Numerical verification of the singularity of Newtonian flow in a 4:1 contraction via the streamfunction-vorticity formulation
DOI:
https://doi.org/10.14393/BEJOM-v5-2024-73402Keywords:
Newtonian flow, 4:1 contraction, streamfunction-vorticity formulation, singularityAbstract
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.
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Copyright (c) 2024 Irineu Lopes Palhares Junior, Larissa Vitória Ribeiro de Andrade
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