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Hydrodynamics and heat transfer in cooling channels of oil-filled power transformers with multicoil windings
Applied Thermal Engineering 63 (2014) 347e353
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Hydrodynamics and heat transfer in cooling channels of oil-filled power transformers with multicoil windings Vitaly A. Yatsevsky* National Academy of Sciences of Ukraine, Institute of Engineering Thermophysics, Department of Heat-and-Mass Transfer Modelling, St. Zhelyabova, 2a, 03680 Kyiv, Ukraine
h i g h l i g h t s The CFD model of the transformer with external cooling circuit has been developed. The model also includes all the cooling channels in the space between coils. The analysis of hydrodynamic processes has revealed self-organizing oil flow. The flow features have an influence on the thermal state of windings coils. Zones with the maximum temperature shift along height and toward the radial velocity.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 March 2013 Accepted 26 October 2013 Available online 7 November 2013
The analysis of heat transfer and oil flow in power transformers at natural convection of cooling oil is carried out by numerical simulation of the fluid dynamic problem in axisymmetrical formulation (CFDapproach). The effects of self-organization structure of oil flowing in the form of the unidirectional flow in the groups of horizontal channels between winding coils have been revealed. The flow features have an influence on the thermal state of winding coils of the transformer with the natural cooling system. At such oil flowing, in different channels, the heat transfer coefficient varies within the limits of 50e100 W/(m2 K), and the radial component of velocity is changed over the range of 2.1$104e2.2$103 m/s. Thus the region with maximum temperature values is removed towards oil flowing along the coil radius. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Power transformers CFD modelling Self-organizing flow Natural cooling Oil flow Thermal and hydrodynamic processes
1. Introduction The key factor in ensuring the high reliability and long-term operation of a power transformer is the effective removal of the energy which is inevitably released as heat in basic constructive elements e in the magnetic system, windings and other active parts (Fig. 1). One of the most important technical parameters is the temperature level of hot spots in windings, exceeding of which (more than 98 C) causes the thermal destruction of the winding insulation. Location and temperature values of hot spots are unpredicted owing to the complex structure of oil circulation in numerous interconnected vertical and horizontal channels inside the oil-filled tank.
* Corresponding author. Tel.: þ38 0681268268. E-mail address: [email protected]. 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.10.055
The problem related to CFD modelling of thermal processes in power transformers as well as special features of cooling fluid flowing in channels has been studied enough well in enough scientific works. For the last ten years more than a hundred and fifty publications have presented the models of different level of detailization and accuracy. The previous works have revealed that the modification and redistribution of fluid flow influence directly and largely on the temperature distribution in transformer component, and the distribution of winding temperature is more uniform when the flow rate of cooling fluid increases. Authors of many works put an emphasis on horizontal channels critical zones that require a particular consideration. The majority of CFD studies are concentrated on examining only separate parts of transformer winding, for example considering one pass. In the present article, the general formulation has been carried out taking into account complete two windings, the core, the
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V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
Nomenclature b Cp g Gr h k P Pr Q R r, z Re T
width of vertical channels [m] specific heat capacity [J/kg K] gravity acceleration [m/s2] Grashof number [e] width of horizontal channels [m] empirical coefficient k in Eq. (4) [e] pressure [Pa] Prandtl number [e] heat source density (heating power per unit volume) [W/m3] radius [m] radial and axial cylindrical coordinates [m] Reynolds number [e] temperature [K or C]
transformer tank and the external cooling radiators. Latest similar research works are considered below. Work [1] gives CFD model for thermal investigation of air ventilation in underground transformer substations and presents the patterns of air flow and temperature distribution inside the substation as well as shows a stagnant zone as a zone with still (static) air. The approach to optimization of mutual configuration of coils (disks) and cooling channels is developed by Smolka [2] for effective cooling of a dry-type transformer. The optimization procedure combines the methods of computational fluid dynamics (CFD) and genetic algorithm to find optimum diameter of channels and coils. In the computer CFD model proposed by Smolka in Ref. [2], the thermal properties of coils and core are considered as anisotropic and
Fig. 1. The scheme of 210 MV A power transformer: 1 e axis of symmetry; 2 e transformer core; 3 e lower voltage winding (LV); 4 e pressing ring above LV winding; 5 e high-voltage winding (HV); 6 e pressing ring above HV winding; 7 e radiator of external cooling subsystem; 8 e shunt under HV winding; 9 e shunt under LV winding; 10 e fan; 11 e oil pump.
Vr Vz
velocity components in radial direction r [m/s] velocity components in axial direction z [m/s]
Greek symbols s time [s] r density [kg/m3] m dynamic viscosity [kg/m s] 4 tangential cylindrical coordinate [rad] l thermal conductivity [W/(m K)] Indices amb in oil out v
ambient inner oil outer per unit volume
temperature-dependent quantities. The heat sources (heating power) for elements are computed by coupled CFD and EMAG (electromagnetic) models. A similar approach is used in the present article. The article by Torriano et al. [3] presents the following results. The data obtained with simplified models differ appreciably from the results of the conjugate heat transfer model. The windings having separate copper wires with paper insulation which form a disk are studied. Unfortunately, this approach is extremely time-consuming and complicated for implementing as for many types of complexstructured wires (transposed wires or subdivided wires). Work [4] (a subsequent paper by the same authors) gives the results of 3D simulation of coupled heat transfer and hydrodynamic flow in a disk-type low-voltage winding of distribution transformer 66 MVAe225/26.4 kV ONAN/ONAF. The low-voltage winding contains 78 disks divided into four passes. All the passes, except the first one, have 19 disks each. The first pass consists of 21 disks, but has an additional block-washer between the second and the third disks. The 3D results are compared with the similar computations by 2D model. It show be noted that 3D model includes all geometrical parts (i.e., sticks, intersticks, duct spacers and oil washers). The comparison is made for the homogeneous and inhomogeneous loss distributions in the winding. The computer models are realized by commercial finite-volume CFD code AnsysCFX v12.1. As computational results show, the significant threedimensional effects take place owing to availability of strips and spacers in the channel and, therefore the flows in cooling channels cannot be considered as completely axially symmetric. The authors of the article [4] emphasize that although 3D computations are very valuable, they need high-speed computer facilities. For this reason, the improved 2D models are proposed. The CFD Code_Saturne developed by Électricité de France (EDF) is used by Skillen et al. in Ref. [5] for studying mixed convection for axisymmetric (2D) problem of cooling flows in a low-voltage transformer winding. Only region with fluid is simulated and the simplified (idealized) 3D model of windings is examined. The computations are realized for both a complete winding with five passes (the winding has 78 disks) and a separate pass. The CFD model discovers hot plumes in some horizontal cooling channels. The radial flows differ in direction for each horizontal channel. As revealed, the solution varies depending even on small deviation of the inlet velocity of the mass flow. That shows a highly unstable flow configuration. It is believed that all flows run in several channels where the cross-flow of fluid are negligible (e.g. less than 1% of inlet flow velocity). This causes the high temperature of disk surface and local hot-spots. The vector of gravitational force and then radial cooling flows in the passes and hot plumes are left out of account.
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
The hot streaks are still available due to high Prandtl number of fluid, but they are passive and have no influence on flow distribution. This proves the importance of the accurate setting of the hydrodynamic lift in the calculations. Moreover, we believe, the use of a simplified model for the analysis of the Boussinesq subtle physical effects is inappropriate. However, according to the author of this work [5], there have not been any experimental studies detailed enough to identify and make the analysis of the flow turns in the horizontal channels. Mufuta et al. in Ref. [6] present rather detailed analysis of cooling processes in the fragment of disk-type transformer winding. The geometrical model (and computational region) consists of an axially symmetric fragment of the winding and uses the array with two columns of 10 (in some variants from 4 to 15) rows of rectangular blocks placed between two impermeable walls. The simplifications of the model consist in idealization of conductor cross-section, constant heat dissipation rate of inlet of each vertical channel. In Ref. [6], the finite-volume method and commercial CFD code are used for computation of the temperature in disk-type windings at variation of mass flow rate and heat losses. The computed results revealed the transverse and horizontal flows from the central vertical channel to the adjacent left and right vertical channels and vice versa. As noted, when the ratio of Reynolds number to Grashof number Re/Gr1/2 increases, the buoyancy force decreases. In this case, the amplitude of cooling flow oscillation decreases monotonically and then the smaller flow runs through the horizontal channel. The flows directed to inwards and outward flows promote heat removal from horizontal channel. For small values of ratio Re/Gr1/2, the mass flow rate varies with a greater amplitude than at higher ratio Re/Gr1/2. It was also found that the temperature of the blocks changes nonlinearly along the height of the part of the winding. The temperature field represents fluctuations of the mass flow. The temperature increases starting from the first to the fifth block, then decreases slightly, and again increases. This profile corresponds to the oscillation of the mass flow in the set of blocks. Block number 6 is less hot as compared to block number 5. This is not an evident fact proceeding from general physical principles without detailed computation and related analysis. In a subsequent paper by the same authors [7], the distribution of mass flow around the set of rectangular blocks which imitate a crosssection (profile) of the fragment of disk-type winding is investigated. Also, the transversal flow through horizontal channels (the space between the blocks) was observed by experimental unit with the use of laser Doppler velocimeter to measure the velocity field. The correlation between the velocity difference in the boundary layer and pressure differential across each horizontal channel was defined. It was noted that the spatial flow oscillations occur in vertical channels because of transversal flow through horizontal channels. In conclusion of Ref. [7], the asymmetry of the heat removal rate can be changed in order to provide coolant flowing through horizontal channels even without any additional oil washers used for flow modification. Thus cooling in critical thermal zones of the oil transformer can be intensified. The article proposes the computer model of thermal and hydrodynamic processes in an oil-filled power transformer with
multi-coil windings and numerous cooling channels. The model is built in axial symmetry. In distinction from previous CFD models, it simulated all the major transformer components including the magnetic part, the insulation system, the tank and the radiators. The heat transfer into the environment by the external cooling system (radiators) is described by parametric relation derived from the experimental data. Much attention is devoted to fine peculiarities of flows in horizontal cooling channels of full-scale windings. 2. Geometric model of power transformer The construction of modern high-power transformers (Fig. 1) is considerably complex [8,9]. It consists of a large number of details which are inhomogeneous according to thermophysical characteristics and of complex geometry (up to 100 constructive units). However, most of the structural elements have a cylindrical symmetry about axis of core in each transformer phase. Therefore, in this article the thermo-hydrodynamic processes in winding channels are studied for two-dimensional axisymmetrical presentation of transformer with the natural convection cooling system. It is the most complicated for numerical simulation of hot spots positions. High power transformers have the windings with coils separated by horizontal channels, and, the number of the channels can be up to 400 (Fig. 1). The windings are separated from each other by oil insulating elements forming a subsystem of vertical channels. Dimensions of both vertical and horizontal channels are in the range of 3e12 mm. For such transformers, the heat removal through the walls of oilfilled tank cannot provide an acceptable level of temperature. Therefore, the tank is connected to the external oil cooling system which can operate under either natural or mixed (natural and forced) convection conditions. Then the cooled oil from the external radiators enters to the bottom of the tank, lifts due to buoyancy force (and, if necessary by means of pumps) through the vertical and horizontal channels in windings and around them, thus, forms the admissible temperature field of structural elements of the transformer (see Figs. 1 and 4). 3. Physical and mathematical models The physical and mathematical models for computations of hydrodynamic and heat transfer processes are the following. It was assumed that the dependent variables (the temperature, velocity and pressure fields) do not change along the axis f of cylindrical coordinate system (r, z, f). Then, in the axisymmetrical formulation, some specific features of the real windings such as availability of distancing gaskets and strips cannot be taken into account properly. However, the special test 3D computations show that the contribution of these structural components to heating of windings is negligible. The mathematical model of coupled processes of hydrodynamics and heat transfer in the transformer, consists of Naviere Stokes equations (conservation of momentum) for a viscous incompressible fluid, mass continuity (conservation equation) and equations of energy conservation:
2$m vVr vVr Vr vVr vVz v v ¼ vP ; vr þ 2$vr m$ vr þ r $ vr r þ vz m$ vz þ vr vVz vVz vVz vVr vVr vVz v v z z r vV ¼ rg vP þ mr $ vV vs þ Vr vr þ Vz vz vr þ vz þ 2$vz m$ vz ; vz þ vr m$ vr þ vz
r
vVr vs
vVr r þ Vr vV vr þ Vz vz
349
(1)
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V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
Fig. 2. Methodology for investigation.
vðrÞ vðrVr Þ rVr vðrVz Þ þ ¼ 0; þ þ vs vr vz r
rCp
(2)
vT vT vT 1v vT v vT lr l ¼ þ þ Qv ðr; zÞ; þ Vr þ Vz vs vr vz r vr vr vz vz (3)
Here, Vr, Vz components of velocity vector in radial (r) and axial (z) directions, P pressure scalar field, r density, Cp specific heat capacity, m dynamic viscosity of cooling fluid, g free fall acceleration, s time. Transport and thermodynamic characteristics of cooling fluid are the functions of temperature according to the experimental data presented in Ref. [9]. 4. Boundary conditions and fluid properties The initial data for thermal computations in addition to detailed geometric parameters are formed with values of ambient temperature, heat generation of coil windings, dimensions of vertical and horizontal channels between the coils, thickness of insulating cylinders, values of thermal conductivity, and parameters of external cooling system for each type of load. The heat sources Qv in the region of coil windings, metal components of magnetic core and tank walls are defined by preliminary electrodynamic computations. In cooling fluid (transformer oil) inside the tank Qv ¼ 0. In the region of heat release in external circuit (with cooling radiators, Fig. 1), the heat sources are assumed to be negative in order to simulate heat removal into the environment: 1:2 Qv ¼ k$DToil amb :
(4)
The empirical coefficient k and the index of a power, at the average temperature difference in radiators above ambient temperature DToil amb in Eq. (4), are determined by experimental data. As the initial conditions the velocity vector components of cooling fluid are set to be zero, and the temperature of all the system elements are equal to ambient temperature. All the solid surfaces contacting with oil are considered to be non-slipping and non-leaking (solid walls), i.e. the velocity
components are set to be zero. The energy equation (3) is valid for description of temperature fields for cooling fluid (oil) and solid construction elements, where velocity components are equal to zero. On the interface between coolant and solid surfaces, conjugation conditions are specified (equality of the temperature and heat fluxes values). On the external surface of the oil-filled tank, mixed conditions of convective heat transfer (heat transfer coefficient and ambient temperature) and radiation heat transfer are assigned. System of Equations (1)e(4) is solved by the implicit finitevolume method in professional code ANSYS FLUENT. In the computational model of a two-phase transformer of 210 MV A power, only one phase consisting of two concentric windings is considered. The low-voltage winding consists of 114 coils separated by horizontal channels with different height, and the high-voltage winding contains 156 coils. The computational region and its subdomains are shown in Fig. 1. The computations were realized for heat generation in coils and other conducting units being specific for rated duty of the transformer under consideration. The computations were made by quad core computer with the use of parallelization by means of decomposition of computational region. 5. Methodology The methodological approach gives an opportunity to develop CFD-models for both theoretical (especially for investigation of the velocity and temperature fields) and applied study aimed at sensor positioning in order to monitor hot spots in real time. CFD modelling of thermal processes in transformers with the external cooling subsystem can be defined as a series of interdependent procedures of physical, geometrical, mathematical and computer models to be performed in a certain sequence (Fig. 2). That modelling enables to obtain and analyze the temperature field, accounting all the basic features and physical mechanisms of heatand-mass transfer processes in the equipment. In order to achieve accurate and reliable results concerning the thermal state and dynamics of the coolant in the equipment, the estimation of computational errors and verification of computer models are required by comparison with previous studies (Fig. 2).
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
351
Fig. 3. The scheme of oil flow through the channels (a); distribution of the total pressure differential along the height of the HV winding starting from the 1-st coil (at the bottom) to the 156-th coil (on top) (b); distribution of the radial component of velocity along the relative height of the HV winding (c); distribution of radial velocity along the height of the HV winding from the 42 coil (at the bottom) to the 57-th coil (on top) (d).
Such empirical data should be concerned with analogous subject area and particular problem statements. In addition to this, the typical range of main characteristics (heat power, cooling conditions, thermal characteristics of coolant) as well as the basic design of comparative objects should be similar. After conjugate problem solving and numerical data averaging, the temperature of surfaces and volumes of windings and other constructive elements and distribution of heat transfer coefficients at selected surfaces are determined. These data can be compared with analogous results presented in scientific-and-technical works. 6. Validation of numerical model In order to verify the adequacy of the developed computer model, the thermal tests were conducted at Public Joint Stock Company (PJSC) “Zaporozhtransformator” (“ZTR”). The experimental data were compared with analytical correlations. The
results of the comparison at 20 C ambient temperature are given in Tables 1 and 2. For the comparison, the analysis of calculational results was made by the CFD computer model. The average temperature of the windings was determined by averaging the temperature values of all the coils in each winding. The average oil temperature was defined as the arithmetic mean between temperature of upper oil and lower oil temperature. “Upper oil” in this context is defined as a region with oil inside the tank located above the upper surface of the upper horizontal yoke and up to the lower surface of the tank cover. And “lower oil” is a region placed below the lower surface of the lower horizontal yoke and down to the upper surface of the tank bottom. The average temperature of the oil in the tank, including the oil between the coil channels (horizontal cooling channels of winding) was defined in the same way. As seen from Tables 1 and 2, the accuracy of computations by developed CFD model is admissible.
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V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353 Table 2 Winding temperature, C (mode ONAN).
Fig. 4. Temperature field over the range of 50e90 C in the LV and HV windings.
7. Discussion of computational results At convective heat transfer, both integral and local characteristics of the heat process depend mainly on the nature and structure of the fluid flow. Patterns of thermal and hydrodynamic fields in the transformer vary depending on cooling conditions and during the non-stationary process. At the same time, there are significant quantitative and qualitative distinctions at different stages of the transient process. The directions of circulation in separate channels during fluid flowing can often be reversed which was found by numerical simulation. The numerical solution of the problem in conjugate formulation in terms of temperature, pressure and velocity gives a very complex flow structure not only in cooling channels, but also inside the oilfilled transformer tank. The main feature of convective flow at thermal gravitational convection in the distributed system with a
Table 1 Oil temperature, C (mode ONAN). Parameter
Experiment CFD
Temperature of upper oil Average temperature of oil Temperature of lower oil Temperature difference between upper and lower oil
84.0 69.5 55.0 27.5
Range 79e84
Average temperature
81.5 67.0 50.0e55.0 52.5 29.0
Parameter
Experiment
CFD
Temperature of coil No. 1 (on top) LV winding Temperature of coil No. 1 (on top) HV winding Average temperature of LV winding Average temperature of HV winding
86.8 84.6 71.9 70.1
83.94 80.58 76.76 72.93
great number of interconnected channels inside the oil-filled tank is simultaneous presence of local zones with different flow patterns. Detailed behaviour of flow and its intensity are determined jointly by the design and operational parameters. In other words, the flow pattern is determined by nonlinear interdependent fields of pressure, temperature and velocity. An additional complicating factor is the presence of a rather complex multi-domain geometrical model (Fig. 1), and oil circulation inside the transformer tank. The complex flow structure in cooling channels was found by numerical simulation (Fig. 3). Fig. 3a shows the qualitative scheme of flow thought channels. Fig. 3b gives the distribution of total pressure differential in the middle of the high-voltage (HV) winding. Fig. 3c presents the distribution of the radial velocity in the HV winding, which depends on the height of the coil. It can be seen from the computational results that 11 groups of channels (approximately 14e15 channels in each group) are formed along the winding height where the oil flow has mainly the same direction e from the axis of symmetry of the transformer to the winding periphery towards the lateral wall of the tank or the opposite direction. Between separate groups of channels, there are channels where the radial velocity is much smaller than in the central channels of the group (stagnation zones). Taking into account a considerable height of a real coil (about 3 m), Fig. 3d shows the fragment on a large scale with distribution of radial velocity for the fourth group of the channels starting from the bottom. The primary flow of coolant from the external vertical cooling channel to the inner channel (even at the same width of the channels) was observed with special physical models by Shvidler et al. [10]. It confirms the possibility to realize behaviour of oil in channels detected by numerical simulation. The detailed distributions of the temperature, pressure and velocity fields give a possibility to explain the real oil flow patterns in channels. Formation of zigzaging oil flow in horizontal windings channels (Fig. 3) can be explained by the interaction between the velocity and pressure fields. Due to the intensive heat release in coils and oil heating, as well as buoyancy force, at first the oil runs in one direction of the horizontal channels. However, with the certain level of pressure gradient and according to mass conservation law, the deceleration of collective flow occurs and the inversion of its direction can be observed. In that way, the macrostructure of flows is formed in consecutive groups of uniform channels (from 3 to 15 channels depending on cooling conditions, power and distribution of volumetric heat dissipation). The flow directions in adjacent channel groups are opposite which is determined by mass conservation law (continuity equation). Fig. 3d shows that the maximum value of the radial velocity component in considered channels is z2.2$103 m/s and takes place approximately in the middle channel of the group. In the other channels of the group the maximum velocity decreases approximately by parabolic law. In the outer channels, the radial component of velocity vector is smaller (1.4$104e2.1$104 m/s) as compared to the central channels and heat transfer in them takes place mainly due to the mechanism of heat conduction. In the other groups of channels with the same direction of radial velocity, the flow patterns are qualitatively similar. Fig. 4 shows the non-uniform temperature field within the range of 50e90 C in LV and HV windings of power transformer
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
with power of about 210 MV A. Here, the temperature field in winding coils has no axial symmetry. That is associated with through flow of cooling oil in the direction along the coil radius, as shown in Fig. 4. The temperature distribution also presents zones with the maximum temperature values. When exceeding the limiting permissible temperature, the number of constructive elements should be reduced. In horizontal channels with the maximum oil velocity, the heat transfer coefficient is around 100 W/(m2 K), while in the outer channels (in stagnant zones) the heat transfer coefficient is reduced to w50 W/ (m2 K). In the region adjacent to the inner and outer vertical cooling channels, due to formation or destruction of boundary layers on the coil vertical surfaces, the difference between the coil surface and oil local temperature is minimized and the heat transfer coefficient increases significantly. 8. Conclusions The computer CFD model of the oil transformer in axial symmetry taking into account the tank with the active part, the insulating system and the radiators of external cooling has been developed. The adequacy of the model is verified by experiments. The specific peculiarities in the structure of the cooling fluid flow in the system of a large number of interconnected channels of the oil-filled transformer have been revealed with the use of the developed model. It has been found that the self-organization in hydrodynamic processes with unidirectional oil flowing along the numerous horizontal channels between the coils takes place. This phenomenon has a considerable influence on the thermal state of the transformer. The region with maximum temperature values in the transformer is displaced along the winding height and in the direction of the radial component of velocity. The proposed computer model along with the numerical results can be used for further investigation of hydrodynamic and thermal processes in oil-filled power transformers at different loads, cooling and external conditions.
353
Acknowledgements This work was funded by the National Academy of Sciences of Ukraine and the Joint Stock Company “Zaporozhtransformator”. I would like to express my sincere gratitude and appreciation to Prof. Artem A. Khalatov and Prof. Pavel G. Krukovsky for useful and valuable discussions and suggestions concerning the article’s content. I am also obliged to Mr. Anatoly S. Polubinsky and Mr. Anton N. Tkachuk for participation in computer models data preparation and their kind-hearted help and support during the work. References [1] J.C. Ramos, M. Beiza, J. Gastelurrutia, A. Rivas, R. Antón, G.S. Larraona, I. de Miguel, Numerical modelling of the natural ventilation of underground transformer substations, Appl. Therm. Eng. 51 (2013) 852e863. [2] J. Smolka, CFD-based 3-D optimization of the mutual coil configuration for the effective cooling of an electrical transformer, Appl. Therm. Eng. 50 (2013) 124e133. [3] F. Torriano, M. Chaaban, P. Picher, Numerical study of parameters affecting the temperature distribution in a disk-type transformer winding, Appl. Therm. Eng. 30 (2010) 2034e2044. [4] F. Torriano, P. Picher, M. Chaaban, Numerical investigation of 3D flow and thermal effects in a disk-type transformer winding, Appl. Therm. Eng. 40 (2012) 121e131. [5] A. Skillen, A. Revell, H. Iacovides, W. Wu, Numerical prediction of local hot-spot phenomena in transformer windings, Appl. Therm. Eng. 36 (2012) 96e105. [6] J.M. Mufuta, E. van den Bulck, Modelling of the mixed convection in the windings of a disk-type power transformer, Appl. Therm. Eng. 20 (2000) 417e437. [7] J.M. Mufuta, E. van den Bulck, Modelling of the mass flow distribution around an array of rectangular blocks in-line arranged and simulating the crosssection of a winding disk-type transformer, Appl. Therm. Eng. 21 (2001) 731e749. [8] P.G. Krukovsky, V.A. Yatsevsky, L.N. Kontorovich, V.F. Ivankov, D.D. Yurchenko, Methodical approaches to the CFD modelling of thermal regimes of power oil transformers, Ind. Heat. Eng. 30 (6) (2008) 57e66 (in Russian). [9] K. Karsai, D. Kerenyi, L. Kiss, Large Power Transformers, Elsevier Science Publishing Company, Amsterdam, Oxford, New York, Tokyo, 1987. [10] A.B. Shvidler, Yu.A. Michaylovsky, G.B. Cherednichenko, L.A. Klimenko, Internal heat transfer coil windings of transformers, Elektroteknika 7 (1980) 19e21 (in Russian).
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Hydrodynamics and heat transfer in cooling channels of oil-filled power transformers with multicoil windings Vitaly A. Yatsevsky* National Academy of Sciences of Ukraine, Institute of Engineering Thermophysics, Department of Heat-and-Mass Transfer Modelling, St. Zhelyabova, 2a, 03680 Kyiv, Ukraine
h i g h l i g h t s The CFD model of the transformer with external cooling circuit has been developed. The model also includes all the cooling channels in the space between coils. The analysis of hydrodynamic processes has revealed self-organizing oil flow. The flow features have an influence on the thermal state of windings coils. Zones with the maximum temperature shift along height and toward the radial velocity.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 March 2013 Accepted 26 October 2013 Available online 7 November 2013
The analysis of heat transfer and oil flow in power transformers at natural convection of cooling oil is carried out by numerical simulation of the fluid dynamic problem in axisymmetrical formulation (CFDapproach). The effects of self-organization structure of oil flowing in the form of the unidirectional flow in the groups of horizontal channels between winding coils have been revealed. The flow features have an influence on the thermal state of winding coils of the transformer with the natural cooling system. At such oil flowing, in different channels, the heat transfer coefficient varies within the limits of 50e100 W/(m2 K), and the radial component of velocity is changed over the range of 2.1$104e2.2$103 m/s. Thus the region with maximum temperature values is removed towards oil flowing along the coil radius. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Power transformers CFD modelling Self-organizing flow Natural cooling Oil flow Thermal and hydrodynamic processes
1. Introduction The key factor in ensuring the high reliability and long-term operation of a power transformer is the effective removal of the energy which is inevitably released as heat in basic constructive elements e in the magnetic system, windings and other active parts (Fig. 1). One of the most important technical parameters is the temperature level of hot spots in windings, exceeding of which (more than 98 C) causes the thermal destruction of the winding insulation. Location and temperature values of hot spots are unpredicted owing to the complex structure of oil circulation in numerous interconnected vertical and horizontal channels inside the oil-filled tank.
* Corresponding author. Tel.: þ38 0681268268. E-mail address: [email protected]. 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.10.055
The problem related to CFD modelling of thermal processes in power transformers as well as special features of cooling fluid flowing in channels has been studied enough well in enough scientific works. For the last ten years more than a hundred and fifty publications have presented the models of different level of detailization and accuracy. The previous works have revealed that the modification and redistribution of fluid flow influence directly and largely on the temperature distribution in transformer component, and the distribution of winding temperature is more uniform when the flow rate of cooling fluid increases. Authors of many works put an emphasis on horizontal channels critical zones that require a particular consideration. The majority of CFD studies are concentrated on examining only separate parts of transformer winding, for example considering one pass. In the present article, the general formulation has been carried out taking into account complete two windings, the core, the
348
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
Nomenclature b Cp g Gr h k P Pr Q R r, z Re T
width of vertical channels [m] specific heat capacity [J/kg K] gravity acceleration [m/s2] Grashof number [e] width of horizontal channels [m] empirical coefficient k in Eq. (4) [e] pressure [Pa] Prandtl number [e] heat source density (heating power per unit volume) [W/m3] radius [m] radial and axial cylindrical coordinates [m] Reynolds number [e] temperature [K or C]
transformer tank and the external cooling radiators. Latest similar research works are considered below. Work [1] gives CFD model for thermal investigation of air ventilation in underground transformer substations and presents the patterns of air flow and temperature distribution inside the substation as well as shows a stagnant zone as a zone with still (static) air. The approach to optimization of mutual configuration of coils (disks) and cooling channels is developed by Smolka [2] for effective cooling of a dry-type transformer. The optimization procedure combines the methods of computational fluid dynamics (CFD) and genetic algorithm to find optimum diameter of channels and coils. In the computer CFD model proposed by Smolka in Ref. [2], the thermal properties of coils and core are considered as anisotropic and
Fig. 1. The scheme of 210 MV A power transformer: 1 e axis of symmetry; 2 e transformer core; 3 e lower voltage winding (LV); 4 e pressing ring above LV winding; 5 e high-voltage winding (HV); 6 e pressing ring above HV winding; 7 e radiator of external cooling subsystem; 8 e shunt under HV winding; 9 e shunt under LV winding; 10 e fan; 11 e oil pump.
Vr Vz
velocity components in radial direction r [m/s] velocity components in axial direction z [m/s]
Greek symbols s time [s] r density [kg/m3] m dynamic viscosity [kg/m s] 4 tangential cylindrical coordinate [rad] l thermal conductivity [W/(m K)] Indices amb in oil out v
ambient inner oil outer per unit volume
temperature-dependent quantities. The heat sources (heating power) for elements are computed by coupled CFD and EMAG (electromagnetic) models. A similar approach is used in the present article. The article by Torriano et al. [3] presents the following results. The data obtained with simplified models differ appreciably from the results of the conjugate heat transfer model. The windings having separate copper wires with paper insulation which form a disk are studied. Unfortunately, this approach is extremely time-consuming and complicated for implementing as for many types of complexstructured wires (transposed wires or subdivided wires). Work [4] (a subsequent paper by the same authors) gives the results of 3D simulation of coupled heat transfer and hydrodynamic flow in a disk-type low-voltage winding of distribution transformer 66 MVAe225/26.4 kV ONAN/ONAF. The low-voltage winding contains 78 disks divided into four passes. All the passes, except the first one, have 19 disks each. The first pass consists of 21 disks, but has an additional block-washer between the second and the third disks. The 3D results are compared with the similar computations by 2D model. It show be noted that 3D model includes all geometrical parts (i.e., sticks, intersticks, duct spacers and oil washers). The comparison is made for the homogeneous and inhomogeneous loss distributions in the winding. The computer models are realized by commercial finite-volume CFD code AnsysCFX v12.1. As computational results show, the significant threedimensional effects take place owing to availability of strips and spacers in the channel and, therefore the flows in cooling channels cannot be considered as completely axially symmetric. The authors of the article [4] emphasize that although 3D computations are very valuable, they need high-speed computer facilities. For this reason, the improved 2D models are proposed. The CFD Code_Saturne developed by Électricité de France (EDF) is used by Skillen et al. in Ref. [5] for studying mixed convection for axisymmetric (2D) problem of cooling flows in a low-voltage transformer winding. Only region with fluid is simulated and the simplified (idealized) 3D model of windings is examined. The computations are realized for both a complete winding with five passes (the winding has 78 disks) and a separate pass. The CFD model discovers hot plumes in some horizontal cooling channels. The radial flows differ in direction for each horizontal channel. As revealed, the solution varies depending even on small deviation of the inlet velocity of the mass flow. That shows a highly unstable flow configuration. It is believed that all flows run in several channels where the cross-flow of fluid are negligible (e.g. less than 1% of inlet flow velocity). This causes the high temperature of disk surface and local hot-spots. The vector of gravitational force and then radial cooling flows in the passes and hot plumes are left out of account.
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The hot streaks are still available due to high Prandtl number of fluid, but they are passive and have no influence on flow distribution. This proves the importance of the accurate setting of the hydrodynamic lift in the calculations. Moreover, we believe, the use of a simplified model for the analysis of the Boussinesq subtle physical effects is inappropriate. However, according to the author of this work [5], there have not been any experimental studies detailed enough to identify and make the analysis of the flow turns in the horizontal channels. Mufuta et al. in Ref. [6] present rather detailed analysis of cooling processes in the fragment of disk-type transformer winding. The geometrical model (and computational region) consists of an axially symmetric fragment of the winding and uses the array with two columns of 10 (in some variants from 4 to 15) rows of rectangular blocks placed between two impermeable walls. The simplifications of the model consist in idealization of conductor cross-section, constant heat dissipation rate of inlet of each vertical channel. In Ref. [6], the finite-volume method and commercial CFD code are used for computation of the temperature in disk-type windings at variation of mass flow rate and heat losses. The computed results revealed the transverse and horizontal flows from the central vertical channel to the adjacent left and right vertical channels and vice versa. As noted, when the ratio of Reynolds number to Grashof number Re/Gr1/2 increases, the buoyancy force decreases. In this case, the amplitude of cooling flow oscillation decreases monotonically and then the smaller flow runs through the horizontal channel. The flows directed to inwards and outward flows promote heat removal from horizontal channel. For small values of ratio Re/Gr1/2, the mass flow rate varies with a greater amplitude than at higher ratio Re/Gr1/2. It was also found that the temperature of the blocks changes nonlinearly along the height of the part of the winding. The temperature field represents fluctuations of the mass flow. The temperature increases starting from the first to the fifth block, then decreases slightly, and again increases. This profile corresponds to the oscillation of the mass flow in the set of blocks. Block number 6 is less hot as compared to block number 5. This is not an evident fact proceeding from general physical principles without detailed computation and related analysis. In a subsequent paper by the same authors [7], the distribution of mass flow around the set of rectangular blocks which imitate a crosssection (profile) of the fragment of disk-type winding is investigated. Also, the transversal flow through horizontal channels (the space between the blocks) was observed by experimental unit with the use of laser Doppler velocimeter to measure the velocity field. The correlation between the velocity difference in the boundary layer and pressure differential across each horizontal channel was defined. It was noted that the spatial flow oscillations occur in vertical channels because of transversal flow through horizontal channels. In conclusion of Ref. [7], the asymmetry of the heat removal rate can be changed in order to provide coolant flowing through horizontal channels even without any additional oil washers used for flow modification. Thus cooling in critical thermal zones of the oil transformer can be intensified. The article proposes the computer model of thermal and hydrodynamic processes in an oil-filled power transformer with
multi-coil windings and numerous cooling channels. The model is built in axial symmetry. In distinction from previous CFD models, it simulated all the major transformer components including the magnetic part, the insulation system, the tank and the radiators. The heat transfer into the environment by the external cooling system (radiators) is described by parametric relation derived from the experimental data. Much attention is devoted to fine peculiarities of flows in horizontal cooling channels of full-scale windings. 2. Geometric model of power transformer The construction of modern high-power transformers (Fig. 1) is considerably complex [8,9]. It consists of a large number of details which are inhomogeneous according to thermophysical characteristics and of complex geometry (up to 100 constructive units). However, most of the structural elements have a cylindrical symmetry about axis of core in each transformer phase. Therefore, in this article the thermo-hydrodynamic processes in winding channels are studied for two-dimensional axisymmetrical presentation of transformer with the natural convection cooling system. It is the most complicated for numerical simulation of hot spots positions. High power transformers have the windings with coils separated by horizontal channels, and, the number of the channels can be up to 400 (Fig. 1). The windings are separated from each other by oil insulating elements forming a subsystem of vertical channels. Dimensions of both vertical and horizontal channels are in the range of 3e12 mm. For such transformers, the heat removal through the walls of oilfilled tank cannot provide an acceptable level of temperature. Therefore, the tank is connected to the external oil cooling system which can operate under either natural or mixed (natural and forced) convection conditions. Then the cooled oil from the external radiators enters to the bottom of the tank, lifts due to buoyancy force (and, if necessary by means of pumps) through the vertical and horizontal channels in windings and around them, thus, forms the admissible temperature field of structural elements of the transformer (see Figs. 1 and 4). 3. Physical and mathematical models The physical and mathematical models for computations of hydrodynamic and heat transfer processes are the following. It was assumed that the dependent variables (the temperature, velocity and pressure fields) do not change along the axis f of cylindrical coordinate system (r, z, f). Then, in the axisymmetrical formulation, some specific features of the real windings such as availability of distancing gaskets and strips cannot be taken into account properly. However, the special test 3D computations show that the contribution of these structural components to heating of windings is negligible. The mathematical model of coupled processes of hydrodynamics and heat transfer in the transformer, consists of Naviere Stokes equations (conservation of momentum) for a viscous incompressible fluid, mass continuity (conservation equation) and equations of energy conservation:
2$m vVr vVr Vr vVr vVz v v ¼ vP ; vr þ 2$vr m$ vr þ r $ vr r þ vz m$ vz þ vr vVz vVz vVz vVr vVr vVz v v z z r vV ¼ rg vP þ mr $ vV vs þ Vr vr þ Vz vz vr þ vz þ 2$vz m$ vz ; vz þ vr m$ vr þ vz
r
vVr vs
vVr r þ Vr vV vr þ Vz vz
349
(1)
350
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
Fig. 2. Methodology for investigation.
vðrÞ vðrVr Þ rVr vðrVz Þ þ ¼ 0; þ þ vs vr vz r
rCp
(2)
vT vT vT 1v vT v vT lr l ¼ þ þ Qv ðr; zÞ; þ Vr þ Vz vs vr vz r vr vr vz vz (3)
Here, Vr, Vz components of velocity vector in radial (r) and axial (z) directions, P pressure scalar field, r density, Cp specific heat capacity, m dynamic viscosity of cooling fluid, g free fall acceleration, s time. Transport and thermodynamic characteristics of cooling fluid are the functions of temperature according to the experimental data presented in Ref. [9]. 4. Boundary conditions and fluid properties The initial data for thermal computations in addition to detailed geometric parameters are formed with values of ambient temperature, heat generation of coil windings, dimensions of vertical and horizontal channels between the coils, thickness of insulating cylinders, values of thermal conductivity, and parameters of external cooling system for each type of load. The heat sources Qv in the region of coil windings, metal components of magnetic core and tank walls are defined by preliminary electrodynamic computations. In cooling fluid (transformer oil) inside the tank Qv ¼ 0. In the region of heat release in external circuit (with cooling radiators, Fig. 1), the heat sources are assumed to be negative in order to simulate heat removal into the environment: 1:2 Qv ¼ k$DToil amb :
(4)
The empirical coefficient k and the index of a power, at the average temperature difference in radiators above ambient temperature DToil amb in Eq. (4), are determined by experimental data. As the initial conditions the velocity vector components of cooling fluid are set to be zero, and the temperature of all the system elements are equal to ambient temperature. All the solid surfaces contacting with oil are considered to be non-slipping and non-leaking (solid walls), i.e. the velocity
components are set to be zero. The energy equation (3) is valid for description of temperature fields for cooling fluid (oil) and solid construction elements, where velocity components are equal to zero. On the interface between coolant and solid surfaces, conjugation conditions are specified (equality of the temperature and heat fluxes values). On the external surface of the oil-filled tank, mixed conditions of convective heat transfer (heat transfer coefficient and ambient temperature) and radiation heat transfer are assigned. System of Equations (1)e(4) is solved by the implicit finitevolume method in professional code ANSYS FLUENT. In the computational model of a two-phase transformer of 210 MV A power, only one phase consisting of two concentric windings is considered. The low-voltage winding consists of 114 coils separated by horizontal channels with different height, and the high-voltage winding contains 156 coils. The computational region and its subdomains are shown in Fig. 1. The computations were realized for heat generation in coils and other conducting units being specific for rated duty of the transformer under consideration. The computations were made by quad core computer with the use of parallelization by means of decomposition of computational region. 5. Methodology The methodological approach gives an opportunity to develop CFD-models for both theoretical (especially for investigation of the velocity and temperature fields) and applied study aimed at sensor positioning in order to monitor hot spots in real time. CFD modelling of thermal processes in transformers with the external cooling subsystem can be defined as a series of interdependent procedures of physical, geometrical, mathematical and computer models to be performed in a certain sequence (Fig. 2). That modelling enables to obtain and analyze the temperature field, accounting all the basic features and physical mechanisms of heatand-mass transfer processes in the equipment. In order to achieve accurate and reliable results concerning the thermal state and dynamics of the coolant in the equipment, the estimation of computational errors and verification of computer models are required by comparison with previous studies (Fig. 2).
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Fig. 3. The scheme of oil flow through the channels (a); distribution of the total pressure differential along the height of the HV winding starting from the 1-st coil (at the bottom) to the 156-th coil (on top) (b); distribution of the radial component of velocity along the relative height of the HV winding (c); distribution of radial velocity along the height of the HV winding from the 42 coil (at the bottom) to the 57-th coil (on top) (d).
Such empirical data should be concerned with analogous subject area and particular problem statements. In addition to this, the typical range of main characteristics (heat power, cooling conditions, thermal characteristics of coolant) as well as the basic design of comparative objects should be similar. After conjugate problem solving and numerical data averaging, the temperature of surfaces and volumes of windings and other constructive elements and distribution of heat transfer coefficients at selected surfaces are determined. These data can be compared with analogous results presented in scientific-and-technical works. 6. Validation of numerical model In order to verify the adequacy of the developed computer model, the thermal tests were conducted at Public Joint Stock Company (PJSC) “Zaporozhtransformator” (“ZTR”). The experimental data were compared with analytical correlations. The
results of the comparison at 20 C ambient temperature are given in Tables 1 and 2. For the comparison, the analysis of calculational results was made by the CFD computer model. The average temperature of the windings was determined by averaging the temperature values of all the coils in each winding. The average oil temperature was defined as the arithmetic mean between temperature of upper oil and lower oil temperature. “Upper oil” in this context is defined as a region with oil inside the tank located above the upper surface of the upper horizontal yoke and up to the lower surface of the tank cover. And “lower oil” is a region placed below the lower surface of the lower horizontal yoke and down to the upper surface of the tank bottom. The average temperature of the oil in the tank, including the oil between the coil channels (horizontal cooling channels of winding) was defined in the same way. As seen from Tables 1 and 2, the accuracy of computations by developed CFD model is admissible.
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V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353 Table 2 Winding temperature, C (mode ONAN).
Fig. 4. Temperature field over the range of 50e90 C in the LV and HV windings.
7. Discussion of computational results At convective heat transfer, both integral and local characteristics of the heat process depend mainly on the nature and structure of the fluid flow. Patterns of thermal and hydrodynamic fields in the transformer vary depending on cooling conditions and during the non-stationary process. At the same time, there are significant quantitative and qualitative distinctions at different stages of the transient process. The directions of circulation in separate channels during fluid flowing can often be reversed which was found by numerical simulation. The numerical solution of the problem in conjugate formulation in terms of temperature, pressure and velocity gives a very complex flow structure not only in cooling channels, but also inside the oilfilled transformer tank. The main feature of convective flow at thermal gravitational convection in the distributed system with a
Table 1 Oil temperature, C (mode ONAN). Parameter
Experiment CFD
Temperature of upper oil Average temperature of oil Temperature of lower oil Temperature difference between upper and lower oil
84.0 69.5 55.0 27.5
Range 79e84
Average temperature
81.5 67.0 50.0e55.0 52.5 29.0
Parameter
Experiment
CFD
Temperature of coil No. 1 (on top) LV winding Temperature of coil No. 1 (on top) HV winding Average temperature of LV winding Average temperature of HV winding
86.8 84.6 71.9 70.1
83.94 80.58 76.76 72.93
great number of interconnected channels inside the oil-filled tank is simultaneous presence of local zones with different flow patterns. Detailed behaviour of flow and its intensity are determined jointly by the design and operational parameters. In other words, the flow pattern is determined by nonlinear interdependent fields of pressure, temperature and velocity. An additional complicating factor is the presence of a rather complex multi-domain geometrical model (Fig. 1), and oil circulation inside the transformer tank. The complex flow structure in cooling channels was found by numerical simulation (Fig. 3). Fig. 3a shows the qualitative scheme of flow thought channels. Fig. 3b gives the distribution of total pressure differential in the middle of the high-voltage (HV) winding. Fig. 3c presents the distribution of the radial velocity in the HV winding, which depends on the height of the coil. It can be seen from the computational results that 11 groups of channels (approximately 14e15 channels in each group) are formed along the winding height where the oil flow has mainly the same direction e from the axis of symmetry of the transformer to the winding periphery towards the lateral wall of the tank or the opposite direction. Between separate groups of channels, there are channels where the radial velocity is much smaller than in the central channels of the group (stagnation zones). Taking into account a considerable height of a real coil (about 3 m), Fig. 3d shows the fragment on a large scale with distribution of radial velocity for the fourth group of the channels starting from the bottom. The primary flow of coolant from the external vertical cooling channel to the inner channel (even at the same width of the channels) was observed with special physical models by Shvidler et al. [10]. It confirms the possibility to realize behaviour of oil in channels detected by numerical simulation. The detailed distributions of the temperature, pressure and velocity fields give a possibility to explain the real oil flow patterns in channels. Formation of zigzaging oil flow in horizontal windings channels (Fig. 3) can be explained by the interaction between the velocity and pressure fields. Due to the intensive heat release in coils and oil heating, as well as buoyancy force, at first the oil runs in one direction of the horizontal channels. However, with the certain level of pressure gradient and according to mass conservation law, the deceleration of collective flow occurs and the inversion of its direction can be observed. In that way, the macrostructure of flows is formed in consecutive groups of uniform channels (from 3 to 15 channels depending on cooling conditions, power and distribution of volumetric heat dissipation). The flow directions in adjacent channel groups are opposite which is determined by mass conservation law (continuity equation). Fig. 3d shows that the maximum value of the radial velocity component in considered channels is z2.2$103 m/s and takes place approximately in the middle channel of the group. In the other channels of the group the maximum velocity decreases approximately by parabolic law. In the outer channels, the radial component of velocity vector is smaller (1.4$104e2.1$104 m/s) as compared to the central channels and heat transfer in them takes place mainly due to the mechanism of heat conduction. In the other groups of channels with the same direction of radial velocity, the flow patterns are qualitatively similar. Fig. 4 shows the non-uniform temperature field within the range of 50e90 C in LV and HV windings of power transformer
V.A. Yatsevsky / Applied Thermal Engineering 63 (2014) 347e353
with power of about 210 MV A. Here, the temperature field in winding coils has no axial symmetry. That is associated with through flow of cooling oil in the direction along the coil radius, as shown in Fig. 4. The temperature distribution also presents zones with the maximum temperature values. When exceeding the limiting permissible temperature, the number of constructive elements should be reduced. In horizontal channels with the maximum oil velocity, the heat transfer coefficient is around 100 W/(m2 K), while in the outer channels (in stagnant zones) the heat transfer coefficient is reduced to w50 W/ (m2 K). In the region adjacent to the inner and outer vertical cooling channels, due to formation or destruction of boundary layers on the coil vertical surfaces, the difference between the coil surface and oil local temperature is minimized and the heat transfer coefficient increases significantly. 8. Conclusions The computer CFD model of the oil transformer in axial symmetry taking into account the tank with the active part, the insulating system and the radiators of external cooling has been developed. The adequacy of the model is verified by experiments. The specific peculiarities in the structure of the cooling fluid flow in the system of a large number of interconnected channels of the oil-filled transformer have been revealed with the use of the developed model. It has been found that the self-organization in hydrodynamic processes with unidirectional oil flowing along the numerous horizontal channels between the coils takes place. This phenomenon has a considerable influence on the thermal state of the transformer. The region with maximum temperature values in the transformer is displaced along the winding height and in the direction of the radial component of velocity. The proposed computer model along with the numerical results can be used for further investigation of hydrodynamic and thermal processes in oil-filled power transformers at different loads, cooling and external conditions.
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Acknowledgements This work was funded by the National Academy of Sciences of Ukraine and the Joint Stock Company “Zaporozhtransformator”. I would like to express my sincere gratitude and appreciation to Prof. Artem A. Khalatov and Prof. Pavel G. Krukovsky for useful and valuable discussions and suggestions concerning the article’s content. I am also obliged to Mr. Anatoly S. Polubinsky and Mr. Anton N. Tkachuk for participation in computer models data preparation and their kind-hearted help and support during the work. References [1] J.C. Ramos, M. Beiza, J. Gastelurrutia, A. Rivas, R. Antón, G.S. Larraona, I. de Miguel, Numerical modelling of the natural ventilation of underground transformer substations, Appl. Therm. Eng. 51 (2013) 852e863. [2] J. Smolka, CFD-based 3-D optimization of the mutual coil configuration for the effective cooling of an electrical transformer, Appl. Therm. Eng. 50 (2013) 124e133. [3] F. Torriano, M. Chaaban, P. Picher, Numerical study of parameters affecting the temperature distribution in a disk-type transformer winding, Appl. Therm. Eng. 30 (2010) 2034e2044. [4] F. Torriano, P. Picher, M. Chaaban, Numerical investigation of 3D flow and thermal effects in a disk-type transformer winding, Appl. Therm. Eng. 40 (2012) 121e131. [5] A. Skillen, A. Revell, H. Iacovides, W. Wu, Numerical prediction of local hot-spot phenomena in transformer windings, Appl. Therm. Eng. 36 (2012) 96e105. [6] J.M. Mufuta, E. van den Bulck, Modelling of the mixed convection in the windings of a disk-type power transformer, Appl. Therm. Eng. 20 (2000) 417e437. [7] J.M. Mufuta, E. van den Bulck, Modelling of the mass flow distribution around an array of rectangular blocks in-line arranged and simulating the crosssection of a winding disk-type transformer, Appl. Therm. Eng. 21 (2001) 731e749. [8] P.G. Krukovsky, V.A. Yatsevsky, L.N. Kontorovich, V.F. Ivankov, D.D. Yurchenko, Methodical approaches to the CFD modelling of thermal regimes of power oil transformers, Ind. Heat. Eng. 30 (6) (2008) 57e66 (in Russian). [9] K. Karsai, D. Kerenyi, L. Kiss, Large Power Transformers, Elsevier Science Publishing Company, Amsterdam, Oxford, New York, Tokyo, 1987. [10] A.B. Shvidler, Yu.A. Michaylovsky, G.B. Cherednichenko, L.A. Klimenko, Internal heat transfer coil windings of transformers, Elektroteknika 7 (1980) 19e21 (in Russian).