scholarly journals Helical Flow of Polymer Melts in Extruders : Model Development and Validation with Experiments

2021 ◽  
Author(s):  
Farshid Sanjabi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Injection Molding ◽  
Natural System ◽  
State Variables ◽  
Melt Temperature ◽  
Coupled Equations ◽  
Simulation Results ◽  
Helical Geometry ◽  
The Mathematical Model

Operating and processing conditions as well as the selection of the screw design in injection molding industry are largely based on trial-and-error exercise, which is expensive and time consuming. A better approach is to develop mathematical models for prediction of the final process performance where the conditions and parameters of a process can be used as inputs in those models. However, most of the models developed and used so far contain unrealistic geometrical and mathematical simplifications. The objective of this work is to develop a steady-state three dimensional mathematical model to describe the flow of an incompressible polymer melt inside a helical geometry, which represents the polymer's true motion in extrusion and injection molding processes. In order to develop the model in helical geometry, where at least two axes are not perpendicular, the mathematical model is first developed in a natural system (i.e. cylindrical) and using transformation tools are then changed to the physical helical one. In this initiative, we develop an iterative computational alogrithm based on shooting Newton-Raphson method in order to simulate the process. The transformation matrices to adapt the equations of change form a natural system (i.e. orthogonal cylindrical systems) to a physical system (i.e. Helical coordinates) are also developed for velocity and derivative profiles. Subsequently the solution approach to solve the indirectly coupled equations of change is explained and the simulation results are compared with experimental data. The simulation results are vallidated against data obtained from ten different experiments with an industrial injection molding machine, processing two different polymers - high density polyethylene (HDPE) and poly ethylene terephthalate (PET). It is observed that the simulation results are in good agreement with experimental data. This outcome demonstrates the utility of the developed mathematical model and simulation approach. Important features of this work are the consideration of the linear backward motion of the screw leading to calculation of proper process shot size and the incorporation of the tapering screw designs with upward and downward sections in the direction of the flow into the model. Another important feature in the development of the mathematical model is that the rheological and physical properties of plastic resins are not constant and change as the melt temperature changes during the process. From the standpoint of industrial practice, the direct benefit of this work is the ability to effectively calculate adequate shot size, recovery rate, and various state variables throughout the extent of the machine.

scholarly journals Helical Flow of Polymer Melts in Extruders : Model Development and Validation with Experiments

2021 ◽  
Author(s):  
Farshid Sanjabi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Injection Molding ◽  
Natural System ◽  
State Variables ◽  
Melt Temperature ◽  
Coupled Equations ◽  
Simulation Results ◽  
Helical Geometry ◽  
The Mathematical Model

Operating and processing conditions as well as the selection of the screw design in injection molding industry are largely based on trial-and-error exercise, which is expensive and time consuming. A better approach is to develop mathematical models for prediction of the final process performance where the conditions and parameters of a process can be used as inputs in those models. However, most of the models developed and used so far contain unrealistic geometrical and mathematical simplifications. The objective of this work is to develop a steady-state three dimensional mathematical model to describe the flow of an incompressible polymer melt inside a helical geometry, which represents the polymer's true motion in extrusion and injection molding processes. In order to develop the model in helical geometry, where at least two axes are not perpendicular, the mathematical model is first developed in a natural system (i.e. cylindrical) and using transformation tools are then changed to the physical helical one. In this initiative, we develop an iterative computational alogrithm based on shooting Newton-Raphson method in order to simulate the process. The transformation matrices to adapt the equations of change form a natural system (i.e. orthogonal cylindrical systems) to a physical system (i.e. Helical coordinates) are also developed for velocity and derivative profiles. Subsequently the solution approach to solve the indirectly coupled equations of change is explained and the simulation results are compared with experimental data. The simulation results are vallidated against data obtained from ten different experiments with an industrial injection molding machine, processing two different polymers - high density polyethylene (HDPE) and poly ethylene terephthalate (PET). It is observed that the simulation results are in good agreement with experimental data. This outcome demonstrates the utility of the developed mathematical model and simulation approach. Important features of this work are the consideration of the linear backward motion of the screw leading to calculation of proper process shot size and the incorporation of the tapering screw designs with upward and downward sections in the direction of the flow into the model. Another important feature in the development of the mathematical model is that the rheological and physical properties of plastic resins are not constant and change as the melt temperature changes during the process. From the standpoint of industrial practice, the direct benefit of this work is the ability to effectively calculate adequate shot size, recovery rate, and various state variables throughout the extent of the machine.

A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level

2018 ◽  
Vol 26 (6) ◽  
pp. 859-873 ◽  
Author(s):  
H. Thomas Banks ◽  
Sergey I. Kabanikhin ◽  
Olga I. Krivorotko ◽  
Darya V. Yermolenko
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Inverse Problem ◽  
Cellular Level ◽  
Free Virus ◽  
Hiv Dynamics ◽  
Infection Parameters ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Fixed Times

Abstract In this paper a problem of specifying HIV-infection parameters and immune response using additional measurements of the concentrations of the T-lymphocytes, the free virus and the immune effectors at fixed times for a mathematical model of HIV dynamics is investigated numerically. The problem of the parameter specifying of the mathematical model (an inverse problem) is reduced to a problem of minimizing an objective function describing the deviation of the simulation results from the experimental data. A genetic algorithm for solving the least squares function minimization problem is implemented and investigated. The results of a numerical solution of the inverse problem are analyzed.

Modeling and Simulation of a Co-current Rotary Dryer

2016 ◽  
Vol 12 (2) ◽  
pp. 189-194 ◽  
Author(s):  
Zhi-gang Huang ◽  
Yun-xuan Weng ◽  
Nan Fu ◽  
Zong-qiang Fu ◽  
Dong Li ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Moisture Content ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Air Temperature ◽  
Good Accuracy ◽  
Rotary Dryer ◽  
Simulation Results ◽  
The Mathematical Model

Abstract Mathematical models including mass and energy conservation were developed in order to predict the outlet particles temperature and moisture. As the inlet air temperature increased, the outlet particles temperature increased as well and the outlet particles moisture decreased quickly. The outlet particles temperature and moisture changed a little as a function of the speed of rotation at the low inlet air temperature, while the outlet particles temperature and moisture increased very apparently with the speed of rotation increased at the high inlet air temperature. The error of the simulation results compared to the experimental data showed good accuracy for particles temperature and moisture content. The mathematical model performs well to predict the outlet particles temperature and moisture content.

scholarly journals EXPERIMENTAL STUDIES OF HEAT EXCHANGE DURING WATER COOLING AND STEAM CONDENSATION IN DEMOVER RADIATOR SECTIONS

2021 ◽  
Vol 1 (38) ◽  
pp. 107-114
Author(s):  
V. Mogila ◽  
M. Kovtanets ◽  
M. Morneva
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Cooling System ◽  
Experimental Studies ◽  
Road Transport ◽  
Thermal Calculation ◽  
Mode Of Operation ◽  
Simulation Results ◽  
The Mathematical Model

The Department of Railwayand Road Transport, lift and care system of Volodymyr Dahl East Ukrainian National University, an energy-saving cooling system for diesel locomotives using phase transitions of the coolant has been developed. The proposed cooling system allows to maintain constant optimal temperatures of cooling objects at ambient temperatures ± 40 ºC and in any mode of operation of the diesel engine. For thermal calculation of the radiator section operating in the mode of the steam condenser, the mathematical model of process of heat transfer from steam to walls of a flat tube at condensation is developed that considers geometrical features of section of a tube. The adequacy of this mathematical model is verified by comparing the simulation results with the obtained experimental data. During the tests, the outlet water temperature, inlet and outlet air temperature, and air pressure in front of and behind the radiator were measured. Having the values of wall temperature, steam temperature and condensate, knowing the value of steam consumption and the experimental heat transfer coefficient, it becomes possible to verify the adequacy of the mathematical model by comparing the simulation results with the obtained experimental data. Schemes of bench equipment, test methods, experimental planning and basic calculation dependences required for testing serial radiator sections of a locomotive in the standard mode of operation and in the mode of steam condensers are presented.

Numerical Study of the Dynamics of Particles Motion with Different Sizes from Coal-Based Thermal Power Plant

2019 ◽  
Vol 20 (2) ◽  
pp. 223-241 ◽  
Author(s):  
Alibek Issakhov ◽  
Ruslan Bulgakov ◽  
Yeldos Zhandaulet
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Power Plant ◽  
Thermal Power Plant ◽  
Thermal Power ◽  
Numerical Results ◽  
Simulation Results ◽  
Turbulent Models ◽  
The Mathematical Model

AbstractIn this paper, the propagation of particles with different sizes from a coal-based thermal power plant was investigated. It was found that the deterioration of the environment is due to the release of a large amount of SOx, NOx and the volatile particles of Suspended Particulate Matter and Respirable Suspended Particles matter, which cause human and animal diseases. This paper presents the numerical simulation results of air pollution by particles which having different sizes from thermal power plants in real sizes using a 3D model. For the adequacy of the mathematical model, a test problem was solved using different turbulent models. To assess the applicability of the mathematical model, the numerical algorithm and the choice of the optimal turbulent model, experimental data and numerical results of other authors were used. The obtained numerical simulation results are in good agreement with the experimental results and the numerical results of other authors. And to obtain more accurate numerical results for the experimental data for turbulent models ($k - \varepsilon $,$k - \omega $), there were certain corresponding boundary conditions for kinetic energy. Also, profiles of all flow characteristics were compared with and without particles and some effects of the particle on the flow were identified.

Research on Dynamic Balance Method of Precision Centrifuge

2014 ◽  
Vol 945-949 ◽  
pp. 777-780
Author(s):  
Tao Liu ◽  
Yong Xu ◽  
Bo Yuan Mao
Keyword(s):  
Mathematical Model ◽  
Balance Control ◽  
Dynamic Balance ◽  
Dynamic Balancing ◽  
Structure Characteristics ◽  
Balance System ◽  
Simulation Results ◽  
Set Up ◽  
System Controller ◽  
The Mathematical Model

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

The Impact Analysis of Revolute Pair Clearance to the End Pose Accuracy of Welding Robot

2015 ◽  
Vol 778 ◽  
pp. 259-263
Author(s):  
Fa Jun Zhang ◽  
Lin Zi Li ◽  
Hui Lin ◽  
Yin Lin Pu ◽  
Zhu Xin
Keyword(s):  
Mathematical Model ◽  
Impact Analysis ◽  
Joint Clearance ◽  
Welding Robot ◽  
Movement Characteristic ◽  
Movement Stability ◽  
Simulation Results ◽  
The Impact ◽  
The Mathematical Model ◽  
Welding Position

Various uncertain factors affect the movement of the welding robot, thus welding gun tend to deviate from the theory of welding position which reduces the welding accuracy, of which the revolute pair clearance have an greater effect on the movement of the welding robot. In order to study the influence of revolute pair clearance to the end pose accuracy of welding robot, the mathematical model of revolute pair clearance was established, and the software SolidWorks was used for establishing the welding robot model, making simulations of the mechanical arm with joint clearance and no joint clearance. At last, the movement characteristic of the hinge shaft is attained. The simulation results showed that the shaft velocity and displacement of mechanical arm with joint clearance has a certain degree of fluctuation, which affecting the end pose accuracy of welding robot , and reducing the movement stability and the welding accuracy of welding robot.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Deep and Shallow Water Low-Speed Maneuvering Tests: Comparison Between Experimental and Simulation Results

2016 ◽  
Author(s):  
Felipe Ribolla Masetti ◽  
Pedro Cardozo de Mello ◽  
Guilherme F. Rosetti ◽  
Eduardo A. Tannuri
Keyword(s):  
Mathematical Model ◽  
Small Scale ◽  
Shallow Waters ◽  
Hydrodynamic Coefficients ◽  
Low Speed ◽  
Tunnel Model ◽  
Oceanographic Research ◽  
Simulation Results ◽  
The University ◽  
The Mathematical Model

This paper presents small-scale low-speed maneuvering tests with an oceanographic research vessel and the comparison with mathematical model using the real time maneuvering simulator developed by the University of São Paulo (USP). The tests are intended to verify the behavior of the vessel and the mathematical model under transient and low speed tests. The small-scale tests were conducted in deep and shallow waters, with a depth-draft ratio equal to 1.28, in order to verify the simulator ability to represent the vessel maneuverability on both depth conditions. The hydrodynamic coefficients used in the simulator model were obtained by CFD calculations and wind tunnel model tests carried out for this vessel. Standard turning circle and accelerating turn maneuvers were used to compare the experimental and numerical results. A fair agreement was achieved for shallow and deep water. Some differences were observed mainly in the initial phase of the accelerating turn test.

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