弱可压缩流体与可压缩流体模型的管路水击研究

Investigation on Water Hammer in Pipes by Slightly Compressible Fluid Model and Compressible Fluid Model

关键词:  管路模型  水击  弱可压缩流体  可压缩流体  有限体积法

Key words:  Pipeline model  Water hammer  Slightly compressible fluid  Compressible fluid  Finite volume method

摘要:

为提升液体推进系统模型对可压缩流体的仿真能力，针对供应管路的瞬变流动，采用一维有限体积法，使用Modelica语言基于MWorks平台分别开发了适用于补燃循环发动机仿真模型库的弱可压缩流体与可压缩流体的管路模型，不同于控制方程中显含声速的弱可压缩流体模型，可压缩流体模型通过将守恒方程与真实流体的SRK型状态方程耦合求解来计算压力波的传播。在管路供应系统中，分别以液氢、液氧及液甲烷为工质进行关阀水击的仿真研究，结果表明：使用SRK状态方程避免了可压缩流体模型对内能拟合公式的依赖，减轻了建模难度；可压缩流体模型对液氧及液甲烷的仿真结果较为准确，最大误差不超过2%，对液氢的最大计算误差约9%；相对于可压缩流体模型，弱可压缩流体模型计算得到的水击压力在振幅及频率上均偏大；可压缩流体模型计算得到的流体密度波动不超过3%，因此工程实践中处理水击问题时将液体假设为弱可压具有一定的合理性。

Abstract:

To improve the simulation capability of the liquid propulsion system model for compressible fluids, the pipeline models for slightly compressible fluid and compressible fluid have been developed respectively to investigate the hydraulic transients of feed lines in the present work. With one-dimensional finite volume method programmed under Modelica on MWorks platform, the models are suitable for a staged combustion cycle engine simulation package. Different from the slightly compressible fluid model, the speed of sound does not appear explicitly in the governing equations of the compressible fluid model. Instead, an equation of state for real fluid, SRK EoS, is solved in conjunction with the conservation equations to simulate the compressibility for modeling the wave propagation. The pressure surges of liquid hydrogen, liquid oxygen and liquid methane in a feed system have been predicted due to valve closing, and the results show that the utilization of SRK equation of state in compressible fluid model avoids the dependence on fitting the internal energy equation, which reduces the difficulty of modeling. And with the compressible model, the simulations of liquid oxygen and liquid methane are more accurate, that the maximum error does not exceed 2%, while the simulating error of liquid hydrogen is about 9%. The amplitude and frequency of impact pressure at the upstream of valve simulated by the slightly compressible fluid model are larger, compared to the compressible fluid model. Since density fluctuation calculated by the compressible fluid model is less than 3%, the assumption that transient flow of liquid is slightly compressible would be acceptable, especially for engineering application.