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<p>This study numerically investigates the effects of bed slope and proximity effects on 30° inclined dense jets in quiescent water using OpenFOAM with a modified pisoFOAM solver and realizable k-ε turbulence model. The results demonstrate that positive slopes (+ 2° to + 5°) shift the impingement point toward the source, while negative slopes (−2° to −5°) displace it downstream, with these effects becoming negligible at Fr ≤ 11. Upward slopes reduce impingement-point dilution by 7–19% compared to horizontal beds, whereas downward slopes enhance it by 5–22%. The results show a progressive increase in dilution from the return to the impact point for far‑bed jets: 7–20% on a horizontal bed (0°), 15–25% at a –2° downward slope, and 30–43% at a –5° downward slope. In contrast, on a + 2° upward slope, this increase is limited to only 1–2%. Parametric analysis reveals strong correlations between impact-point dilution, vertical impingement position, and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F\)</EquationSource> </InlineEquation> -slope interactions. While the model predicts flow characteristics reasonably well, it underestimates terminal rise height compared to experimental data and shows limited capability in resolving Coanda effects, indicating the need for improved turbulence modeling. These findings provide valuable insights for optimizing outfall designs in sloped environments, predicting environmental impacts through dilution analysis, and developing coastal discharge regulations.</p>

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Numerical Investigation of Bed Slope and Proximity Effects on the Dynamics of Inclined Dense Jets

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Mahshid Goodarzi,
  • Seyed Mostafa Siadatmousavi,
  • Ebrahim Jabbari

摘要

This study numerically investigates the effects of bed slope and proximity effects on 30° inclined dense jets in quiescent water using OpenFOAM with a modified pisoFOAM solver and realizable k-ε turbulence model. The results demonstrate that positive slopes (+ 2° to + 5°) shift the impingement point toward the source, while negative slopes (−2° to −5°) displace it downstream, with these effects becoming negligible at Fr ≤ 11. Upward slopes reduce impingement-point dilution by 7–19% compared to horizontal beds, whereas downward slopes enhance it by 5–22%. The results show a progressive increase in dilution from the return to the impact point for far‑bed jets: 7–20% on a horizontal bed (0°), 15–25% at a –2° downward slope, and 30–43% at a –5° downward slope. In contrast, on a + 2° upward slope, this increase is limited to only 1–2%. Parametric analysis reveals strong correlations between impact-point dilution, vertical impingement position, and \(F\) -slope interactions. While the model predicts flow characteristics reasonably well, it underestimates terminal rise height compared to experimental data and shows limited capability in resolving Coanda effects, indicating the need for improved turbulence modeling. These findings provide valuable insights for optimizing outfall designs in sloped environments, predicting environmental impacts through dilution analysis, and developing coastal discharge regulations.