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1
Model of magnetic gun with respecting eddy currents
EN
A sophisticated mathematical model of the magnetic gun is presented and solved numerically. The model consists of three strongly non-linear and non-stationary differential equations describing the time-dependent distribution of magnetic field in the device, current in the field circuit and movement of the projectile. The numerical solution is carried out in the application Agros2D based on a fully adaptive higher-order finite element method. The results are processed in Wolfram Mathematica. The methodology is illustrated by an example and selected results are compared with experiment.
2
Model of magnetic gun with respecting eddy currents
EN
A sophisticated mathematical model of the magnetic gun is presented and solved numerically. The model consists of three strongly non-linear and non-stationary differential equations describing the time-dependent distribution of magnetic field in the device, current in the field circuit and movement of the projectile. The numerical solution is carried out in the application Agros2D based on a fully adaptive higher-order finite element method. The results are processed in Wolfram Mathematica. The methodology is illustrated with an example and selected results are compared with experiment.
EN
An electromagnetic valve for control of flow of electrically non-conductive liquids is proposed and modeled. The device contains only one movable part (a cylindrical plunger) whose movement is controlled by a secondary magnetic circuit with a high-parameter permanent magnet and current in the field coil. The paper presents its mathematical model that is solved numerically. For computations we used our own code Agros2D based on a fully adaptive higher-order finite element method. The static characteristics of the device are calculated using a modified version of the Eggshell method in order to avoid undesirable peaks and oscillations. The principal results are evaluated and discussed.
EN
An electromagnetic valve for control of flow of electrically non-conductive liquids is proposed and modeled. The device contains only one movable part (a cylindrical plunger) whose movement is controlled by a secondary magnetic circuit with a high-parameter permanent magnet and current in the field coil. The paper presents its mathematical model that is solved numerically. For computations we used our own code Agros2D based on a fully adaptive higher-order finite element method. The static characteristics of the device are calculated using a modified version of the Eggshell method in order to avoid undesirable peaks and oscillations. The principal results are evaluated and discussed.
EN
A complete overview of results is presented concerning induction heating of nonmagnetic cylindrical billets in magnetic field produced by permanent magnets. The authors proposed and modelled two possible ways of the process. The billet either rotates inside a system of appropriately arranged static permanent magnets or a ring containing such magnets rotates around an unmoving billet. Both arrangements were modelled numerically using fully adaptive higher-order finite element method and some results were verified by experiments on a physical model built in our lab.
PL
W pracy opisano rezultaty modelowania procesu nagrzewania indukcyjnego kęsów aluminiowych w polu magnetycznym wytwarzanym przez magnesy stałe. Autorzy proponują i modelują dwa warianty technologii. Kęs może być obracany wewnątrz zestawu odpowiednio ustawionych magnesów lub pierścień magnesów jest obracany względem nieruchomego kęsa. Oba warianty były symulowane przy pomocy w pełni adaptacyjnej metody elementów skończonych wyższych rzędów. Niektóre wyniki symulacji porównano z modelem fizycznym zbudowanym przez autorów.
EN
Comparison of several types of electrostatic micro-actuators is carried out, particularly with respect to their resultant force effects. The continuous mathematical model of such actuators is mostly described by the Laplace equation. In this paper, its numerical solution is performed by a fully adaptive higher-order finite element method, using a code developed by the authors. The methodology is illustrated by typical examples whose results are discussed.
7
Higher-Order Modeling of Electrostatic Separator of Plastic Particles
EN
Optimization of a separator of plastic particles is carried out. The objective function maximizes the number of particles falling down to the corresponding bins. Electric field in the system is solved numerically, using the fully adaptive higher-order finite element method. The trajectories of particles are determined by means of an adaptive Runge-Kutta-Fehlberg method with a time varying time step. The shape of the electrodes is performed by a technique based on higher-order conjugate gradients.
PL
. W artykule przeprowadzono optymalizację separatora cząstek plastycznych. Funkcja celu maksymalizuje liczę cząstek spadających do odpowiednich pojemników. Pole elektryczne w tym systemie wyznaczane jest numerycznie, poprzez zastosowanie pełno adaptacyjnej metody elementów skończonych wyższego rzędu. Trajektorie ruchu cząstek zostały wyznaczone za pomocą adaptacyjneh metody Runge-Kutta-Fehlberga ze zmiennym krokiem czasowym. Kształt elektrod jest wyznaczany techniką gradientów sprzężonych wyższego rzędu. (Modelowanie wyższego rzędu elektrostatycznego separatora cząstek plastycznych)
EN
Simulation of movement of a large number of charged particles in external electrostatic field is of great importance for a correct design of separators whose aim is to select them according to the sign of their charge. The paper deals with modeling of their trajectories in a specific arrangement consisting of a profile vessel equipped with two electrodes and several collecting bins. Electric field between the electrodes is determined using a fully adaptive higher-order finite element method. The movement (velocities and trajectories) of the particles affected by electric field, gravity and aerodynamic resistance is modeled by an adaptive Runge-Kutta-Fehlberg method with an appropriately varying time step. On the other hand, their charges are rather low, so that it is possible to neglect the Coulomb forces acting among them. The methodology is illustrated by a typical example whose results are discussed.
EN
Induction heating of nonmagnetic cylindrical billets by rotation in magnetic field produced by static permanent magnets is modeled. Numerical analysis of the process is carried out in the hard-coupled formulation, using own code based on higher-order finite element method. The methodology is illustrated by a typical example and the most important results are validated by an experiment.
PL
W artykule przedstawiono model grzania indukcyjnego wkładu cylindrycznego poprzez rotację w polu magnetycznym magnesu trwałego. Analiza numeryczna przeprowadzona jest dla sformułowania bazującego na silnym sprzężeniu przy użyciu własnego kodu wykorzystującego metodę elementów skończonych wyższych rzędów. Metodykę analizy zilustrowano typowym przykładem a najważniejsze wyniki są skonfrontowane z wynikami eksperymentu.
EN
Incompressible flow of electrically conductive medium driven by time-variable magnetic field in an axisymmetric channel is modeled. Numerical solution of the model is carried out by a higher-order finite element method in the monolithic formulation by our own code Hermes.
PL
W artykule modelowany jest nieściśliwy przepływ cieczy elektrycznie przewodzącej wywołany polem magnetycznym zmiennym w czasie. Rozwiązanie numeryczne wykorzystuje metodę elementów skończonych wyższych rzędów w sformułowaniu monolitycznym przy użyciu własnego kodu Hermes.
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