Abstract

It is very important to study the steady and unsteady flow through porous media and fluid- particle interactions. In the present study, using the experimental data obtained from experiments performed in a steel cylinder on small, medium and large materials, using Particle Swarm Optimization (PSO) algorithm was first used to optimize the coefficients of binomial equations (a, b) and three parameter equations (a, b, c) to calculate changes of hydraulic gradient (i) versus flow velocity (V) in the steady and unsteady flow conditions, respectively. If, using experimental results of unsteady flow, three parameter equation is used to calculate the hydraulic gradient in the unsteady flow condition instead of the binomial equation (by assuming a negligible value for the third term), the mean relative error (MRE) of the above mentioned gradations is improved by 22, 38 and 19%, respectively. Since the Drag coefficient (C_d) and consequently the Drag force (F_d) is a function of the coefficient of friction (f), in the present study, using Darcy-Weisbach equations binomial and three parameter equations were presented for the steady and unsteady flow conditions, respectively. In addition, using the analytical equations proposed by Ahmed and Sunada for coefficients a and b, high accuracy equations were presented to calculate coefficient of friction (f) in terms of the Reynolds number (Re) in the steady and especially unsteady flow conditions in the porous media with all gradation types and Reynolds numbers. As a results, MRE between the calculated (using the proposed equations in the present study) and observed (using experimental data) coefficients of friction for the small, medium and large materials in the steady flow condition was calculated as 1.913, 3.614 and 3.322%, respectively. The corresponding values of 7.806, 14.106 and 10.506% were calculated in the unsteady flow condition, respectively.