<p>This study employs the Smoothed Particle Hydrodynamics (SPH) method to investigate hydraulic transient phenomena in pipelines. The Corrected SPH (CSPH) technique effectively addresses domain support boundary imbalances, while the introduction of artificial viscosity suppresses spurious oscillations. A thorough assessment of unsteady friction models underscores their accuracy, showing the model based on two empirical coefficients — <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7113_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{x}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation>, influencing the pressure wave damping ratio, and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7113_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{t}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation>, which governs pressure wave celerity — as the best among the unsteady friction models. The research optimizes critical parameters to minimize discrepancies between numerical simulations and experimental outcomes, revealing the significant effects of coefficients <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7113_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$K_x$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7113_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{t}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> on the accuracy of simulation responses. Furthermore, the study highlights the importance of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7113_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">$\Delta x$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation>, the initial particle spacing, alongside the number of particles, to enhance both accuracy and stability in simulations. The proposed methodology demonstrates promising capabilities in simulating hydraulic transients, offering valuable insights for more precise modeling of fluid dynamics phenomena.</p>

Hydraulic transient analysis with the Smoothed Particle Hydrodynamics method coupled with unsteady friction model

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2025年6月11日

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Almério José Venâncio Pains Soares Pamplona,
José Fernandes Júnior,
Joel Roberto Guimarães Vasco,
Andreia Aoyagui Nascimento

摘要

This study employs the Smoothed Particle Hydrodynamics (SPH) method to investigate hydraulic transient phenomena in pipelines. The Corrected SPH (CSPH) technique effectively addresses domain support boundary imbalances, while the introduction of artificial viscosity suppresses spurious oscillations. A thorough assessment of unsteady friction models underscores their accuracy, showing the model based on two empirical coefficients — $K_{x}$ $K_{x}$ , influencing the pressure wave damping ratio, and $K_{t}$ $K_{t}$ , which governs pressure wave celerity — as the best among the unsteady friction models. The research optimizes critical parameters to minimize discrepancies between numerical simulations and experimental outcomes, revealing the significant effects of coefficients $K_x$ $K_{x}$ and $K_{t}$ $K_{t}$ on the accuracy of simulation responses. Furthermore, the study highlights the importance of $\Delta x$ $Δ x$ , the initial particle spacing, alongside the number of particles, to enhance both accuracy and stability in simulations. The proposed methodology demonstrates promising capabilities in simulating hydraulic transients, offering valuable insights for more precise modeling of fluid dynamics phenomena.