جستجوی مقالات مرتبط با کلیدواژه « جریان آشفته ی کاملا توسعه یافته » در نشریات گروه « آب و خاک »

The increase of flow velocity and Reynolds number in coarse porous media and the subsequent violation of Darcy's law, force to analyze the flow based on nonlinear relations of hydraulic slope and flow velocity. So, it is necessary to study nonlinear relationships more accurately. The purpose of this study was to investigate the performance of fractional-order model and the effect of conformable derivatives on improving the relationship between flow velocity and hydraulic gradient. Therefore, by determining the acceptable range for the fractional-order model, a nonlinear model based on conformable derivatives of the Izbash equation for the fully developed turbulent flow was presented and solved analytically and the parameters of the proposed model were determined using laboratory data analysis. The optimal values of the model parameters including coefficient a and the order of fractional derivative α, which can be varied in the range of (0-2), were calculated for each laboratory data set. The results were compared with the experimental data and the analytical solution of Izbash equation and a good agreement was found to the non-Darcian flow laboratory data. Moreover, using dimensional analysis method, Reynolds number was introduced as an effective factor on α coefficient and a suitable relationship was observed between the order of fractional derivative α and Reynolds number indicating the hydraulic concept of fractional-order model. According to the present study, the fractional order α is not only a fitting coefficient, but it represents a physical concept.

In this study, the fractional-order differential equations in range of (0,1) were used to model the water surface profile under Darcy's law condition in porous medium for a fully developed turbulent flow. The developed equation is solved analytically. The laboratory model used in this study consists of a coarse-grained porous medium with 6.4 m length, 0.8 m width and 1 m height, including rounded corner materials, which are tested for different flow rates and three longitudinal slopes of 0, 4, 20.3%. Then, parameters of model and porous media were calibrated based on laboratory data. In order to evaluate the proposed analytical solution, the obtained results from fractional-order differential model were compared with the laboratory data. The results showed a satisfactory agreement with experimental data of water surface profile (seepage line) in all three slopes. The maximum error of the proposed model is 3.5% compared to the experimental data. It can be concluded that the proposed method can provide better description of water surface profile analysis under non-Darcy flow conditions as compared to Darcy model in porous media.