## 4 Actual Detected Temperature and Numerical Simulation Results
### Finite Element Simulation Results  
The revelation of the distributed temperature information inside an operating power transformer has provided massive detailed data for both researchers and field staff. However, the DOFS detecting method only has great advantages in the temperature sensing and it is still hard to fully understand what is happening inside the power transformer. Thus, the FEM (Finite Element Method) has been utilized to further analyze the internal physical process. The transformer internal transient process was mainly focused in this simulation based on the hydrokinetics theories. The corresponding parameters used in the calculation are all from the manufacturers and are listed in Table 3. The simulation results are exhibited in Figure 14.  
According to the real structure of the studied 35 kV oil-immersed power transformer, a 3D thermal-fluid simulation model has been established. The calculation model maintains as much as structural components as possible, such as wood padding blocks, insulation cardboards, detailed iron core (composed of many layers of laminates), insulation washers, cooling fins, oil tank, windings, etc. However, it is impossible to totally and accurately reconstruct a real transformer due to the model complexity and the calculating time (or rather the convergence). Thereby, some necessary simplifications are inevitable. In this model, the windings are considered as coaxial cylinders, ignoring the detailed electromagnetic wire structures and the insulating papers wrapped around due to that it has adopted the layered winding structure. This simplification can leave out plenty of tiny components which only add the calculating difficulties and weaken the convergence. The whole simulation was based on the COMSOL MUTIPHYSICS software (5.4, COMSOL AB, Stockholm, Sweden) and it took around 60 h according to our current hardware facility. The whole model has around 6 million elements in total, including 1.66 million mesh vertices, 70 thousand edge units, etc. The mesh independency was also proven when further increasing the element density (no more than 3% changes in the result). Meanwhile, the structured grid (mainly the hexahedral  
Figure 13: Hotspots transient temperature changes of (**a**) HV windings and (**b**) LV windings. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Properties** & **Density (kg\(\cdot\)m\({}^{-3}\))** & **Heat Capacity (\(\mathbf{J}\)-kg\({}^{-1}\).K\({}^{-1}\))** & **Thermal Conductivity (\(\mathbf{W}\)-m\({}^{-1}\).K\({}^{-1}\))** \\ \hline Tank/Fins & 7900 & 460 & 47 \\ Windings & 8940 & 386 & 340 \\ Cardboards & 900 & 2000 & 0.21 \\ Washers & 750 & 2310 & 0.17 \\ Blocks & 960 & 1720 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Corresponding parameters for the simulation. elements) and unstructured grid (basically the tetrahedral elements) were applied for different areas according to their characteristics. The thermal field transient simulation result (Figure 14a) showed a similar temperature distribution to the actual detected data. The HV winding hottest temperature reached about 57 \({}^{\circ}\)C, a little higher than the measured value. The flow field simulation result is exhibited in Figure 14b. There were several obvious vortexes appearing in the top area of the windings with a maximum flow velocity of 2 cm/s. For an ONAN power transformer, the circulation of insulating oil is mainly driven by the heat generated from the windings. Thus, the heated oil flows tend to climb up along the windings or the cardboards and gather in the top area where the heat emission conditions are relatively better. Then, part of the cooled oil begins to sink along the cooling fins while the rest would fall down directly and meet the upward streams to continuously form the vortexes (shown in detail in Figure 14c).