冰盖下梯形及抛物线形输水明渠正常水深显式迭代算法

Explicit iterative algorithm of normal water depth for trapezoid and parabolic open channels under ice cover

随着冬季用水量的增加,越来越多的输水工程在冬季冰盖下输水,冰盖下输水已经成为一种常态化输水方式,但目前对明渠正常水深的显式计算方法的研究主要针对不结冰渠道的,缺少对冰盖下输水时正常水深的显式计算方面的研究。该文推导了梯形断面冰盖下输水时正常水深和流量关系,提出了正常水深的简易显式迭代算法,并经过证明,此迭代算法是收敛的。用同样的方法,推导了抛物线形断面冰盖下输水时正常水深和流量关系,提出了计算正常水深的简易显式迭代算法。算例表明,该文提出的冰盖下梯形断面和抛物线形断面的显式迭代算法具有形式简单、计算量小、精度高,收敛性好的特点,一般需要3~5次迭代就可使误差小于0.01 m,当增大迭代次数时,误差进一步减小。研究为冰盖下输水渠道正常水深计算提供了便捷的计算方法,对冰期输水渠道的设计及运行管理具有理论和实践意义。

With the increase of water demand in winter in northern China, more and more open-channel water diversion projects transport water under the ice cover in winter such as the Middle Route of South-to-North Water Diversion Project. The method of transporting water using open channel under the ice cover has become increasingly common to delivery water from reservoirs, rivers and lakes to cities. The normal water depth is an important parameter in channel design, operation, flood control, and flow measurement and maintenance of the open channel or sewage systems. The explicit calculation algorithms of the normal water depth for the open channel are mainly for free-ice channels. This paper proposed algorithm of normal water depth of open channel under ice cover. The expression of the synthesis roughness for the flow of the channel under the ice cover was determined based on the studies of Sabaneev. The relationship between the normal water depth and the flow rate of the trapezoid section under the ice cover was derived. A simple explicit iterative algorithm to compute the normal water depth was then proposed. It proved that the new iterative algorithm was convergent using the convergence theory of iteration. The formula to getting the initial value was proposed using the best hydraulic section. The application examples were given to compute the normal depth under the ice cover by using the new iterative algorithm. The results showed that the explicit iterative algorithm proposed had a fast convergence speed. In general, the error would be less than 0.01 m with only 3-5 times iterations. The number of the iteration decreased when using the initial value from the best hydraulic section. When the number of iterations was increased, the iterative value would be closer to the theoretical value of the normal depth. By using the same method, the relationship between the normal water depth and the flow rate under the ice cover was derived for the parabolic section, and a simple explicit iterative algorithm for calculating the normal depth of water was proposed too. The examples showed that the explicit iterative formula of the parabolic section proposed was simple and had a fast convergence speed too. In general, the error would be less than 0.01 m with only 3-5 times iterations as well as trapezoid section. The study of this paper provides a convenient method for the calculation of the normal water depth of the water conveyance channel under the ice cover. The research has theoretical and practical significance for the design, operation and management of the water conveyance channels under the ice cover because the normal depth is most widely used in the water conservancy project.