utilization. | Challenges in high-Re turbulence and unsteady cases. | |
Data Assimilation | Cylinder, [107] | Method innovation; relevance to practical applications. | Statistical dependence issues; computational efficiency and scalability. |
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Hao, X.; He, X.; Zhang, Z.; Li, J. A Review of Simulations and Machine Learning Approaches for Flow Separation Analysis. Aerospace 2025, 12, 238. https://doi.org/10.3390/aerospace12030238
Hao X, He X, Zhang Z, Li J. A Review of Simulations and Machine Learning Approaches for Flow Separation Analysis. Aerospace. 2025; 12(3):238. https://doi.org/10.3390/aerospace12030238
Chicago/Turabian StyleHao, Xueru, Xiaodong He, Zhan Zhang, and Juan Li. 2025. "A Review of Simulations and Machine Learning Approaches for Flow Separation Analysis" Aerospace 12, no. 3: 238. https://doi.org/10.3390/aerospace12030238
APA StyleHao, X., He, X., Zhang, Z., & Li, J. (2025). A Review of Simulations and Machine Learning Approaches for Flow Separation Analysis. Aerospace, 12(3), 238. https://doi.org/10.3390/aerospace12030238