FINITE VOLUME MODEL OF WATER COLUMN SEPARATION AND REJOINING WATER HAMMER IN VISCOELASTIC PIPES
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摘要: 基于有限体积法二阶Godunov求解格式对黏弹性输水管道中水柱分离弥合现象进行建模和模拟研究. 在传统的弹性管道模型基础上考虑管道黏弹性效应的影响. 在瞬变流控制方程中引入管道黏弹性项和动态摩阻项, 采用有限体积法进行求解, 考虑压力修正系数来模拟自由气体对计算单元的影响, 同时为避免数值模拟结果产生虚假震荡引入斜率限制器MINMOD函数; 通过虚拟单元法进行边界构建, 实现了计算区域的统一计算. 将所建模型计算结果与已有模型结果、试验结果进行对比, 并对影响模型的各参数进行敏感性分析. 结果表明, 本文模型能够准确模拟出纯水锤、水柱分离弥合水锤两种情况下的瞬态压力变化, 均能与试验数据高度吻合; 与传统的特征线方法相比, 当库朗数Cr小于1时, 有限体积法二阶Godunov格式计算结果更准确、稳定; 在压力波动的衰减过程中, 黏弹性效应相比于管道摩阻起主导作用; 与弹性管道模型相比, 考虑管道黏弹性效应后可显著提高模拟结果的准确性, 尤其是压力波峰值的相对误差明显降低.Abstract: Finite Volume Method with second-order Godunov-type scheme was developed to simulate the Water Column Separation and Rejoining phenomenon in viscoelastic water pipes. Based on the traditional elastic pipe model, the viscoelastic effect was considered in the process of numerical simulation. The viscoelasticity term and unsteady friction term were introduced into the governing equation of hydraulic transient flow, and the finite volume method with second-order Godunov scheme was used to solve the problem of numerical discretization and calculation. The pressure adjustment coefficient was considered to calculate the influence of free gas on the calculation unit, meanwhile the slope limiter MINMOD function was introduced for the sake of avoiding the spurious oscillations of numerical simulation results; The ghost cell method was used to construct the boundary and realize the unified computation of computing area at the same time. The calculation results of the model established in this paper were compared with those of the existing model and the experimental results, and the sensitivity analysis of the influencing parameters was also carried out. The results show that the proposed model can accurately simulate the transient pressures fluctuation and changes in the cases of both pure water hammer and water column separation and rejoining water hammer, which were basically identical with the experimental data; Compared with the traditional MOC method, when the Courant number Cr is less than 1, the results of Finite Volume Method's second-order Godunov scheme are more accurate and stable; In the process of pressure attenuation, viscoelastic effect plays a dominant role compared with pipeline friction; Compared with the mathematical model which only considers the elasticity of the pipe, the accuracy of simulation results can be significantly improved by considering the viscoelastic effect of the pipe, especially the relative error of the peak value of the pressure wave is significantly reduced.
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图 4 工况1下游阀门处计算值与试验结果
Figure 4. Calculation value and test result at downstream valve in Case 1
图 7 FVM-DGCM VE中α0对上游阀门压力的影响
Figure 7. Effects of α0 in FVM-DGCM VE on pressure at upstream valve
图 8 工况2上游阀门处计算值与试验结果
Figure 8. Calculation value and test result at upstream valve in Case 2
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