Thermal-fluid characterization of alternative liquids of power transformers: A numerical approach

The transformers lifespan depends importantly on its refrigeration. Mineral oils perform this work in the majority of the power transformers. However, this type of coolant has two main drawbacks: low biodegradability and low ignition point. Several alternative liquids are being developed in order to overcome these drawbacks. This paper compares their thermal-fluid behavior with a mineral oil by means of several parameters, such as temperature, flow rate, fluids velocity, convective heat transfer coefficient (h) and the cooling criterion (P). These are calculated using the numerical results of the simulation of a 3D-model of a Low Voltage Winding that belongs to a power transformer with ONAN cooling. The software COMSOL Multiphysics has allowed the simulation of the geometry using a physical model in which buoyancies and viscous forces are the only considered establishing the natural convection. As a result of the comparison, it is clear that the mineral oil is the best coolant liquid. Among the alternative liquids, silicone oil would be the second best coolant fluid, followed by the synthetic and natural esters, respectively. On the other hand, it seems to be clear that the 3D simulations can be used to compare properly the cooling capacities of the liquids.


INTRODUCTION
1 MINERAL oil is the most common option as a cooling 2 and dielectric liquid in the majority of the power transformers 3 worldwide. However, in cases where fire risk is an important 4 concern, this type of liquid is not so recommendable. Fire 5 resistant oils (with higher flash and fire points than those of the 6 mineral oils) should be used. Environmental reasons are also 7 supporting the development of new transformer oils with 8 improved biodegradability, so that in the event of a failure or 9 leakage the impact would be lower. Thus, the growing 10 demands for improved fire safety and environmental 11 sustainability have encouraged the research and development 12 of alternative fluids. 13 The main research lines of these liquids are focused in 14 silicone oils, natural and synthetic esters. The characterization 15 of silicone oils and synthetic esters has been studied by a few 16 authors [1][2][3][4][5]. However, the majority of the studies has been 17 focused in the physicochemical characterization of some 18 commercial natural esters, [6][7][8], or based on some specific 19 crop (coconut, palm, rapeseed…) [9 -10]. Finally, some authors 20 have compared the main properties of these new fluids with 21 mineral oil in order to evaluate their suitability [11]. 22 On the other hand, there has been a lot of research about 23 cooling improvement in power transformers. The reason is 24 simple, high temperatures degrade the dielectric materials, oil 25 and paper, shortening their lifespan. In order to ensure a long 26 life for these machines, there are two types of approximations 27 for the calculation of their temperature and velocity 28 distributions: lumped parameter models and Computational 29 Finite Element-based Tools (CFET). The first method provides 30 fast and approximate results based on several simplifications 31 and empirical data. By contrast, the second one is more 32 accurate since it is based on the solution of the differential 33 equations governing processes. 34 Several papers have been published in last decade using CFET. 35 Nonetheless, we have to mention that the main goal of 36 practically all these papers is the determination of the velocity 37 and temperature profiles of a mineral oil inside a 2D section of 38 one winding. For instance, Mufuta  The self-explanatory Figure 1 (left side) and Figure 2  113 (bottom right corner) shows the three windings of a phase 114 of a three-phase transformer: LVW in the inner part; on-115 load tap winding in the outer part; finally, the High Voltage 116 Winding in the middle of both of them. 117 118 that are wrapped with a dielectric paper of 0.3 mm width. 127 The layers are separated by means of 48 wooden sticks and 128 inter-sticks of 3 mm thick. This way, 48 cooling ducts of 129 7.5 degrees of amplitude are created between internal 130 cylinder and first layer, other 48 cooling channels between 131 first layer and second layer, and so on. Finally, the total 132 height of the LVW is 1,056 mm. 133 Self-explanatory Figure 3 allows understanding how the 134 geometrical design has evolved to achieve the optimal 135 model for solving numerically. In fact, the results 136 comparison of both models (15-degree model and 7.5-137 degree model) allows to demonstrate that there are no 138 significant differences between their temperatures and 139 velocities distributions. This way, 7.5-degree model has 140 been chosen. 141 142

GOVERNING EQUATIONS 147
This study is based on the numerical solution of the 148 momentum and continuity equations, (1) and (2)  149 respectively. It also solves the heat transfer equation, which 150 for a fluid is (3). 151 152 The symbols ρ, u, p, I, µ, F, Cp T and q of (1), (2) and

PHYSICAL MODEL AND BOUNDARY
No-slip condition is considered in the contact surfaces 176 between oil and the solid surfaces in the ducts (see (6)). 177 178 = 0 (6) 179 Natural convection due to oil decreasing density with the 180 increase of the temperature is the main phenomenon that 181 determines the thermodynamic behavior inside the ducts 182 (see (7) in which g is the gravity acceleration). Also, 183 boundary conditions in inlets and outlets of the cooling 184 channels are pressure-based (see (8) for inlet pressure and 185 (9) for outlet pressure in which Toil,∞, and H are the 186 reference temperature of the model (35ºC) and the total 187 height of the ducts, respectively). 188 189 Thermal-fluid symmetry has been modeled using (10)  191 and (11) (see detail in right-side of Figure 3). 192 193 The wrapping paper is considered mathematically as a 195 thin thermally resistive layer whose thermal behavior is 196 modeled according (12) in which kp, Ti, To and dp are the 197 conductivity, the temperatures in the inside and outside 198 surfaces and the thickness of the paper, respectively (see 199 detail in right-side of Figure 3). 200 201 laminar or turbulent flow. The similarity between the 215 geometric and physical models of our article and El-216 Morshedy's paper [21], in addition to the higher viscosities 217 of our coolants (water is the coolant of the reference 218 article), allows us to establish that the heat transfer is going 219 to be carried out by natural convection under laminar flow 220 regime. 221

COMPUTATIONAL DOMAIN AND MESH 222
The computational domain considers both the liquid and 223 solid parts of the geometry in order to calculate the 224 temperature distribution in the entire model and the fluid 225 behavior inside the channels. The simulations took between 226 90 and 120 minutes using a workstation with two 227 processors at 2.66 GHz and 48 Gbytes of RAM with a 228 convergence criterion of 10-4 for the residuals values. 229 Initially, in the meshing convergence study, several mesh 230 types with different meshing densities are studied, thus 231 obtaining several configurations with similar solutions. In 232 this paper, among these last configurations, the simplest one 233 from the computational standpoint is selected.  The densities of these liquids decrease linearly with the 263 temperature. In the case of the viscosities, those of the 264

322
The model validation is shown in the first subsection. In 323 next subsection, temperatures and flow rates of the ducts 324 are presented. Finally, in third subsection, h a P results are 325 compared. 326

MODEL VALIDATION 327
The comparison of the average velocities of the ducts 2-328 6, shown in Table 2, with those of the El-Morshedy's article 329 [21] confirms the hypothesis that is initially supposed: the 330 flow regime of all the studied liquids is laminar in those 331 channels of our model that are similar, from the physical 332 and geometric standpoint, to that of the aforementioned 333 paper. 334 335

TEMPERATURES AND FLOW RATES 337
As initial point, it is necessary to point out that there are 338 two types of channels from the geometrical standpoint: 339 those ducts with narrow cross-section (channels 1-7), and 340 those with wide cross-section (channels 8-10). It is clear 341 that this geometrical feature has a major influence in the 342 flow rates and velocities of the channels, therefore, in their 343 temperatures (See Tables 2 and 3). Also, we can see that the 344 velocities of those fluids with higher viscosities in the 345 operating temperature range (ester-based liquid sand HKV 346 silicone oil) are lower than those of the other two liquids, 347 both in narrow and wide channels. 348 Table 3 shows the maximum temperature of the 349 geometry (Tmax,model), the Tavg,outlet and the ṁℎ in all the 350 ducts for all the liquids. In relation to the former, it can be 351  Tavg,outlet for the same fluid (See Table 3 and Figure 7). Also, 370 these channels have the highest temperatures if the same 371 liquid is considered. 372 Then, it is perceived that the use of alternative fluids 373 gives rise to an increase both in Tavg higher temperatures in the winding, as can be seen in Table  406 3 and Figure 7. In the same way that in the Figure 8, the average values 418 of the P of the five studied liquids in the channels two to 419 five are shown in Figure 9. Again, according this parameter, 420 mineral oil is the best coolant, followed by the LKV 421 silicone oil, synthetic and natural esters, and HKV silicone 422 oil (27%, 43%, 48% and 68% smaller values than mineral 423 oil, respectively). 424 425 There