Proposição da equação do coeficiente politrópico e do coeficiente de abertura de válvula para a modelagem computacional do esvaziamento de condutos forçados

Abstract

This study aims to analyze the adiabatic thermodynamic process during the emptying of a forced conduit, concurrently with the influence of downstream valve opening in the process. Recent studies propose the use of the polytropic coefficient as a fixed value for gases in adiabatic processes, however, this can lead to inadequate modeling. Therefore, the development of equations to calculate the polytropic coefficient, k, and the valve opening coefficient, α, is proposed to improve the computational modeling of forced conduit emptying using the Rigid Water Column Model (RWCM). The methodological study involved a literature review to explore the theory of pipeline emptying, using data from experimental research. A set of experimental research works was selected for analysis, aiming to apply their quantitative solutions in computational modeling. In these works, 12 experiments without air admission and 23 experiments with air admission were conducted, simulating an air valve for air admission. Based on the results of these experiments, a simplified solution was developed from RWCM under emptying conditions without air admission. Subsequently, the hypothesis that the polytropic coefficient varies from the values of k for atmospheric air and water vapor (1,40 and 1,33) was evaluated. A new understanding of the valve opening law was developed, considering a coefficient, α, as a function of computational time step. The findings are presented in three segments. The first part presents graphs comparing the findings of the simplified solution with data from 12 experiments without air admission, including the results of three numerical methods for comparison. In the second part of the results, the calibration of coefficients k and α was performed using the developed methodology for each of the 35 analyzed experiments. In the third and final part, equations for predicting coefficients k and α were developed, generating Nash-Sutcliffe Error above 0,90; these are considered good results regarding the proposed equations. Such results contribute to a better understanding of the thermodynamic process of the air pocket during water column emptying, regarding the sensitivity of the polytropic coefficient. Also, it scientifically contributes to the proposal of the valve opening coefficient for modeling the emptying of forced conduits.