Experimental-numerical simulation of longitudinal water surface profile through large porous media

Rock fill materials are among the useful materials in operation of hydraulic structures that are being frequently used by engineers and designers of hydraulic structures, because of lower cost and environmental sustainability. Knowing of water profile is valuable for practical purposes and designing, sometimes observed that because of mining or roadway operations in vicinity of rivers, the rock materials were fallen to river bed and changed the flow regime from open channel flow to the None-Darcy inner flow. Another use with these materials is in building of rock fill detention dams for flood mitigation in river downstream, which nowadays become so common in Iran. These dams temporary reserves the flood in its low capacity reservoir and then passes from its body with delay. Flow through large porous media could be interpreted with both equations of pipe and open channel flow. Since the flow in rock drains or detention dams have a free surface, it is usual to apply open channel equations like GVF in profile estimation. Different types of numerical or theoretical equations have been employed by previous researchers for its solving, but it should be mention that in these type problems, the method would be valuable which could be applied easily. Therefore, single step direct numerical methods were selected in the present study. Furthermore, because of nature of water surface profiles inside the rock fill dumps, the method of calculation could be capable for estimation of the flow depth according to the profile length.
For laboratory data collection, an experimental setup was created in which the semi crashed riddled rock materials placed between two vertical screen walls such that a grid of Piezometric tubes had been positioned in the centerline of rock media. By changing of media size and length, the different type of physical configurations created. Then by employing of four different discharges, the surface profile acquired. The photography and digitizing technic have been used for experimental data extraction. Moreover, water supply system of the flume has been connected to the constant head tank of laboratory, and the discharges were measured by means of pre-calibrated V notch. In this research, water surface profiles were obtained experimentally by two rock diameter, two media length and four operation discharges. Then, by using of gradually varied flow equation and three numerical methods including Euler, modified Euler and 4th order Range-Kutta, The water surface profiles were simulated numerically and compared with experimental profiles. In all of these methods the exit point height from the experimental data series were employed as the boundary condition. The flow condition at that point is generally different from other parts of rock body. Different researchers have presented some relationships for exit height, but most of them related it to the critical height in the particular discharge. By focus on experimental observations, Because of existing of large slope in surface profile, the flow regime changes rapidly and the GVF equation may be unsuitable in the mentioned regions but because of low length of it the discrepancy in profile calculations is negligible. Therefore, more research is needed to investigate it in details and disquisition around it is not from the purposes of this research. One of the most important subjects of profile estimation is to calculate pore velocity which is dependent on media size and porosity. Previously, several types of pore velocity equations have been presented, but the most famous one is the Wilkins relationship. Because of None-Darcy and turbulent nature of inflow, the relationship between hydraulic gradient and pore velocity is quadratic and the effect of first term of Forchheimer’s equation is negligible.
After acquisition of experimental surface profile in different flow and physical configuration of laboratory setup and programming of the selected numerical methods in MATHLAB software, the comparisons of results were done. Then it was observed that 4th order Range-Kutta method with 4th order accuracy has the better estimation accuracy rather than other two methods with average RMSE equal to 1.19 and average R2 equal to 0.9. Also, it should be mentioned that because of the large magnitude of hydraulic grade in exit regions of porous media, use of Range-Kutta method imposes some errors in the profile estimation in the exit region. Therefore, application of modified Euler at the aforementioned zone has the better conclusions.