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Praks Pavel - One of the best experts on this subject based on the ideXlab platform.
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright ω-function
2020Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y=W(ex), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright omega-function
'MDPI AG', 2019Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright omega-function. The Wright omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = W (e(x)), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient.Web of Science71art. no. 3
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright-Omega function
'MDPI AG', 2019Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor f. To date, the captured flow friction factor f can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright Omega-function. The Wright Omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term y=W(e^x) of the Lambert W-function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in term of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.Comment: 15 pages, 58 references, 1 figure, 2 table
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Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function
HAL CCSD, 2018Co-Authors: Brkić Dejan, Praks PavelAbstract:International audienceThe Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W -function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y=W(ex) , of the Lambert W -function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W -function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient
Y. H. Zhao - One of the best experts on this subject based on the ideXlab platform.
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Time-frequency analysis of enhanced GPR detection of RF tagged buried plastic Pipes
NDT and E International, 2017Co-Authors: W.y. Zhang, T. Hao, Y Chang, Y. H. ZhaoAbstract:Ground Penetrating Radar (GPR) is a well-received non-destructive technique for the detection of underground utilities, such as water/Gas Pipes, sewers, power cables, and telecommunication ducts. However, radar signatures of plastic Pipes are generally weak when the surrounding soils are attenuative and/or the pipe and soils have similar electromagnetic characteristics. In order to increase the radar visibility of these Pipes, attaching Radio-Frequency (RF) tags to them is a useful method. In this paper we designed two types of Bowtie-Omega shaped RF tags. The finite element method (FEM) simulation and measurement of the designed tags show strong resonances in the GPR spectrum, and by conducting GPR B-scans stronger radar signatures are observed when the RF tags are buried in our 2.0×1.5×0.75 m tank filled with dry sand. Furthermore, we implement a simple processing procedure based on Short-time Fourier Transform (STFT), by which strong time-frequency domain response of the tags is clearly seen at those designed resonant frequencies, and disappear when tags are not inserted. The resulting detection of the hollow plastic pipe in both time and frequency domains due to the co-located tag is evidently enhanced.
Roland Piques - One of the best experts on this subject based on the ideXlab platform.
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Creep damage mechanisms in polyethylene Gas Pipes
Polymer, 2001Co-Authors: Hedi Ben Hadj Hamouda, Maria Simoes-betbeder, François Grillon, P. Blouet, Noëlle Billon, Roland PiquesAbstract:This study deals with the creep damaging processes of two polyethylene (PE) resins. One is a ductile material while the other is a brittle one. Scanning electron microscopic (SEM) observations as well as chemical analysis are used to identify elementary process involved in the crack initiation and propagation. Of the two considered resins, only the second exhibits a lifetime controlled by slow crack growth (SCG). It is shown that catalytic residues act as initiating agents for the damage. Nevertheless, the presence of such particles in an extruded resin does not lead to a creep damage in every case. Intraspherulitic micro-cracks (mirror zones) can then propagate. Propagation takes place between the lamellae, seemingly through a disentanglement of tie molecules connecting the lamellae. The orientation of the micro-cracks is perpendicular to the largest principal stress. Cryogenic fracture surfaces indicate that the mirror zone gives rise to discontinuous crack growth bands (DCGB). In a pre-cracked specimen, only the DCGB stage takes place in the crack tip.
Reza Khademi-zahedi - One of the best experts on this subject based on the ideXlab platform.
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Application of a finite element method to stress distribution in buried patch repaired polyethylene Gas Pipes
Elsevier, 2019Co-Authors: Reza Khademi-zahedi, M. ShishesazAbstract:Advantages of polyethylene Pipes over traditional steel or metal Pipes have increased industry interest in the use of polyethylene (PE) pipelines for underground applications and especially in Gas distribution networks. In this study, finite element analysis is used to calculate the stress distribution in a patch repaired defective Gas pipe under internal pressure. The pipe is assumed to be buried at a depth of 125 cm. The material is assumed to be medium density PE80B, where the patch material was selected from high density polyethylene (HDPE). During the loading process, the seasonal pipe temperature changes, surcharge loads, soil column weight, and soil–pipe interaction were included in the analysis. Four types of patch arrangements were selected to repair the damaged pipe. The shape of the defect hole was deemed as circular or elliptic. With respect to elliptic defects, various minor to major diameter ratios, a/b, were selected to simulate a circular to a crack shaped defect. Based on the results, the semi-circular and saddle fusion patches decrease the peak von Mises stress in the pipe by almost the same amount. However, the minimum peak von Mises stress in the patch corresponds to the saddle fusion repair arrangement. Based on the results, with respect to a saddle fusion repair, when the shape of the defect approaches a crack, the peak von Mises stress in the pipe almost doubles and exceeds the pipe allowable stress for a working life of 50 years. With respect to higher values of a/b, the stress level in the patch repaired pipe is significantly below its limiting value for the same life expectancy. Keywords: Patch repair, Buried Gas pipe, MDPE, HDPE, Temperature variatio
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Application of the finite element method for evaluating the stress distribution in buried damaged polyethylene Gas Pipes
Elsevier, 2019Co-Authors: Reza Khademi-zahediAbstract:During the loading process, buried Gas Pipes can experience severe stresses due to soil- structure interaction, the presence of traffic load, the soil’s column weight, daily and/or seasonal temperature changes and uniform internal pressure. In this research, the finite element method is employed to evaluate the behavior of buried Medium Density Polyethylene (MDPE) Pipes which have been subjected to damage at the pipe crown. The modeled pipe damage ranges from a very small circular hole to a large circular hole and elliptic holes with various minor to major diameter ratios, a/b, to simulate circular to crack-shaped defects. The computer simulation and stress analyses were performed using the ANSYS software finite element package. The stress distribution around the defect was determined under the aforementioned mechanical and thermal loading conditions. Then, the maximum values of Von Mises stresses in the damaged buried PE Pipes, which were evaluated by finite element solution, were compared with their corresponding reduced strength for safe operation with a life expectancy of fifty years. Based on the results, the maximum Von Mises stress values in the defective buried polyethylene Gas pipeline are significantly above the pipe strength limit at 35 °C. The previously mentioned stress values increase with the following factors: temperature increase, increase in circular hole diameter and decrease in elliptic hole diameter ratio (a/b). The maximum stress in the damaged PE pipe is due to the simultaneous loading effects of soil column weight, internal pressure, vehicle wheel load and pipe temperature increase. Additionally, the novel finite element models and stress plots for the buried damaged pipe and the pipe material allowable strength will be used to investigate the correct repair method for the damaged Gas pipeline and to choose the best patch arrangement which will assure a safe repair. Keywords: Buried Gas distribution Pipes, Circular and elliptical defects, Medium Density Polyethylene (MDPE), Von Mises stress, Finite element method, Temperature variatio
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Finite Element Analysis to the Effect of Thermo-Mechanical Loads on Stress Distribution in Buried Polyethylene Gas Pipes Jointed by Electrofusion Sockets, Repaired by PE Patches
MDPI AG, 2018Co-Authors: Reza Khademi-zahedi, Pouyan AlimouriAbstract:Polyethylene (PE) Gas Pipes can be jointed together by electrofusion PE fittings, which have sockets that are fused onto the pipe. Additionally, electrofused PE patches can be used to repair defected Pipes. When these pipelines are buried under the ground, they can experience sever local stresses due to the presence of pipe joints, which is superimposed on the other effects including the soil-structure interaction, traffic load, soil’s column weight, a uniform internal pressure, and thermal loads imposed by daily and/or seasonal temperature changes. The present contribution includes two cases. At first, stress variations in buried polyethylene Gas pipe and its socket due to the aforementioned loading condition is estimated using finite element. The pipe is assumed to be made of PE80 material and its jointing socket material is PE100. Afterward, the effects of aforementioned thermo-mechanical loads on the stress distribution in patch repaired buried Pipes are well investigated. The soil physical properties and the underground polyethylene pipe installation method are based on the American association of state highway and transportation officials and American society for testing and material standards. The computer simulation and analysis of stresses are performed through the finite element package of ANSYS Software. Stress concentrations can be observed in both components due to the presence of the socket or the repair patch. According to the results, the electrofusion sockets can be used for joining PE Gas Pipes even in hot climate areas. The maximum values of these stresses happen to be in the pipe. Also, the PE100 socket is more sensitive to a temperature drop. Additionally, all four studied patch arrangements show significant reinforcing effects on the defected section of the buried PE Gas pipe to withstand applied loads. Meanwhile, the defected buried medium density polyethylene (MDPE) Gas pipe and its saddle fused patch can resist the imposed mechanical and thermal loads of +22 °C temperature increase
Brkić Dejan - One of the best experts on this subject based on the ideXlab platform.
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright ω-function
2020Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y=W(ex), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright omega-function
'MDPI AG', 2019Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright omega-function. The Wright omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = W (e(x)), of the Lambert W-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient.Web of Science71art. no. 3
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Accurate and efficient explicit approximations of the Colebrook flow friction equation based on the Wright-Omega function
'MDPI AG', 2019Co-Authors: Brkić Dejan, Praks PavelAbstract:The Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor f. To date, the captured flow friction factor f can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright Omega-function. The Wright Omega-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term y=W(e^x) of the Lambert W-function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W-function is identical to the original expression in term of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.Comment: 15 pages, 58 references, 1 figure, 2 table
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Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function
HAL CCSD, 2018Co-Authors: Brkić Dejan, Praks PavelAbstract:International audienceThe Colebrook equation is a popular model for estimating friction loss coefficients in water and Gas Pipes. The model is implicit in the unknown flow friction factor, f . To date, the captured flow friction factor, f , can be extracted from the logarithmic form analytically only in the term of the Lambert W -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W -function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y=W(ex) , of the Lambert W -function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert W -function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient
