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<p>This article presents a detailed comparison between 1D and Q2D models used for simulating unsteady flows in pressurized conduits, commonly known as water hammer. The 1D model incorporates the effects of unsteady friction through a convolution integral, whereas the Q2D model is a recently developed approach based on the continuum theory of mixtures. Pressure responses from both models were compared against eight selected experimental studies (four for laminar flows and four for turbulent flows). The study qualitatively assessed the models' accuracy in simulating dynamic pressure, average velocity, and shear stress histories, with quantitative analysis focused on dynamic pressure responses. Both models exhibited high accuracy for simulating laminar flows. Additional numerical studies performed for turbulent flows highlighted the influence of the Ghidaoui parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>P</mi> </math></EquationSource> </InlineEquation> on the accuracy of both models. These studies underscored the need for experimental research in the range of low <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(P\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>P</mi> </math></EquationSource> </InlineEquation> values and indicated that the Q2D model is suitable for calculations when <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(P\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. Computational time analysis demonstrated that the Q2D model outperform the 1D model in relatively long tests in terms of efficiency, primarily because the 1D approach relies on a computationally expensive full convolution-based friction formulation. Furthermore, this work showed that the 1D model does not satisfy the Clausius–Duhem inequality criterion because, relying solely on average velocities, it cannot account for the contributions of the inner layers of fluid flow to total energy dissipation.</p>

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Accuracy and limitations of 1D and Q2D water hammer models for laminar and turbulent flows

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月17日

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  • Kamil Urbanowicz,
  • Douglas Monteiro Andrade,
  • Michał Kubrak,
  • Apoloniusz Kodura

摘要

This article presents a detailed comparison between 1D and Q2D models used for simulating unsteady flows in pressurized conduits, commonly known as water hammer. The 1D model incorporates the effects of unsteady friction through a convolution integral, whereas the Q2D model is a recently developed approach based on the continuum theory of mixtures. Pressure responses from both models were compared against eight selected experimental studies (four for laminar flows and four for turbulent flows). The study qualitatively assessed the models' accuracy in simulating dynamic pressure, average velocity, and shear stress histories, with quantitative analysis focused on dynamic pressure responses. Both models exhibited high accuracy for simulating laminar flows. Additional numerical studies performed for turbulent flows highlighted the influence of the Ghidaoui parameter \(P\) P on the accuracy of both models. These studies underscored the need for experimental research in the range of low \(P\) P values and indicated that the Q2D model is suitable for calculations when \(P\ge 3\) P ≥ 3 . Computational time analysis demonstrated that the Q2D model outperform the 1D model in relatively long tests in terms of efficiency, primarily because the 1D approach relies on a computationally expensive full convolution-based friction formulation. Furthermore, this work showed that the 1D model does not satisfy the Clausius–Duhem inequality criterion because, relying solely on average velocities, it cannot account for the contributions of the inner layers of fluid flow to total energy dissipation.