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  • 1
    Publication Date: 2020
    Description: Thermal performance development, heat transfer structure, and flow behavior in the heat exchanger square duct equipped with a 45° inclined square ring are investigated numerically. The effects of flow blockage ratios and spacing ratios for the inclined square ring on fluid flow and heat transfer are considered. The Reynolds number (Re = 100–2000, laminar regime) based on the hydraulic diameter of the square duct is selected for the present work. The numerical domain of the square duct inserted with the 45° inclined square ring is solved with the finite volume method. The SIMPLE algorithm is picked for the numerical investigation. The heat transfer characteristics and flow topologies in the square duct inserted with the inclined square ring are plotted in the numerical report. The heat transfer rate, pressure loss, and efficiency for the square duct placed with the inclined square ring are presented in forms of Nusselt number, friction factor, and thermal enhancement factor, respectively. As the numerical results, it is detected that the heat transfer rate of the heat exchanger square duct inserted with the inclined square ring is around 1.00–10.05 times over the smooth duct with no inclined square ring. Additionally, the maximum thermal enhancement factor for the heat exchanger square duct inserted with the inclined square ring is around 2.84.
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  • 2
    Publication Date: 2020
    Description: In the present work, the statistical dispersion of the mortar compressive strength as a function of the geometric parameters of the specimens as well as the effect of the mortar workability difference on the compressive strength was investigated. For this purpose, specimens were prepared for six types of mortars: two conventional mortars in the proportions of 1 : 1 : 6 and 1 : 2 : 9 of cement, hydrated lime, and sand, respectively, two with clay replacing lime, and two with marble waste in place of lime. The results confirm the difference between the results found for the two geometries due to the differences in the heights of the molding layers and show that the workability of the mortar modifies the resistance properties, especially in the cylindrical mold where the molding of the specimens is more complex. By comparing the differences between the destructive test results and those defined by the Finite Element Modeling (FEM) for conventional mortars, it was clear that the effect of excess material in the sample during the compression tests did not change the strength properties studied. This facilitates the performance of the assay as specimens may be used excessively on the side without the need for sample rectification.
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  • 3
    Publication Date: 2020
    Description: The current study performs an explicit nonlinear finite element simulation to predict temperature distribution and consequent stresses during the friction stir welding (FSW) of AA 7075-T651 alloy. The ABAQUS® finite element software was used to model and analyze the process steps that involve plunging, dwelling, and traverse stages. Techniques such as Arbitrary Lagrangian–Eulerian (ALE) formulation, adaptive meshing, and computational feature of mass scaling were utilized to simulate sequence events during the friction stir welding process. The contact between the welding tool and workpiece was modelled through applying Coulomb’s friction model with a nonlinear friction coefficient value. Also, the model considered the effect of nonlinear material properties as well as heat transfer conditions such as heat losses due to convection and thermal contact conductance between the workpiece and the backing plate interface on the thermal history. To validate the computational model results, an experimental procedure was carried out to measure temperature history on both sides of the specimen as well as the plunging force throughout the whole process time. The results obtained showed that symmetrical temperature distribution throughout the workpiece width was distinguished, implying that the tool rotation has a minor effect on the final temperature distribution. In addition, asymptotic V shape with high gradient temperature value in the weld nugget region after the full plunging was distinguished. Mechanical stresses and related plastic deformations generated, while achieving the FSW samples were evaluated in addition to the tool reaction force and heat generated to protect against tool failure.
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  • 4
    Publication Date: 2020
    Description: Thermal performance development, heat transfer structure, and flow behavior in the heat exchanger square duct equipped with a 45° inclined square ring are investigated numerically. The effects of flow blockage ratios and spacing ratios for the inclined square ring on fluid flow and heat transfer are considered. The Reynolds number (Re = 100–2000, laminar regime) based on the hydraulic diameter of the square duct is selected for the present work. The numerical domain of the square duct inserted with the 45° inclined square ring is solved with the finite volume method. The SIMPLE algorithm is picked for the numerical investigation. The heat transfer characteristics and flow topologies in the square duct inserted with the inclined square ring are plotted in the numerical report. The heat transfer rate, pressure loss, and efficiency for the square duct placed with the inclined square ring are presented in forms of Nusselt number, friction factor, and thermal enhancement factor, respectively. As the numerical results, it is detected that the heat transfer rate of the heat exchanger square duct inserted with the inclined square ring is around 1.00–10.05 times over the smooth duct with no inclined square ring. Additionally, the maximum thermal enhancement factor for the heat exchanger square duct inserted with the inclined square ring is around 2.84.
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  • 5
    Publication Date: 2020
    Description: Darrieus wind rotor is a vertical axis wind turbine that is a very promising kind of wind converters at remote and domestic locations that have soft and weak wind potential and speed, but from the quantitative comparison with horizontal axis wind turbines, this type of turbines has a weak performance. Additional researches are still needed to develop its efficiency to identify all the requirements of the generated power in low power demands. The aim of the current investigation is to analyze all the acting forces on the main parts of Darrieus rotor over the rotations as well as in maintenance and stationary conditions. Aerodynamic forces assessment will be executed for 3 different blade shapes (nonsymmetric and symmetric airfoils) like the airfoil section shapes of the Darrieus rotor blades. NACA 0021, LS413, and S1046 are selected as cross-sectional profile in this work. CFD simulations have been used in this work to get the different aerodynamic forces on the rotor blades of the Darrieus turbines. The present results indicated that the symmetric S1046 blade has higher forces during the rotation and stagnant (static) conditions. Moreover, the self-starting capability of NACA 0021 is better than S1046 due to low aerodynamic torsion on the S1046 blades.
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  • 6
    Publication Date: 2020
    Description: A cellular automaton (CA) model is proposed to simulate the egress of pedestrians while gaseous hazardous material is spreading. The advection-diffusion with source term is used to describe the propagation of gaseous hazardous material. It is incorporated into the CA model. The navigation field in our model is determined by the solution of the Eikonal equation. The state transition of a pedestrian relies on the arrival time of cells in the Moore neighborhood. Numerical experiments are investigated in a room with multiple exits, and their results are shown.
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  • 7
    Publication Date: 2020
    Description: In the present paper, we report a numerical study of dynamic and thermal behavior of the incompressible turbulent air flow by forced convection in a two-dimensional horizontal channel. This one contains the complicated form of the deflector which has been studied by varying the inclination angle from φ = 40°, φ = 55° to φ = 65°. The baffles are mounted on lower and upper walls of the channel. The walls are maintained at a constant temperature (375 K), the inlet velocity of air is Uint = 7.8 m/s, and the Reynolds number Re = 8.73 × 104. A specifically developed numerical model was based on the finite-volume method to solve the coupled governing equations and the SIMPLE (Semi Implicit Method for Pressure Linked Equation) algorithm for the treatment of velocity-pressure coupling. For Pr = 0.71, the results obtained show that (i) the streamlines and isotherms are strongly affected by the inclinations angles at Re = 8.73 × 104, (ii) the friction coefficient near the baffles increases under the angle exchange effect, and (iii) for a constant Re, the local Nusselt number at the walls of the channel varies with increasing the inclination angle of the deflector. Furthermore, the deflectors are generally used to change the direction of the structure of flow and also to increase the turbulence levels. We can conclude that the contribution of inclined baffles improves the increase of heat and mass transfer in which the Nusselt number at a certain angle increases noticeably.
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  • 8
    Publication Date: 2020
    Description: Darrieus wind rotor is a vertical axis wind turbine that is a very promising kind of wind converters at remote and domestic locations that have soft and weak wind potential and speed, but from the quantitative comparison with horizontal axis wind turbines, this type of turbines has a weak performance. Additional researches are still needed to develop its efficiency to identify all the requirements of the generated power in low power demands. The aim of the current investigation is to analyze all the acting forces on the main parts of Darrieus rotor over the rotations as well as in maintenance and stationary conditions. Aerodynamic forces assessment will be executed for 3 different blade shapes (nonsymmetric and symmetric airfoils) like the airfoil section shapes of the Darrieus rotor blades. NACA 0021, LS413, and S1046 are selected as cross-sectional profile in this work. CFD simulations have been used in this work to get the different aerodynamic forces on the rotor blades of the Darrieus turbines. The present results indicated that the symmetric S1046 blade has higher forces during the rotation and stagnant (static) conditions. Moreover, the self-starting capability of NACA 0021 is better than S1046 due to low aerodynamic torsion on the S1046 blades.
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  • 9
    Publication Date: 2020
    Description: Wet snow accumulation on bridge cables and its shedding due to external phenomena such as rise in temperature, wind, and gravity is a serious threat to the safety of cars and pedestrians crossing the bridge. Commonly the accumulated snow on bridge cables is removed by external means such as mechanical removal or heat treatment which are expensive, time-consuming, and high-risk processes and are conducted based on little or no information available regarding the actual size and shape of the accumulated snow. In addition, cleaning of cables using the mechanical methods can potentially lead to erosion of cable materials when applied over years, resulting in enhanced surface roughness and potentially increased wet snow/ice accumulation during future precipitation events, and sometimes might require replacement of cable stays, which is an extremely costly and complicated task. Optimizing the number of mechanical cleaning procedures such as chain release through predicting the shape and thickness of the accumulated snow on the cable stays reduces the cost, time, and risk associated with the process. In this study, wet snow accumulation on torsionally rigid inclined cylinders of high-density polyethylene (HDPE) has been studied experimentally and numerically. A 2-D numerical model has been developed utilizing weather data to predict the thickness and the shape of the accumulated wet snow on inclined cylindrical surfaces. Outdoor experiments were also conducted to measure the density and thickness of accumulated snow, while monitoring the weather data real time. Overall, snow density was found to be linearly increasing with an increase in wind velocity, during snow precipitation. The maximum thickness and shape of the accumulated snow on cables obtained from the numerical model were found to be in good agreement with the outdoor experimental data. This work aims to provide a mean for prediction of snow accumulation on surfaces for optimizing the efficiency of the costly and high-risk snow removal procedures.
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  • 10
    Publication Date: 2020-05-26
    Description: The deterioration of polycarbonate (PC) depends on various environmental factors. Meanwhile, the complexity of the related weathering processes inhibits the prediction of service life based on the environmental factors. To elucidate the nonlinear correlation between PC weathering and the environmental factors, three-year-long natural weathering tests were conducted at eight experimental stations in China. The relationship between tensile-property data of PC and environmental and pollutant data is analyzed by extra-trees and multilayer perceptron networks implemented in Python. The results indicated that (1) the degradation of PC tensile properties is mainly affected by the experimental period (76.37%), whilst the effect of the environmental or pollutant factors on the degradation is less pronounced (23.63%); (2) the classification accuracy of the trained model on the training set is 91% (91/100), and on the testing set is 72.13% (44/61); and lastly, (3) it is inferred from the error analysis of the classification results that the performance change of polycarbonate in Qionghai and Wuhan is characterized by an initial reduction followed by a slight improvement. Lastly, we show that the proposed method performs well, especially in the case of areas with incomplete data available.
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  • 11
    Publication Date: 2020-08-26
    Description: In this research, a comparative study of two recurrent neural networks, nonlinear autoregressive with exogenous input (NARX) neural network and nonlinear autoregressive moving average (NARMA-L2), and a feedforward neural network (FFNN) is performed for their ability to provide adaptive control of nonlinear systems. Three dynamical nonlinear systems of different complexity are considered. The aim of this work is to make the output of the plant follow the desired reference trajectory. The problem becomes more challenging when the dynamics of the plants are assumed to be unknown, and to tackle this problem, a multilayer neural network-based approximate model is set up which will work in parallel to the plant and the control scheme. The network parameters are updated using the dynamic backpropagation (BP) algorithm.
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  • 12
    Publication Date: 2020-06-17
    Description: In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques.
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  • 13
    Publication Date: 2020-09-18
    Description: HAPS (high-altitude pseudosatellites) are flight machines, airplane type, generally without pilot which fly in a definite zone at 18-22 km altitude, providing communication and surveillance services. These flight machines do not leave the atmosphere, and their purpose is to maintain a constant flight level for as long time as possible in the interest zone (e.g., five years) to fulfill their mission. HAPS energetic system proposed in this paper has to feed the electric propulsion system of HAPS (12.5 kW) and also to feed on-board equipment (navigation, data links, scientific equipment, etc.). On-board energy sources have to maintain HAPS in the interest zone for long periods. For this reason, it is used in the present solar power sources. A part of the generated energy is consumed on board; the rest is stored daytime and consumed nighttime. So, the system is provided with energy generation systems and also with storage and management systems. HAPS energetic system is a hybrid type, with two or more power sources. In this case, power sources are photovoltaic panels are used daytime and fuel cell are used nighttime, and also, a battery and/or a supercapacitor is used in transition periods from day to night and in peak load periods. In this paper, an electric power system used nighttime is designed and analysed. In this situation, the primary power source is the fuel cell and the secondary power sources are battery and/or supercapacitor. There are used numerical simulations models, developed in Matlab/Simulink, for all hybrid power source components: fuel cell stack, battery system, supercapacitors, conversion system, and fuzzy logic power management system. For a part of these components, there are used existing simulation models in Matlab/Simulink, adapted to these simulation requirements, and for others, there are designed and implemented simulation schemes according to these simulation requirements. An important component of the hybrid power source is the power conversion system which adapts the power sources parameters to consumer input requirements. A fuzzy logic power management system is designed.
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  • 14
    Publication Date: 2020-07-30
    Description: Three-dimensional modelling of biological systems is imperative to study the behaviour of dynamic systems that require the analysis of how their components interact in space. However, there are only a few formal tools that offer a convenient modelling of such systems. The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. Indeed, a visual modelling can help to conceive a mental image which eventually contributes to the understanding of the problem under study. Coloured Hybrid Petri Nets (HPNC) are a high-level representation of classical Petri nets that offer hybrid as well as spatial modelling of biological systems. In addition to their graphical representations, HPNC models are also scalable. This paper shows how HPNC can be used to construct and simulate systems that require three-dimensional as well as hybrid (stochastic/continuous) modelling. We use calcium diffusion in three dimensions to illustrate our main ideas. More specifically, we show that creating 3D models using HPNC can yield more flexible models as the structure can be easily scaled up and down by just modifying a few parameters. This advantage of convenient model configuration facilitates the design of different experiments without the need to alter the model structure.
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  • 15
    Publication Date: 2020-08-19
    Description: Motivated by the ridge regression (Hoerl and Kennard, 1970) and Liu (1993) estimators, this paper proposes a modified Liu estimator to solve the multicollinearity problem for the linear regression model. This modification places this estimator in the class of the ridge and Liu estimators with a single biasing parameter. Theoretical comparisons, real-life application, and simulation results show that it consistently dominates the usual Liu estimator. Under some conditions, it performs better than the ridge regression estimators in the smaller MSE sense. Two real-life data are analyzed to illustrate the findings of the paper and the performances of the estimators assessed by MSE and the mean squared prediction error. The application result agrees with the theoretical and simulation results.
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  • 16
    Publication Date: 2020-09-03
    Description: With advancements in computer-aided design, simulation of internal combustion engines has become a vital tool for product development and design innovation. Among the simulation software packages currently available, MATLAB/Simulink is widely used for automotive system simulations, but does not contain a comprehensive engine modeling toolbox. To leverage MATLAB/Simulink’s capabilities, a Simulink-based 1D flow engine modeling framework has been developed. The framework allows engine component blocks to be connected in a physically representative manner in the Simulink environment, reducing model build time. Each component block, derived from physical laws, interacts with other blocks according to block connection. In this Part 1 of series papers, a comprehensive gas dynamics model is presented and integrated in the engine modeling framework based on MATLAB/Simulink. Then, the gas dynamics model is validated with commercial engine simulation software by conducting a simple 1D flow simulation.
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  • 17
    Publication Date: 2020-03-17
    Description: In this paper, we present, in detail, how a mathematical model that simulates the probable scenarios of intimate partner violence is linked to the application of any questionnaire of domestic violence already in use. This questionnaire assigns a weight of severity to each proposed inquiry for the types of psychological, physical, and sexual violence. We show a numerical procedure that must be performed to obtain the probable scenarios of violence in which the victim is involved, taking as key factor the loss of control of the perpetrator. With the numerical data obtained from the application of the mathematical model, the probable levels of violence that the victim could experience month to month for two cycles of violence are plotted, as well as the behaviors of the probable states of loss of control that the perpetrator would have during the next twelve months. Based on the results obtained, we generated a help table of indicators that could be used by victim assistance centers and/or health experts for decision-making schemes.
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  • 18
    Publication Date: 2020-02-18
    Description: The current study performs an explicit nonlinear finite element simulation to predict temperature distribution and consequent stresses during the friction stir welding (FSW) of AA 7075-T651 alloy. The ABAQUS® finite element software was used to model and analyze the process steps that involve plunging, dwelling, and traverse stages. Techniques such as Arbitrary Lagrangian–Eulerian (ALE) formulation, adaptive meshing, and computational feature of mass scaling were utilized to simulate sequence events during the friction stir welding process. The contact between the welding tool and workpiece was modelled through applying Coulomb’s friction model with a nonlinear friction coefficient value. Also, the model considered the effect of nonlinear material properties as well as heat transfer conditions such as heat losses due to convection and thermal contact conductance between the workpiece and the backing plate interface on the thermal history. To validate the computational model results, an experimental procedure was carried out to measure temperature history on both sides of the specimen as well as the plunging force throughout the whole process time. The results obtained showed that symmetrical temperature distribution throughout the workpiece width was distinguished, implying that the tool rotation has a minor effect on the final temperature distribution. In addition, asymptotic V shape with high gradient temperature value in the weld nugget region after the full plunging was distinguished. Mechanical stresses and related plastic deformations generated, while achieving the FSW samples were evaluated in addition to the tool reaction force and heat generated to protect against tool failure.
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  • 19
    Publication Date: 2020-02-11
    Description: In the present work, the statistical dispersion of the mortar compressive strength as a function of the geometric parameters of the specimens as well as the effect of the mortar workability difference on the compressive strength was investigated. For this purpose, specimens were prepared for six types of mortars: two conventional mortars in the proportions of 1 : 1 : 6 and 1 : 2 : 9 of cement, hydrated lime, and sand, respectively, two with clay replacing lime, and two with marble waste in place of lime. The results confirm the difference between the results found for the two geometries due to the differences in the heights of the molding layers and show that the workability of the mortar modifies the resistance properties, especially in the cylindrical mold where the molding of the specimens is more complex. By comparing the differences between the destructive test results and those defined by the Finite Element Modeling (FEM) for conventional mortars, it was clear that the effect of excess material in the sample during the compression tests did not change the strength properties studied. This facilitates the performance of the assay as specimens may be used excessively on the side without the need for sample rectification.
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  • 20
    Publication Date: 2020-01-28
    Description: In the present paper, we report a numerical study of dynamic and thermal behavior of the incompressible turbulent air flow by forced convection in a two-dimensional horizontal channel. This one contains the complicated form of the deflector which has been studied by varying the inclination angle from φ = 40°, φ = 55° to φ = 65°. The baffles are mounted on lower and upper walls of the channel. The walls are maintained at a constant temperature (375 K), the inlet velocity of air is Uint = 7.8 m/s, and the Reynolds number Re = 8.73 × 104. A specifically developed numerical model was based on the finite-volume method to solve the coupled governing equations and the SIMPLE (Semi Implicit Method for Pressure Linked Equation) algorithm for the treatment of velocity-pressure coupling. For Pr = 0.71, the results obtained show that (i) the streamlines and isotherms are strongly affected by the inclinations angles at Re = 8.73 × 104, (ii) the friction coefficient near the baffles increases under the angle exchange effect, and (iii) for a constant Re, the local Nusselt number at the walls of the channel varies with increasing the inclination angle of the deflector. Furthermore, the deflectors are generally used to change the direction of the structure of flow and also to increase the turbulence levels. We can conclude that the contribution of inclined baffles improves the increase of heat and mass transfer in which the Nusselt number at a certain angle increases noticeably.
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  • 21
    Publication Date: 2020-02-20
    Description: Wet snow accumulation on bridge cables and its shedding due to external phenomena such as rise in temperature, wind, and gravity is a serious threat to the safety of cars and pedestrians crossing the bridge. Commonly the accumulated snow on bridge cables is removed by external means such as mechanical removal or heat treatment which are expensive, time-consuming, and high-risk processes and are conducted based on little or no information available regarding the actual size and shape of the accumulated snow. In addition, cleaning of cables using the mechanical methods can potentially lead to erosion of cable materials when applied over years, resulting in enhanced surface roughness and potentially increased wet snow/ice accumulation during future precipitation events, and sometimes might require replacement of cable stays, which is an extremely costly and complicated task. Optimizing the number of mechanical cleaning procedures such as chain release through predicting the shape and thickness of the accumulated snow on the cable stays reduces the cost, time, and risk associated with the process. In this study, wet snow accumulation on torsionally rigid inclined cylinders of high-density polyethylene (HDPE) has been studied experimentally and numerically. A 2-D numerical model has been developed utilizing weather data to predict the thickness and the shape of the accumulated wet snow on inclined cylindrical surfaces. Outdoor experiments were also conducted to measure the density and thickness of accumulated snow, while monitoring the weather data real time. Overall, snow density was found to be linearly increasing with an increase in wind velocity, during snow precipitation. The maximum thickness and shape of the accumulated snow on cables obtained from the numerical model were found to be in good agreement with the outdoor experimental data. This work aims to provide a mean for prediction of snow accumulation on surfaces for optimizing the efficiency of the costly and high-risk snow removal procedures.
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  • 22
    Publication Date: 2020-01-25
    Description: A cellular automaton (CA) model is proposed to simulate the egress of pedestrians while gaseous hazardous material is spreading. The advection-diffusion with source term is used to describe the propagation of gaseous hazardous material. It is incorporated into the CA model. The navigation field in our model is determined by the solution of the Eikonal equation. The state transition of a pedestrian relies on the arrival time of cells in the Moore neighborhood. Numerical experiments are investigated in a room with multiple exits, and their results are shown.
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  • 23
    Publication Date: 2020-01-11
    Description: Darrieus wind rotor is a vertical axis wind turbine that is a very promising kind of wind converters at remote and domestic locations that have soft and weak wind potential and speed, but from the quantitative comparison with horizontal axis wind turbines, this type of turbines has a weak performance. Additional researches are still needed to develop its efficiency to identify all the requirements of the generated power in low power demands. The aim of the current investigation is to analyze all the acting forces on the main parts of Darrieus rotor over the rotations as well as in maintenance and stationary conditions. Aerodynamic forces assessment will be executed for 3 different blade shapes (nonsymmetric and symmetric airfoils) like the airfoil section shapes of the Darrieus rotor blades. NACA 0021, LS413, and S1046 are selected as cross-sectional profile in this work. CFD simulations have been used in this work to get the different aerodynamic forces on the rotor blades of the Darrieus turbines. The present results indicated that the symmetric S1046 blade has higher forces during the rotation and stagnant (static) conditions. Moreover, the self-starting capability of NACA 0021 is better than S1046 due to low aerodynamic torsion on the S1046 blades.
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  • 24
    Publication Date: 2020-01-13
    Description: Thermal performance development, heat transfer structure, and flow behavior in the heat exchanger square duct equipped with a 45° inclined square ring are investigated numerically. The effects of flow blockage ratios and spacing ratios for the inclined square ring on fluid flow and heat transfer are considered. The Reynolds number (Re = 100–2000, laminar regime) based on the hydraulic diameter of the square duct is selected for the present work. The numerical domain of the square duct inserted with the 45° inclined square ring is solved with the finite volume method. The SIMPLE algorithm is picked for the numerical investigation. The heat transfer characteristics and flow topologies in the square duct inserted with the inclined square ring are plotted in the numerical report. The heat transfer rate, pressure loss, and efficiency for the square duct placed with the inclined square ring are presented in forms of Nusselt number, friction factor, and thermal enhancement factor, respectively. As the numerical results, it is detected that the heat transfer rate of the heat exchanger square duct inserted with the inclined square ring is around 1.00–10.05 times over the smooth duct with no inclined square ring. Additionally, the maximum thermal enhancement factor for the heat exchanger square duct inserted with the inclined square ring is around 2.84.
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