## 3 Modeling of Equivalent Radiation Sources Based on the Huygens Principle  
The Huygens principle states that the fields at points on any closed surface surrounding a field source can serve as a secondary source to radiate electromagnetic fields outside the closed surface again. That is, the electromagnetic field at any point outside the closed surface is generated by the contribution of all the electromagnetic fields present on the closed surface. Hence, the computation of electromagnetic radiation can be achieved through twice numerical calculations. Firstly, the near-field electromagnetic field of the axial flow fan is calculated by the field-circuit coupled FIT. Subsequently, the near-field radiation source obtained is utilized as the secondary excitation source and the electromagnetic field distribution characteristics in the target domain are further calculated. Figure 9 presents a schematic diagram of the equivalent modeling of the near-far field radiation from the fan. The near-field radiation source of the fan is computed by the field-circuit coupling FIT method from Equations (2)-(4) for the enclosed hexahedral domain surrounding the fan. The surface current source \(\mathbf{J}_{s}\) and the surface magnetic flux source \(\mathbf{J}_{s}^{m}\) of the near-field closed domain \(S\) are obtained:  
\[ \begin{array}{l}\mathbf{J}_{s}=\mathbf{e}_{n}\times(\mathbf{H}_{s}-\mathbf{ H}_{s}^{\prime})\\ \mathbf{J}_{s}^{m}=(\mathbf{E}_{s}-\mathbf{E}_{s}^{\prime})\times\mathbf{e}_{n }\end{array}  \tag{5}\]  
where \(\mathbf{e}_{n}\) is the unit vector in the direction normal to the outside  
Similarly, the expression for the intensity of the magnetic field can be obtained as follows:  
\[\mathbf{H}(\mathbf{r})=\oint_{S}\left[-j\omega\mu(\mathbf{e}_{n}\times\mathbf{E}_ {S})+(\mathbf{e}_{n}\times\mathbf{H}_{S})\times\
abla^{\prime}+\left(\mathbf{e} _{n}\cdot\mathbf{H}_{S}\right)\times\
abla^{\prime}\right]G\big{(}\mathbf{r}, \mathbf{r}^{\prime}\big{)}dS \tag{12}\]  
Therefore, when calculating the electromagnetic field distribution in a large space, the surface electromagnetic field distribution \(\mathbf{E}_{s}\) and \(\mathbf{H}_{s}\) can be obtained by calculating the near-field radiation source of the fan numerically. The calculation results are then used as an excitation source to obtain the electromagnetic field distribution in the target space through secondary calculation. During the numerical calculations, the computational domain is divided into two parts: the near-field domain and the target computational domain. The near-field domain is first refined with grid discretization and computation. Then, the obtained surface electromagnetic field data from the near-field source are imported into the target computational domain as a secondary excitation source. To simulate the electromagnetic field within the target domain, it is necessary to compute the surface electromagnetic field data propagating in each direction within the near-field domain. The equivalent currents and magnetic flux on six surfaces are calculated utilizing the hexahedral near-field domain, where the equivalent surface current \(\mathbf{J}_{e,x}\) and the equivalent magnetic flux \(\mathbf{J}_{m,x}\) in the positive direction of the \(x\)-axis are as follows:  
\[ \begin{array}{l}\mathbf{J}_{e,x}=\mathbf{e}_{x}\times\mathbf{H}=\mathbf{e}_{ x}\times\left(0,H_{y},H_{z}\right)=-H_{z}\mathbf{e}_{y}+H_{y}\mathbf{e}_{z}\\ \mathbf{J}_{m,x}=-\mathbf{e}_{x}\times\mathbf{E}=-\mathbf{e}_{x}\times\left( 0,E_{y},E_{z}\right)=-E_{y}\mathbf{e}_{z}+E_{z}\mathbf{e}_{y}\end{array}  \tag{13}\]  
The equivalent surface current \(\mathbf{J}_{e,y}\) and the equivalent magnetic flux \(\mathbf{J}_{m,y}\) in the positive direction of the \(y\)-axis are as follows:  
\[ \begin{array}{l}\mathbf{J}_{e,y}=\mathbf{e}_{y}\times\mathbf{H}=\mathbf{e}_ {y}\times\left(H_{x},0,H_{z}\right)=H_{z}\mathbf{e}_{x}-H_{x}\mathbf{e}_{z}\\ \mathbf{J}_{m,y}=-\mathbf{e}_{y}\times\mathbf{E}=-\mathbf{e}_{y}\times\left( E_{x},0,E_{z}\right)=E_{z}\mathbf{e}_{x}-E_{x}\mathbf{e}_{z}\end{array}