Water Hammer Simulation Using Simplified Convolution-Based Unsteady Friction Model

Kamil Urbanowicz, Anton Bergant, Michał Stosiak, Adam Deptuła, Mykola Karpenko, Michał Kubrak, Apoloniusz Kodura

Omission of frequency-dependent hydraulic resistance (skin friction) during modelling of the water hammer phenomenon is unacceptable. This resistance plays a major role when the transient liquid flow occurs in rigid-walled pipes (steel, copper, etc.). In the literature, there are at least two different modelling approaches to skin friction. The first group consists of models based on instantaneous changes in local and convective velocity derivatives, and the second group are models based on the convolution integral and full history of the flow. To date, more popular models are those from the first group, but their use requires empirical coefficients. The second group is still undervalued, even if based on good theoretical foundations and does not require any empirical coefficients. This is undoubtedly related to the calculation complexity of the convolution integral. In this work, a new improved effective solution of this integral is further validated, which is characterised with the use of a simplified weighting function consisting of just two exponential terms. This approach speeds the numerical calculations of the basic flow parameters (pressure and velocity) significantly. Presented comparisons of calculations using the new procedure with experimental pressure runs show the usefulness of the proposed solution and prove that it maintains sufficient accuracy.

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