Solving Water Hammer equations by Chebyshev super-spectral viscosity method and unsteady roughness coefficient

Document Type : Original Article

Authors

Department of Water Engineering, College of Agriculture, Razi University, Kermanshah, Iran

Abstract

Predicting the impact due to the Water Hammer phenomenon is very important in the design of the pipe line and Water Hammer control equipment. Different numerical methods are used to solve Water Hammer equations. In this research, Chebyshev spectral method and Chebyshev super-spectral viscosity method have been used to solve these equations in the case of sudden and slow closing of the valve with steady, quasi-steady and unsteady roughness coefficient and were compared with experimental data. In the case of rapid closing of the valve, both spectral methods with unsteady roughness coefficient have high accuracy in predicting the pressure and the results of both methods are same. However, in the case of slow closing of the valve with unsteady roughness coefficient, at the beginning of the Water Hammer, there is an error in calculating the minimum and maximum pressure, and over time, the error decreases and the pressure values are predicted later than the real time. Comparison of the results of Chebyshev super spectral viscosity method with the finite difference method shows that the spectral method has a higher accuracy in fast closing of the valve than the finite difference method. While in the case of slow closing of the valve at the beginning of the Water Hammer, the finite difference method has a higher accuracy in calculating the minimum and maximum pressure values. But over time, the results of the Chebyshev viscosity spectral method conform to the results of the finite difference method, and both methods predict pressure values later.

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References

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