Coil Conductor region without losses

Introduction

This chapter discusses the creation of coil conductor regions without a model for evaluating Joule losses. This type of coil region is the simplest available in Flux, allowing the user to create a coil model from only a few parameters. Most remarkably, the user does not need to provide a material to create such a coil conductor region.

The following topics are covered in this documentation:

What this type of region models.
How to create a coil conductor region without losses in a Flux project.
Limitations.
Example of application.

What this type of region models

The coil conductor region without losses allows the user to represent a coil in the finite element domain. The region behaves as a magnetic field source and may be driven either by a coupled circuit or have its current imposed by the user.

A noteworthy feature of this coil region is the fact that it requires a minimal set of parameters for its creation. Consequently, it is well adapted to situations in which the designer does not want or does not know how to describe a coil or winding in its full detail.

As a tradeoff, due to its concise definition, this type of coil conductor region is only well suited for devices in which the Joule losses distribution in the winding is neither relevant nor frequency dependant. Since a material is not included among the parameters required for its creation, the coil conductor region without losses accounts only for the coil losses dissipated in the additional resistance of its associated FE coupling component.

The definition of this kind of coil model in a Flux project may also be regarded as a preliminary step for building more elaborate coil conductor regions, which in turn can account for the increased losses arising from the skin and proximity effects. For further details on extending the capabilities of a coil conductor region without a model for Joule losses, the user is referred to the following documentation topics:

How to create it in a Flux project

In Flux 2D and in Flux Skew, the coil conductor region without losses is a surface region, while in Flux 3D it becomes a volume region. The availability of these regions in Flux FEM applications is discussed in the following documentation topic: Coil models and their availability in Flux projects.

In any case, this region may be created as follows:

while creating a new region, select Coil Conductor Region in the drop-down menu Type of region;
then, in the Basic Definition tab, provide the following inputs:
- the FE coupling component (coil conductor type) associated with the coil;
- the number of turns in the coil (either a number or an I/O Parameter);
- set the option allowing Flux to account appropriately for symmetries and periodicities.
in the Coil Loss Models tab, leave the option Compute coil losses (winding geometry details required) unchecked.

Note: In Flux 2D and in Flux Skew, the region's current orientation must also be informed in the Basic Definition tab. However, in Flux 3D, the current orientation in the volume region is adjusted in the Physics menu, by choosing the option Orient wires of coil conductor regions. For further information on the procedure for selecting the input and output terminals and orienting the wires in 3D, please refer to the following documentation page: Current orientation of coil conductor regions in Flux 3D.

Note: In projects that do not contain any periodicities or symmetries, the user may leave the field Symmetries and periodicities: conductors in series or parallel unchanged (that is, set to the default option All the symmetrical and periodical conductors are in series). For further information on adjusting this field, please refer to the documentation topic discussing how symmetries and periodicities affect the creation of coil entities in Flux.

Limitations

Since this coil model does not include a material in its description, it is impossible to post-process quantities related to the resistivity in the associated surface (in 2D) or volume (in 3D) regions (e.g., the power loss density in the winding or the total dissipated power).

As a matter of fact, this modeling approach forces the user interested in evaluating the Joule losses of a coil to choose the FE coil conductor component as the computation support. Flux post-processing module provides at least two ways to evaluate the Joule losses dissipated in a FE coupling component of the Stranded Coil Conductor type:

Using the Computation menu, followed by the following choices: On physical entity → Compute → Circuit.
With a sensor (Predefined type: Losses by Joule effect) on a Stranded Coil Conductor component.

It is highly advisable to provide a non-zero additional resistance to the FE Element Coupling component assigned to a coil conductor region without losses, especially in the case of coils or circuits fed by a voltage source.

In Flux coupled magneto-thermal applications (AC Steady State Magnetic - Transient Thermal) do not take the power dissipated in the additional resistance of a FE coupling component into account. For this reason, coil conductor regions without losses linked to a FE coupling component with an additional resistance should not be used in this kind of Flux application. Under such circumstances, the recommended coil conductor regions are the coil conductor region with losses with simplified and detailed geometrical descriptions.

The coil conductor region does not take the skin and proximity effects into account. Consequently, its use is not recommended in projects requiring a detailed evaluation of the current and loss densities distributions in a winding.

Example of application

The magnetic field intensity H created by the current density J in a solenoid is governed by Ampère’s law:

$\overset{}{\nabla} \times \vec{H} = \vec{J}$ .

In its integral form, this law may be rewritten as

$\oint \vec{H} . d \vec{l} = \int \vec{J} . d \vec{s}$

and, if the solenoid is sufficiently long, the magnetic field inside it is expected to be uniform and parallel to the solenoid axis.

Now let N, ℓ, r and I represent respectively the number of turns, length, radius and current of the solenoid. Under such circumstances, and if the winding is immersed in the air, the magnetic flux density B is related to H by the constitutive relation B = μ₀H (with μ₀ = 4π.10^-7H/m) and Ampère’s law becomes

B = μ₀N I / ℓ.

Moreover, the inductance of the solenoid is given by

L = μ₀N²(π r²) / ℓ .

Let’s now consider the modeling of a real, finite-length solenoid with the help of a coil conductor region without losses in Flux 3D. Since the creation of this region requires only the number of turns (and, of course, the dimensions of the solenoid for building the geometry), the results yielded by Flux 3D may be easily compared to the analytical expressions above.

Figure 1 shows the construction of a Flux 3D project and the result of a computation of the magnetic flux density for a solenoid with geometrical parameters r = 8 mm, ℓ = 250 mm, N = 500 turns and traversed by a current of 1A.

Figure 1. Modeling a finite length solenoid in Flux 3D with a coil conductor region without losses: (a) Geometry and physics descriptions; (b) the coupled circuit feeding the solenoid; (c) the discretization of the meshed coil region and (d) evaluation of the magnetic flux density in the post-processing stage.

Table 1 compares the values of the inductance and of the magnetic field density yielded by sensors in Flux 3D to the analytical approximations given by the two previous equations.

Table 1. Evaluation of the magnetic flux density and of the inductance in Flux 3D with sensors: comparison with analytical values for an infinitely long solenoid.
	Axial magnetic flux density	Inductance
Infinite solenoid (analytical approximation)	B = 2.513 mT (everywhere inside the coil)	L = 1.579 mH
Finite length solenoid (Flux 3D computation)	B = 2.474 mT (at the coil center)	L = 1.555 mH