Fast meshless solution with lumped friction for water hammer

The water hammer in pipelines, with the absence of fluid friction, could be solved by a time-domain exact solution, using a simple recursive process. No computational grid was needed, but the calculation time cost was extremely high. Its improved method, named as the fast meshless solution (FMS), was developed to speed the computation by introducing the time-line interpolation. For the purpose of practical applications, the attempt to consider fluid friction in the FMS is presented here. As there is no mesh grid in the distance-time plane, the distributed friction model can not be employed upon the presented method directly. The fluid friction lumped at the pipe end is proposed, and both steady and unsteady friction are studied. A benchmark problem of the water hammer in a reservoir-pipe-valve (RPV) system is employed for the validation and comparison. The water hammer considering lumped friction can be calculated fast by the FMS, and the accuracy is acceptable. The method discussed here may be of interest in a quick assessment of the piping water hammer.