Crank2Nicolson discrete form of pipeline water hammer equation and its engineering application
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Abstract:
In or der t o simulate the hydraulic tr ansit ion pro cess in the pipeline, a new model o f hydraulic calculation of pressur e pipe w as established. The finite v olume metho d was used to conduct the spatial and t em po ral integ ratio ns for the o ne2dimension2 al equation of water hammer pr essure pipe , the implicit Crank2Nicolso n scheme of central difference of time w as used to treat the pa rtial differ ential items, and the discrete format of w ater hammer equatio ns with the second or der accuracy and unco ndit ion2 al stability was obtained. The ex ample w ith analytic solutions w as used to v erify the met ho d accuracy . Thr ough the simulation of opening and closing pro cesses o f H uinanzhuang pum ping station o f t he South2to2Nor th Water Div ersio n Project in Beijing , pres2 sure fluctuatio n can be predicted, therefor e ear ly respo nse measur es can be pro po sed to reduce the o ccur rence probability o f w a2 ter hammer and the adver se effects of pressur e fluctuatio n, and t he trainset co nditions can be chang ed into no rmal o per ation. T he met ho d has go od eng ineering applicat ion.
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