Computational characterization of turbulent flow in a microfluidic actuator

In this contribution, an unsteady numerical simulation of the flow in a microfluidic oscillator has been performed. The transient turbulent flow inside the device is described by the Unsteady Reynolds Averaged Navier–Stokes equations (URANS) coupled with proper turbulence models. The main characteri...

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Autores:
Laín Beatove, Santiago
Lozano Parada, Jaime H.
Guzmán, Javier
Tipo de recurso:
Article of journal
Fecha de publicación:
2022
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/14697
Acceso en línea:
https://hdl.handle.net/10614/14697
https://red.uao.edu.co/
Palabra clave:
Dinámica de fluidos
Fluid dynamics
Computational fluid dynamics (CFD) numerical simulation
2D and 3D unsteady analysis
Fluidic actuator
Turbulent flow
Rights
openAccess
License
Derechos reservados - MDPI, 2022
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oai_identifier_str oai:red.uao.edu.co:10614/14697
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network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Computational characterization of turbulent flow in a microfluidic actuator
title Computational characterization of turbulent flow in a microfluidic actuator
spellingShingle Computational characterization of turbulent flow in a microfluidic actuator
Dinámica de fluidos
Fluid dynamics
Computational fluid dynamics (CFD) numerical simulation
2D and 3D unsteady analysis
Fluidic actuator
Turbulent flow
title_short Computational characterization of turbulent flow in a microfluidic actuator
title_full Computational characterization of turbulent flow in a microfluidic actuator
title_fullStr Computational characterization of turbulent flow in a microfluidic actuator
title_full_unstemmed Computational characterization of turbulent flow in a microfluidic actuator
title_sort Computational characterization of turbulent flow in a microfluidic actuator
dc.creator.fl_str_mv Laín Beatove, Santiago
Lozano Parada, Jaime H.
Guzmán, Javier
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
Lozano Parada, Jaime H.
Guzmán, Javier
dc.subject.armarc.spa.fl_str_mv Dinámica de fluidos
topic Dinámica de fluidos
Fluid dynamics
Computational fluid dynamics (CFD) numerical simulation
2D and 3D unsteady analysis
Fluidic actuator
Turbulent flow
dc.subject.armarc.eng.fl_str_mv Fluid dynamics
dc.subject.proposal.eng.fl_str_mv Computational fluid dynamics (CFD) numerical simulation
2D and 3D unsteady analysis
Fluidic actuator
Turbulent flow
description In this contribution, an unsteady numerical simulation of the flow in a microfluidic oscillator has been performed. The transient turbulent flow inside the device is described by the Unsteady Reynolds Averaged Navier–Stokes equations (URANS) coupled with proper turbulence models. The main characteristics of the complex fluid flow inside the device along one oscillation cycle was analyzed in detail, including not only velocity contours but also the pressure and turbulent kinetic energy fields. As a result, two-dimensional simulations provided good estimations of the operating frequency of the fluidic actuator when compared with experimental measurements in a range of Reynolds numbers. Moreover, with the objective of altering the operating frequency of the apparatus and, in order to adapt it to different applications, geometrical modifications of the feedback channels were proposed and evaluated. Finally, a fully three-dimensional simulation was carried out, which allowed for the identification of intricate coherent structures revealing the complexity of the turbulent flow dynamics inside the fluidic oscillator
publishDate 2022
dc.date.issued.none.fl_str_mv 2022-04
dc.date.accessioned.none.fl_str_mv 2023-05-04T20:21:11Z
dc.date.available.none.fl_str_mv 2023-05-04T20:21:11Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv 20763417
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/14697
dc.identifier.doi.none.fl_str_mv doi.org/10.3390/app12073589
dc.identifier.instname.spa.fl_str_mv Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv Repositorio Educativo Digital UAO
dc.identifier.repourl.spa.fl_str_mv https://red.uao.edu.co/
identifier_str_mv 20763417
doi.org/10.3390/app12073589
Universidad Autónoma de Occidente
Repositorio Educativo Digital UAO
url https://hdl.handle.net/10614/14697
https://red.uao.edu.co/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 16
dc.relation.citationissue.spa.fl_str_mv 7
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv 12
dc.relation.cites.none.fl_str_mv Laín Beatove, S., Lozano Parada, J.H., Guzmán, J. (2022). Computational Characterization of Turbulent Flow in a Microfluidic Actuator. Applied sciences, vol. 12,(7), pp. 1-16
dc.relation.ispartofjournal.eng.fl_str_mv Applied sciences
dc.relation.references.none.fl_str_mv 1. Tesar, V. Taxonomic trees of fluidic oscillators. EPJ Web Conf. 2017, 143, 02128. [CrossRef]
2. Ghanami, S.; Farhadi, M. Fluidic Oscillators Applications, Structures and Mechanisms—A review. Trans. Phenom. Nano Micro Scales 2019, 7, 9–27.
3. Guzmán, J.; Lozano-Parada, J.H.; Zimmerman, W.B.J.; Laín, S. Numerical simulation of the transient behavior of the turbulent flow in a microfluidic oscillator. J. Braz. Soc. Mech. Sci. Eng. 2021, 43, 29. [CrossRef]
4. Adhikari, A.; Schweitzer, T.; Lückoff, F.; Oberleithner, K. Design of a Fluidic Actuator with Independent Frequency and Amplitude Modulation for Control of Swirl Flame Dynamics. Fluids 2021, 6, 128. [CrossRef]
5. Cosi´c, B.; Waßmer, D.; Genin, F. Integration of Fluidic Nozzles in the New Low Emission Dual Fuel Combustion System for MGT ´ Gas Turbines. Fluids 2021, 6, 129. [CrossRef]
6. Koklu, M. Performance Assessment of Fluidic Oscillators Tested on the NASA Hump Model. Fluids 2021, 6, 74. [CrossRef]
7. Schweitzer, T.; Hörmann, M.; Bühling, B.; Bobusch, B. Switching Action of a Bistable Fluidic Amplifier for Ultrasonic Testing. Fluids 2021, 6, 171. [CrossRef]
8. Löffler, S.; Ebert, C.; Weiss, J. Fluidic-Oscillator-Based Pulsed Jet Actuators for Flow Separation Control. Fluids 2021, 6, 166. [CrossRef]
9. Fink, A.; Nett, O.; Schmidt, S.; Krüger, O.; Ebert, T.; Trottner, A.; Jander, B. Free Stream Behavior of Hydrogen Released from a Fluidic Oscillating Nozzle. Fluids 2021, 6, 245. [CrossRef]
10. Liebsch, J.; Paschereit, C.O. Oscillating Wall Jets for Active Flow Control in a Laboratory Fume Hood—Experimental Investigations. Fluids 2021, 6, 279. [CrossRef]
11. Pandhal, J.; Siswanto, A.; Kuvshinov, D.; Zimmerman, W.B.; Lawton, L.; Edwards, C. Cell Lysis and Detoxification of Cyanotoxins Using a Novel Combination of Microbubble Generation and Plasma Microreactor Technology for Ozonation. Front. Microbiol. 2018, 9, 678. [CrossRef]
12. Lozano-Parada, J.H.; Zimmerman, W.B.J. The role of kinetics in the design of plasma microreactors. Chem. Eng. Sci. 2010, 65, 4925–4930. [CrossRef]
13. Tesar, V. Fluidic Oscillators Mediating Generation of Microbubbles (Survey). Fluids 2021, 6, 77. [CrossRef]
14. Bobusch, B.C.; Woszidlo, R.; Bergada, J.M.; Nayeri, C.N.; Paschereit, C.O. Experimental Study of the Internal Flow Structures inside a Fluidic Oscillator. Exp. Fluids 2013, 54, 1559. [CrossRef]
15. Krüger, O.; Bobusch, B.; Woszidlo, R.; Paschereit, C. Numerical Modeling and Validation of the Flow in a Fluidic Oscillator. In Proceedings of the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, USA, 27 June 2013; p. AIAA2013-3087.
16. Baghaei, M.; Bergada, J.M.; del Campo, D.; del Campo, V. Research on Fluidic Amplifiers Dimensional Modifications via Computer Simulation (CFD). In Proceedings of the 9th International Conference on Computational Fluid Dynamics (ICCFD9), Istanbul, Turkey, 11–15 July 2016; p. 256.
17. Laín, S.; García, J.A. Study of four-way coupling on turbulent particle-laden jet flows. Chem. Eng. Sci. 2006, 61, 6775–6785. [CrossRef]
18. Menter, F. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA. J. 1994, 32, 269–289. [CrossRef]
19. Launder, B.E.; Spalding, D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974, 3, 269–289. [CrossRef]
20. Launder, B.E.; Reece, G.J.; Rodi, W. Progress in the Development of a Reynolds-stress Turbulence Closure. J. Fluid Mech. 1975, 68, 537–566. [CrossRef]
21. Langtry, R.B.; Menter, F. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J. 2009, 47, 2894–2906. [CrossRef]
22. Jizu Lv, P.W.; Bai, M.; Wang, Y.; Hu, C. Numerical investigation of the flow and heat behaviours of an impinging jet. Int. J. Comput. Fluid Dyn. 2014, 28, 301–315.
23. Laín, S.; Taborda, M.A.; López, O.D. Numerical study of the effect of winglets on the performance of a straight blade Darrieus water turbine. Energies 2018, 11, 297. [CrossRef]
24. Karbasian, H.R.; Kim, K.C. Numerical investigations on flow structure and behavior of vortices in the dynamic stall of an oscillating pitching hydrofoil. Ocean. Eng. 2016, 127, 200–211. [CrossRef]
25. Hærvig, J.; Sørensen, K.; Condra, T.J. On the fully-developed heat transfer enhancing flow field in sinusoidally, spirally corrugated tubes using computational fluid dynamics. Int. J. Heat Mass Transf. 2017, 106, 1051–1062. [CrossRef]
26. Sudo, K.; Sumida, M.; Hibara, H. Experimental investigation of turbulent flow in a square-sectioned 90-degree bend. Exp. Fluids 2001, 30, 246–252. [CrossRef]
27. Sommerfeld, M.; Laín, S. Parameters influencing dilute-phase pneumatic conveying through pipe systems: A computational study by the Euler/Lagrange approach. Can. J. Chem. Eng. 2015, 93, 1–17. [CrossRef]
28. Hunt, J.C.R.; Wray, A.A.; Moin, P. Eddies, streams, and convergence zones in turbulent flows. Cent. Turbul. Res. Proc. Summer Program. 1988, 1, 193–208.
dc.rights.spa.fl_str_mv Derechos reservados - MDPI, 2022
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rights_invalid_str_mv Derechos reservados - MDPI, 2022
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spelling Laín Beatove, Santiagovirtual::2576-1Lozano Parada, Jaime H.9ed5492cb1f07c16916fafe2c5663a7aGuzmán, Javier48badecca42ebb675d0c58f7b5719b952023-05-04T20:21:11Z2023-05-04T20:21:11Z2022-0420763417https://hdl.handle.net/10614/14697doi.org/10.3390/app12073589Universidad Autónoma de OccidenteRepositorio Educativo Digital UAOhttps://red.uao.edu.co/In this contribution, an unsteady numerical simulation of the flow in a microfluidic oscillator has been performed. The transient turbulent flow inside the device is described by the Unsteady Reynolds Averaged Navier–Stokes equations (URANS) coupled with proper turbulence models. The main characteristics of the complex fluid flow inside the device along one oscillation cycle was analyzed in detail, including not only velocity contours but also the pressure and turbulent kinetic energy fields. As a result, two-dimensional simulations provided good estimations of the operating frequency of the fluidic actuator when compared with experimental measurements in a range of Reynolds numbers. Moreover, with the objective of altering the operating frequency of the apparatus and, in order to adapt it to different applications, geometrical modifications of the feedback channels were proposed and evaluated. Finally, a fully three-dimensional simulation was carried out, which allowed for the identification of intricate coherent structures revealing the complexity of the turbulent flow dynamics inside the fluidic oscillator 16 páginasapplication/pdfengMDPIBasel, SuizaDerechos reservados - MDPI, 2022https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Computational characterization of turbulent flow in a microfluidic actuatorArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Dinámica de fluidosFluid dynamicsComputational fluid dynamics (CFD) numerical simulation2D and 3D unsteady analysisFluidic actuatorTurbulent flow167112Laín Beatove, S., Lozano Parada, J.H., Guzmán, J. (2022). Computational Characterization of Turbulent Flow in a Microfluidic Actuator. Applied sciences, vol. 12,(7), pp. 1-16Applied sciences1. Tesar, V. Taxonomic trees of fluidic oscillators. EPJ Web Conf. 2017, 143, 02128. [CrossRef]2. Ghanami, S.; Farhadi, M. Fluidic Oscillators Applications, Structures and Mechanisms—A review. Trans. Phenom. Nano Micro Scales 2019, 7, 9–27.3. Guzmán, J.; Lozano-Parada, J.H.; Zimmerman, W.B.J.; Laín, S. Numerical simulation of the transient behavior of the turbulent flow in a microfluidic oscillator. J. Braz. Soc. Mech. Sci. Eng. 2021, 43, 29. [CrossRef]4. Adhikari, A.; Schweitzer, T.; Lückoff, F.; Oberleithner, K. Design of a Fluidic Actuator with Independent Frequency and Amplitude Modulation for Control of Swirl Flame Dynamics. Fluids 2021, 6, 128. [CrossRef]5. Cosi´c, B.; Waßmer, D.; Genin, F. Integration of Fluidic Nozzles in the New Low Emission Dual Fuel Combustion System for MGT ´ Gas Turbines. Fluids 2021, 6, 129. [CrossRef]6. Koklu, M. Performance Assessment of Fluidic Oscillators Tested on the NASA Hump Model. Fluids 2021, 6, 74. [CrossRef]7. Schweitzer, T.; Hörmann, M.; Bühling, B.; Bobusch, B. Switching Action of a Bistable Fluidic Amplifier for Ultrasonic Testing. Fluids 2021, 6, 171. [CrossRef]8. Löffler, S.; Ebert, C.; Weiss, J. Fluidic-Oscillator-Based Pulsed Jet Actuators for Flow Separation Control. Fluids 2021, 6, 166. [CrossRef]9. Fink, A.; Nett, O.; Schmidt, S.; Krüger, O.; Ebert, T.; Trottner, A.; Jander, B. Free Stream Behavior of Hydrogen Released from a Fluidic Oscillating Nozzle. Fluids 2021, 6, 245. [CrossRef]10. Liebsch, J.; Paschereit, C.O. Oscillating Wall Jets for Active Flow Control in a Laboratory Fume Hood—Experimental Investigations. Fluids 2021, 6, 279. [CrossRef]11. Pandhal, J.; Siswanto, A.; Kuvshinov, D.; Zimmerman, W.B.; Lawton, L.; Edwards, C. Cell Lysis and Detoxification of Cyanotoxins Using a Novel Combination of Microbubble Generation and Plasma Microreactor Technology for Ozonation. Front. Microbiol. 2018, 9, 678. [CrossRef]12. Lozano-Parada, J.H.; Zimmerman, W.B.J. The role of kinetics in the design of plasma microreactors. Chem. Eng. Sci. 2010, 65, 4925–4930. [CrossRef]13. Tesar, V. Fluidic Oscillators Mediating Generation of Microbubbles (Survey). Fluids 2021, 6, 77. [CrossRef]14. Bobusch, B.C.; Woszidlo, R.; Bergada, J.M.; Nayeri, C.N.; Paschereit, C.O. Experimental Study of the Internal Flow Structures inside a Fluidic Oscillator. Exp. Fluids 2013, 54, 1559. [CrossRef]15. Krüger, O.; Bobusch, B.; Woszidlo, R.; Paschereit, C. Numerical Modeling and Validation of the Flow in a Fluidic Oscillator. In Proceedings of the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, USA, 27 June 2013; p. AIAA2013-3087.16. Baghaei, M.; Bergada, J.M.; del Campo, D.; del Campo, V. Research on Fluidic Amplifiers Dimensional Modifications via Computer Simulation (CFD). In Proceedings of the 9th International Conference on Computational Fluid Dynamics (ICCFD9), Istanbul, Turkey, 11–15 July 2016; p. 256.17. Laín, S.; García, J.A. Study of four-way coupling on turbulent particle-laden jet flows. Chem. Eng. Sci. 2006, 61, 6775–6785. [CrossRef]18. Menter, F. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA. J. 1994, 32, 269–289. [CrossRef]19. Launder, B.E.; Spalding, D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974, 3, 269–289. [CrossRef]20. Launder, B.E.; Reece, G.J.; Rodi, W. Progress in the Development of a Reynolds-stress Turbulence Closure. J. Fluid Mech. 1975, 68, 537–566. [CrossRef]21. Langtry, R.B.; Menter, F. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J. 2009, 47, 2894–2906. [CrossRef]22. Jizu Lv, P.W.; Bai, M.; Wang, Y.; Hu, C. Numerical investigation of the flow and heat behaviours of an impinging jet. Int. J. Comput. Fluid Dyn. 2014, 28, 301–315.23. Laín, S.; Taborda, M.A.; López, O.D. Numerical study of the effect of winglets on the performance of a straight blade Darrieus water turbine. Energies 2018, 11, 297. [CrossRef]24. Karbasian, H.R.; Kim, K.C. Numerical investigations on flow structure and behavior of vortices in the dynamic stall of an oscillating pitching hydrofoil. Ocean. Eng. 2016, 127, 200–211. [CrossRef]25. Hærvig, J.; Sørensen, K.; Condra, T.J. On the fully-developed heat transfer enhancing flow field in sinusoidally, spirally corrugated tubes using computational fluid dynamics. Int. J. Heat Mass Transf. 2017, 106, 1051–1062. [CrossRef]26. Sudo, K.; Sumida, M.; Hibara, H. Experimental investigation of turbulent flow in a square-sectioned 90-degree bend. Exp. Fluids 2001, 30, 246–252. [CrossRef]27. Sommerfeld, M.; Laín, S. Parameters influencing dilute-phase pneumatic conveying through pipe systems: A computational study by the Euler/Lagrange approach. Can. J. Chem. Eng. 2015, 93, 1–17. [CrossRef]28. Hunt, J.C.R.; Wray, A.A.; Moin, P. Eddies, streams, and convergence zones in turbulent flows. Cent. Turbul. Res. Proc. Summer Program. 1988, 1, 193–208.Comunidad generalPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::2576-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::2576-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::2576-10000-0002-0269-2608virtual::2576-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::2576-1ORIGINALComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdfComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdftexto completo del artículoapplication/pdf5470297https://red.uao.edu.co/bitstreams/863de2e2-fcc0-4c21-9701-93938a984c50/downloade442aa9514920279c14ce538ad172cf9MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/21e4a707-28ad-492c-b3e4-7b1ecef38946/download20b5ba22b1117f71589c7318baa2c560MD52TEXTComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdf.txtComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdf.txtExtracted texttext/plain78296https://red.uao.edu.co/bitstreams/e7c280a9-4db5-4aaf-afce-f54d44583890/download9cb0e51bd36a77c2d81086ce9245ffaaMD53THUMBNAILComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdf.jpgComputational_Characterization_of_Turbulent_Flow_in_a_Microfluidic_Actuator.pdf.jpgGenerated Thumbnailimage/jpeg15820https://red.uao.edu.co/bitstreams/c09e7889-cdcd-41c0-b191-90ed80a7f9d1/download8a78a08e77473d732e75246421d7df36MD5410614/14697oai:red.uao.edu.co:10614/146972024-03-19 11:34:44.808https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - MDPI, 2022open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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