改进的Preissmann狭缝法在明满流负压模拟中的研究

Research on improved Preissmann slot method for negative pressure simulation of free-surface-pressurized flow

摘要

【目的】Preissmann狭缝法在明满流数值模拟中运用非常广泛，然而该方法无法直接用于模拟负压现象。在现有方法分析的基础上，对Preissmann狭缝法进行改进，以实现包含负压的明满流过程模拟。【方法】模型首先通过初始状态的水头和通气条件进行流态判别，若初始状态的水头低于管道顶部，并且管道不与大气相通，则判定水流为负压流。对于出现的负压流，按满管流冻结过流断面面积，方程求解仍采用Preissmann狭缝法统一模式，但方程中的水位转换为水头，随后刻画了明渠流、有压流和负压流的计算方法及其统一控制方程，并采用Preissmann四点隐格式进行离散求解，以此建立改进的一维明满流模型。【结果】通过多个经典算例、某多级串联电站尾水衔接段数值模拟进行对比验证，结果显示：改进的Preissmann狭缝法可有效模拟明渠流、有压流、负压流以及明满流过渡过程，并且对计算效率没有明显影响，对于某实际案例而言，计算时长仅慢0.243 s。【结论】结果表明：传统的Preissmann狭缝法中水头和水位始终保持一致，但对于负压流而言，水头与水位应相互分离；在改进的Preissmann狭缝法中，对于出现的负压流按满管流冻结过流面积，而方程求解与传统方法一致，只需将方程中的水位转换为水头，从而实现负压模拟。

Abstract

[Objective] The Preissmann slot method is widely used in numerical simulation of free-surface-pressurized flow. However, it cannot directly simulate negative pressure. Based on the analysis of existing method, the Preissmann slot method is improved to enable the simulation of free-surface-pressurized flow process involving negative pressure. [Methods] The model was used to determine the different flow patterns based on the initial state of water head and aeration conditions. If the initial water head was lower than the top of the pipeline and the pipeline was not connected to the atmosphere, the flow was determined as negative pressure flow. For negative pressure flow, the flow cross-sectional area was treated as a frozen full-pipe flow. The Preissmann slot method was still used to solve the equation, but the water level in the equation was converted to water head. Subsequently, the calculation method for open channel flow, pressurized flow, and negative pressure flow were described, along with the unified controlling equations. The Preissmann four-point implicit scheme was used for discrete solution, so as to establish an improved one-dimensional free-surface-pressurized flow model. [Results] Multiple classic cases and numerical simulations of the tailwater transition section of a multi-stage cascade hydropower station were used for comparison and validation. The result showed that the improved Preissmann slot method could effectively simulate the transition processes of open channel flow, pressurized flow, negative pressure flow, and free-surface-pressurized flow, with no significant impact on calculation efficiency. For a specific real-world case, the calculation time was only 0.243 s longer. [Conclusion] The research indicates that in the traditional Preissmann slot method, the water head and water level remain consistent. However, for negative pressure flow, the water head and water level should be separated. In the improved Preissmann slot method, the flow cross-sectional area is treated as a frozen full-pipe flow for negative pressure conditions, and the equation solving remains consistent with the traditional method. The only modification required is converting the water level in the equation to water head, thus enabling the simulation of negative pressure flow.

关键词

水力学 / 明满流 / 负压模拟 / 数值模拟 / 改进Preissmann狭缝法

Key words

hydraulics / free-surface-pressurized flow / negative pressure simulation / numerical simulation / improved Preissmann slot method

基金资助

国家自然科学基金项目(52209105)

中国水科院基本科研业务费项目(HY110145B0012024)

流域水循环模拟与调控国家重点实验室自主研究课题(SKL2022ZD03)