磁绝缘边界条件.doc

发布时间：2022-06-08 发布人：admin 分类：说明书资料大小：0.84M 资料格式：doc 举报版权申诉

weixin_44305804-11972738-4744302543416615957.doc.pdf-第1页.png

第1页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第2页.png

第2页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第3页.png

第3页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第4页.png

第4页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第5页.png

第5页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第6页.png

第6页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第7页.png

第7页 / 共13页

weixin_44305804-11972738-4744302543416615957.doc.pdf-第8页.png

第8页 / 共13页

How to Choose Between Boundary Conditions for Coil

Boundary Conditions for Modeling Coils: An Overvie

Replacing Boundary Conditions with Domain Conditio

Closing Remarks on Choosing Boundary Conditions fo

Further Resources

How to Choose Between Boundary Conditions for Coil Modeling 22, 2016 Walter Frei March Whenever you are modeling coils with the AC/DC Module in COMSOL Multiphysics, you need to consider what type of boundary conditions to use to truncate your modeling domain. In this blog post, we will introduce the different boundary conditions that you can use and how to choose between them.

Boundary Conditions for Modeling Coils: An Overview As we introduced in our previous blog post on the basics of coil modeling, whenever you are modeling an electromagnetic coil, you need to think in terms of a closed current loop. The current loop can be entirely within the modeling domain or closed via a boundary condition, as illustrated in the figure below. A coil connected to a voltage source (left) and two different approaches to closing the current loop (right). As we learned earlier, if the coil extends to the boundaries of the modeling domain, then the current flowing through the coil will return

along the modeling domain boundaries. Otherwise, to close the current loop, the coil must loop within the modeling domain. Here, we will concern ourselves with two questions. First, what boundary conditions should we use? And second, how far away from the coil should these boundaries be? We will start by thinking of our coil as sitting in a space that extends to infinity and does not contain anything else. Obviously, we cannot model an infinitely large domain. We must truncate our modeling domain to some finite size that will give reasonably accurate results but will not require too much computational effort to solve. First, let us consider the case of an axisymmetric coil that is closed within the modeling domain. This case can be analyzed via a 2D axisymmetric model, as shown below.

A circular coil in a spherical modeling domain can be modeled via a 2D axisymmetric model. The domain radius is normalized with respect to the coil radius. We will consider two different boundary conditions along the outside radius of the modeling domain shown above: the Magnetic Insulation (MI) boundary condition and the Perfect Magnetic Conductor (PMC) boundary condition. The Magnetic Insulation condition can be physically interpreted as a boundary to a domain that has infinite electrical conductivity. That is, the Magnetic Insulation condition implies that our coil is enclosed

within a sphere of very high conductivity. Currents can flow and be induced on a magnetic insulation boundary. Mathematically speaking, the magnetic insulation fixes the field variable that is being solved for to be zero at the boundary; it is a homogeneous Dirichlet boundary condition. On the other hand, the Perfect Magnetic Conductor boundary condition can be thought of as the opposite boundary condition. Mathematically, it enforces the homogeneous Neumann condition, meaning the derivative of the solution field in the direction normal to the boundary is zero. No current can flow, nor be induced on, a perfect magnetic conductor boundary. Since these two boundary conditions can be thought of as opposites, let’s take a look at what happens to the solution as we solve the above problem with an increasing radius of the surrounding air sphere and monitor the

computed coil inductance. We can perform a parametric sweep over the domain radius and then take the average of the solutions for the two different boundary conditions by joining solutions. These results are shown in the plot below, and we can observe that the solution for the inductance converges with increasing domain radius. We can also observe that the average of the two solutions converges even faster. Normalized inductance of a coil with an

increasing radius for different boundary conditions. From the above plot, we can conclude that it doesn’t matter which boundary condition we use for this axisymmetric problem, as long as we study the solution with an increasing domain radius. We can also conclude that we can run the model with a relatively smaller domain radius and with both Magnetic Insulation and Perfect Magnetic Conductor boundary conditions to take the average of the two cases. This average, even for a small radius, will give a good prediction of the solution at larger domain radii. Replacing Boundary Conditions with Domain Conditions

We can, in fact, avoid the question of boundary conditions entirely by truncating our modeling domain with a domain condition known as an infinite element domain. The infinite element domain requires that you add an additional domain as a layer around the exterior of the modeling domain. The software then internally performs a coordinate stretching within this domain such that the domain is infinitely large, for all practical purposes. Thus, the solution from a model with infinite element domains will be the same as when the domain radius is increased. The advantage of the infinite element domain is that it obviates the question of choosing between boundary conditions as well as the question of the domain size. The infinite element domain can be placed in very close proximity to the coil — it could even be touching. The only additional work that the

分享到：

赞收藏

资料库

磁绝缘边界条件.doc

相关推荐

课程资源

热门标签

最新资料