CFD analysis of directed oil flow in power transformers.
Pupaza, Cristina ; Stancu, Octavian ; Parpala, Radu Constantin 等
1. INTRODUCTION
Large power transformers as generator step-up (GSU) are operating
life time under full load. An efficient cooling system is a crucial
factor determining the operational safety. Actually, the best solution
is the Oil Directed (OD) cooling system. It improves cooling, lowers the
hot-spot temperature and reduces the thermal aging of the insulation.
The design task is to assure sufficient oil flow in all the parts of the
system, while keeping the pressure drop as small as possible.
Recommendations for the design of power transformers are found in
loading guides (IEC 60076-7, 2005), but this standard does not address
the local distribution of the coolant flow inside the windings. It is
thus up to each transformer manufacturer to make use of appropriate
tools such as Computational Fluid Dynamics (CFD) in the design process.
Detailed studies were undertaken with regular CFD solvers on two
dimensional models. However, CFD is considered unfeasible for the daily
design work due to the required computer time (Kranenborg et al., 2008).
One complication for CFD models of transformer cooling is that the flow
in the tank is three dimensional and unsteady. Although OD cooling has
already been calculated in the past (Karsai et al., 1987), (Zhang &
Li, 2004) and experiments were described in the literature (Felber et
al., 1984), (Weinlaser & Tenbohlen, 2008), we promote a method to
rapidly calculate the cooling system using 3D modeling of the windings
in an early stage of the design. The simulation takes advantage of the
axisymmetry, the cylindrical shape and the repetitive pattern of the
winding sections in the flow path. Different oil patterns were performed
in order to obtain a balanced pressure drop on each winding. The results
were compared with analytical calculations and a good accuracy was
found. The method proved to be efficient in a simulation driven design
approach.
2. CFD PROCEDURE
The fluid flow problem is defined by the laws of conservation of
mass (1) and momentum (2) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [v.sub.x], [v.sub.x], [v.sub.x] are components of the
velocity vector, [rho] density and t--time. The rate of change of
density is replaced by the rate of change of pressure. In a Newtonian
fluid flow the relationship between the stress and the rate of
deformation of the fluid is:
[[tau].sub.ij] - [rho][[delta].sub.ij] + [mu] ([[partial
derivative]u.sub.i] [[partial derivative]x.sub.j] + [[partial
derivative]u.sub.j] [[partial derivative]x.sub.i] (2)
where [[tau].sub.ij] is the stress tensor and [u.sub.i],
[u.sub.j]--the orthogonal velocities and [mu]--the dynamic viscosity.
These laws are expressed in terms of partial differential equations
which are discretized with a finite element based technique. The
solution method used in CFD codes is known as the Finite Volume
technique (ANSYS CFX, 2005).
3. MODELING AND SIMULATION
The CFD analysis aimed to determine the pressure loss for several
oil patterns in the Low Voltage (LV) and High Voltage (HV) windings of a
440 MVA GSU transformer. The 3D models were processed in CATIA V.5.18
and imported in ANSYS CFX using a neutral file.
[FIGURE 1 OMITTED]
Because the symmetry and the vertical pattern of the models only 11
and respectively 8 disc sectors of the HV and LV windings were
processed, as shown in Fig. 1.
3.1 Mesh definition
The models were meshed using advanced front and inflation 3D
methods combined with controlled body, edge and face spacing. A proper
angular resolution option was set in order to obtain a sufficiently
refined mesh (Fig. 2).
[FIGURE 2 OMITTED]
Some faces and edges were declared in a virtual topology
environment to eliminate narrow or short edges.
Finally the HV and LV cooling system models had 281652 nodes and
1306187 elements and 135312 nodes corresponding to 616485 elements,
respectively. Mesh quality control checks were performed and no
inconsistencies were found.
3.2 Simulation conditions
The oil flow capacity at the inlet was imposed as shown in Table 1,
in order to eliminate the copper losses using the temperature drop in
each winding. The simulation conditions were laminar flow of pure and
nearly incompressible substance. The wall influence on the flow was set
no slip. The uninhibited oil transformer met the required specifications
(IEC 60296, 2003). Oil properties were assumed to be at the average
temperature of the windings. The convergence criterion was chosen the
RMS residuals, with a suitable residual target. For adequate convergence
the physical timescale was calculated taking into account the average
residence time. The residuals were plotted each time step in order to
monitor the solution convergence. All the computations terminated with a
normal convergence, after 70-80 iterations. No parallel computing was
needed and the solver enabled the calculation in a practical amount of
time.
4. RESULTS
A balanced pressure drop on each winding was obtained. The windings
were calculated for both flow directions, when the oil enters from the
inner and outer section, because the flow conditions were different.
The oil velocity in each cylindrical sector was processed in order
to avoid stagnant regions and to check the risk of oil electrisation at
cold start. Figure 3 shows the velocity distribution for the HV and LV
calculated segments, when the oil enters from the inner section. The
velocities were also displayed in a horizontal plane (P1) located in the
neighborhood of the inlet (Fig. 4). Results were included in Table 2
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
When calculating the total pressure loss not only the number of
calculated sections, but also the relative position of the flow path
were considered. The numerical results of the pressure drop were
compared with the analytical values and this verification confirmed that
the prediction of the pressure loss was accurate.
5. CONCLUSION
The proposed CFD procedure enforces traditional capital intensive
design processes of power transformers with a simulation driven design
method. It is performed on a three dimensional model, which is the most
reliable simulation for the power transformer cooling system. It avoids
late design changes and takes advantage of the parametrical modeling of
the transformer windings, enabling the optimization of the cooling
system.
At this stage of the research we neglected the dependence of the
oil properties with the temperature. The next step of the simulation
will be a multiphysics approach, coupling the fluid dynamic analysis
with the thermal-electromagnetic solution.
This approach provides a proper understanding of the cooling
system, reduces the need for expensive prototypes and gives
comprehensive data that is not easily obtainable from experimental
tests. When optimizing new power transformer designs, many "what
if' scenarios can be analyzed in a short time. The result is an
improved performance of the power transformer, as well as a reliable and
a durable design.
6. REFERENCES
ANSYS CFX. (2005). Fluids Analysis Guide, ANSYS Inc., Southpointe,
275 Technology Drive, Canonsburg, PA15317
Felber, W.; Damm, B.; Loderer, K. & Preininger, G. (1984).
Evaluation of Thermal Conditions of Large Transformers, CIGRE
International Conference on Large High Voltage Electric Systems,
Imprimerie Louis-Jean, Paris
IEC 60076-7. (2005). Power transformers. Part 7: Loading guide for
oil-immersed power transformers, International Electrotechnical
Commission, December 1, 2005
IEC 60296. (2003). Fluids for electrotechnical applications. Unused
mineral insulating oils for transformers and switchgear, Int.
Electrotechnical Commission, Nov. 1, 2005
Karsai, K.; Kerenyi, D. & Kiss, L. (1987). Large Power
Transformers, Akademiai Kiado, ISBN 963-05-4112-2, Budapest
Kranenborg, E.J.; Olsson, C.O.; Samuelsson, B.R.; Lundin, L.A.
& Missing, R.M. (2008). Numerical Study on Mixed Convection and
Thermal Streaking in Power Transformer Windings, Available from:
www.eurotherm2008.tue.nl/
Proceedings_Eurotherm2008/papers/Mixed_Convection/M CV_3.pdf, Accessed:
2009-03-15
Weinlaser, A. & Tenbohlen, S. (2008). Thermohydraulische
Untersuchung von Transformatorwicklungen durch Messung und Simulation.
Thermal-hydraulic Analysis of Transformer Development, Available from:
www.unistuttgart.de/ieh/forschung/veroeffentlichungen/30_Weinlae
der%20Andreas.pdf Accessed on: 2009-02-20
Zhang, J. & Li, X. (2004). Coolant Flow Distribution and
Pressure Loss in ONAN Transformer Windings, IEEE Trans. on Power
Delivery, pp. 186-199, Vol. 19, No. 1, Jan. 2004
Tab. 1. Inlet input data
Model Flow capacity Surface [m2] Speed [m/s]
[[m.sup.3]/s]
HV 2.576 x [10.sub.-4] 6.46 x [10.sub.-4] 0.39878
LV 1.554 x [10.sub.-4] 4.36 x [10.sub.-4] 0.35655
Tab. 2. Simulation results
HV LV
Flow Pressure Min. Pressure Min.
case loss Velocity [Pa] Velocity
[Pa] [m/s] [m/s]
1 247.853 9.942-[10.sup.-5] 163.392 1.002-[10.sup.-5]
2 489.836 4.079-[10.sup.-5] 335.630 1.913-[10.sup.-5]