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<p>Precise quantification of discharge capacity is essential for flood routing and reservoir safety. However, conventional design practices commonly assume a constant discharge coefficient (<i>µ</i>), neglecting the nonlinear variations that emerge during partial gate operations. This simplification introduces systematic errors in hydrological calculations and compromises downstream flow stability. This study employs a 1:45 geometrically undistorted hydraulic model of the EG Reservoir to investigate the nonlinear evolution of the bottom outlet discharge coefficient and to optimize the associated energy dissipation system. Experimental results reveal a pronounced “<i>U</i>-shaped” variation in <i>µ</i> relative to gate opening (<i>G</i>). While small openings (<i>G</i> &lt; 2.0&#xa0;m) maintain high discharge efficiency (<i>µ =</i> 0.77–0.82), a hydraulically “sensitive zone” emerges at intermediate openings (2.0&#xa0;m &lt; <i>G</i>&lt;3.0&#xa0;m). In this zone, intensified vertical jet contraction drives <i>µ</i> down to a minimum of 0.67, approximately 21% lower than standard design code recommendations. Accordingly, a cubic polynomial correction model (R<sup>2</sup> &gt; 0.99) was derived for real-time discharge prediction. This study provides a systematic quantification of the <i>U</i>-shaped nonlinear evolution mechanism of the discharge coefficient with gate opening for the radial-gated bottom outlet of the EG Reservoir and quantifies the discharge deviation amplitude (up to approximately 21%) in the hydraulic sensitive zone (<i>G</i> = 2.0–3.0&#xa0;m). To mitigate the hydraulic instability exacerbated by these discharge fluctuations, the stilling basin geometry was optimized by deepening the apron (from 5.0&#xa0;m to 7.4&#xa0;m) and raising the end sill. This geometric optimization transformed the flow regime from an unstable swept-out jump to a stable submerged jump, increasing energy dissipation efficiency from 46.3% to 64.5% under design flood conditions. These findings establish a quantitative framework for refined gate operation protocols and resilient energy dissipation design, with the correction model applicable for gate openings <i>G</i> = 0.96–4.80&#xa0;m (R² &gt; 0.99) under the tested geometric conditions, and demonstrated downstream scour reduction of 35–40%.</p>

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Nonlinear variation of discharge coefficient and energy dissipation optimization for bottom outlet of EG reservoir: an integral hydraulic model study

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月22日

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  • Ying Li,
  • Jiwei Zhao,
  • Yongshuai Yan,
  • Shihao Shen,
  • Xiaolei Zhang,
  • Quansheng Luo

摘要

Precise quantification of discharge capacity is essential for flood routing and reservoir safety. However, conventional design practices commonly assume a constant discharge coefficient (µ), neglecting the nonlinear variations that emerge during partial gate operations. This simplification introduces systematic errors in hydrological calculations and compromises downstream flow stability. This study employs a 1:45 geometrically undistorted hydraulic model of the EG Reservoir to investigate the nonlinear evolution of the bottom outlet discharge coefficient and to optimize the associated energy dissipation system. Experimental results reveal a pronounced “U-shaped” variation in µ relative to gate opening (G). While small openings (G < 2.0 m) maintain high discharge efficiency (µ = 0.77–0.82), a hydraulically “sensitive zone” emerges at intermediate openings (2.0 m < G<3.0 m). In this zone, intensified vertical jet contraction drives µ down to a minimum of 0.67, approximately 21% lower than standard design code recommendations. Accordingly, a cubic polynomial correction model (R2 > 0.99) was derived for real-time discharge prediction. This study provides a systematic quantification of the U-shaped nonlinear evolution mechanism of the discharge coefficient with gate opening for the radial-gated bottom outlet of the EG Reservoir and quantifies the discharge deviation amplitude (up to approximately 21%) in the hydraulic sensitive zone (G = 2.0–3.0 m). To mitigate the hydraulic instability exacerbated by these discharge fluctuations, the stilling basin geometry was optimized by deepening the apron (from 5.0 m to 7.4 m) and raising the end sill. This geometric optimization transformed the flow regime from an unstable swept-out jump to a stable submerged jump, increasing energy dissipation efficiency from 46.3% to 64.5% under design flood conditions. These findings establish a quantitative framework for refined gate operation protocols and resilient energy dissipation design, with the correction model applicable for gate openings G = 0.96–4.80 m (R² > 0.99) under the tested geometric conditions, and demonstrated downstream scour reduction of 35–40%.