May 7, 2018 - (M. Hassanine Aissa, TU Delft, October 2017). Quantifying ... Mikhael Balabane, for the time spent in front of the blackboard of Classroom 1 or ...
VON
K ARMAN I NSTITUTE FOR F LUID DYNAMICS E NVIRONMENTAL & A PPLIED F LUID DYNAMICS U NIVERSIT E´ L IBRE DE B RUXELLES A ERO -T HERMO -M ECHANICS
Dynamics of Gas Jet Impinging on Falling Liquid Films
Thesis presented by Miguel Alfonso Mendez, M.Sc. in Energy Engineering, in order to obtain the degree of Doctor of Engineering Science and Technology of the Universit`e Libre de Bruxelles, on May 7th , 2018. Supervisor: Prof. Jean- Marie Buchlin, von Karman Institute for Fluid Dynamics, Belgium. Promotor: Prof. Herman Deconinck, von Karman Institute for Fluid Dynamics, and Universit´e Libre de Bruxelles, Belgium Doctoral Committee: Prof. Pierre Colinet, Universit´e Libre de Bruxelles, Belgium Prof. Benoit Scheid, Universit´e Libre de Bruxelles, Belgium Prof. Alessandro Parente, Universit´e Libre de Bruxelles, Belgium Prof. Anne Gosset, University of A Coru˜na, Spain Prof. Mikhael Balabanne, Universit´e Paris 13, France Ing. Jean-Michel Mataigne, ArcelorMittal Global R&D, Luxemburg Dr. Pascal Gardin, ArcelorMittal Global R&D, Luxemburg
A selection of doctoral theses published by the von Karman Institute: GPU-accelerated CFD Simulations for Turbomachinery Design Optimization (M. Hassanine Aissa, TU Delft, October 2017) Quantifying inflow uncertainties for CFD simulations of dispersion in the atmospheric boundary layer (C. Garcia Snchez, U. Antwerpen, September 2017) Flow field and heat transfer in a rotating rib-roughened cooling passage (I. Mayo Yage, Institut Polytechnique de Toulouse, July 2017) Experimental characterization of instability onsets in a high speed axial compressor (G. DellEra, Universit Catholique de Louvain, April 2017) Large-Eddy Simulation, Stability and Optimization of the Conjugate Heat Transfer for Cooling Channels (S. Scholl, RWTH Aachen, February 2017) A full catalogue of publications is available from the library.
Dynamics of Gas Jet Impinging on Falling Liquid Films Keywords: Stability of Impinging Gas Jets, Coating Flows, Falling Liquid Films, Data-Driven Modal Analysis, Flow Control
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2018 by Miguel Alfonso Mendez D/2018/0238/706, T. Magin, Editor-in-Chief Published by the von Karman Institute for Fluid Dynamics with permission. All rights reserved. Permission to use a maximum of two figures or tables and brief excerpts in scientific and educational works is hereby granted provided the source is acknowledged. This consent does not extend to other kinds of copying and reproduction, for which permission requests should be addressed to the Director of the von Karman Institute. ISBN 978-2-87516-136-9
Acknowledgements
Bruxelles, 1th May 2018 This was a wonderful journey. For four years, I have been doing research; I have been learning how to learn. If this is currently the activity I love the most, it is only thanks to the people who have walked down this road together with me. These were colleagues and friends, as well as experts who have been enjoying this path –with all its setbacks and rewards– for decades. Thanks to all of you. Thank you, Prof. Jean Marie Buchlin, for being my supervisor and mentor. For teaching me to be driven by questions, no matter what technical challenge hides behind the answer nor how much new things one must learn to have one. Thank you for transmitting your passion for this work, for giving me the freedom to explore my scientific interests and tailor my work accordingly, and for teaching me to keep always a positive attitude to recognize any struggle for what it is– a learning experience. Thank you, Prof. Mikhael Balabane, for the time spent in front of the blackboard of Classroom 1 or in the courts of VKI and the Institut Henri Poincar´e; thinking, arguing, planning, computing, discussing. Thank you for teaching me the importance of questioning everything and the need and the beauty of proving things. Thank you for supporting and fostering my most naive and idealistic thoughts with the patience of a great teacher, and for shaping my thinking with your remarkable questions. Thank you, Prof. Anne Gosset, for all the time you have spent reading my work, always providing interesting and generous feedbacks, insights, suggestions, and corrections with impressive attention to details. Your Thesis was an important source of motivation for my work and an example I always tried to follow. Thank you, Prof. Benoit Scheid, for the time we spent in your office and at the VKI canteen, discussing liquid film modeling, dynamical systems, and stability analysis; your brilliant introduction to these topics have placed them among my major interests and at the center of my next journey. Thanks to the EA-VKI technical team Dani, Mohamed, Karl, Alain, Didier, and Laurent, expertly managed by Ir. Mathieu Delsipee, for the amazing and fundamental support in the design, construction and instrumentation of all the facilities involved in this study. Thanks to the VKI Computer Center and the endless resourcefulness and patience of Dr. Raimondo Giammanco, for the support in the cluster computing and in every imaginable IT-related problem that arose in four years.
ii Thanks to all the members of the VKI-ArcelorMittal meetings, Pascal Gardin, Jean-Michel Mataigne, and Marc Anderhuber, for supporting this work and for all the interesting discussions we had during these years. Thanks to all the other members of the Ph.D. Committee, Prof. Deconinck, Prof. Colinet, Prof. Parente, who have made my private defense a pleasant afternoon of discussion rather than a just an examination. Finally, thanks to all the VKI family for making my working place so enjoyable, supportive and inspiring. To my office mates, Mohamed, Guillaume, Tal, Zdenek, Davide, my STP/RM students Ozan, Marin, David B., Lorenzo, Adriana, Ahmad, David R., Kamila, Denis, Massimiliano, Maria Teresa, Ivan, Lorinc, Hulya, Jacque, Alejandro, my ‘lunchmates’ Mathieu, Gertjan, Laura and Alessia and my ‘RM brother’ and ‘paranimf’ Beppe. Last, but not surely not least, thanks to my pillars: Mamma Francesca e Babbo Guido, for their endless support, encouragement, trust, and love.
Abstract
This thesis describes the unstable dynamics of a gas jet impinging on a falling liquid film. This flow configuration is encountered in the jet wiping process, used in continuous coating applications such as the hot-dip galvanizing to control the thickness of a liquid coat on a moving substrate. The interaction between these flows generates a non-uniform coating layer, of great concern for the quality of industrial products, and results from a complex coupling between the interface instabilities of the liquid film and the confinement-driven instabilities of the impinging jet. Combining experimental and numerical methods, this thesis studied the dynamics of these flows on three simplified flow configurations, designed to isolate the key features of their respective instabilities and to provide complementary information on their mutual interaction. These configurations include the gas jet impingement on a falling liquid film perturbed with controlled flow rate pulsation, the gas jet impingement on a solid interface reproducing stable and unstable liquid film interfaces and a laboratory scaled model of the jet wiping process. Each of these configurations was reproduced on dedicated experimental set-up, instrumented for non-intrusive measurement techniques such as High-Speed Flow Visualization (HSFV) and Time-resolved Particle Image Velocimetry (TR-PIV) for the gas jet flow analysis, Laser Induced Fluorescence (LIF) tracking of the liquid interface, and 3D Light Absorption (LAbs) measurement of the liquid film thickness. To optimize the performances of these measurement techniques, several advanced data processing routines were developed, including a novel image pre-processing method for background removal in PIV and a dynamic feature tracking for the automatic detection of the jet flow and the liquid film interface from HSFV, LIF, and PIV videos. To identify the flow structures driving the unstable response of the jet flow, a novel data-driven modal decomposition was developed. This decomposition, referred to as Multiscale Proper Orthogonal Decomposition (mPOD), was validated on synthetic, numerical and experimental test cases and allowed for better feature extraction than classical alternatives such as Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). The experimental work on these laboratory models was complemented with the analysis of several numerical simulations, including a classical 2D Unsteady Reynolds Averaged Navier Stokes (URANS) modeling of the gas jet impingement on a fixed interface, a 2D Variational Multiscale Simulation (VMS) with anisotropic mesh refinement of the gas jet impingement on a pulsing interface, and a 3D simulation
iv of the jet wiping process combining Large Eddy Simulation (LES) on the gas side with Volume of Fluid (VOF) treatment of the liquid film flow. The experimental modal analysis on the dynamic response of the gas jet and the characterization of the pressure-velocity coupling in the numerical investigation allowed for a complete picture of the mechanism driving the jet oscillation and its possible impact on the liquid film flow. In parallel, several flow control strategies to prevent the jet oscillation were developed, tested numerically and experimentally in simplified conditions, and later implemented on the design of a new nozzle for the jet wiping process. This new nozzle was finally tested on a laboratory scale of the wiping process and its performances compared to single jet and multiple jet wiping configurations. In these three cases, the experimental work presents the modal analysis of the gas field using TR-PIV and mPOD, the liquid interface tracking via LIF, and the final coating thickness characterization via LAbs. The large spatiotemporally resolved experimental database allowed to give a detailed description of the jet wiping instability and to provide new insights on this fascinating fundamental and applied problem of fluid dynamics.
Contents
1. Introduction 1.1. Research Framework, Motivation and Aims . . . . . 1.2. Fundamentals of the Jet Wiping Process . . . . . . . 1.2.1. Pressure and Shear Stress Distributions . . . 1.2.2. The Far field and the Free Drag-Out Problem 1.2.3. 0D Model and Process Similarity . . . . . . . 1.3. Literature Review on the Undulation Problem . . . . 1.4. Thesis Overview and Manuscript Organization . . .
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1 1 4 6 10 12 16 19
2. Experimental Methods 2.1. Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. The VKI Liquid Film Facility and Related Nozzle Set-Up 2.1.2. The VKI Membrane Facility . . . . . . . . . . . . . . . . 2.1.3. The VKI Ondule Facility . . . . . . . . . . . . . . . . . . 2.2. Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . 2.2.1. The Light Absorption Method . . . . . . . . . . . . . . . 2.2.2. Planar Laser Interface Detection . . . . . . . . . . . . . . 2.2.3. Gas Jet Centerline Tracking (GJT) . . . . . . . . . . . . . 2.2.4. Time Resolved Particle Image Velocimetry (TR-PIV) . .
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23 24 24 33 36 38 38 44 51 52
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55 56 58 61 61 64 67 74 79
4. Multiscale Modal Analysis of Complex Fluid Flows 4.1. The Algebra of Discrete Modal Analysis . . . . . . . . . . . . . . . . 4.1.1. The Discrete Fourier Transform (DFT) . . . . . . . . . . . . 4.1.2. The Proper Orthogonal Decomposition (POD) . . . . . . . .
81 82 84 87
3. Gas 3.1. 3.2. 3.3.
Jet Impinging on a Pulsing Liquid Films Literature on Low Kapitza Falling Liquid Films . . . Facility Calibration and Scaling Laws . . . . . . . . Characterization of Liquid Film Perturbations . . . . 3.3.1. Operational Maps . . . . . . . . . . . . . . . 3.3.2. Data Processing for Traveling Waves . . . . . 3.3.3. Correlations for Liquid Film Traveling Wave 3.4. Response of the Impinging Jet Flow . . . . . . . . . 3.5. Summary and Conclusions . . . . . . . . . . . . . . .
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4.1.3. The Dynamic Mode Decomposition (DMD) . . . . . . . . 4.1.4. The Spectral Proper Orthogonal Decomposition (SPOD) 4.2. An illustrative synthetic test case . . . . . . . . . . . . . . . . . . 4.3. The multi-scale POD (mPOD) . . . . . . . . . . . . . . . . . . . 4.3.1. The Filtered Eigenvalue Decomposition . . . . . . . . . . 4.3.2. Multiresolution Analysis (MRA) via 2D Wavelets . . . . . 4.3.3. Re-orthogonalization and Final Assembly . . . . . . . . . 4.4. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 5. Gas Jet Impinging on a Deformable Wall 5.1. Literature on Oscillating Impinging Jet Flows . . 5.2. Data Processing . . . . . . . . . . . . . . . . . . 5.2.1. Time-Frequency Analysis via CWT . . . . 5.2.2. Modal Analysis via mPOD . . . . . . . . 5.3. Time-Frequency Characterization . . . . . . . . . 5.4. Flow Field Modal Analysis . . . . . . . . . . . . 5.4.1. Quasi-Steady Response . . . . . . . . . . 5.4.2. Dynamic Condition: Mixed Response . . 5.4.3. Dynamic Condition: Harmonic Response 5.5. Summary and Conclusions . . . . . . . . . . . . .
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90 95 96 105 107 109 113 119
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121 122 124 124 126 128 137 138 144 149 151
6. Numerical Investigation of the Hydrodynamic Feedback 6.1. Oscillating Gas Jet Impinging on a Stationary Interface 6.1.1. Geometry and Numerical Settings . . . . . . . . 6.1.2. Phase Portrait of the Hydrodynamic Feedback . 6.1.3. Flow Field Modal Analysis . . . . . . . . . . . . 6.2. Oscillating Gas Jet Impinging on a Pulsing Interface . . 6.2.1. Geometry and Numerical Settings . . . . . . . . 6.2.2. Flow Field Modal Analysis . . . . . . . . . . . . 6.3. 3D Simulation of the Jet Wiping Process . . . . . . . . . 6.3.1. Geometry and Numerical Settings . . . . . . . . 6.3.2. Liquid Film Characterization . . . . . . . . . . . 6.3.3. Multi-scale POD Analysis of Gas Flow . . . . . . 6.3.4. Gas Jet-Liquid film Interaction . . . . . . . . . . 6.4. Summary and Conclusions . . . . . . . . . . . . . . . . .
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155 156 157 159 164 167 169 171 173 173 174 180 180 186
7. Development of a Flow Control Strategy (CONFIDENTIAL) 7.1. Selected Control Strategies and Related Literature . . . . 7.2. Vectoring a Turbulent Jet Flow . . . . . . . . . . . . . . . 7.2.1. A General Vectoring Law . . . . . . . . . . . . . . 7.2.2. Vectoring performance of the Secondary Jet . . . . 7.2.3. Momentum exchange between jet flows . . . . . . 7.2.4. Model Formulation . . . . . . . . . . . . . . . . . . 7.2.5. Numerical Methods for Model Validation . . . . . 7.2.6. Preliminary Design and Set-Up . . . . . . . . . . .
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191 192 197 198 200 201 202 203 204
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7.2.7. Vectoring performances in free jet conditions 7.3. The CFV Nozzle Design . . . . . . . . . . . . . . . . 7.4. Analysis of the Jet Stabilization Methods . . . . . . 7.4.1. Numerical Analysis . . . . . . . . . . . . . . . 7.5. Experimental Analysis . . . . . . . . . . . . . . . . . 7.6. Summary and Conclusions . . . . . . . . . . . . . . .
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206 212 212 214 219 223
8. Experimental Analysis of The Jet Wiping (CONFIDENTIAL) 8.1. Measured Quantities and Related Data Processing . . . . 8.1.1. TR-PIV of the Gas Jet Flow . . . . . . . . . . . . 8.1.2. Run-Back Liquid Film Analysis . . . . . . . . . . . 8.1.3. Final Coating Film Analysis . . . . . . . . . . . . . 8.2. The Uncontrolled Jet Wiping Process . . . . . . . . . . . 8.2.1. Mean Film and Wave Amplitudes . . . . . . . . . 8.2.2. Wave frequency and traveling speed . . . . . . . . 8.2.3. Modal Analysis of Selected Test Case . . . . . . . 8.3. The HS Controllet Jet Wiping Process . . . . . . . . . . . 8.3.1. Mean Film and Wave Amplitude . . . . . . . . . . 8.3.2. Wave frequency and traveling speed . . . . . . . . 8.3.3. Modal Analysis of Selected Test Case . . . . . . . 8.4. The CFV Controlled Jet Wiping Process . . . . . . . . . . 8.4.1. Mean Film and Wave Amplitude . . . . . . . . . . 8.4.2. Wave Frequency and Traveling Speeds . . . . . . . 8.4.3. Modal Analysis of Selected Test Case . . . . . . . 8.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
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227 228 228 228 232 234 234 239 246 251 252 254 260 263 263 265 266 273
9. Conclusions and Future Work (CONFIDENTIAL) 275 9.1. Summary and Major Contributions . . . . . . . . . . . . . . . . . . . 275 9.2. Perspectives and Future Work . . . . . . . . . . . . . . . . . . . . . . 282 A. Notes on the Modeling of the Jet Wiping Process A.I. The full set of equations . . . . . . . . . . . . . . A.II. The Long Wave Set Of Dimensionless Equations A.III.Integral form of the Unsteady Wiping Model . . A.III.1.Integration of Continuity Equation . . . . A.III.2.Integration of Momentum Equation . . .
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285 285 287 292 292 293
B. POD-based background removal for particle image velocimetry B.I. Algorithm Formulation . . . . . . . . . . . . . . . . . . . . . . B.I.1. Decomposition of Ideal PIV Sequence . . . . . . . . . B.I.2. Removal of Correlated Background Noise . . . . . . . B.I.3. Proposed Algorithm and Error Estimation . . . . . . . B.II. Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.II.1. Statistical Convergence of an Ideal PIV sequence . . . B.II.2. Background Removal in a Synthetic Test Case . . . .
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Contents
B.II.3. Background removal in an Experimental Test Case . . . . . . 309 B.III.Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 C. mPOD Analysis of an Advection-Diffusion Problem 313 C.I. Validation on a Nonlinear Advection-Diffusion Problem . . . . . . . 313 C.II. Geometry and Numerical Settings . . . . . . . . . . . . . . . . . . . 315 C.III.Vorticity Field Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 318 D. Modeling of Oscillating/Meandering Shear Layers D.I. Dimensionless Formulation and Change of Variables . . . . . . . . . D.II. Analytical Solution via Laplace Trasform(s) . . . . . . . . . . . . . . D.III.Oder Of Magnitudes and General considerations . . . . . . . . . . .
333 333 334 337
E. List of Publications
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Bibliography
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