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An Implicit Approach for Numerical Simulation of Water Hammer Induced Pressure in a Straight Pipe

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Abstract

An accurate prediction of propagation speed and the magnitude induced pressure in water hammer is very critical for the analysis, design, and operation of pipeline transmissions. A new numerical scheme based on an implicit discretization of the method of characteristics solution (IMOC) was proposed in this study. The numerical results were compared with the experimental data and the explicitly discretized solution of the method of characteristics (MOC). Due to the transient nature of the problem, accurate estimation of the head loss can significantly alter the performance of numerical models. In this regards, the performance of both numerical models (i.e., MOC and IMOC) were tested. Four equations were employed based on the steady, quasi-steady, unsteady, and the simplified unsteady algorithms. An acceptable prediction of pressure head with a minimum relative error of −2% and a maximum error of 11% was achieved by using a quasi-steady algorithm for prediction of head loss term in the IMOC model whereas, the relative error of the MOC model was between −11% and +30%. The IMOC model in combination with the simplified unsteady algorithm for estimation of the head loss term had an error range between −20% and +2%, whereas the error range of the MOC model was between −35% and −3%. The numerical results indicated that the MOC model is less accurate than the IMOC in properly modeling the wave propagation speed which resulted in a time lag accumulation between numerical results and the measurements. It was found that the best combination of the numerical scheme and the head loss prediction equation was the IMOC model and the unsteady algorithm, which accurately simulated the time-history of pressure head within ±3% error.

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Authors and Affiliations

  1. Department of Civil Engineering, Razi University, Kermanshah, Iran

    Mohammad Bostan & Ali Akbar Akhtari

  2. Department of Civil Engineering, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    Amir Hossein Azimi

  3. Department of Soils and Agri-Food Engineering, Université Laval, Québec, QC, G1V 0A6, Canada

    Hossein Bonakdari

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  1. Mohammad Bostan
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  2. Amir Hossein Azimi
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  3. Ali Akbar Akhtari
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  4. Hossein Bonakdari
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Contributions

The first author performed the numerical simulation, the analysis of data, and wrote the manuscript. The second author finalized the figures and supervised the presentation of data, reviewed the manuscript, and addressed the Reviewers’ comments. The third and fourth authors supervised the technical content of the paper and reviewed the manuscript.

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Correspondence to Amir Hossein Azimi.

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Bostan, M., Azimi, A.H., Akhtari, A.A. et al. An Implicit Approach for Numerical Simulation of Water Hammer Induced Pressure in a Straight Pipe. Water Resour Manage 35, 5155–5167 (2021). https://doi.org/10.1007/s11269-021-02992-3

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