| 摘要: |
| 【目的】针对马蹄形断面几何形式复杂，其临界水深为高次超越方程，难以直接求解，现有公式多为分段函数且存在误差大、适用范围小等问题，以期提出一种方便实用且具有较高精度的临界水深直接算法。【方法】通过对明渠临界流方程进行恒等变换，统一标准I、II型马蹄形断面临界水深计算方程，基于数学理论构造替代函数模型，并通过带粒子释放的优化PSO算法对研究范围内的真值按照预设函数模型进行逼近。【结果】建立了标准I、II型马蹄形断面临界水深直接计算式。通过对现有公式的归纳比选、误差分析及实例计算表明：该式形式简单不分段、计算方便快捷且物理概念明确，在工程实用范围内计算相对误差绝对值最大分别为0.37%和0.40%，具有较高的计算精度。【结论】建立的马蹄形断面临界水深直接计算式在简捷性、适用范围、精度等方面综合评价较好，实用推广性强。同时为灌区引水工程和水利水电输水隧洞工程其他断面设计中临界水深计算提供有益参考。 |
| 关键词: 水力学；临界水深；马蹄形断面；PSO算法 |
| DOI： |
| 分类号:TV131.4 |
| 基金项目: |
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| Direct calculation formula for critical water depth of standard I and II horseshoe-shaped section |
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liuxile, zhaomingyan
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Hebei Provincial Academy of Water Resources
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| Abstract: |
| 【Background】Critical water depth is an important parameter for the determination of open channel flow patterns, and it is an inevitable element in open channel hydraulic section design and hydraulic calculation. It has a wide range of applications and high accuracy requirements. The standard horseshoe-shaped section requires low geological conditions, is convenient for construction, and has superior hydraulic conditions. It is one of the commonly used sections of water diversion tunnels in irrigation areas.【Objective】 In view of the complex geometry of the horseshoe section, the critical water depth of the horseshoe section is a higher-order transcendental equation, which is difficult to solve directly, and the existing formulas are mostly piecewise functions with large errors and small scope of application. Therefore, a convenient and practical direct critical water depth algorithm with high accuracy is proposed.The critical water depth is a high-order transcendental equation, which is difficult to solve directly. The existing formulas are mostly piecewise functions and have problems such as large errors and small scope of application.【Method】 To this end, this paper transformed the critical water depth solution problem into solving a nonlinear constrained optimization problem through the identity transformation of the open channel critical flow equation, and constructed an inverse function model. MATLAB software programming was used to realize the optimized PSO algorithm with particle release. The true value calculated in the practical range was approximated according to the preset function model, and the direct calculation formula for the critical water depth of the standard I and II horseshoe-shaped section is established.【Result】 Through induction and comparison of the existing formulas, error analysis and calculation of examples, The results showed that: (1) The formula is simple in form and not segmented, and the calculation is convenient and quick and the physical concept is clear. The formula adopts the form of compound power function, and it can be directly calculated without segmentation discrimination. The scope of application includes part of the bottom arch section, side arch section and top arch section to meet the requirements of common engineering scope. It overcomes the cumbersome and slow convergence of the iterative calculation method, and reduces the workload of the grassroots engineering and technical personnel. (2) Through accuracy comparison and example calculation, the maximum absolute value of relative error calculated within the applicable range is 0.37% and 0.40%, respectively, which has high calculation accuracy. The existing alternative formulas are comprehensively evaluated in terms of simplicity, scope of application and accuracy.【Conclusion】 The formulas in this paper have good comprehensive performance and can provide a useful reference for the design and operation management of horseshoe-shaped cross-sections of water diversion projects in irrigation areas and water conservancy and hydropower tunnel projects. |
| Key words: Hydraulics; critical water depth; horseshoe-shaped section; PSO algorithm |
