Numerical modeling and discharge coefficient analysis of semi-elliptical sharp-crested weirs

IF 2.7 3区工程技术 Q2 ENGINEERING, MECHANICAL

Flow Measurement and Instrumentation Pub Date : 2025-08-23 DOI:10.1016/j.flowmeasinst.2025.103035

Abbas Parsaie, Mahziar BasitNejad, Mohammad Bahrami-Yarahmadi

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Abstract

Sharp-crested weirs are commonly used for flow measurement in confined channels and low-velocity hydraulic systems, where the head-discharge relationship (H-Q) and discharge coefficient (Cd) are vital for performance assessment. While deriving the H-Q equation analytically involves integrating the velocity profile across the weir's flow section, complex geometries like semi-elliptical weirs introduce elliptic integrals that need numerical solutions. This study introduces a computational framework using Simpson's numerical integration (implemented in Python via Google Colab) to analyze the H-Q relationship for semi-elliptical sharp-crested weirs (SCSCWs). The calibrated model showed an average deviation of 10.2 % from experimental data, indicating acceptable predictive accuracy. Results indicate Cd values between 1.5 and 2.2 for relative heads (H/P = 0.1–0.8), with orientation-dependent trends: horizontal major axis (HMA) configurations show increasing Cd with head, while vertical major axis (VMA) configurations display decreasing Cd. Two orientation-specific regression models were developed and validated against laboratory data, achieving ∼4 % accuracy for HMA and ∼13 % for VMA.

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半椭圆尖顶堰数值模拟及流量系数分析

尖峰堰通常用于密闭通道和低速液压系统的流量测量，其中水头-流量关系（H-Q）和流量系数（Cd）对性能评估至关重要。虽然解析推导H-Q方程涉及对堰流段的速度剖面进行积分，但像半椭圆堰这样的复杂几何形状引入了需要数值解的椭圆积分。本研究引入了一个使用Simpson数值积分（通过谷歌Colab在Python中实现）的计算框架来分析半椭圆尖顶堰（SCSCWs）的H-Q关系。校正后的模型与实验数据的平均偏差为10.2%，预测精度可接受。结果表明，相对水头的Cd值在1.5和2.2之间（H/P = 0.1-0.8），具有方向依赖的趋势：水平长轴（HMA）配置显示Cd随水头增加，而垂直长轴（VMA）配置显示Cd减少。根据实验室数据开发并验证了两个方向特异性回归模型，HMA和VMA的准确度分别为~ 4%和~ 13%。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Flow Measurement and Instrumentation 工程技术-工程：机械

CiteScore

4.30

自引率

13.60%

发文量

123

审稿时长

6 months

期刊介绍： Flow Measurement and Instrumentation is dedicated to disseminating the latest research results on all aspects of flow measurement, in both closed conduits and open channels. The design of flow measurement systems involves a wide variety of multidisciplinary activities including modelling the flow sensor, the fluid flow and the sensor/fluid interactions through the use of computation techniques; the development of advanced transducer systems and their associated signal processing and the laboratory and field assessment of the overall system under ideal and disturbed conditions. FMI is the essential forum for critical information exchange, and contributions are particularly encouraged in the following areas of interest: Modelling: the application of mathematical and computational modelling to the interaction of fluid dynamics with flowmeters, including flowmeter behaviour, improved flowmeter design and installation problems. Application of CAD/CAE techniques to flowmeter modelling are eligible. Design and development: the detailed design of the flowmeter head and/or signal processing aspects of novel flowmeters. Emphasis is given to papers identifying new sensor configurations, multisensor flow measurement systems, non-intrusive flow metering techniques and the application of microelectronic techniques in smart or intelligent systems. Calibration techniques: including descriptions of new or existing calibration facilities and techniques, calibration data from different flowmeter types, and calibration intercomparison data from different laboratories. Installation effect data: dealing with the effects of non-ideal flow conditions on flowmeters. Papers combining a theoretical understanding of flowmeter behaviour with experimental work are particularly welcome.