Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional

ilustraciones, gráficas, tablas

Autores:
Tovar Tuirán, Jair Hernando
Tipo de recurso:
Fecha de publicación:
2022
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/81966
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/81966
https://repositorio.unal.edu.co/
Palabra clave:
530 - Física::532 - Mecánica de fluidos
620 - Ingeniería y operaciones afines::621 - Física aplicada
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación
510 - Matemáticas::518 - Análisis numérico
Numerical analysis
Generación numérica de mallas
Análisis numérico
Numerical grid generation
Dinámica de fluidos computacional
Chorros supersónicos
chorros sub-expandidos
Flujo turbulento
Reenganche
Computational Fluid Dynamics
under-resolved Direct Numerical Simulation
Large-Eddy Simulation
Lid-Driven Cavity
Differentially Heated Cavity
OpenFoam
Supersonic jets
Under-expanded jets
Turbulent flow
Backward-facing step
Separation
Reattachment
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 4.0 Internacional
id UNACIONAL2_5152065d22b83826c4970ac5719901d9
oai_identifier_str oai:repositorio.unal.edu.co:unal/81966
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
dc.title.translated.eng.fl_str_mv Meshing methodology for numerical simulations of turbulent flows at low computational cost
title Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
spellingShingle Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
530 - Física::532 - Mecánica de fluidos
620 - Ingeniería y operaciones afines::621 - Física aplicada
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación
510 - Matemáticas::518 - Análisis numérico
Numerical analysis
Generación numérica de mallas
Análisis numérico
Numerical grid generation
Dinámica de fluidos computacional
Chorros supersónicos
chorros sub-expandidos
Flujo turbulento
Reenganche
Computational Fluid Dynamics
under-resolved Direct Numerical Simulation
Large-Eddy Simulation
Lid-Driven Cavity
Differentially Heated Cavity
OpenFoam
Supersonic jets
Under-expanded jets
Turbulent flow
Backward-facing step
Separation
Reattachment
title_short Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
title_full Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
title_fullStr Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
title_full_unstemmed Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
title_sort Metodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacional
dc.creator.fl_str_mv Tovar Tuirán, Jair Hernando
dc.contributor.advisor.none.fl_str_mv Duque Daza, Carlos Alberto
dc.contributor.author.none.fl_str_mv Tovar Tuirán, Jair Hernando
dc.contributor.researchgroup.spa.fl_str_mv Gnum Grupo de Modelado y Métodos Numericos en Ingeniería
dc.subject.ddc.spa.fl_str_mv 530 - Física::532 - Mecánica de fluidos
620 - Ingeniería y operaciones afines::621 - Física aplicada
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación
510 - Matemáticas::518 - Análisis numérico
topic 530 - Física::532 - Mecánica de fluidos
620 - Ingeniería y operaciones afines::621 - Física aplicada
620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería
000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación
510 - Matemáticas::518 - Análisis numérico
Numerical analysis
Generación numérica de mallas
Análisis numérico
Numerical grid generation
Dinámica de fluidos computacional
Chorros supersónicos
chorros sub-expandidos
Flujo turbulento
Reenganche
Computational Fluid Dynamics
under-resolved Direct Numerical Simulation
Large-Eddy Simulation
Lid-Driven Cavity
Differentially Heated Cavity
OpenFoam
Supersonic jets
Under-expanded jets
Turbulent flow
Backward-facing step
Separation
Reattachment
dc.subject.armarc.none.fl_str_mv Numerical analysis
dc.subject.lemb.spa.fl_str_mv Generación numérica de mallas
Análisis numérico
dc.subject.lemb.eng.fl_str_mv Numerical grid generation
dc.subject.proposal.spa.fl_str_mv Dinámica de fluidos computacional
Chorros supersónicos
chorros sub-expandidos
Flujo turbulento
Reenganche
dc.subject.proposal.eng.fl_str_mv Computational Fluid Dynamics
under-resolved Direct Numerical Simulation
Large-Eddy Simulation
Lid-Driven Cavity
Differentially Heated Cavity
OpenFoam
Supersonic jets
Under-expanded jets
Turbulent flow
Backward-facing step
Separation
Reattachment
description ilustraciones, gráficas, tablas
publishDate 2022
dc.date.accessioned.none.fl_str_mv 2022-08-18T20:32:40Z
dc.date.available.none.fl_str_mv 2022-08-18T20:32:40Z
dc.date.issued.none.fl_str_mv 2022-03
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/81966
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/81966
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.references.spa.fl_str_mv B. F. Armaly, F. Durst, J. C. F. Pereira, and B. Schönung. Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech., 127(-1):473{496, feb 1983. doi: 10.1017/s0022112083002839
J. Bellan. Large-Eddy Simulation of Supersonic Round Jets: Effects of Reynolds and Mach Numbers. AIAA Journal, 54(5):1482{1498, may 2016. doi: 10.2514/1.j054548.
G. Biswas, M. Breuer, and F. Durst. Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers. J. Fluids Eng., 126(3):362-374, may 2004. doi: 10.1115/1.1760532.
Blog Ingeniería. Blog Ingeniería, el blog para ingenieros. https://blogingenieria.com/curiosidades/supercavitacion-velocidad-supersonica/, 2021. Online; Accesado en 08 de Noviembre de 2021.
D. J. Bodony and S. K. Lele. On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets. Physics of Fluids, 17(8):085103, aug 2005. doi: 10.1063/1.2001689.
F. Bonelli, A. Viggiano, and V. Magi. High-speed turbulent gas jets: an LES investigation of Mach and Reynolds number effects on the velocity decay and spreading rate. Flow, Turbulence and Combustion, 107(3):519-550, feb 2021. doi: 10.1007/s10494-021-00242-5.
C. Bosshard, A. Dehbi, M. Deville, E. Leriche, R. Puragliesi, and A. Soldati. Large Eddy Simulation of the Differentially Heated Cubic Cavity Flow by the Spectral Element Method. Computers and Fluids, 86:210-227, 2013. doi: 10.1016/j.compuid.2013.07.007.
C. Bosshard, M. O. Deville, A. Dehbi, and E. Leriche. UDNS or LES, That Is the Question. Open Journal of Fluid Dynamics, 5:339-352, 12 2015. doi: 10.4236/ojfd.2015.54034.
R. Bouffanais, M. O. Deville, and E. Leriche. Large-Eddy Simulation of the Flow in a Lid-Driven Cubical Cavity. Phys. Fluids, 19, 2007. doi: 10.1063/1.2723153.
G. A. Brès, F. E. Ham, J. W. Nichols, and S. K. Lele. Unstructured Large-Eddy Simulations of Supersonic Jets. AIAA Journal, 55(4):1164-1184, apr 2017. doi: 10.2514/1.j055084.
J. Bridges and M. Wernet. Turbulence Associated with Broadband Shock Noise in Hot Jets. In AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, may 2008. doi: 10.2514/6.2008-2834.
G. Castiglioni and J. A. Domaradzki. A numerical dissipation rate and viscosity in flow simulations with realistic geometry using low-order compressible Navier-Stokes solvers. Computers and Fluids, 119:37-46, 2015. doi: 10.1016/j.compfluid.2015.07.004.
A. Darisse, J. Lemay, and A. Benaïssa. Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet. Journal of Fluid Mechanics, 774:95-142, jun 2015. doi: 10.1017/jfm.2015.245.
J. R. DeBonis and J. N. Scott. Large-Eddy Simulation of a Turbulent Compressible Round Jet. AIAA Journal, 40(7):1346-1354, jul 2002. doi: 10.2514/2.1794.
C. D. Donaldson and R. S. Snedeker. A study of free jet impingement. Part 1. Mean properties of free and impinging jets. J. Fluid Mech., 45(02):281, jan 1971. doi: 10.1017/s0022112071000053.
J. Freund, S. Lele, and P. Moin. Direct simulation of a Mach 1.92 jet and its sound field. AIAA, jun 1998. doi: 10.2514/6.1998-2291.
D. V. Gaitonde. Analysis of the Near Field in a Plasma-Actuator-Controlled Supersonic Jet. J. Propul. Power, 28(2):281-292, mar 2012. doi: 10.2514/1.b34289.
L. Gamet and J. L. Estivalezes. Application of Large-Eddy Simulations and Kirchhoff Method to Jet Noise Prediction. AIAA Journal, 36(12):2170-2178, dec 1998. doi: 10.2514/2.341.
W. K. George. Lectures in Turbulence for the 21st Century. Department of Thermo and Fluid Engineering, Chalmers University of Technology, Göteborg, Sweden, 2005.
D. González, D. Gaitonde, and M. Lewis. Large-eddy simulations of plasma-based asymmetric control of supersonic round jets. International Journal of Computational Fluid Dynamics, 29(3-5):240-256, mar 2015. doi: 10.1080/10618562.2015.1053877.
C. J. Greenshields, H. G. Weller, L. Gasparini, and J. M. Reese. Implementation of semidiscrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows. Int. J. Numer. Methods Fluids, 63:1-21, May 2009. doi: 10.1002/fld.2069.
J. Hart. Comparison of Turbulence Modeling Approaches to the Simulation of a Dimpled Sphere. Procedia Engineering, 147:68-73, 2016. doi: 10.1016/j.proeng.2016.06.191.
J. I. Hileman, B. S. Thurow, E. J. Caraballo, and M. Samimy. Large-scale structure evolution and sound emission in high-speed jets: real-time visualization with simultaneous acoustic measurements. J. Fluid Mech., 544(-1):277-307, nov 2005. doi: 10.1017/s002211200500666x.
D. Jehad, G. Hashim, A. Kadhim Zarzoor, and N. A. Che Sidik. Numerical Study of Turbulent Flow over Backward-Facing Step with Different Turbulence Models. Journal of Advanced Research Design, 4:2289-7984, 01 2015.
S. Jovic and D. M. Driver. Backward-facing step measurements at low Reynolds number, Re(sub h)=5000. In NASA Technical Memorandum 108807, 1994.
N. Kasagi and A. Matsunaga. Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow. Int. J. Heat and Fluid Flow, 16(6):477-485, dec 1995. doi: 10.1016/0142-727x(95)00041-n.
A. Khavaran, E. Krejsa, and C. Kim. Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model. In 30th Aeroespace Sciences Meeting and Exhibit. AIAA-92-0500, jan 1992. doi: 10.2514/6.1992-500.
J. Kim, S. J. Kline, and J. P. Johnston. Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step. J. Fluids Eng., 102(3):302-308, sep 1980. doi: 10.1115/1.3240686.
J. Kostas, J. Soria, and M. Chong. Particle image velocimetry measurements of a backward-facing step flow. Experiments in Fluids, 33(6):838-853, dec 2002. doi: 10.1007/s00348-002-0521-9.
A. Kurganov and E. Tadmor. New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations. J. Comput. Phys., 160(1):241-282, may 2000. doi: 10.1006/jcph.2000.6459.
J. C. Lau, P. J. Morris, and M. J. Fisher. Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech., 93(1):1-27, jul 1979. doi: 10.1017/s0022112079001750.
H. Le, P. Moin, and J. Kim. Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech., 330:349-374, jan 1997. doi: 10.1017/s0022112096003941.
E. Leriche. Direct Numerical Simulation of Lid Driven Cavity at High Reynolds Numbers. J. Sci. Comput., 27:335-345, 2006. doi: 10.1007/s10915-005-9032-1.
J. Liu, K. Kailasanath, R. Ramamurti, D. Munday, E. Gutmark, and R. Lohner. Large-Eddy Simulations of a Supersonic Jet and Its Near-Field Acoustic Properties. AIAA Journal, 47(8):1849-1865, aug 2009. doi: 10.2514/1.43281.
S.-C. Lo, G. Blaisdell, and A. Lyrintzis. Numerical Simulation of Supersonic Jet Flows and their Noise. In 14th AIAA/CEAS Aeroacoustics Conference. AIAA 2008-2970, may 2008. doi: 10.2514/6.2008-2970.
S.-C. Lo, G. Blaisdell, and A. Lyrintzis. Numerical Investigation of 3-D Supersonic Jet Flows Using Large Eddy Simulation. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA 2011-1155, jan 2011. doi: 10.2514/6.2011-1155.
C. Loh and L. Hultgren. Near-Field Noise Computation for a Supersonic Circular Jet. In 11th AIAA/CEAS Aeroacoustics Conference. AIAA 2005-3042, may 2005. doi: 10.2514/6.2005-3042.
R. R. Mankbadi, M. E. Hayer, and L. A. Povinelli. Structure of supersonic jet flow and its radiated sound. AIAA Journal, 32(5):897-906, may 1994. doi: 10.2514/3.12072.
L. F. G. Marcantoni, J. P. Tamagno, and S. A. Elaskar. High Speed Flow Simulation using OpenFOAM. Asociación Argentina de Mecánica Computacional, XXXI:2939-2959, nov 2012.
R. Maulik and O. San. Explicit and implicit LES closures for Burgers turbulence. J. Comput. Appl. Math., 327:12-40, 2018. doi: 10.1016/j.cam.2017.06.003.
R. C. Moura, S. J. Sherwin, and J. Peiró. Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods. J. Comput. Phys., 298:695-710, 2015. doi: 10.1016/j.jcp.2015.06.020.
E. Murakami and D. Papamoschou. Eddy Convection in Coaxial Supersonic Jets. AIAA Journal, 38(4):628-635, apr 2000. doi: 10.2514/2.1034.
A. Nigro, C. D. Bartolo, A. Crivellini, M. Franciolini, A. Colombo, and F. Bassi. A low-dissipation DG method for the under-resolved simulation of low Mach number turbulent flows. Computers and Mathematics with Applications, 77:1739-1755, 2019. doi: 10.1016/j.camwa.2018.09.049.
OpenFOAM. OpenFOAM v5 User Guide. https://cfd.direct/openfoam/user-guide, 2021. Online; Accesado en Octubre de 2021.
J. Panda and R. Seasholtz. Velocity and temperature measurement in supersonic free jets using spectrally resolved Rayleigh scattering. In 37th AIAA Aerospace Sciences Meeting and Exhibit. AIAA-99-0296, jan 1999. doi: 10.2514/6.1999-296.
B. Panjwani, I. S. Ertesvag, A. Gruber, and K. E. Rian. Large Eddy Simulation of Backward Facing Step Flow. In Fifth National Conference on Computational Mechanics, Trondheim 26-27, pages 353-369, may 2009.
S. B. Pope. Turbulent Flows. Cambridge University Press, 2000. ISBN 9780521598866. URL https://books.google.com.co/books?id=HZsTw9SMx-0C.
H. P. Rani, T. W. H. Sheu, and E. S. F. Tsai. Eddy structures in a transitional backward-facing step flow. J. Fluid Mech., 588:43-58, sep 2007. doi: 10.1017/s002211200700763x.
S. Rodriguez. LES and DNS Turbulence Modeling. Springer International Publishing, 2019. doi: 10.1007/978-3-030-28691-0_5.
A. Rona and X. Zhang. Time accurate numerical study of turbulent supersonic jets. J. Sound Vib., 270(1-2):297-321, feb 2004. doi: 10.1016/s0022-460x(03)00537-6.
M. Samimy, J.-H. Kim, J. Kastner, I. Adamovich, and Y. Utikn. Active control of high-speed and high-Reynolds-number jets using plasma actuators. J. Fluid Mech., 578:305-330, apr 2007. doi: 10.1017/s0022112007004867.
J. M. Seiner. Fluid Dynamics and Noise Emission Associated With Supersonic Jets. In T. G. Gatski et al. (eds.), Studies in Turbulence, pages 297-323. Springer New York, 1992. doi: 10.1007/978-1-4612-2792-2_22.
E. Shehadi. Large Eddy Simulation of Turbulent Flow over a Backward-Facing Step. Master's thesis, Uppsala Universitet, Mar. 2018.
S. Shih, D. Hixon, R. Mankbadi, and L. Povinelli. Prediction of flow and acoustic fields of a supersonic jet. In AIAA Paper 96-0751, jan 1996. doi: 10.2514/6.1996-751.
C. Tam, M. Golebiowski, and J. Seiner. On the two components of turbulent mixing noise from supersonic jets. In AIAA Meeting Papers on Disc, NAG1-1776, AIAA Paper 96-1716, may 1996. doi: 10.2514/6.1996-1716.
B. A. Toms. Large-eddy Simulation of Flow over a Backward Facing Step: Assessment of Inflow Boundary Conditions, Eddy Viscosity Models, and Wall Functions. J. Appl. Mech. Eng., 04(03), 2015. doi: 10.4172/2168-9873.1000169.
K. Viswanathan, N. Reddy, and L. Sankar. A fluid/acoustic coupled simulation of supersonic jet noise. In 32nd Aerospace Sciences Meeting and Exhibit, jan 1994. doi: 10.2514/6.1994-137.
J. C. Vogel and J. K. Eaton. Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step. J. Heat Transfer, 107(4):922-929, nov 1985. doi: 10.1115/1.3247522.
P. O. Witze. Centerline Velocity Decay of Compressible Free Jets. AIAA Journal, 12(4):417-418, apr 1974. doi: 10.2514/3.49262.
S. Ye, Y. Lin, L. Xu, and J. Wu. Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow. Mathematics, 8(1):119, jan 2020. doi: 10.3390/math8010119.
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv xiv, 118 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ingeniería - Maestría en Ingeniería - Ingeniería Mecánica
dc.publisher.department.spa.fl_str_mv Departamento de Ingeniería Mecánica y Mecatrónica
dc.publisher.faculty.spa.fl_str_mv Facultad de Ingeniería
dc.publisher.place.spa.fl_str_mv Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/81966/3/1022416879.2022.pdf
https://repositorio.unal.edu.co/bitstream/unal/81966/4/license.txt
https://repositorio.unal.edu.co/bitstream/unal/81966/5/1022416879.2022.pdf.jpg
bitstream.checksum.fl_str_mv 890a2ca0aeec56a3c13b92ef20e87ee3
8153f7789df02f0a4c9e079953658ab2
255b468cc360535d9d1a861ca350128e
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
_version_ 1814089265949179904
spelling Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Duque Daza, Carlos Alberto2af3fa9fc1551951a8ddefbc637c4cd8Tovar Tuirán, Jair Hernandoabf90697dacca90bb5153bd4b83f4a92Gnum Grupo de Modelado y Métodos Numericos en Ingeniería2022-08-18T20:32:40Z2022-08-18T20:32:40Z2022-03https://repositorio.unal.edu.co/handle/unal/81966Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasEn este trabajo de investigación se construyeron mallas computacionales estructuradas paramétricas, para la solución numérica de dos casos de flujo turbulento. El propósito principal de este trabajo fue analizar la influencia de ciertos parámetros de mallado, en la predicción numérica de variables de flujo turbulento. Para ello se llevaron a cabo simulaciones UDNS con mallas de bajo costo computacional, las cuales fueron definidas a partir de parámetros de mallado tales como: tamaños de malla, relaciones de aspecto y secciones de refinamiento. El primer caso seleccionado consistió en un chorro circular supersónico expulsado de una tobera, para flujo compresible; y el segundo caso de interés se fundamentó en un flujo interno a través de un canal con un cambio de sección abrupto, para flujo incompresible. Se analizaron estadísticas de turbulencia de primer y segundo orden obtenidas con experimentos numéricos realizados usando diferentes topologías de malla. Los resultados fueron validados con datos experimentales y resultados numéricos LES y DNS reportados por otros investigadores. Se encontró que mediante el ajuste paramétrico de mallado, es posible obtener discretizaciones espaciales de bajo costo computacional pero que permiten la predicción de las características de flujos turbulentos, sin la necesidad de recurrir a modelos de turbulencia explícitos. Los resultados muestran que, en efecto, aunque no se alcanzan los niveles de precisión numérica de enfoques DNS, es posible tener predicciones comparables con aquellas dadas por tales enfoques numéricos de alta precisión. (Texto tomado de la fuente)In this research work, parametric structured computational grids were constructed for the numerical solution of two turbulent flow cases. The main purpose of this work was to analyze the influence of certain meshing parameters in the numerical prediction of turbulent flow variables. For this purpose, UDNS simulations were carried out with low computational cost meshes, which were defined from meshing parameters such as: mesh sizes, aspect ratios and refinement sections. The first case selected consisted of a supersonic circular jet ejected from a nozzle, for compressible flow; and the second case of interest was based on an internal flow through a channel with an abrupt section change, for incompressible flow. First and second order turbulence statistics obtained from numerical experiments using different mesh topologies were analyzed. The results were validated with experimental data and numerical LES and DNS results reported by other researchers. It was found that by means of parametric mesh adjustment, it is possible to obtain spatial discretizations of low computational cost but which allow the prediction of turbulent flow characteristics, without the need to resort to explicit turbulence models. The results show that, indeed, although the numerical accuracy levels of DNS approaches are not reached, it is possible to have predictions comparable to those given by such high-accuracy numerical approaches.MaestríaMaestría en Ingeniería MecánicaSimulación Computacionalxiv, 118 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ingeniería - Maestría en Ingeniería - Ingeniería MecánicaDepartamento de Ingeniería Mecánica y MecatrónicaFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá530 - Física::532 - Mecánica de fluidos620 - Ingeniería y operaciones afines::621 - Física aplicada620 - Ingeniería y operaciones afines::629 - Otras ramas de la ingeniería000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación510 - Matemáticas::518 - Análisis numéricoNumerical analysisGeneración numérica de mallasAnálisis numéricoNumerical grid generationDinámica de fluidos computacionalChorros supersónicoschorros sub-expandidosFlujo turbulentoReengancheComputational Fluid Dynamicsunder-resolved Direct Numerical SimulationLarge-Eddy SimulationLid-Driven CavityDifferentially Heated CavityOpenFoamSupersonic jetsUnder-expanded jetsTurbulent flowBackward-facing stepSeparationReattachmentMetodología de mallado para simulaciones numéricas de flujos turbulentos a bajo costo computacionalMeshing methodology for numerical simulations of turbulent flows at low computational costTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMB. F. Armaly, F. Durst, J. C. F. Pereira, and B. Schönung. Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech., 127(-1):473{496, feb 1983. doi: 10.1017/s0022112083002839J. Bellan. Large-Eddy Simulation of Supersonic Round Jets: Effects of Reynolds and Mach Numbers. AIAA Journal, 54(5):1482{1498, may 2016. doi: 10.2514/1.j054548.G. Biswas, M. Breuer, and F. Durst. Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers. J. Fluids Eng., 126(3):362-374, may 2004. doi: 10.1115/1.1760532.Blog Ingeniería. Blog Ingeniería, el blog para ingenieros. https://blogingenieria.com/curiosidades/supercavitacion-velocidad-supersonica/, 2021. Online; Accesado en 08 de Noviembre de 2021.D. J. Bodony and S. K. Lele. On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets. Physics of Fluids, 17(8):085103, aug 2005. doi: 10.1063/1.2001689.F. Bonelli, A. Viggiano, and V. Magi. High-speed turbulent gas jets: an LES investigation of Mach and Reynolds number effects on the velocity decay and spreading rate. Flow, Turbulence and Combustion, 107(3):519-550, feb 2021. doi: 10.1007/s10494-021-00242-5.C. Bosshard, A. Dehbi, M. Deville, E. Leriche, R. Puragliesi, and A. Soldati. Large Eddy Simulation of the Differentially Heated Cubic Cavity Flow by the Spectral Element Method. Computers and Fluids, 86:210-227, 2013. doi: 10.1016/j.compuid.2013.07.007.C. Bosshard, M. O. Deville, A. Dehbi, and E. Leriche. UDNS or LES, That Is the Question. Open Journal of Fluid Dynamics, 5:339-352, 12 2015. doi: 10.4236/ojfd.2015.54034.R. Bouffanais, M. O. Deville, and E. Leriche. Large-Eddy Simulation of the Flow in a Lid-Driven Cubical Cavity. Phys. Fluids, 19, 2007. doi: 10.1063/1.2723153.G. A. Brès, F. E. Ham, J. W. Nichols, and S. K. Lele. Unstructured Large-Eddy Simulations of Supersonic Jets. AIAA Journal, 55(4):1164-1184, apr 2017. doi: 10.2514/1.j055084.J. Bridges and M. Wernet. Turbulence Associated with Broadband Shock Noise in Hot Jets. In AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, may 2008. doi: 10.2514/6.2008-2834.G. Castiglioni and J. A. Domaradzki. A numerical dissipation rate and viscosity in flow simulations with realistic geometry using low-order compressible Navier-Stokes solvers. Computers and Fluids, 119:37-46, 2015. doi: 10.1016/j.compfluid.2015.07.004.A. Darisse, J. Lemay, and A. Benaïssa. Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet. Journal of Fluid Mechanics, 774:95-142, jun 2015. doi: 10.1017/jfm.2015.245.J. R. DeBonis and J. N. Scott. Large-Eddy Simulation of a Turbulent Compressible Round Jet. AIAA Journal, 40(7):1346-1354, jul 2002. doi: 10.2514/2.1794.C. D. Donaldson and R. S. Snedeker. A study of free jet impingement. Part 1. Mean properties of free and impinging jets. J. Fluid Mech., 45(02):281, jan 1971. doi: 10.1017/s0022112071000053.J. Freund, S. Lele, and P. Moin. Direct simulation of a Mach 1.92 jet and its sound field. AIAA, jun 1998. doi: 10.2514/6.1998-2291.D. V. Gaitonde. Analysis of the Near Field in a Plasma-Actuator-Controlled Supersonic Jet. J. Propul. Power, 28(2):281-292, mar 2012. doi: 10.2514/1.b34289.L. Gamet and J. L. Estivalezes. Application of Large-Eddy Simulations and Kirchhoff Method to Jet Noise Prediction. AIAA Journal, 36(12):2170-2178, dec 1998. doi: 10.2514/2.341.W. K. George. Lectures in Turbulence for the 21st Century. Department of Thermo and Fluid Engineering, Chalmers University of Technology, Göteborg, Sweden, 2005.D. González, D. Gaitonde, and M. Lewis. Large-eddy simulations of plasma-based asymmetric control of supersonic round jets. International Journal of Computational Fluid Dynamics, 29(3-5):240-256, mar 2015. doi: 10.1080/10618562.2015.1053877.C. J. Greenshields, H. G. Weller, L. Gasparini, and J. M. Reese. Implementation of semidiscrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows. Int. J. Numer. Methods Fluids, 63:1-21, May 2009. doi: 10.1002/fld.2069.J. Hart. Comparison of Turbulence Modeling Approaches to the Simulation of a Dimpled Sphere. Procedia Engineering, 147:68-73, 2016. doi: 10.1016/j.proeng.2016.06.191.J. I. Hileman, B. S. Thurow, E. J. Caraballo, and M. Samimy. Large-scale structure evolution and sound emission in high-speed jets: real-time visualization with simultaneous acoustic measurements. J. Fluid Mech., 544(-1):277-307, nov 2005. doi: 10.1017/s002211200500666x.D. Jehad, G. Hashim, A. Kadhim Zarzoor, and N. A. Che Sidik. Numerical Study of Turbulent Flow over Backward-Facing Step with Different Turbulence Models. Journal of Advanced Research Design, 4:2289-7984, 01 2015.S. Jovic and D. M. Driver. Backward-facing step measurements at low Reynolds number, Re(sub h)=5000. In NASA Technical Memorandum 108807, 1994.N. Kasagi and A. Matsunaga. Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow. Int. J. Heat and Fluid Flow, 16(6):477-485, dec 1995. doi: 10.1016/0142-727x(95)00041-n.A. Khavaran, E. Krejsa, and C. Kim. Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model. In 30th Aeroespace Sciences Meeting and Exhibit. AIAA-92-0500, jan 1992. doi: 10.2514/6.1992-500.J. Kim, S. J. Kline, and J. P. Johnston. Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step. J. Fluids Eng., 102(3):302-308, sep 1980. doi: 10.1115/1.3240686.J. Kostas, J. Soria, and M. Chong. Particle image velocimetry measurements of a backward-facing step flow. Experiments in Fluids, 33(6):838-853, dec 2002. doi: 10.1007/s00348-002-0521-9.A. Kurganov and E. Tadmor. New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations. J. Comput. Phys., 160(1):241-282, may 2000. doi: 10.1006/jcph.2000.6459.J. C. Lau, P. J. Morris, and M. J. Fisher. Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech., 93(1):1-27, jul 1979. doi: 10.1017/s0022112079001750.H. Le, P. Moin, and J. Kim. Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech., 330:349-374, jan 1997. doi: 10.1017/s0022112096003941.E. Leriche. Direct Numerical Simulation of Lid Driven Cavity at High Reynolds Numbers. J. Sci. Comput., 27:335-345, 2006. doi: 10.1007/s10915-005-9032-1.J. Liu, K. Kailasanath, R. Ramamurti, D. Munday, E. Gutmark, and R. Lohner. Large-Eddy Simulations of a Supersonic Jet and Its Near-Field Acoustic Properties. AIAA Journal, 47(8):1849-1865, aug 2009. doi: 10.2514/1.43281.S.-C. Lo, G. Blaisdell, and A. Lyrintzis. Numerical Simulation of Supersonic Jet Flows and their Noise. In 14th AIAA/CEAS Aeroacoustics Conference. AIAA 2008-2970, may 2008. doi: 10.2514/6.2008-2970.S.-C. Lo, G. Blaisdell, and A. Lyrintzis. Numerical Investigation of 3-D Supersonic Jet Flows Using Large Eddy Simulation. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA 2011-1155, jan 2011. doi: 10.2514/6.2011-1155.C. Loh and L. Hultgren. Near-Field Noise Computation for a Supersonic Circular Jet. In 11th AIAA/CEAS Aeroacoustics Conference. AIAA 2005-3042, may 2005. doi: 10.2514/6.2005-3042.R. R. Mankbadi, M. E. Hayer, and L. A. Povinelli. Structure of supersonic jet flow and its radiated sound. AIAA Journal, 32(5):897-906, may 1994. doi: 10.2514/3.12072.L. F. G. Marcantoni, J. P. Tamagno, and S. A. Elaskar. High Speed Flow Simulation using OpenFOAM. Asociación Argentina de Mecánica Computacional, XXXI:2939-2959, nov 2012.R. Maulik and O. San. Explicit and implicit LES closures for Burgers turbulence. J. Comput. Appl. Math., 327:12-40, 2018. doi: 10.1016/j.cam.2017.06.003.R. C. Moura, S. J. Sherwin, and J. Peiró. Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods. J. Comput. Phys., 298:695-710, 2015. doi: 10.1016/j.jcp.2015.06.020.E. Murakami and D. Papamoschou. Eddy Convection in Coaxial Supersonic Jets. AIAA Journal, 38(4):628-635, apr 2000. doi: 10.2514/2.1034.A. Nigro, C. D. Bartolo, A. Crivellini, M. Franciolini, A. Colombo, and F. Bassi. A low-dissipation DG method for the under-resolved simulation of low Mach number turbulent flows. Computers and Mathematics with Applications, 77:1739-1755, 2019. doi: 10.1016/j.camwa.2018.09.049.OpenFOAM. OpenFOAM v5 User Guide. https://cfd.direct/openfoam/user-guide, 2021. Online; Accesado en Octubre de 2021.J. Panda and R. Seasholtz. Velocity and temperature measurement in supersonic free jets using spectrally resolved Rayleigh scattering. In 37th AIAA Aerospace Sciences Meeting and Exhibit. AIAA-99-0296, jan 1999. doi: 10.2514/6.1999-296.B. Panjwani, I. S. Ertesvag, A. Gruber, and K. E. Rian. Large Eddy Simulation of Backward Facing Step Flow. In Fifth National Conference on Computational Mechanics, Trondheim 26-27, pages 353-369, may 2009.S. B. Pope. Turbulent Flows. Cambridge University Press, 2000. ISBN 9780521598866. URL https://books.google.com.co/books?id=HZsTw9SMx-0C.H. P. Rani, T. W. H. Sheu, and E. S. F. Tsai. Eddy structures in a transitional backward-facing step flow. J. Fluid Mech., 588:43-58, sep 2007. doi: 10.1017/s002211200700763x.S. Rodriguez. LES and DNS Turbulence Modeling. Springer International Publishing, 2019. doi: 10.1007/978-3-030-28691-0_5.A. Rona and X. Zhang. Time accurate numerical study of turbulent supersonic jets. J. Sound Vib., 270(1-2):297-321, feb 2004. doi: 10.1016/s0022-460x(03)00537-6.M. Samimy, J.-H. Kim, J. Kastner, I. Adamovich, and Y. Utikn. Active control of high-speed and high-Reynolds-number jets using plasma actuators. J. Fluid Mech., 578:305-330, apr 2007. doi: 10.1017/s0022112007004867.J. M. Seiner. Fluid Dynamics and Noise Emission Associated With Supersonic Jets. In T. G. Gatski et al. (eds.), Studies in Turbulence, pages 297-323. Springer New York, 1992. doi: 10.1007/978-1-4612-2792-2_22.E. Shehadi. Large Eddy Simulation of Turbulent Flow over a Backward-Facing Step. Master's thesis, Uppsala Universitet, Mar. 2018.S. Shih, D. Hixon, R. Mankbadi, and L. Povinelli. Prediction of flow and acoustic fields of a supersonic jet. In AIAA Paper 96-0751, jan 1996. doi: 10.2514/6.1996-751.C. Tam, M. Golebiowski, and J. Seiner. On the two components of turbulent mixing noise from supersonic jets. In AIAA Meeting Papers on Disc, NAG1-1776, AIAA Paper 96-1716, may 1996. doi: 10.2514/6.1996-1716.B. A. Toms. Large-eddy Simulation of Flow over a Backward Facing Step: Assessment of Inflow Boundary Conditions, Eddy Viscosity Models, and Wall Functions. J. Appl. Mech. Eng., 04(03), 2015. doi: 10.4172/2168-9873.1000169.K. Viswanathan, N. Reddy, and L. Sankar. A fluid/acoustic coupled simulation of supersonic jet noise. In 32nd Aerospace Sciences Meeting and Exhibit, jan 1994. doi: 10.2514/6.1994-137.J. C. Vogel and J. K. Eaton. Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step. J. Heat Transfer, 107(4):922-929, nov 1985. doi: 10.1115/1.3247522.P. O. Witze. Centerline Velocity Decay of Compressible Free Jets. AIAA Journal, 12(4):417-418, apr 1974. doi: 10.2514/3.49262.S. Ye, Y. Lin, L. Xu, and J. Wu. Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow. Mathematics, 8(1):119, jan 2020. doi: 10.3390/math8010119.EstudiantesInvestigadoresORIGINAL1022416879.2022.pdf1022416879.2022.pdfTesis de Maestría en Ingeniería Mecánicaapplication/pdf17829996https://repositorio.unal.edu.co/bitstream/unal/81966/3/1022416879.2022.pdf890a2ca0aeec56a3c13b92ef20e87ee3MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/81966/4/license.txt8153f7789df02f0a4c9e079953658ab2MD54THUMBNAIL1022416879.2022.pdf.jpg1022416879.2022.pdf.jpgGenerated Thumbnailimage/jpeg5295https://repositorio.unal.edu.co/bitstream/unal/81966/5/1022416879.2022.pdf.jpg255b468cc360535d9d1a861ca350128eMD55unal/81966oai:repositorio.unal.edu.co:unal/819662023-08-07 23:03:42.288Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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

Publicaciones similares