Figure 6 - uploaded by Jalal Bazargan
Content may be subject to copyright.
Source publication
To calculate the hydraulic gradient (i) in steady-non Darcy regimes, the validity of the binomial relationship is confirmed using dimensional analysis and Navier-Stokes equations. According to St. Venant equations, the experimental data used in the present study are of the diffusion wave type and the changes in flow depth (h) in terms of changes in...
Contexts in source publication
Context 1
... in the case of the diffusion and dynamic wave, changes of the flow depth relative to the flow discharge are expressed as a loop (Jain, 2001). As can be seen from Figure 6, the variations of the flow depth in terms of the flow discharge for the Small, Medium and Large grain size in the present study are in the form of a loop, indicating a diffusion wave type in all the three gradation types. Figure 6 shows the formed wave is of a diffusion type. ...
Context 2
... can be seen from Figure 6, the variations of the flow depth in terms of the flow discharge for the Small, Medium and Large grain size in the present study are in the form of a loop, indicating a diffusion wave type in all the three gradation types. Figure 6 shows the formed wave is of a diffusion type. In previous studies conducted by (Hannoura & McCor- quodale, 1985;Hassanizadeh & Gray, 1987; Hall et al., 1994; Burcharth & Andersen, 1995;Moutsopoulos, 2007;Shokri et al. 2013), it was recommended to use a trinomial equation (Eq. ...
Context 3
... results presented in Table 4 shows the insignificance of the third or the last term of the SaintVenant equation, and in the present study, a new approach is proposed to increase the accuracy of the binomial equation. Figure 6 shows that for a Input discharge (I), or in other words, for a input flow velocity (V ), there are two different flow depths (h) so that in the ascending area of the hydrograph (red colour in Figure 6), the flow depth is less than the recession area of the hydrograph (blue colour in Figure 6). ...
Context 4
... results presented in Table 4 shows the insignificance of the third or the last term of the SaintVenant equation, and in the present study, a new approach is proposed to increase the accuracy of the binomial equation. Figure 6 shows that for a Input discharge (I), or in other words, for a input flow velocity (V ), there are two different flow depths (h) so that in the ascending area of the hydrograph (red colour in Figure 6), the flow depth is less than the recession area of the hydrograph (blue colour in Figure 6). ...
Context 5
... results presented in Table 4 shows the insignificance of the third or the last term of the SaintVenant equation, and in the present study, a new approach is proposed to increase the accuracy of the binomial equation. Figure 6 shows that for a Input discharge (I), or in other words, for a input flow velocity (V ), there are two different flow depths (h) so that in the ascending area of the hydrograph (red colour in Figure 6), the flow depth is less than the recession area of the hydrograph (blue colour in Figure 6). ...
Context 6
... Determining the type of wave is very important in the study of unsteady flow and the calculations indicate that the flow related to the experimental data used in the present study is of the diffusion wave type. (3) Since in the diffusion wave, the changes in flow depth in terms of the flow rate (flow-depth curve) are loop, for the flow rate or flow velocity (V ), there are two different values for flow depth (h), as shown in Figure 6. (4) According to the diffusion wave relation (S f = S 0 − ∂h ∂x ), the value of S f or i depends on the changes in flow depth (h). ...
Citations
... Calculation of the exact values of the coefficients ''a'' and ''b'' in the binomial equation is very important for calculating the hydraulic gradient and consequently, the unsteady flow analysis (Safarian et al. 2021). ...
... Calculation of the coefficients ''a'' and ''b'' of the binomial equation and consequently, calculation of the hydraulic gradient is of great importance in the unsteady flow analysis (Safarian et al. 2021). In the unsteady flow condition, there are variable temporal changes in the flow discharge and water surface profile and consequently, variable changes in the hydraulic gradient with respect to the flow velocity as well as the coefficients ''a'' and ''b'' of the binomial equation and therefore, different values must be optimized for the coefficients (Fig. 8 shows the temporal changes in the coefficients ''a' ' and ''b''). ...
Rockfill materials are widely used in construction of rockfill dams and flood control structures. Analysis of the unsteady flow through rockfill materials is of great importance. Calculations of water surface profile at different times, flood hydrographs (temporal changes in flow discharge) at different reaches and temporal changes of depth at different intervals through the rockfill materials are widely used in the design of the hydraulic structures. In the present study, using the experimental data and the Saint–Venant equations, the unsteady flow through the rockfill materials was studied. Since the hydraulic gradient inside the rockfill materials is equal to the slope of the energy line in open channels, considering the temporal changes of the unsteady flow discharge and depth and consequently, temporal changes in the hydraulic gradient with respect to the flow velocity, different values of the binomial equation coefficients "a" and "b" were optimized every 1 s using the Particle Swarm Optimization (PSO) algorithm and combining it with the Saint–Venant equations. In addition, the sensitivity analysis as well as the effects of spatial step (dx) and time step (dt) on calculation of the unsteady flow characteristics were also addressed. The results indicated that if instead of using the fixed values for the coefficients "a" and "b", variable values are used for the mentioned coefficients at different times, the Saint–Venant equations are more accurate in the analysis of the unsteady Non-Darcy flow.
... Particle swarm optimization (PSO) algorithm is a population-based evolutionary algorithm and is used in civil engineering and water resources optimization problems such as reservoir performance (Nagesh Kumar & Janga Reddy 2007), water quality management (Lu et al. 2002;Chau 2005;Afshar et al. 2011), optimization of the Muskingum method coefficients (Chu & Chang 2009;Moghaddam et al. 2016;Bazargan & Norouzi 2018;Norouzi & Bazargan 2020;) and optimization of the parameters of the porous media equations Safarian et al. 2021). ...
The outflow depth from the radial porous media (inflow to the well) is very useful as the downstream boundary condition and the starting point for water surface profile calculations. Based on the studies, unlike the Stephenson's hypothesis (the outflow depth is equal to the critical depth), the outflow depth from the rockfill media is a coefficient (Γ) of the critical depth. In the present study, using several (large scale and almost real) experimental data in the radial non-Darcy flow condition, dimensional analysis and the particle swarm optimization (PSO) algorithm, an equation was presented to calculate the mentioned coefficient based on upstream water depth (h) and distance between the well center and the upstream (R). Then, using the calculated outflow depth and the 1D flow analysis equations, the water surface profile in the radial non-Darcy condition was calculated for the first time. The results showed that considering an outflow depth equal to the critical depth and using the proposed solution in the present study, the mean relative error (MRE) values of 83.43% and 3.53% were obtained, respectively. In addition, using the proposed solution for different experimental conditions, an average MRE of 2.58% was calculated for the water surface profile.
HIGHLIGHTS
Using the experimental data with almost real scale.;
Calculation of the output flow depth from the radial porous media.;
Providing a relationship based on the upstream water depth (h) and the distance of well center from upstream (R) to calculate the output flow depth.;
Calculation of water surface profile in radial non-Darcy flow using gradually varied flow theory.;
Using PSO algorithm in calculations.;
... (Hu et al. 2019) Kriging-approximation simulated annealing (KASA) optimization algorithm has been used to optimize flow parameters in the porous media. Particle swarm optimization (PSO) algorithm is a population-based evolutionary algorithm and is used in civil engineering and water resources optimization problems such as reservoir performance (Nagesh Kumar & Janga Reddy 2007), water quality management (Lu et al. 2002;Chau 2005;Afshar et al. 2011), optimization of the Muskingum method coefficients (Chu & Chang 2009;Moghaddam et al. 2016;Bazargan & Norouzi 2018;Norouzi & Bazargan 2020;) and optimization of the parameters of the porous media equations Safarian et al. 2021). Therefore, in the present study, the Particle Swarm Optimization (PSO) algorithm was used to optimize the coefficients of the proposed equation. ...
To analyze the flow in a rockfill porous media using the Gradually Varied Flows theory (one-dimensional flow analysis) and solving the Parkin equation (two-dimensional flow analysis), calculation of the output flow depth as the downstream boundary condition is of great importance. In most previous studies, the output flow depth has been considered equal to the critical depth. In the rockfill porous media, unlike free surface channels, the fluid weight is exerted to the aggregates in addition to the flow, and therefore, the output flow depth from the rockfill is always greater than the critical depth (flow leaves the rockfill with a specific energy greater than the critical energy), and is expressed as a coefficient (Γ) of the critical depth. In the present study, using dimensional analysis and particle swarm optimization (PSO) algorithm and experimental data in different conditions (a total of 178 experimental data for rounded, crashed, Glass artificial materials with rhomboid structure, Glass artificial materials with cubic structure, sandy natural materials), an equation was presented to calculate the mentioned coefficient as a function of the physical characteristics of the rockfill porous media as well as the flow that can be used for all experimental conditions with high accuracy. If the output flow depth is considered to be equal to the critical depth, the mean relative error (MRE) in terms of using the experimental data of the mentioned materials separately and for the data of all the mentioned materials together was equal to 84.40, 83.81, 60.62, 67.68, 74.82 and 69.96%, respectively. In the case of using the proposed equation in the present study, the corresponding values of 5.49, 4.72, 6.24, 4.41, 6.42 and 8.99% were calculated, respectively. HIGHLIGHTS
Presenting an approach to increase the accuracy of one-dimensional and two-dimensional analysis of steady flow in coarse-grained porous media.;
Using the dimensional analysis, particle swarm optimization (PSO) algorithm and experimental data in different conditions.;
Presenting an equation applicable to all porous media with different conditions to calculate the output flow depth.;
