Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (7): 811-822.doi: https://doi.org/10.1007/s10483-013-1709-x

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Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

陈明 焦光伟 邓松圣 王建华   

  1. Department of Petroleum Supply Engineering, Logistical Engineering University of PLA, Chongqing 401311, P. R. China
  • 出版日期:2013-07-03 发布日期:2013-07-03
  • 通讯作者: Ming CHEN E-mail:chenchen8201@126.com

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

Ming CHEN, Guang-wei JIAO, Song-sheng DENG, Jian-hua WANG   

  1. Department of Petroleum Supply Engineering, Logistical Engineering University of PLA, Chongqing 401311, P. R. China
  • Online:2013-07-03 Published:2013-07-03
  • Contact: Ming CHEN E-mail:chenchen8201@126.com

摘要: The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

关键词: ssler振子, 非线性耦合, Liapunov指数, 相位同步, Rö, gas-liquid-solid three-phase flow, fluid-structure interaction, hydraulic transient, flux vector splitting, second-order precision

Abstract: The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

Key words: Lyapunov exponent, phase synchronization, Rö, ssler oscillator, nonlinearly coupled, gas-liquid-solid three-phase flow, fluid-structure interaction, hydraulic transient, flux vector splitting, second-order precision

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