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Numerical verification of the singularity of Newtonian flow in a 4:1 contraction via the streamfunction-vorticity formulation ; Verificación numérica de la singularidad del flujo Newtoniano en una contracción 4:1 mediante la formulación corriente-vorticidad ; Verificação numérica da singularidade do escoamento Newtoniano em uma contração 4:1 por meio da formulação corrente-vorticidade

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Title: Numerical verification of the singularity of Newtonian flow in a 4:1 contraction via the streamfunction-vorticity formulation ; Verificación numérica de la singularidad del flujo Newtoniano en una contracción 4:1 mediante la formulación corriente-vorticidad ; Verificação numérica da singularidade do escoamento Newtoniano em uma contração 4:1 por meio da formulação corrente-vorticidade
Authors: Palhares Junior, Irineu Lopes, de Andrade, Larissa Vitória Ribeiro
Source: BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS; Vol. 5 (2024): Brazilian Electronic Journal of Mathematics; 1-17 ; BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS; v. 5 (2024): Brazilian Electronic Journal of Mathematics; 1-17 ; 2675-1313
Publisher Information: Portal de Periódicos UFU
Publication Year: 2024
Collection: Universidade Federal de Uberlândia (UFU): Sistema Eletrônico de Editoração de Revistas
Subject Terms: Escoamento Newtoniano, contração 4:1, formulação corrente-vorticidade, singularidade, Newtonian flow, 4:1 contraction, streamfunction-vorticity formulation, singularity, Flujo Newtoniano, contracción 4:1, formulación corriente-vorticidad, singularidad
Description: In this study, the asymptotic behavior of the velocity field and vorticity around a reentrant corner is investigated. The analysis is conducted through numerical simulations of Newtonian flow in a 4:1 contraction, using the streamfunction-vorticity formulation.The equations describing this flow were discretized using the finite difference method, and the numerical code was implemented in the C programming language. The robustness of the asymptotic behavior is evaluated under three distinct conditions: variations in the Reynolds number, the use of geometries with different lengths, and the comparison of results with those obtained by the Marker-And-Cell (MAC) approach.The main objective of this work is to validate the prediction of the asymptotic behavior near the geometric singularity and to demonstrate the independence of this phenomenon concerning variations in operational parameters and the extension of the contraction geometry. The investigation also addresses the comparative effectiveness of the streamfunction-vorticity and MAC methodologies, highlighting the good agreement between the formulations.The results indicate that, although both approaches can capture the fundamental behavior of the flow, differences still exist at points closest to the singularity, suggesting the need for improvements in computational models for simulating flows with complex geometric characteristics. ; En este estudio se investiga el comportamiento asintótico del campo de velocidad y la vorticidad en torno a una esquina reentrante. El análisis se realiza mediante simulaciones numéricas de flujo Newtoniano en una contracción con una razón 4:1, utilizando la formulación corriente-vorticidad. Las ecuaciones que describen este flujo se discretizaron utilizando la técnica de diferencias finitas, y el código numérico fue implementado en lenguaje C. La robustez del comportamiento asintótico se evalúa bajo tres condiciones distintas: variaciones en el número de Reynolds, el uso de geometrías con diferentes longitudes y la comparación de ...
Document Type: article in journal/newspaper
File Description: application/pdf
Language: Portuguese
Relation: https://seer.ufu.br/index.php/BEJOM/article/view/73402/39979; https://seer.ufu.br/index.php/BEJOM/article/view/73402
DOI: 10.14393/BEJOM-v5-2024-73402
Availability: https://seer.ufu.br/index.php/BEJOM/article/view/73402
https://doi.org/10.14393/BEJOM-v5-2024-73402
Rights: Copyright (c) 2024 Irineu Lopes Palhares Junior, Larissa Vitória Ribeiro de Andrade ; https://creativecommons.org/licenses/by-nc/4.0
Accession Number: edsbas.51FB5D13
Database: BASE
Description
Abstract:In this study, the asymptotic behavior of the velocity field and vorticity around a reentrant corner is investigated. The analysis is conducted through numerical simulations of Newtonian flow in a 4:1 contraction, using the streamfunction-vorticity formulation.The equations describing this flow were discretized using the finite difference method, and the numerical code was implemented in the C programming language. The robustness of the asymptotic behavior is evaluated under three distinct conditions: variations in the Reynolds number, the use of geometries with different lengths, and the comparison of results with those obtained by the Marker-And-Cell (MAC) approach.The main objective of this work is to validate the prediction of the asymptotic behavior near the geometric singularity and to demonstrate the independence of this phenomenon concerning variations in operational parameters and the extension of the contraction geometry. The investigation also addresses the comparative effectiveness of the streamfunction-vorticity and MAC methodologies, highlighting the good agreement between the formulations.The results indicate that, although both approaches can capture the fundamental behavior of the flow, differences still exist at points closest to the singularity, suggesting the need for improvements in computational models for simulating flows with complex geometric characteristics. ; En este estudio se investiga el comportamiento asintótico del campo de velocidad y la vorticidad en torno a una esquina reentrante. El análisis se realiza mediante simulaciones numéricas de flujo Newtoniano en una contracción con una razón 4:1, utilizando la formulación corriente-vorticidad. Las ecuaciones que describen este flujo se discretizaron utilizando la técnica de diferencias finitas, y el código numérico fue implementado en lenguaje C. La robustez del comportamiento asintótico se evalúa bajo tres condiciones distintas: variaciones en el número de Reynolds, el uso de geometrías con diferentes longitudes y la comparación de ...
DOI:10.14393/BEJOM-v5-2024-73402