تحلیل نیمرخ سطح آب در محیط متخلخل درشت‌دانه با جریان شعاعی با استفاده از فرضیه جریان‌های متغیر تدریجی

تحلیل یک بعدی جریان ماندگار در حالت غیردارسی موازی و شعاعی (همگرا) با استفاده از تئوری جریان‌های متغیر تدریجی و تحلیل دو بعدی آنها با استفاده از حل معادله پارکین صورت می‌گیرد. جهت تحلیل دوبعدی جریان ماندگار، به داده‌های فراوانی مانند شرایط مرزی در بالادست و پایین دست و همچنین شرط مرزی پروفیل سطح آب نیاز بوده و روند محاسبات آن پیچیده و زمانبر است. به‌عبارت دیگر، تئوری جریان‌های متغیر تدریجی نسبت به حل معادله پارکین به داده‌های بسیار کمتری نیاز داشته و پروفیل سطح آب به‌دست آمده از آن نیز به‌عنوان اصلی‌ترین شرط مرزی در حل معادله پارکین مورد استفاده قرار می‌گیرد. اکثر پژوهش‌های قبلی جریان غیردارسی موازی را بررسی کرده‌اند. درحالیکه در پژوهش حاضر، برای اولین بار با استفاده از داده‌های آزمایشگاهی در مقیاس تقریبا واقعی (دستگاه آزمایش نیمه استوانه‌ای شکل به قطر 6 و ارتفاع 3 متر و 10 حالت مختلق برای عمق آب پمپاژ شده در بالادست) و تئوری جریان‌های متغیر تدریجی و رابطه‌ی نمایی بین گرادیان هیدرولیکی و سرعت جریان، پروفیل سطح آب جریان ماندگار در حالت جریان غیردارسی شعاعی با سطح آزاد بررسی شده است. نتایج بیانگر آنست که؛ متوسط میانگین خطای نسبی (mre) 10 داده‌ی ثبت شده در آزمایشگاه برابر با 0/45 درصد محاسبه شده است.

analysis of water surface profiles in coarse-grained porous media with radial flow using the gradually varied flow theory

introductionnon-darcy flows into two categories: parallel flows (such as gravel dams, gabions, etc.) and radial flows (such as flows near wells drilled in coarse-grained alluvial beds, etc.) are divided. in the first category, streamlines are almost parallel so that there is no curvature or contraction of streamlines in the plan view. this type of flow is found in both pressurized and free-surface modes. radial non-darcy flow analysis has many applications in the fields of civil engineering, geology, oil, and gas. the equations governing the radial non-darcy flow are solved using numerical methods of finite differences, finite elements and finite volumes. solving these equations requires boundary conditions and a lot of data and is almost bulky, time consuming and costly. while, gradually varied flow theory, requires much less data and is easier and less expensive. for this reason, in the present study, for the first time, using experimental data recorded in a large-scale (almost real) device, the application of the gradually varied flow theory in radial non-darcy flows with free surface has been investigated. in other words, since the calculation of water surface profiles in a radial rockfill is of great importance. in the present study, using large-scale (almost real) experimental data and the gradually varied flow theory, the water surface profile in radial non-darcy flow with free surface and in steady state has been investigated.methodologyin the present study, due to the compatibility of cylindrical coordinates and its adaptation to the physics of problems related to radial flows, a device has been constructed in the laboratory of bu ali sina university in the form of a semi-cylinder with a diameter of 6 meters and a height of 3 meters. the dimensions of this device are made on a large scale and the effects limitations have practically no effect on the testing process. to measure piezometric pressure, piezometric grids have been used. the device has a volume of 14,000 liters and a capacity of materials weighing approximately 40 tons. four pumps are installed in parallel at the top of the device to generate the required flow. coarse-grained river materials with a diameter between 2 to 10 cm, a porosity of 40%, a cu of 2.13, and a cc of 1.016 have been used. to perform the tests, the model is first filled to a certain height (53, 60, 70, 85, 95, 110, 120, 140, 150, and 160 cm) by pumping operations. the flow rate created in these experiments is in the range of 49.94 to 53.16 l/s.results and discussionone-dimensional analysis of steady-non-darcy flow using gradually varied flow theory and two-dimensional analysis using parkin equation solution. most research has been done in parallel flow rockfills. also, solving the parkin equation in both parallel and radial flows requires a lot of data such as boundary conditions upstream and downstream, as well as the boundary condition of the water surface profile, and the calculation process is complex and time-consuming. the gradually varied flow theory requires much less data than solving the parkin equation, and the water surface profile obtained from it is also used as the main boundary condition in solving the parkin equation. in other words, calculating the water surface profile in a radial rockfill is very important to studying the movement of water.