Modeling of Velocity and Hydraulic Gradient in Non-Darcian Flows Using the Concept of Conformable Fractional Derivatives

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ESLAHI NOOSHIN; VATANKHAH ALIREZA; SEDGHI ASL MOHAMMAD

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Journal: Iranian Journal of Soil and Water Research Year:2021 | Volume:51 | Issue:12 Page(s): 2987-2998

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Title

Modeling of Velocity and Hydraulic Gradient in Non-Darcian Flows Using the Concept of Conformable Fractional Derivatives

Author(s)

ESLAHI NOOSHIN | VATANKHAH ALIREZA | SEDGHI ASL MOHAMMAD | Issue Writer Certificate

Keywords

Conformable DerivativesQ1

Fractional OrderQ1

Fully Developed Turbulent FlowQ1

Non-Darcian FlowQ1

Analytical SolutionQ2

Abstract

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 fractionalorder 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.

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APA: Copy

ESLAHI, NOOSHIN, VATANKHAH, ALIREZA, & SEDGHI ASL, MOHAMMAD. (2021). Modeling of Velocity and Hydraulic Gradient in Non-Darcian Flows Using the Concept of Conformable Fractional Derivatives. IRANIAN JOURNAL OF SOIL AND WATER RESEARCH, 51(12 ), 2987-2998. SID. https://sid.ir/paper/372485/en

Vancouver: Copy

ESLAHI NOOSHIN, VATANKHAH ALIREZA, SEDGHI ASL MOHAMMAD. Modeling of Velocity and Hydraulic Gradient in Non-Darcian Flows Using the Concept of Conformable Fractional Derivatives. IRANIAN JOURNAL OF SOIL AND WATER RESEARCH[Internet]. 2021;51(12 ):2987-2998. Available from: https://sid.ir/paper/372485/en

IEEE: Copy

NOOSHIN ESLAHI, ALIREZA VATANKHAH, and MOHAMMAD SEDGHI ASL, “Modeling of Velocity and Hydraulic Gradient in Non-Darcian Flows Using the Concept of Conformable Fractional Derivatives,” IRANIAN JOURNAL OF SOIL AND WATER RESEARCH, vol. 51, no. 12 , pp. 2987–2998, 2021, [Online]. Available: https://sid.ir/paper/372485/en

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