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

Abstract

Abstract 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 (R 2  > 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%.