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ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
ANALYTICAL SOLUTION OF ZIELKE’S UNSTEADY FRICTION MODEL FOR ONE-DIMENSIONAL PIPE FLOW IN LIGHT OF THE SECOND LAW OF THERMODYNAMICS
Submission Author:
Jaguarê Smith Gonzaga Filho , RJ
Co-Authors:
Jaguarê Smith Gonzaga Filho, Felipe Bastos de Freitas Rachid
Presenter: Jaguarê Smith Gonzaga Filho
doi://10.26678/ABCM.ENCIT2022.CIT22-0144
Abstract
Although different authors have been developing distinct unsteady friction models in one-dimensional pipe flow, there is no consensus about which model class better describes the water-hammer phenomenon. This disagreement happens due to the lack of analysis criteria. Over the decades, researchers usually compare the unsteady hydraulic head numerical results of distinct classes of models to the measured data of a particular experiment, pointing out the error of wave peak amplitude, or the wave shape resemblance. So, it is relevant to show the application of new criteria in order to reveal inconsistencies inside the models or even rule out physically wrong ones. The classical Second Law of Thermodynamics (SLT) must be used as a criterion since it does not admit negative rates of energy dissipation generated by the friction force for any particular case. Therefore, an analysis using the SLT needs to be carried out to identify issues and maybe suggest corrections. A classical SLT inequality to properly evaluate those models was derived. Then, two unsteady friction models were applied to it, reaching an analytical solution for both. The famous Zielke’s original model failed according to the classical SLT, and the Nucci and Spena’s model satisfied it.
Keywords
unsteady friction model, transient flow in pipes, Zielke’s model, Nucci and Spena’s model
