ABSTRACT A thermal design of transformers has been performed using an empirical formula. In order to reduce the developing cost and time, CFD analysis is used in thermal design process for gas-insulated transformers. We calculated the pressure loss of coolant and the temperature rise of winding with empirical formulas and CFD analysis. Also, we constructed some real machines and compared the analytic results with the experimental data. The comparison shows a good agreement between the CFD calculations and experimental results

D J Lee

I S Park

J H Kim

J H Woo

S B Shin

S S Seol

CiteSeerX

 
 
 
 
 
Downloaded From: https://proceedProceedings of HTFED04 
2004 ASME Heat Transfer/Fluids Engineering Summer Conference 
July 11-15, 2004, Charlotte, North Carolina USA 
HT-FED2004-56184 
CFD ANALYSIS OF GAS-INSULATED TRANSFORMERS 
D.J. Lee, S.S. Seol, I.S. Park, J.H. Kim, S.B. Shin, and J.H. Woo 
Hyundai Heavy Industries Co. Ltd.  
1, Cheonha-dong, Dong-ku, Ulsan, 682-792 ,Republic of Korea 
Tel. 82-52-230-6188, Fax. 82-52-250-9578 
einstein@hhi.co.kr 
Proceedings of HT-FED04 
2004 ASME Heat Transfer/Fluids Engineering Summer Conference 
July 11-15, 2004, Charlotte, North Carolina USA 
 
 
HT-FED04-56184 
 
Keywords : CFD, Gas-insulated transformer, SF6 gas 
 
ABSTRACT 
A thermal design of transformers has been performed using 
an empirical formula. In order to reduce the developing cost 
and time, CFD analysis is used in thermal design process for 
gas-insulated transformers. We calculated the pressure loss of 
coolant and the temperature rise of winding with empirical 
formulas and CFD analysis. Also, we constructed some real 
machines and compared the analytic results with the 
experimental data. The comparison shows a good agreement 
between the CFD calculations and experimental results. 
 
INTRODUCTION 
Today, electric power demand in cities has been 
continually increased. To save the transmission cost of 
electricity, transformer substations have been built in urban 
regions. But it is difficult to find areas to install a transformer 
substation in urban region, because of the people’s hatred for 
those dangerous electric plants. So transformer substations 
have usually being installed inside a building or a basement. 
Because an oil type transformer has possibilities bringing 
to a big disaster such as fire or explosion, it is inappropriate as 
an urban transformer. Therefore, gas-insulated transformers 
using SF6 gas with non-flammable and non-explosive natures 
were developed. 
Gas type transformers also have other advantages such as 
compact installation space and simplification of facilities. On 
the other hand, gas type transformers have a poorer cooling 
performance than oil type due to its small heat capacity and 
thermal conductivity. To compensate for these defects, various 
studies have being conducted in the fields of gas type 
transformers in recent years[1]. ings.asmedigitalcollection.asme.org on 06/30/2019 Terms of UsUnder all circumstances, the temperature of windings must 
be kept below the maximum permissible temperature to 
maintain reliability and prolonged durability of the gas type 
transformer. In the design process, the accurate prediction for 
the winding temperature is very important in the face of 
determining the adequate capacity of cooling system[2]. 
HHI gas type transformers have been designed using the 
empirical formula set and manufactured after the validation 
through an experimental model test. The model test process is 
required to guarantee a reliability of product but very expensive 
and laborious. In this study, we try to reduce the cost of the 
iterative trial and error course by adding the CFD analysis 
process between the design and model test processes. For this 
purpose we established the CFD model for gas type 
transformer and compared the simulated and hand-calculated 
(empirical formula) results to experimental data. 
In this paper, the results for the flow rate distribution of 
coolant into each channel (magnetic core, TV, LV, HV, and Tap) 
of gas-insulated transformer and the temperature rise of 
windings under the given pressure loss conditions are obtained 
by empirical formula and CFD analysis. Also, the tested results 
for two real transformers (development type and commercial 
type) are included. The comparisons for each result are 
discussed. 
 
NOMENCLATURE 
A  : surface area [m2] 
Cv : specific heat capacity of SF6 gas [J/kg·K] 
De  : equivalent diameter of cooling duct section [m] 
f : friction factor [-] 
h  : heat transfer coefficient, [W/m2·K] 
Nu  : Nusselt number [-] 
P : power loss at winding, [W] 1 Copyright © 2004 by ASME 
e: http://www.asme.org/about-asme/terms-of-use
D
Pr  : Prandtl number [-] 
△p  : pressure drop [Pa] 
q  : heat flux surface density [W/m2] 
Q  : SF6 gas flow rate [m3/hr] 
Re  : Reynolds number [-] 
V  : velocity [m/s] 
 
Greek Letters 
ρ : SF6 gas density [kg/m3] 
δ : insulation thickness [mm] 
λ : heat conductivity [W/m·K] 
 
Subscripts 
gas : SF6 gas 
w : winding 
i : coolant channel 
 
EXPERIMENTS AND NUMERICAL METHODS 
The configuration of gas-insulated transformer is shown in 
Fig. 1. The transformer consists of the main part that changes 
voltage, and heat exchanger that controls the coolant 
temperature. The main part is composed of magnetic cores, 
windings, and insulations, etc. The coolant, SF6 gas, makes the 
temperature in the transformer stay below a specific value by 
removing heat generated at the magnetic cores and windings.  
The coolant of the transformer flows through magnetic 
cores, TV winding, LV winding, HV winding and TAP 
winding, respectively. The geometry of the coolant channel and 
the coolant flow passage in the transformer are shown in Fig. 2. 
Empirical formulas applied to find out the pressure loss of 
coolant channels and the temperature rise of the winding are  
 
gasv tC
PQ
∆
=
ρ
    (1) 
 
2
2
2
22 ii
i
i QA
fVfP ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
==∆
ρρ
   (2) 
 
iQQ ∑=      (3) 
 
λ
δ
2
10 3−×
=∆
qtw     (4) 
 
λ
Deh
Nu gas== 43.08.0 PrRe021.0   (5) 
 
Experiments are carried out on the transformers. The 
temperatures of coolant at the inlet and outlet of the 
transformer are measured by K-type thermocouple with 0.05 oC  
ownloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of Useprecision. The total flow rate of coolant is governed by the 
performance of the fan installed. The flow rates of coolant in 
each channel cannot be measured because the flow meter 
cannot be installed due to the complicated structure of 
transformer. The heat losses at each winding are calculated by 
measuring electric power loss of the transformer. 
Numerical analysis of flow field is performed using a 
commercial CFD package, Fluent. All simulations are 
performed using a three-dimensional, structured grid with 
Cartesian coordinates. The flow fields for the steady state, 
three-dimensional, incompressible, and turbulent flow are 
analyzed. In order to solve the flow fields, the conservation 
equations for mass, momentum, energy, and turbulent 
properties are selected as the governing equations. The 
standard k-ε model is applied to simulate the turbulent flow.  
The computational domain of the transformer used in this 
study is modeled as shown in Fig. 3. The computational 
domain, a quarter of whole flow field, is sufficient to 
investigate the flow characteristics due to its symmetry. Two 
million cells are used in whole domain. 
RESULTS AND DISCUSSIONS 
The total coolant flow rate is calculated by equation (1). 
The coolant inlet and outlet temperatures are given in table 1 as 
the design conditions. The heat losses of the windings are 
tabulated in table 2. In this case, the required flow rate of 
coolant is 1806 m3/hr. Table 3 shows the properties of the 
coolant and insulation applied to the empirical formula and 
CFD analysis. 
We can express the pressure losses in each coolant channel 
as equation (6). 
 
21 mmHVLVTVm PPPPPPP ∆=∆=∆=∆=∆=∆=∆    (6) 
 
For calculating the pressure losses and flow rates of each 
coolant channel, the pressure losses are assumed.  
From equation (2), we can obtain the coolant flow rates 
through magnetic cores, TV winding, LV winding, HV winding 
and TAP winding, respectively. A friction factor, f, in equation 
(2) follows the HHI’s design standard. 
The flow rates vs. the pressure losses of the coolant at each 
channel are shown in Fig. 4. 
The total coolant flow rate is the sum of all coolant flow 
rates. In order to adjust the sum of all coolant flow rates to 
1806 m3/hr, we calculate equation (2) iteratively for the various 
pressure drops. The results are summarized in table 4. The 
pressure drop, 1735 Pa is suitable to this case. 
The parts of magnetic core with complex coolant paths are 
excluded in CFD analysis. Since the magnetic core parts 
generate much less thermal energy than others and are 
completely insulated by insulation, they can be assumed to be 
thermally independent components. The coolant flow rate, 
1618.5 m3/hr, except the flow rates through the magnetic cores 
in table 4 is applied to CFD analysis.  2 Copyright © 2004 by ASME 
: http://www.asme.org/about-asme/terms-of-use
DowThe flow rate distribution through each coolant path 
calculated by empirical formula and CFD analysis is shown in 
table 5. The result shows a large different flow rate for TV 
winding. It can be considered due to the assumption of same 
pressure drop at each coolant channel in the empirical formula. 
In real facility, the coolant is provided to each channel from a 
main pipe, and the pressures at the inlet of each channel have 
different values.  
The measuring data of the temperature rise at each winding 
are compared with the results from the empirical formula and 
CFD analysis in table 6. The permissible winding temperature 
is 160 oC and all results satisfy that condition. The temperature 
rises predicted by CFD analysis are closer to the experimental 
results than the results using the empirical formula. The 
differences in the temperature rise between experimental and 
CFD analysis results are less 10 %. 
 
CONCLUSIONS 
For a gas-insulated transformer, we calculated the flow rate 
distribution of coolant into each channel for the given pressure 
loss and the temperature rises of windings using empirical 
formulas. CFD analysis was simultaneously conducted to get 
the coolant flow rate distributions, the pressure drops, and the 
temperature rises at each winding. The test results of real 
facilities were compared with the results calculated using the 
CFD analysis and the empirical formula. The empirical formula 
predicted very large flow rate at TV winding compared to CFD 
analysis. Although we could not measure the flow rates at each 
channel, the temperature rises were gauged with highly 
accurate thermometry. The results of CFD analysis showed 
good agreement with the measuring data. 
By analyzing the thermal flow fields of transformer with 
CFD before the model test process, we could predict more 
accurately the cooling performance of transformer. Through the 
feedback of the results to design stage and the appropriate 
design change, we could improve the thermal performance of 
transformer. 
 
 
 
REFERENCES 
[1] Takahashi, E., Tanaka, K., Toda, K., Ikeda, M., Teranishi, 
T., Inaba M., and Yanari, T., 1996, “Development of Large-
Capacity Gas-Insulated Transformer”, IEEE Transactions 
on Power Delivery, 11, pp. 895-902. 
[2] Nakadate, M., Toda, K., Sato, K., Biswas, D., Nakagawa, 
C., and Yanari, T., 1996, “Gas Cooling Performance in Disc 
Winding of Large-Capacity Gas-Insulated Transformer”, 
IEEE Transactions on Power Delivery, 11, pp. 903-908. 
 
 
 
 
 
nloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of UTable 1  Coolant and cooling water design 
temperature 
 Temperature [oC] 
Coolant inlet 74.8 
Coolant outlet 91 
Cooling water 35 
 
 
Table 2  Heat losses of windings 
 Heat loss of winding 
 KW kW/m3
TV 9.7 134.2 
LV 20.9 200.5 
 27.1 226.2 
HV 76.5 173.0 
TAP 11.2 157.5 
 
 
Table 3  Properties of coolant and insulation 
Coolant, SF6 Density [kg/m3] 22.3 
 Heat capacity [J/kg oC] 756.2 
 Heat conductivity 
[W/m oC] 
1.780×10-2
 Viscosity [kg/m s] 1.886×10-5
Insulation Heat conductivity 
[W/m oC] 
0.24 
 Thickness [mm] 0.6~1.2 
 
 
Table 4  Coolant flow rates through each channel at 
various pressure drops 
Pressure 
drop 
[Pa] 
 
Coolant flow rate [m3/hr] 
 Qm QTV QLV QHV Qm1 Qm2 QTotal
1400 89 115 575 765 40 40 1624
1735 99.5 127.5 643 848 44 44 1806
1800 102 130 657 862 45 45 1841
 
 
Table 5  Flow rate distribution in the transformer 
 Empirical Formula 
[m3/hr] 
CFD analysis
[m3/hr] 
Error 
[%] 
TV 127.5 92.3 27.6 
LV 643 598.3 7 
HV 848 927.9 8.6 
Total 1618.5 1618.5 - 
 
3 Copyright © 2004 by ASME 
se: http://www.asme.org/about-asme/terms-of-use
DownloaTable 6  Comparison of winding temperature rise data 
in the transformer 
 Winding temperature rise [oC] 
 Experiment 
(Development) 
Experiment 
(Commercial) 
Empirical 
Formula 
CFD 
analysis
TV 129 127 105 119.7 
LV 141 149 113 129.3 
HV 119 126 107 112.3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of Use: 
Figure 1 Gas-insulated transformer 
 
 
 
 
 
Figure 2  Geometry of the coolant channel and the flow 
passage in the transformer 
 
 
 
 
 
Figure 3  Computational domain of gas-insulated 
transformer 
 
4 Copyright © 2004 by ASME 
 http://www.asme.org/about-asme/terms-of-use
Down 
Flow rate (m3/h)
0 50 100 150 600 700 800 900
Pr
es
su
re
 d
ro
p 
(P
a)
1300
1400
1500
1600
1700
1800
1900
DelP-m1
DelP-m
DelP-TV
DelP-LV
DelP-HV
 
Figure 4  Distribution of coolant flow rates to TV, LV, HV 
windings and magnetic cores 
 
 
 5 Copyright © 2004 by ASME 
loaded From: https://proceedings.asmedigitalcollection.asme.org on 06/30/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use


HT-FED2004-56184 CFD ANALYSIS OF GAS-INSULATED TRANSFORMERS

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HT-FED2004-56184 CFD ANALYSIS OF GAS-INSULATED TRANSFORMERS

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