准一维可压缩瞬变管流的有限体积模型(Ⅰ)流场的有限体积模型
Finite volume model for quasi one-dimensional compressible transient pipe flow (Ⅰ) Finite volume model of flow field
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摘要: 针对现有流体系统一维动力学模型缺乏统一的理论推导过程和能够涵盖众多模型的基本方程组的现象,从适用于连续介质控制体的欧拉型积分形式的流动守恒方程出发,经过合理模化推导得到了可压缩变截面管流准一维瞬变流动积分形式和微分形式的守恒方程.通过保留能量方程中的变体积项考虑了由于控制体体积的改变所输出的膨胀功.通过对守恒方程在空间交错网格上的有限体积离散建立了一种计算准一维可压缩变截面管流瞬变流场的有限体积模型,该模型可考虑变体积、变物性、轴向热传导、重力场影响,一方面,在深化和阐明了有限元状态变量模型体系的理论基础的同时,拓宽了其对瞬变流动的适用范围,另一方面,结合阀芯节流模型,从此模型出发可推导出管路系统常见元件的流场模型.Abstract: Given the fact that there is lack of a uniform deduction process in theory and an all-embracing base equation group for existing one-dimensional dynamic models of flow system,the integral and differential conservative equations of quasi one-dimensional compressible transient flow in pipe with variable section were derived by rational modeling based on integral conservative equations in Eulerian type of specification suitable for control volume of continuous fluid media.The expansion work resulted from variation of control volume was taken into account by reserving the variable volume term in energy equation.With two kinds of finite volume grids which are interlaced in discrete space,a finite volume model was established to describe quasi one-dimensional compressible transient pipe flow field.Actions derived from variable volume,variable fluid properties,axial heat conductivity and gravity were considered in the model.This reinforces and clarifies the theoretical foundation for the numerical system of finite element state-variable model,and also improves the scope of application.On the other hand,the model can be further developed to establish flow field models of common components in pipe system in collaboration with throttling model of valve core.
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