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Axisymmetry r,z vs 2D x,y in the same conditions.
Posted 8 nov. 2010, 07:22 UTC−5 6 Replies
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I modeled a circular cross-sectional area wire forming a loop (a coil) carrying current in 2D axisymmetric mode (azimuthal induction current, vector potential). . The model is just a circle which represents the cross-sectional area of the coil wire and this small circle is inside a big rectangle which represents the surroundings.
I solved the model and also revolved and mapped the solutions into 3D using extrusion coupling variables
Then I did the same model but instead of starting in 2D axisymmetric mode, I started in just 2D (x,y) coordinates using perpendicular induction currents, vector potential.
In both models, All the geometric parameters are the same, and also the subdomains sub domain settings, but THE VALUES FOR THE FIELD VARIABLE FOR THE SAME COORDINATES, Magnetic Flux Density, B, (BOTH IN THE MODELING PLANE AND ALSO IN 3D) ARE DIFFERENT in both models.
QUESTIONS:
1- In 2D axisymmetric mode (r,z coordinates) I used in z, the axis around which I later I revolved the circle (cross-section of the coil loop) AXISYMMETRY as boundary condition, and the rest of the sides of the rectangle that represent the surroundings I used Magnetic Insulation as a boundary condition. But in 2D (x,y coordinates) I don't have Axisymmetry as one of the options for boundary conditions. Which condition is equivalent to the Axisymmetry in order for the both models to be equivalent. (I used Magnetic Insulation and the values didn't match, and I also change the Axisymmetry condition in z axis in Axisymmetric Mode, for both models to be the same, and it didn't work either: the values were different).
2- In a plane, around a wire carrying a current I, the magnetic flux density at a distance r from the center of the wire should be, according to books, B= mu*I /(2*pi*r). In any of the models the magnetic flux density has the value given by this equation and I think it should be the same, because in both cases the current is perpendicular to the modeling plane, and the Magnetic Flux Lines are concentric circles around the wire. What's happening?
Thank you ALL,
P.S. I am attaching two images of the models for the differences to be shown.
I solved the model and also revolved and mapped the solutions into 3D using extrusion coupling variables
Then I did the same model but instead of starting in 2D axisymmetric mode, I started in just 2D (x,y) coordinates using perpendicular induction currents, vector potential.
In both models, All the geometric parameters are the same, and also the subdomains sub domain settings, but THE VALUES FOR THE FIELD VARIABLE FOR THE SAME COORDINATES, Magnetic Flux Density, B, (BOTH IN THE MODELING PLANE AND ALSO IN 3D) ARE DIFFERENT in both models.
QUESTIONS:
1- In 2D axisymmetric mode (r,z coordinates) I used in z, the axis around which I later I revolved the circle (cross-section of the coil loop) AXISYMMETRY as boundary condition, and the rest of the sides of the rectangle that represent the surroundings I used Magnetic Insulation as a boundary condition. But in 2D (x,y coordinates) I don't have Axisymmetry as one of the options for boundary conditions. Which condition is equivalent to the Axisymmetry in order for the both models to be equivalent. (I used Magnetic Insulation and the values didn't match, and I also change the Axisymmetry condition in z axis in Axisymmetric Mode, for both models to be the same, and it didn't work either: the values were different).
2- In a plane, around a wire carrying a current I, the magnetic flux density at a distance r from the center of the wire should be, according to books, B= mu*I /(2*pi*r). In any of the models the magnetic flux density has the value given by this equation and I think it should be the same, because in both cases the current is perpendicular to the modeling plane, and the Magnetic Flux Lines are concentric circles around the wire. What's happening?
Thank you ALL,
P.S. I am attaching two images of the models for the differences to be shown.
Attachments:
6 Replies Last Post 9 nov. 2010, 08:05 UTC−5
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Posted:
1 decade ago
Hi
I do not really catch your issue here, in 2D you are claculating a infinitely depth problem expressed as 1/m deep system. in 2D axi you are on a thorus with a loop length (corresponding to the previous depth value) that is 2*pi*r, hence varying.
So for me you should not get the same results, or am I missing a point ?
--
Good luck
Ivar
I do not really catch your issue here, in 2D you are claculating a infinitely depth problem expressed as 1/m deep system. in 2D axi you are on a thorus with a loop length (corresponding to the previous depth value) that is 2*pi*r, hence varying.
So for me you should not get the same results, or am I missing a point ?
--
Good luck
Ivar
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Posted:
1 decade ago
What I think (of course I maybe wrong) is that after I revolve both planar models I get the same geometry for both: a coil with a circular cross-section (a toroid ) both around the y-Cartesian coordinate. The geometry is exactly the same for both models. See attachments.
Anyway, what I want to do is built the Cartesian Coordinates Model which is equivalent to the model in 2D axisymmetry, and get the same results for both.
Can you give me at least a hint on how to do it (I need a special help about what boundary condition to use in the symmetry axis, I mean the axis I am going to revolve the rectangle (surroundings) and the circle (cross-section of the coil) around to get the 3D model, because that option is not available for boundary conditions in 2D? What should be the equivalent boundary condition in 2D of the "Axisymmetry boundary condition of the r,z axisymmetric mode?
By the way, and in relation to my question No 2, in any case:
Even if the models are not the same in my case, why the results in any of those models, in the modeling plane, don't meet the result of the equation for the magnetic flux density, B, produce in a plane by a wire carrying a current I, when the current is perpendicular to the plane, B = µ0 * I / 2*pi * r, where r is the distance from the center of the wire? Both produce circular magnetic lines around the wire but the values don't match those one yield for the equation.
Thank you for your help.
Anyway, what I want to do is built the Cartesian Coordinates Model which is equivalent to the model in 2D axisymmetry, and get the same results for both.
Can you give me at least a hint on how to do it (I need a special help about what boundary condition to use in the symmetry axis, I mean the axis I am going to revolve the rectangle (surroundings) and the circle (cross-section of the coil) around to get the 3D model, because that option is not available for boundary conditions in 2D? What should be the equivalent boundary condition in 2D of the "Axisymmetry boundary condition of the r,z axisymmetric mode?
By the way, and in relation to my question No 2, in any case:
Even if the models are not the same in my case, why the results in any of those models, in the modeling plane, don't meet the result of the equation for the magnetic flux density, B, produce in a plane by a wire carrying a current I, when the current is perpendicular to the plane, B = µ0 * I / 2*pi * r, where r is the distance from the center of the wire? Both produce circular magnetic lines around the wire but the values don't match those one yield for the equation.
Thank you for your help.
Attachments:
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Posted:
1 decade ago
Hi
Well my physics understanding tells me that tese cases are not the same, you have a different topology and must adapt the all physics correspondingly, not just a postprocessing loop revolve
What is wrong using 2D axi ? ANd then revolve that ?
--
Good luck
Ivar
Well my physics understanding tells me that tese cases are not the same, you have a different topology and must adapt the all physics correspondingly, not just a postprocessing loop revolve
What is wrong using 2D axi ? ANd then revolve that ?
--
Good luck
Ivar
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Posted:
1 decade ago
Thank you for your answer.
In 2D axisymmetry, at Quasi-Static Magnetic>transient analysis> azimuthal induction currents, vector potential mode, if I draw a circle in THE MODELING PLANE (that's the cross-section of the wire I am going to revolve later to form a coil), if I SET THE CURRENT DENSITY TO A VALUE in that PLANE the current is PERPENDICULAR to the circle, so the magnetic flux density around the circle should be concentric circles and the value of B should be equal to the value yield by the equation
B (r) = µ0 * I
---------
2*pi*r
Why the values COMSOL yields are not the same as the values yield by this equation?
If I understand well, even though the current is Azimuthal, IN THAT PLANE (THE MODELING PLANE) it is perpendicular to the plane.
Thank you again Ivar.
In 2D axisymmetry, at Quasi-Static Magnetic>transient analysis> azimuthal induction currents, vector potential mode, if I draw a circle in THE MODELING PLANE (that's the cross-section of the wire I am going to revolve later to form a coil), if I SET THE CURRENT DENSITY TO A VALUE in that PLANE the current is PERPENDICULAR to the circle, so the magnetic flux density around the circle should be concentric circles and the value of B should be equal to the value yield by the equation
B (r) = µ0 * I
---------
2*pi*r
Why the values COMSOL yields are not the same as the values yield by this equation?
If I understand well, even though the current is Azimuthal, IN THAT PLANE (THE MODELING PLANE) it is perpendicular to the plane.
Thank you again Ivar.
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Posted:
1 decade ago
Igor,
what you model is a circular loop, not a single wire. The opposite part of the loop contributes to the result. COMSOL of course calculates the 3D structure that is represented by your 2D axially symmetric cross section. So, what you can expect is a dipole field at large distance and not the field of a straight wire.
Regards
Edgar
what you model is a circular loop, not a single wire. The opposite part of the loop contributes to the result. COMSOL of course calculates the 3D structure that is represented by your 2D axially symmetric cross section. So, what you can expect is a dipole field at large distance and not the field of a straight wire.
Regards
Edgar
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Posted:
1 decade ago
Thank you very much. You are right. This is very interesting.