Numerical estimates of the adequacy of a mathematical model of hydroelastic oscillations in curved pipelines

The problem was set in the research context of water hammer in the pipeline system with complex configuration. Usually, the experimental data in the literature on such pipelines are limited to the charts of the unknown functions. Numerical criteria of the adequacy of a mathematical model for a pipeline and an algorithm for its quantitative verification are selected for the case where data is presented in a reference source only by the charts of functions. A new mathematical model is presented and a series of numerical experiments for the water hammer in a variety of curved pipelines have been performed. To verify the model, two pipelines are taken: a pipeline consisting of seven sections of the total length of 48 m, and a smoothly curved pipe of the total length of 624 mm. In addition, acoustic oscillations of a bent pipe of 300 mm in length are calculated. Based on the published data on these pipelines and the results of numerical experiments, quantitative characteristics of the adequacy of the mathematical model proposed are found. These characteristics are the results from statistical analysis of discrete time series of fluid pressure, which are obtained by digitizing charts from the articles referenced here and by solving equations of the tested model. It has been found that the description of the results of field experiments by the proposed mathematical model exhibits accuracy close to that of a mathematical description of the reference sources. In the case when a pipe consists of seven sections, its accuracy can be improved using the parameter identification methods. Thus, the proposed mathematical model adequately describes the results obtained for hydraulic shock in pipes and covers different cases of hydro-elastic vibrations from a unified viewpoint.