Abstract

Unsteady flow analysis is performed using the equations of St. Venant. Calculating the slope of the energy line (S_f) is of great importance in the analysis of unsteady flow. Since S_f is equal to the hydraulic gradient (i) in a coarse porous media, the calculation of i is of great importance. In the present study, using experimental data recorded in a steel cylinder with a diameter of 16 cm and a length of 70 cm, 40 cm of which is filled with rockfill with three small, medium, and large grains, investigated the unsteady flow in a confined porous media. The particle swarm optimization (PSO) algorithm is used to optimize the Forchheimer binomial relation coefficients used in steady flow (a, b) and the triplet relation used in unsteady flow (a, b, c). The results of the present study indicate that the values related to the mean relative error (MRE) in the case of using a triple relation to the binomial relation to calculate the hydraulic gradient of unsteady flow, in small materials 14.5, in medium materials 14.7 and in large material, it has improved by 12.2%. The value of the third sentence is a triple relation to the hydraulic gradient ((cdv/dt)/i) in 7.23% in small materials, 14.79% in medium materials, and 17.01% in large materials. In other words, since with increasing the diameter of the material, the efficiency of the nonlinear (non-Darcy) relation increases compared to the linear (Darcy) relation, the third sentence of the triple relation also has a greater effect on the hydraulic gradient calculations.