15. INDUCTION_SOURCE_FIELD Namelist

The INDUCTION_SOURCE_FIELD namelist defines the external magnetic field that serves as the applied source in the computation of Joule heat for induction heating simulations. The field is a continuous wave (CW) function with frequency \(f\) of the form

\[\vec{H}_\text{ext}(\tau,\mathbf{x}) = \sin(2\pi f\tau)\,\vec{h}(\mathbf{x}), \quad\text{where}\quad \vec{h}(\mathbf{x}) = A\hat{e} + \sum_{i=1}^{m}\vec{h}_i(\mathbf{x})\]

is the superposition of a uniform field of strength \(A\) oriented in the unit direction \(\hat{e}\), and the magnetic fields \(\vec{h}_i\) generated by a collection of induction coils with electric currents \(c_i\).

Besides a steady CW source that is used for an entire induction heating simulation, a CW source that changes abruptly at a sequence of heat transfer times \(t_1,\ldots,t_n\) may be defined by specifying addtional values for the source parameters (\(f\), \(A\), and \(c_i\)) to use at those times.

Namelist Usage

Required/Optional:

Required when electromagnetics is enabled.

Single/Multiple Instances:

Single

15.1. Namelist Variables

orientation

The orientation \(\hat{e}\) of the uniform field. For simplicity this is currently restricted to one of the coordinates axes, \(\hat{x}\), \(\hat{y}\), or \(\hat{z}\). This value also defines the orientation of the induction coil axes.

Type:

string

Default:

“z”

Valid Values:

“x”, “y”, or “z”

times

An optional list of one or more heat transfer times \(t_1<\ldots<t_n\) when the CW source field changes.

Type:

real

Default:

none

Valid Values:

any strictly increasing sequence

Notes:

When this is specified, corresponding lists of values must also be specified for frequency, uniform_strength, and the current component of each coil defined by coils. The number of values in those lists must be one more than the number of values specified here.

frequency

The frequency \(f\) (cycles per unit time) of the sinusoidally-varying source field. When times is specified, additional values to use at each of those times must also be specified.

Type:

real

Default:

none

Valid Values:

any sequence of one or more postive values

uniform_strength

The strength \(A\) of the uniform source field. The field is oriented in the direction specified by orientation. When times is specified, additional values to use at each of those times must also be specified.

Type:

real

Default:

0

Valid Values:

any sequence of one or more values

Notes:

A negative value essentially shifts the phase by 180 degrees.

For reference, the magnitude of the magnetic field within an infinitely-long, finely-wound coil with linear current density \(I\) is simply \(I\). The field magnitude at the center of a circular current loop of radius \(r\) with current \(I\) is \(I/{2r}\). In both cases the field is directed along the axis of the coil/loop.

coils

Optional data that defines the geometry and current of one or more induction coils. Figure 15.1.1 shows the idealized model of a coil that is used to analytically evaluate the magnetic field it generates. This parameter is a structure array. Each element defines a coil and consists of the following components. Note that the axis orientation is defined by the orientation parameter above and is common to all coils.

Component	Description
%num_loops	The number of current loops.
%radius	The radius \(r>0\) of the coil loops.
%length	The length \(l>0\) of the coil. This is only required when the number of coil loops is greater than 1.
%center	A 3-vector giving the position of the center \(x_0\) of the coil; the default is 0, 0, 0.
%current	The amplitude \(c_i\) of the sinusoidally-varying current in each coil loop. A negative value essentially shifts the phase by 180 degrees. When times is specified, additional values to use at each of those times must also be specified.

Figure 15.1.1 Physical 4-turn helical coil with extended wire cross section (left), and its idealized model as a stacked array of circular current loops (right).