Abstract To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.
{"title":"Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow","authors":"W. Artichowicz, Patrycja Mikos-Studnicka","doi":"10.1515/heem-2015-0006","DOIUrl":"https://doi.org/10.1515/heem-2015-0006","url":null,"abstract":"Abstract To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"109 - 89"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66834318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Drainage plays an extremely important role in hydraulic structures, such as earth dams. Observations of drainage in hydraulic structures under various soil conditions indicate that the phenomenon of clogging can lead to a radical reduction in the efficiency of drainage, making it non-functional within a few years after construction. This article describes the problems of drainage clogging by iron oxide in the examples of the Żur and Podgaje dams.
{"title":"Problem of Clogging in Drainage Systems in the Examples of the Żur and Podgaje Dams","authors":"Witold Sterpejkowicz-Wersocki","doi":"10.1515/heem-2015-0012","DOIUrl":"https://doi.org/10.1515/heem-2015-0012","url":null,"abstract":"Abstract Drainage plays an extremely important role in hydraulic structures, such as earth dams. Observations of drainage in hydraulic structures under various soil conditions indicate that the phenomenon of clogging can lead to a radical reduction in the efficiency of drainage, making it non-functional within a few years after construction. This article describes the problems of drainage clogging by iron oxide in the examples of the Żur and Podgaje dams.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"183 - 192"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66834448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. This makes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a constant value of unknown functions was assumed. The verification was carried out for the case of flow in a square cavity with one moving wall. The results obtained show that the use of approximations by simple linear functions is relatively easy for different shapes of the area, but the result may be affected by significant errors.
{"title":"Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow","authors":"Dzmitry Prybytak","doi":"10.1515/heem-2015-0010","DOIUrl":"https://doi.org/10.1515/heem-2015-0010","url":null,"abstract":"Abstract The paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. This makes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a constant value of unknown functions was assumed. The verification was carried out for the case of flow in a square cavity with one moving wall. The results obtained show that the use of approximations by simple linear functions is relatively easy for different shapes of the area, but the result may be affected by significant errors.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"163 - 173"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66834428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The slip boundary condition can be a very useful relation when some specific problems of hydromechanics are considered. According to the classical form of this condition, the slip of a fluid with respect to the solid wall should occur even at a very low velocity of motion. However, both theoretical analysis and certain empirical data suggest that there must be a limit value of the wall shear stress, below which the slip does not occur. According to the simplified balance of adhesive and gravitational forces, a simple experimental method for determining this stress has been proposed and applied in this paper.
{"title":"Experimental Determination of Limit Adhesive Shear Stress between Solid Wall and Liquid","authors":"J. Sawicki","doi":"10.1515/heem-2015-0011","DOIUrl":"https://doi.org/10.1515/heem-2015-0011","url":null,"abstract":"Abstract The slip boundary condition can be a very useful relation when some specific problems of hydromechanics are considered. According to the classical form of this condition, the slip of a fluid with respect to the solid wall should occur even at a very low velocity of motion. However, both theoretical analysis and certain empirical data suggest that there must be a limit value of the wall shear stress, below which the slip does not occur. According to the simplified balance of adhesive and gravitational forces, a simple experimental method for determining this stress has been proposed and applied in this paper.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"175 - 181"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66834438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The outlet flow velocity in the end section of the culvert barrel depends in most cases on the culvert geometry, including the barrel slope, as well as on upstream and downstream channel parameters. Flowing water can create pressure flow or free surface flow in the culvert barrel. In the case of an unsubmerged barrel outlet, the free-surface flow is more frequent than the full flow. Increased velocities can cause channel bed scour and bank erosion downstream of the culvert outlet. Different culvert flow cases in which the barrel outlet is unsubmerged are presented in this paper. The influence of the flow regime on the outlet velocity is also discussed.
{"title":"Outlet Flow Velocity in Circular Culvert","authors":"W. Szpakowski","doi":"10.1515/heem-2015-0013","DOIUrl":"https://doi.org/10.1515/heem-2015-0013","url":null,"abstract":"Abstract The outlet flow velocity in the end section of the culvert barrel depends in most cases on the culvert geometry, including the barrel slope, as well as on upstream and downstream channel parameters. Flowing water can create pressure flow or free surface flow in the culvert barrel. In the case of an unsubmerged barrel outlet, the free-surface flow is more frequent than the full flow. Increased velocities can cause channel bed scour and bank erosion downstream of the culvert outlet. Different culvert flow cases in which the barrel outlet is unsubmerged are presented in this paper. The influence of the flow regime on the outlet velocity is also discussed.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"193 - 203"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66833964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper focuses mainly on laboratory investigations of transient and transcritical flow in a single pipe of a sewer system. The aim of this paper is to present a comparison between pressure values calculated by an improved McCormack scheme and those measured at the hydraulic laboratory of the Gdańsk University of Technology, which were observed inside a pipe in an experiment for water flow with pressurization. The analysis proves that the numerical approach applied to flow simulation is a sufficiently accurate and reliable technique for predicting the basic parameters of storm sewer flow
{"title":"Experimental Verification of Storm Sewer Transient Flow Simulation","authors":"M. Szydłowski","doi":"10.1515/heem-2015-0014","DOIUrl":"https://doi.org/10.1515/heem-2015-0014","url":null,"abstract":"Abstract The paper focuses mainly on laboratory investigations of transient and transcritical flow in a single pipe of a sewer system. The aim of this paper is to present a comparison between pressure values calculated by an improved McCormack scheme and those measured at the hydraulic laboratory of the Gdańsk University of Technology, which were observed inside a pipe in an experiment for water flow with pressurization. The analysis proves that the numerical approach applied to flow simulation is a sufficiently accurate and reliable technique for predicting the basic parameters of storm sewer flow","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"205 - 215"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/heem-2015-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66833982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A poorly designed culvert inlet structure causes scouring, which can lead to the collapse of the culvert and significant damage to the neighboring land. A set of laboratory tests was evaluated to examine velocity distribution at the culvert inlet. A three-dimensional acoustic Doppler velocimeter was used to measure instantaneous flow velocity upstream of the culvert. The analysis of mean velocities, turbulence strength, and Reynolds stresses was performed to understand the flow structure near the culvert entrance.
{"title":"Velocity Field Characteristics at the Inlet to a Pipe Culvert","authors":"T. Kolerski, P. Wielgat","doi":"10.1515/heem-2015-0008","DOIUrl":"https://doi.org/10.1515/heem-2015-0008","url":null,"abstract":"Abstract A poorly designed culvert inlet structure causes scouring, which can lead to the collapse of the culvert and significant damage to the neighboring land. A set of laboratory tests was evaluated to examine velocity distribution at the culvert inlet. A three-dimensional acoustic Doppler velocimeter was used to measure instantaneous flow velocity upstream of the culvert. The analysis of mean velocities, turbulence strength, and Reynolds stresses was performed to understand the flow structure near the culvert entrance.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"61 1","pages":"127 - 140"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66834386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A mathematical model for the continuous saltation of a particle near the granular bed in an open-channel flow is developed in detail. The model is based on the Lagrangian equations governing particle motion, and it takes into account the following forces: drag, lift, gravitation, virtual mass and the force responsible for particle-particle interactions. A model of particle-particle collisions is developed and used to determine the mean impulsive force acting upon a particle flowing and rebounding from the channel bed. The model can simulate the continuous saltation trajectories of a single particle in the near-bed region of turbulent flows, in which particle motion is controlled by collisions. The model has been calibrated and verified with available published data in a rather wide range of grain sizes from 0.53 mm to 15 mm. All parameters, such as lift, drag, restitution, friction coefficients and roughness height, have been set on the basis of a reanalysis of these published data.
{"title":"Lagrangian Model for a Single Saltating Grain in the Near-Wall Region of an Open-Channel Flow","authors":"W. Czernuszenko","doi":"10.2478/heem-2013-0007","DOIUrl":"https://doi.org/10.2478/heem-2013-0007","url":null,"abstract":"Abstract A mathematical model for the continuous saltation of a particle near the granular bed in an open-channel flow is developed in detail. The model is based on the Lagrangian equations governing particle motion, and it takes into account the following forces: drag, lift, gravitation, virtual mass and the force responsible for particle-particle interactions. A model of particle-particle collisions is developed and used to determine the mean impulsive force acting upon a particle flowing and rebounding from the channel bed. The model can simulate the continuous saltation trajectories of a single particle in the near-bed region of turbulent flows, in which particle motion is controlled by collisions. The model has been calibrated and verified with available published data in a rather wide range of grain sizes from 0.53 mm to 15 mm. All parameters, such as lift, drag, restitution, friction coefficients and roughness height, have been set on the basis of a reanalysis of these published data.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"60 1","pages":"31 - 50"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69209423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper presents an examination of approximation aspects of the Smoothed Particle Hydrodynamics (SPH) in modeling the water wave phenomenon. Close attention is paid on consistency of the SPH formulation and its relation with a correction technique applied to improve the method accuracy. The considerations are confined to flow fields within finite domains with a free surface and fixed solid boundaries with free slip boundary conditions. In spite of a wide application of the SPH method in fluid mechanics, the appropriate modeling of the boundaries is still not clear. For solid straight line boundaries, a natural way is to use additional (virtual, ghost) particles outside the boundary and take into account mirror reflection of associated field variables. Such a method leads to good results, except for a vicinity of solid horizontal bottoms where, because of the SPH approximations in the description of pressure, a stratification of the fluid material particles may occur. In order to illustrate the last phenomenon, some numerical tests have been made. These numerical experiments show that the solid fluid bottom attracts the material particles and thus, to prevent these particles from penetration into the bottom, a mutual exchange of positions of real and ghost particles has been used in a computation procedure.
{"title":"On the SPH Approximations in Modeling Water Waves","authors":"K. Szmidt","doi":"10.2478/heem-2013-0009","DOIUrl":"https://doi.org/10.2478/heem-2013-0009","url":null,"abstract":"Abstract This paper presents an examination of approximation aspects of the Smoothed Particle Hydrodynamics (SPH) in modeling the water wave phenomenon. Close attention is paid on consistency of the SPH formulation and its relation with a correction technique applied to improve the method accuracy. The considerations are confined to flow fields within finite domains with a free surface and fixed solid boundaries with free slip boundary conditions. In spite of a wide application of the SPH method in fluid mechanics, the appropriate modeling of the boundaries is still not clear. For solid straight line boundaries, a natural way is to use additional (virtual, ghost) particles outside the boundary and take into account mirror reflection of associated field variables. Such a method leads to good results, except for a vicinity of solid horizontal bottoms where, because of the SPH approximations in the description of pressure, a stratification of the fluid material particles may occur. In order to illustrate the last phenomenon, some numerical tests have been made. These numerical experiments show that the solid fluid bottom attracts the material particles and thus, to prevent these particles from penetration into the bottom, a mutual exchange of positions of real and ghost particles has been used in a computation procedure.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"60 1","pages":"63 - 86"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69209479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.
{"title":"Application of an Element-free Galerkin Method to Water Wave Propagation Problems","authors":"R. Staroszczyk","doi":"10.2478/heem-2013-0010","DOIUrl":"https://doi.org/10.2478/heem-2013-0010","url":null,"abstract":"Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.","PeriodicalId":53658,"journal":{"name":"Archives of Hydroengineering and Environmental Mechanics","volume":"60 1","pages":"105 - 87"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69209488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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