Hostname: page-component-5db58dd55d-mhzq2 Total loading time: 0 Render date: 2026-06-10T10:33:10.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Jet mixing enhancement with Bayesian optimization, deep learning and persistent data topology

Published online by Cambridge University Press:  20 August 2024

Yiqing Li Open the ORCID record for Yiqing Li [Opens in a new window] ,
Bernd R. Noack Open the ORCID record for Bernd R. Noack [Opens in a new window] ,
Tianyu Wang Open the ORCID record for Tianyu Wang [Opens in a new window] ,
Guy Y. Cornejo Maceda Open the ORCID record for Guy Y. Cornejo Maceda [Opens in a new window] ,
Ethan Pickering Open the ORCID record for Ethan Pickering [Opens in a new window] ,
Tamir Shaqarin Open the ORCID record for Tamir Shaqarin [Opens in a new window]  and
Artur Tyliszczak Open the ORCID record for Artur Tyliszczak [Opens in a new window]
Yiqing Li
Affiliation:
Chair of Artificial Intelligence and Aerodynamics, School of Mechanical Engineering and Automation, Harbin Institute of Technology, 518055 Shenzhen, PR China
Bernd R. Noack*
Affiliation:
Chair of Artificial Intelligence and Aerodynamics, School of Mechanical Engineering and Automation, Harbin Institute of Technology, 518055 Shenzhen, PR China Guangdong Provincial Key Laboratory of Intelligent Morphing Mechanisms and Adaptive Robotics, Harbin Institute of Technology, 518055 Shenzhen, PR China
Tianyu Wang
Affiliation:
Chair of Artificial Intelligence and Aerodynamics, School of Mechanical Engineering and Automation, Harbin Institute of Technology, 518055 Shenzhen, PR China
Guy Y. Cornejo Maceda*
Affiliation:
Chair of Artificial Intelligence and Aerodynamics, School of Mechanical Engineering and Automation, Harbin Institute of Technology, 518055 Shenzhen, PR China
Ethan Pickering
Affiliation:
Independent Scholar
Tamir Shaqarin
Affiliation:
Department of Mechanical Engineering, Tafila Technical University, 66110 Tafila, Jordan
Artur Tyliszczak
Affiliation:
Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, 42-201 Czestochowa, Poland
*
†Email addresses for correspondence: bernd.noack@hit.edu.cn, yoslan@hit.edu.cn
†Email addresses for correspondence: bernd.noack@hit.edu.cn, yoslan@hit.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We optimize jet mixing using large eddy simulations (LES) at a Reynolds number of $3000$. Key methodological enablers consist of Bayesian optimization, a surrogate model enhanced by deep learning and persistent data topology for physical interpretation. The mixing performance is characterized by an equivalent jet radius ($R_{eq}$) derived from the streamwise velocity in a plane located $8$ diameters downstream. The optimization is performed in a 22-dimensional actuation space that comprises most known excitations. This search space parameterizes the distributed actuation imposed on the bulk flow and at the periphery of the nozzle in the streamwise and radial directions. The momentum flux measures the energy input of the actuation. The optimization quadruples the jet radius $R_{eq}$ with a $7$-armed blooming jet after around $570$ evaluations. The control input requires $2\,\%$ momentum flux of the main flow, which is one order of magnitude lower than an ad hoc dual-mode excitation. Intriguingly, a pronounced suboptimum in the search space is associated with a double-helix jet, a new flow pattern. This jet pattern results in a mixing improvement comparable to the blooming jet. A state-of-the-art Bayesian optimization converges towards this double-helix solution. The learning is accelerated and converges to another better optimum by including a deep-learning-enhanced surrogate model trained along the optimization. Persistent data topology extracts the global and many local minima in the actuation space. These minima can be identified with flow patterns beneficial to the mixing.

JFM classification

Flow Control: Mixing enhancement Mathematical Foundations: Machine learning Turbulent Flows: Turbulence control

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 991 , 25 July 2024 , A5
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ball, C.G., Fellouah, H. & Pollard, A. 2012 The flow field in turbulent round free jets. Prog. Aerosp. Sci. 50, 1–26.CrossRefGoogle Scholar
Blanchard, A. & Sapsis, T. 2021 Bayesian optimization with output-weighted optimal sampling. J. Comput. Phys. 425, 109901.CrossRefGoogle Scholar
Blanchard, A.B., Cornejo Maceda, G.Y., Fan, D., Li, Y., Zhou, Y., Noack, B.R. & Sapsis, T.P. 2021 Bayesian optimization for active flow control. Acta Mechanica Sin. 37, 1786–1798.CrossRefGoogle Scholar
Boguslawski, A., Wawrzak, K. & Tyliszczak, A. 2019 A new insight into understanding the crow and champagne preferred mode: a numerical study. J. Fluid Mech. 869, 385–416.CrossRefGoogle Scholar
Brunton, S.L., Noack, B.R. & Koumoutsakos, P. 2020 Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52, 477–508.CrossRefGoogle Scholar
Corke, T.C. & Kusek, S.M. 1993 Resonance in axisymmetric jets with controlled helical-mode input. J. Fluid Mech. 249, 307–336.CrossRefGoogle Scholar
Cornejo Maceda, G.Y., Li, Y., Lusseyran, F., Morzyński, M. & Noack, B.R. 2021 Stabilization of the fluidic pinball with gradient-based machine learning control. J. Fluid Mech. 917, A42.CrossRefGoogle Scholar
Crow, S.C. & Champagne, F.H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.CrossRefGoogle Scholar
Danaila, I. & Boersma, B.J. 2000 Direct numerical simulation of bifurcating jets. Phys. Fluids 12 (5), 1255–1257.CrossRefGoogle Scholar
Duriez, T., Brunton, S.L. & Noack, B.R. 2017 Machine Learning Control – Taming Nonlinear Dynamics and Turbulence. Fluid Mechanics and Its Applications, vol. 116. Springer.CrossRefGoogle Scholar
Edelsbrunner, H. & Harer, J. 2008 Persistent homology – a survey. Contemp. Maths 453 (26), 257–282.CrossRefGoogle Scholar
Gohil, T.B., Saha, A.K. & Muralidhar, K. 2015 Simulation of the blooming phenomenon in forced circular jets. J. Fluid Mech. 783, 567–604.CrossRefGoogle Scholar
Guastoni, L., Rabault, J., Schlatter, P., Azizpour, H., & Vinuesa, R. 2023 Deep reinforcement learning for turbulent drag reduction in channel flows. Eur. Phys. J. E 46, 27.CrossRefGoogle ScholarPubMed
Gutmark, E. & Ho, C.M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26, 2932–2938.CrossRefGoogle Scholar
Hilgers, A. & Boersma, B.J. 2001 Optimization of turbulent jet mixing. Fluid Dyn. Res. 29 (6), 345.CrossRefGoogle Scholar
Hussain, A.K.M.F. & Zaman, K.B.M.Q. 1980 Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics. J. Fluid Mech. 101 (3), 493–544.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45 (1), 173–195.CrossRefGoogle Scholar
Kempf, A., Klein, M. & Janicka, J. 2005 Efficient generation of initial- and inflow-conditions for transient turbulent flows in arbitrary geometries. Flow Turbul. Combust. 74, 67–84.CrossRefGoogle Scholar
Koumoutsakos, P., Freund, J. & Parekh, D. 2001 Evolution strategies for automatic optimization of jet mixing. AIAA J. 39 (5), 967–969.CrossRefGoogle Scholar
Lee, M. & Reynolds, W.C. 1985 Bifurcating and blooming jets. Tech. Rep.. Thermosciences Division, Department of Mechanical Engineering, Stanford University.Google Scholar
Lu, L., Jin, P., Pang, G., Zhang, Z. & Karniadakis, G.E. 2021 Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3 (3), 218–229.CrossRefGoogle Scholar
Mankbadi, R. & Liu, J.T.C. 1981 A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet. Phil. Trans. R. Soc. A 298 (1443), 541–602.Google Scholar
Nair, N.J. & Goza, A. 2023 Bio-inspired variable-stiffness flaps for hybrid flow control, tuned via reinforcement learning. J. Fluid Mech. 956, R4.CrossRefGoogle Scholar
Nathan, G.J., Mi, J., Alwahabi, Z.T., Newbold, G.J.R. & Nobes, D.S. 2006 Impacts of a jet's exit flow pattern on mixing and combustion performance. Prog. Energy Combust. Sci. 32 (5), 496–538.CrossRefGoogle Scholar
Parekh, D.E. 1989 Bifurcating Jets at High Reynolds Numbers. Stanford University.Google Scholar
Pickering, E., Guth, S., Karniadakis, G.E. & Sapsis, T.P. 2022 Discovering and forecasting extreme events via active learning in neural operators. Nat. Comput. Sci. 2 (12), 823–833.CrossRefGoogle ScholarPubMed
Pino, F., Schena, L., Rabault, J. & Mendez, M.A. 2023 Comparative analysis of machine learning methods for active flow control. J. Fluid Mech. 958, A39.CrossRefGoogle Scholar
Rabault, J., Kuchta, M., Jensen, A., Réglade, U. & Cerardi, N. 2019 Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J. Fluid Mech. 865, 281–302.CrossRefGoogle Scholar
Sadeghi, H. & Pollard, A. 2012 Effects of passive control rings positioned in the shear layer and potential core of a turbulent round jet. Phys. Fluids 24 (11), 115103.CrossRefGoogle Scholar
Shaabani-Ardali, L., Sipp, D. & Lesshafft, L. 2020 Optimal triggering of jet bifurcation: an example of optimal forcing applied to a time-periodic base flow. J. Fluid Mech. 885, A34.CrossRefGoogle Scholar
Shahriari, B., Swersky, K., Wang, Z., Adams, R.P. & De Freitas, N. 2015 Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104 (1), 148–175.CrossRefGoogle Scholar
Shaqarin, T. & Noack, B.R. 2023 A fast-converging particle swarm optimization through targeted, position-mutated, elitism (PSO-TPME). Intl J. Comput. Intell. Syst. 16, 6.CrossRefGoogle Scholar
da Silva, C.B. & Métais, O. 2002 Vortex control of bifurcating jets: a numerical study. Phys. Fluids 14 (11), 3798–3819.CrossRefGoogle Scholar
Sonoda, T., Liu, Z., Itoh, T. & Hasegawa, Y. 2023 Reinforcement learning of control strategies for reducing skin friction drag in a fully developed turbulent channel flow. J. Fluid Mech. 960, A30.CrossRefGoogle Scholar
Suzuki, H., Kasagi, N. & Suzuki, Y. 1999 Active control of an axisymmetric jet with an intelligent nozzle. In First Symposium on Turbulence and Shear Flow Phenomena. Begell House.CrossRefGoogle Scholar
Tyliszczak, A. 2014 A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows. J. Comput. Phys. 276, 438–467.CrossRefGoogle Scholar
Tyliszczak, A. 2015 a LES-CMC study of an excited hydrogen flame. Combust. Flame 162 (10), 3864–3883.CrossRefGoogle Scholar
Tyliszczak, A. 2015 b Multi-armed jets: a subset of the blooming jets. Phys. Fluids 27 (4), 041703.CrossRefGoogle Scholar
Tyliszczak, A. 2018 Parametric study of multi-armed jets. Intl J. Heat Fluid Flow 73, 82–100.CrossRefGoogle Scholar
Tyliszczak, A. & Geurts, B.J. 2014 Parametric analysis of excited round jets-numerical study. Flow Turbul. Combust. 93, 221–247.CrossRefGoogle Scholar
Utkin, Y.G., Keshav, S., Kim, J.H., Kastner, J., Adamovich, I.V. & Samimy, M. 2006 Development and use of localized arc filament plasma actuators for high-speed flow control. J. Phys. D: Appl. Phys. 40 (3), 685.CrossRefGoogle Scholar
Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M. & Vinuesa, R. 2023 a Effective control of two-dimensional Rayleigh–Bénard convection: invariant multi-agent reinforcement learning is all you need. Phys. Fluids 35 (6), 065146.CrossRefGoogle Scholar
Vignon, C., Rabault, J. & Vinuesa, R. 2023 b Recent advances in applying deep reinforcement learning for flow control: perspectives and future directions. Phys. Fluids 35 (3), 031301.CrossRefGoogle Scholar
Wahde, M. 2008 Biologically Inspired Optimization Methods: An Introduction. WIT Press.Google Scholar
Wang, T., Cornejo Maceda, G.Y. & Noack, B.R. 2023 a XPDT: A Toolkit for Persistent Data Topology. Universitätsbibliothek der Technischen Universität Braunschweig.Google Scholar
Wang, T., Yang, Y., Chen, X., Li, P., Iollo, A., Cornejo Maceda, G.Y. & Noack, B.R. 2023 b Topologically assisted optimization for rotor design. Phys. Fluids 35 (5), 055105.Google Scholar
Wawrzak, K., Boguslawski, A. & Tyliszczak, A. 2015 LES predictions of self-sustained oscillations in homogeneous density round free jet. Flow Turbul. Combust. 95, 437–459.CrossRefGoogle Scholar
Williams, C.K. & Rasmussen, C.E. 2006 Gaussian Processes for Machine Learning. MIT Press.Google Scholar
Wright, A.H. 1991 Genetic algorithms for real parameter optimization. In Foundations of Genetic Algorithms, vol. 1, pp. 205–218. Elsevier.Google Scholar
Xu, D. & Zhang, M. 2023 Reinforcement-learning-based control of convectively unstable flows. J. Fluid Mech. 954, A37.CrossRefGoogle Scholar
Zhou, Y., Fan, D., Zhang, B., Li, R. & Noack, B.R. 2020 Artificial intelligence control of a turbulent jet. J. Fluid Mech. 897, A27.CrossRefGoogle Scholar