M. Moradi Tayyebi; E. Amiri Tokaldany
Abstract
Introduction: Study of flow characteristics in rock porous media is one the most interesting issues for scientists and engineering dealing with river engineering works. So, there is no surprise that many models to describe the relationship between the flow velocity of clear water with hydraulic gradient, ...
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Introduction: Study of flow characteristics in rock porous media is one the most interesting issues for scientists and engineering dealing with river engineering works. So, there is no surprise that many models to describe the relationship between the flow velocity of clear water with hydraulic gradient, rock size, porosity, Reynolds number, and kinematic viscosity, have been introduced. Due to the large spaces between the coarse materials, flow velocity passing through the materials is high which in turn results in higher amounts of Reynolds number of flow. This type of flow classified as turbulent flow. Although Darcy law rules the flow in porous media, it is used for laminar flow in fine porous media and its application is not recommended for turbulent flows. Moreover, as the flow parameters in turbulent flows vary against time, the state of the flow is not steady. The equations describing the turbulent flows are obtained using equations defining basic concepts of hydrodynamics and turbulence effects. Due to complexity of the turbulent flow, these equations are described in the form of the partial differential equations. In order to introduce the specifications of this type of flow, various relationships have been provided by many researchers. However, their applications are confined to the limited conditions of porosity and size materials. In this study, we aim to provide a relationship which can be applied for a wide range of porosity and material size of porous media.
Materials and Methods: To describe the relation between effective hydraulic parameters in coarse porous media, we used dimensional analysis theorem of Buckingham. In this regard six dimensionless parameters have been provided from which a relationship including four constant parameters has been obtained. We used a part of (70 percent) several available sets of data, provided from Soil Conservation and Watershed Management Research Institute, Irrigation and Reclamation Engineering Department of the University of Tehran, and mostly from published results, to find the magnitude of the constant parameters. So, we introduced a new equation which expresses a relationship between hydraulic gradient, porosity, and Froud number. Finally, using the remained part of (30 percent) available data, we compared the results of the new equation with those obtained from available models.
Results and Discussion: To evaluate the new introduced equation and comparing the results obtained from the new equation and those obtained from available equations, we computed the magnitude of relative errors as well as the mean relative errors of the hydraulic gradient estimated from all equations versus the hydraulic gradients provided from field and laboratory observations. It is found that the new equation has the least mean of relative error (15.3 percent) among all equations. Moreover, for various magnitudes of rock size as well as porosity, we computed the mean relative error of estimated hydraulic gradients according to observed data. We found that the new equation has the second largest accuracy (with the mean error of 11.64%) among all evaluated models in this research. Finally, we developed two relationships between hydraulic gradient and Froud number using actual as well as apparent velocities. Again, it is found that the new relationship has the least mean of relative error (14.03 percent) among all equations.
Conclusion: Since all available equations introduced to express the flow characteristics in coarse porous media, can be used in a defined limits of porosity, rock size, etc., in this research we aimed to provide a new relationship which can be used for a wider range of porous media specifications. So, based on dimensional analysis and using several sets of available field and laboratory data, a new equation has been introduced in this research which can be used for a wide range of rock size, Reynolds number, and porosity; i.e. rock diameter of 0.5 to 20 cm, Reynolds number greater than 100, and porosity of 0.35 to 0.55. Moreover, we introduced two equations to demonstrate the relationship between hydraulic gradient and actual velocity as well as apparent velocity. When we evaluated the results obtained from the new relationship with those obtained from some available equations, we found that the relative error of the new equation is 14 percent, which illustrates that the error of the results produced by the new equation is less than those produced by the available equations.
S.A. Mousavi; E. Amiri Tokaladany; M.H. Davoudi
Abstract
Abstract
Rockfill dams are a type of hydraulic control structures used to protect river bed in cases where a considerable reservoir volume is available behind these structures; it could mitigate the floods and provide a gradual depletion of incoming volume of water so that the discharge passing downstream ...
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Abstract
Rockfill dams are a type of hydraulic control structures used to protect river bed in cases where a considerable reservoir volume is available behind these structures; it could mitigate the floods and provide a gradual depletion of incoming volume of water so that the discharge passing downstream is decreased. One of the main issues on utilizing rockfill dams is to keep its permeability enough so that it could be able to pass the flow as well as the sediment load through its body during flooding, avoiding sediments resettlement inside the pores. In this regard, the design of rockfill dams should be carried out so that the available hydraulic gradient is always kept greater than the critical hydraulic gradient, which consequently results in transporting the sediment through the dam body. In this research, a relationship to estimate the critical hydraulic gradient to transport noncohesive sediment through rockfill dam body is introduced. We tested the new equation using a set of published data. Also, using laboratory data obtained from tests on a rectangular rockfill dam, performing dimensional analysis, and using linear regression, an exponential relationship between the required discharge to transport the sediments through the body of rockfill dam, the physical characteristics of rockfill dam, size of the sediments, and the hydraulic characteristics of the flow passing the dam, is prevented. When we investigated the validity of exponential relationship, we found a good accuracy for the equation indicating that the introduced relation predicts the nondimensional sediment transport capacity well.
Keywords: Control structures, Rockfill dams, Critical hydraulic gradient, Noncohesive sediments
M. Safarpour; E. Amiri Tokaldany; M. Abolghasemi; A. Hoorfar
Abstract
Abstract
Naturally, rivers are rarely straight and more likely to take a winding course, called meandering. Because of presence of strong secondary currents in meanders, flow in river meanders is a complicated phenomenon, making it interesting for many researchers and engineers to investigate the equations ...
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Abstract
Naturally, rivers are rarely straight and more likely to take a winding course, called meandering. Because of presence of strong secondary currents in meanders, flow in river meanders is a complicated phenomenon, making it interesting for many researchers and engineers to investigate the equations governing this kind of flow. Many studies have been carried out by different researches during the last 45 years, and consequently, different relations have been published to determine the hydraulic parameters of the flow. In this research, a laboratory trapezoidal channel with a central radius curve of 5 m and central angle of 94 degrees was used to measure the hydraulic parameters for 120, 180, and 230 l/sec flows over a sandy movable bed having rigid walls. The results of this experiment were compared to the results of different models developed to estimate the flow characteristics. Finally, the most suitable model to determine the flow characteristics was introduced.
Key words: Meander, Erodible bed, River engineering, Secondary currents, Sandy bed, Numerical models
