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<p>In two-dimensional domains, apertures represent bounded cross-sections that control transport in diverse engineering applications. While shape factors of regular apertures are well established, those of irregular boundaries remain poorly determined due to experimental limitations and modeling inadequacies. This paper introduces a Galerkin-based integral model to compute shape factors for arbitrary apertures, addressing this gap. The approach combines high-order piecewise polynomial boundary reconstruction with recovery of flow properties through the Poiseuille number, assuming fully developed laminar flows. We applied the method to four sandstone-derived apertures, with dimensionless areas ranging from 0.085 to 0.170 and hydraulic diameters from 0.076 to 0.163. Computed dimensionless velocities over the apertures varied between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1.4 \times 10^{-4}\,\hbox {and}\,6.7 \times 10^{-4}\)</EquationSource> </InlineEquation>, while Poiseuille numbers spanned 15.8–23.9, approaching the theoretical limit of 24. The resulting shape factors lay between 1.96 and 2.73, showing discrepancies below 5% when compared with finite element validations. The current approach enhances quantitative understanding of cross-sectional dynamics in fractured media and provides a practical tool for applications involving ducts, fissures, or cracks across biotechnology, engineering, and medical contexts.</p>

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Irregularly-bounded cross sections’ shape factors from high-order piecewise-polynomials

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Valdecir Alves dos Santos Júnior,
  • José One de Oliveira,
  • Juan Galvis,
  • Gustavo Peixoto de Oliveira

摘要

In two-dimensional domains, apertures represent bounded cross-sections that control transport in diverse engineering applications. While shape factors of regular apertures are well established, those of irregular boundaries remain poorly determined due to experimental limitations and modeling inadequacies. This paper introduces a Galerkin-based integral model to compute shape factors for arbitrary apertures, addressing this gap. The approach combines high-order piecewise polynomial boundary reconstruction with recovery of flow properties through the Poiseuille number, assuming fully developed laminar flows. We applied the method to four sandstone-derived apertures, with dimensionless areas ranging from 0.085 to 0.170 and hydraulic diameters from 0.076 to 0.163. Computed dimensionless velocities over the apertures varied between \(1.4 \times 10^{-4}\,\hbox {and}\,6.7 \times 10^{-4}\) , while Poiseuille numbers spanned 15.8–23.9, approaching the theoretical limit of 24. The resulting shape factors lay between 1.96 and 2.73, showing discrepancies below 5% when compared with finite element validations. The current approach enhances quantitative understanding of cross-sectional dynamics in fractured media and provides a practical tool for applications involving ducts, fissures, or cracks across biotechnology, engineering, and medical contexts.