非恒定摩阻的TVD格式数值模拟水击衰减研究

Numerical simulations of water hammer attenuation due to unsteady friction using a TVD scheme

传统拟恒定摩阻模型的TVD格式虽能精确捕捉水击压力峰值,但无法准确描述水击波衰减和畸变过程,这对管线设计及管理十分不利,因此考虑非恒定摩阻的TVD格式值得深入研究。本文基于Brunone的IAB经验摩阻模型,结合Sweby的TVD格式给出了一维水击方程新的数值解法,将其运用到经典模型试验和工程实例中,并与传统拟恒定摩阻模型TVD格式和非恒定摩阻模型的特征线法的模拟效果进行对比分析。计算结果表明:考虑非恒定摩阻的TVD格式可以更加准确地捕捉水击波各周期压力峰值衰减和畸变的全过程,且模拟偏差随时间增加无增大趋势。其中各周期压力峰值捕捉误差不超过3%,相位偏移不超过0.5弧度,计算精度显著提高。该模型计算耗时和传统模型相差不大,具有良好的工程应用潜力和研究价值。

The peak pressure of water hammer waves can be accurately captured by using traditional TVD schemes solving a quasi-constant friction model, but their attenuation and distortion cannot be exactly described by such models. Further studies on TVD schemes solving unsteady friction models are needed to eliminate the shortcoming of traditional models in pipeline design and management. In this work, we have developed a new numerical method for solving the one-dimensional water hammer equations based on the Sweby＇s TVD scheme and Brunone＇s IAB unsteady friction model and verified it through comparison with previous studies of classical water hammer experiment and application to engineering examples. It was compared with a traditional TVD scheme solving a quasi-constant friction model and the method of characteristics solving the unsteady friction model. Results show that our new method can capture the attenuation and distortion of water hammer waves in each of the calculated wave cycles and improve the accuracy in calculation of the resulting pressure peaks. And its numerical errors do not increase with simulation time, remaining less than 3% in peak pressure and no larger than 0.5 radian in phase shift for all the calculated wave cycles. With its computational cost comparable to that of traditional models, the new model is obviously superior for engineering application and research.