IET Electric Power Applications Research Article
Finite element method-based modelling of flow rate and temperature distribution in an oil-filled disc-type winding transformer using COMSOL multiphysics
ISSN 1751-8660 Received on 14th July 2016 Revised on 6th February 2017 Accepted on 12th February 2017 doi: 10.1049/iet-epa.2016.0446 www.ietdl.org
Anu Kumar Das ✉, Saibal Chatterjee Department of Electrical Engineering, NERIST, Nirjuli, Arunachal Pradesh, India ✉ E-mail:
[email protected]
Abstract: Thermal design of oil filled distribution and power transformers is essential for obtaining the location of ‘hot-spot’ of the transformers. This study presents the analysis of 2D and 3D model for the simplified section of an oilfilled disc-type winding power transformer. Both models developed using COMSOL Multiphysics 5.1 were validated with the experimental and numerical results available in literatures. The analysis of the flow rate and the temperature distribution accurately reveals the location and the temperature of the ‘hot-spot’. Further, the parametric study using the 3D model shows that the combined effect of variation in the vertical cooling duct width and the local cross-section area in the horizontal cooling duct has a significant influence on the location of the ‘hot-spot’ and a minor influence on its temperature (i.e. ±3%). The analysis results in this study shall be beneficial from the point of view of design development in transformers.
1
Introduction
Power transformers are one of the most expensive components in an electricity system. An extensive transmission system with efficient transformers is indispensable to ensure a reliable supply of power. The insulation system age at a normal rate and provide the standard transformer life when a transformer operates at a temperature which are specific to the fluid and the insulating materials, for example mineral oil and thermally upgraded kraft paper operated at 110°C or FR3 fluid and thermally upgraded kraft paper operated at 131°C results in normal and safe thermal life [1]. The heat generated inside a transformer is due to the energy losses in the transformer, which are the iron losses in the core and the ohmic losses in the coils [2]. The transformer oil in the process of heat transfer gets heated up and its temperature rises which is detrimental to its operation. Through external means, this heat in the oil is dissipated and then cooled oil is circulated back into the transformer. Depending upon the quantity of heat to be handled, different cooling methods with suitable heat exchangers are preferred, such as – oil natural air natural (ONAN) cooling, oil natural air forced cooling, oil natural water forced cooling, cooling by separate radiator banks, etc. [3, 4]. Although the ANSI/IEEE loading guides are used to determine the top-oil rise, the ‘hot-spot’ temperature, the loss of life of the transformer, and so on, the standard’s approximation cause the transformers to be oversized as the temperatures estimated are well above the real values. Thus to improve the accuracy of the loading guide, several modifications are proposed by several authors, Pierce, Buchan, and Green, to name a few [5–9]. In 1986, Allen and Childs [10] developed a thermal model of disc type winding transformer based on finite difference and lumped models. The fluid flow and thermal model were solved iteratively, and the prediction were in good agreement with their test results. In another thermal model, Alegi and Black [11] investigated the oil-immersed, forced-air cooled transformer under real operating conditions by validating the tested results available from 75 kVA transformer. Later, the model was used to analyse 5 MVA transformer run for 24 h load cycle, and the temperature distributions of transformer core, coil windings in real time were obtained using convective heat transfer co-efficient available in steady state. Recently, Susa et al., [12] developed a
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new method to determine the location and the temperature of ‘hot-spot’ in the transformer by considering the temperature dependent properties of oil, and taking the temperature of the top-oil as the reference. A network model based on heat and mass flow in natural oil cooled disc-type transformer under non-isothermal flow conditions was presented by Imre et al. [13], and obtained the steady state temperature by solving the networks iteratively. Later, in order to optimise the flow in cooling duct, Szpiro et al. [14] designed a prototype model of a pass, made of Perspex, of a disc-type winding and measured oil flow rate. The predicted oil flow distribution indicates a minimum flow in the duct at the centre of the pass and maximum flow in the duct at the top and bottom of the pass. Tenyenhuis et al., [15] presented a method based on finite element method (FEM) to determine and analyse the temperature distribution, and thereby obtained the location and temperature of the ‘hot-spot’ in the transformer. In another work, to analyse the thermal behaviour of ONAN distribution transformer, Rosillo et al. [16] developed a numerical model based on FEM. Their model considered all the modes of heat transfer, and the predicted flow rate along with temperature distributions were experimentally validated as per IEEE-1995 loading guide. In summary, some approaches were based on empirical co-relation, lumped models, coupled thermal and flow models, others include direct measurement of temperatures using sensors or thermocouples located in the windings, and others were based on numerical methods such as FEM. Unlike empirical method, which is easy to implement but not very precise, the direct measurement although costly and time consuming, provides a very accurate and reliable results. However, recently the FEM-based numerical method is gaining importance and has become a valuable tool which can be applied on a complex geometries, and provide an approximate solutions of high accuracy. A detailed numerical solution, therefore, would be very cost effective to improve the transformer design. A better understanding of the flow rate and the temperature distribution in a disc-type winding would aid significantly in the design of improved cooling of transformers. Thus it becomes necessary to predict the complicated heat transfer mechanism, flow
IET Electr. Power Appl., 2017, Vol. 11, Iss. 4, pp. 664–673 & The Institution of Engineering and Technology 2017
Table 1 Properties of transformer oil Dynamic viscosity, m, (Pa.s) Density, ρ, kg/m3 Specific heat capacity, Cp , J/ kg.K
ρ10 875.6-0.63T 1960 + 4.005T
(−4.726-0.0091T)
distributions in the windings, and the changes in the bulk fluid temperatures. Another important aspect is the analysis of necessary variations in the duct width, which, if optimised properly, can have beneficial effects and thus reduces the temperature of ‘hot-spot’. By considering all the possible modes of heat transfer, variation in vertical duct width and its influence on flow distribution, as well as the temperature dependent properties of oil, this study presents a detailed analysis results of axisymmetric disc-type winding, using 2D and 3D model in COMSOL Multiphysics 5.1 software [17], for future corrections and development in design.
2
Mathematical model
The mathematical model consists of the following three governing equations simplified from the general expressions for conservation of mass, momentum, and energy ∇.(ru) = 0
(1)
r(u.∇)u = −∇p + ∇(m∇u) + F rCp u.∇T = ∇(k∇T ) + Q
(2) (3)
where ρ is the temperature-dependent density (kg/m3) of the transformer oil, u is the flow velocity (m/s), T is the temperature (°K), p is the pressure (Pa), m is the temperature-dependent viscosity (Pa.s) and F is the volume force (N), k is the thermal conductivity W/(m.K), and Q is the heat flux density (W/m3). The temperature dependent expressions for the density, ρ, the viscosity, m and the specific heat capacity, Cp of transformer oil used in the model are given in Table 1 [18].
The model thus simulates the momentum transport and mass conservation with weakly compressible Navier–Stokes equations that describe the fluid velocity, u and the pressure field, p. Mineral oil used in transformer is normally present in the two distinct categories: paraffinic and naphthenic oils. While naphthenic oils are nearly free from N-alkanes, its presence in paraffinic oils crystallise upon cooling which obstruct the free flow of the oil. When the cloud point is reached (i.e. the crystallisation point at near about −10 to −15°C), the oil loses its Newtonian behaviour [19]. In practice the operating temperature in a transformer is much too high for wax crystallites to occur, and therefore the non-Newtonian behaviour is not present in most cases. The Reynolds number is a very important dimensionless number and gives a useful insight into when the fluid flow transitions takes place from laminar to turbulent flow. For a fluid flow in a horizontal duct, the range of ‘Re’ can be estimated to be much W1 (inner width) as shown in Fig. 1b. The velocity variations, which is a function of a duct width, is given by, U (x) = U1 ∗
W1 U1 W 1 = w W1 + (x/L)(W2 − W1 )
† Oil inlet temperature is 20°C for all the horizontal ducts. † Constant heat flux density applied on disc domains, Q = 32,400 W/m3, [27]. † Only convective heat flux is considered at the outlet boundaries: n.( − k∇T) = 0). † The remaining outer boundaries are insulated. In this work the focus in 2D and 3D model is to address the local distribution of temperature and coolant flow inside the windings which is laminar and steady, and ignoring the bulk oil flow in the tank which is 3D, and can often be turbulent and thus appear unsteady. In order to set the initial condition that closely resemble the flow, a constant velocity of 0.01 m/s is chosen at the inlet of the cooling duct, while the reference pressure at the outlet is constant and set equal to zero. Due to the zigzag flow pattern of the transformer oil through the cooling duct of the disc winding, heat transfer takes place almost entirely from the horizontal surfaces, so called the major surfaces of the disc coils, as can be seen in Fig. 1, and also the coolant temperature rise from the bottom to the top of a winding is negligibly small [14, 28]. Consequently, for a single pass the initial temperature field is set equal to the inlet temperature of 20°C for all the horizontal ducts, and heat dissipation from disc to vertical duct can be safely ignored. Constant heat flux density of Q = 32,400 W/m3 is applied on the disc domain whose surface is also the duct surface, and neglecting the effect of radiation [16]. The Reynold number ‘Re’ can be expressed as
(9)
where ‘w’ is the duct width at location ‘x’ [see Fig. 1b]. The average velocity and percentage relative flow along the duct can be expressed as, = 0.5 ∗ ( U1 + U2 ) U
(10)
U %relative flow = ∗ 100 U
(11)
and
respectively.
Re =
rvL , m
(12)
where the characteristic length, L = 4A/P, the cross-sectional area, A = (duct width, b). (duct height, d) and wetted perimeter, P = 2(b + d). In the present study, for a given density and viscosity of a transformer oil in a horizontal cooling duct of height, d = 4 mm, and duct width variation, b = 50 to 100 mm, Re number can be estimated to be in the range of 10 to 100 for the inlet velocity varying between 0.01 to 0.1 m/s. Therefore, the laminar flow interface is selected in COMSOL Multiphysics. The COMSOL software has all the details of the interfaces available to model various flow regimes using latest numerical techniques as given in [17].
Table 3 Abbreviations and symbol used in calculating RMSE [14, 23] Type Case-1 (Left vertical duct, width = 8 mm) Case-2 (Right vertical duct, width = 8 mm)
Table Tables 4–a and 5–a
Abbreviation and symbol used MV Szpiro-A
PV Szpiro-B NA Zhang-C COMSOL-D For case- 1, RMSE calculated against the measured results by Szpiro are labelled as RMSE-B1, RMSE-C1, and RMSE-D1 Tables 4–b and 5–b PV Szpiro-A NA Zhang-B COMSOL-C – For case-2, RMSE calculated against the predicted results by Szpiro are labelled as RMSE-B2, and RMSE-C2
MV Szpiro-measured values obtained by Szpiro PV Szpiro-predicted values obtained by Szpiro NA Zhang-numerical analysis value obtained by Zhang
IET Electr. Power Appl., 2017, Vol. 11, Iss. 4, pp. 664–673 & The Institution of Engineering and Technology 2017
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Fig. 3 Comparisons of flow rate distribution in % relative flow against the height of the duct (in mm) with the experimental and predicted results of Szpiro and Zhang [14, 23] obtained in the a 2D-model b 3D-model. [In both 2D and 3D model results, (i) refers to Case 1-left vertical duct of width = 8 mm, and (ii) refers to Case 2-right vertical duct of width = 8 mm, respectively]
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IET Electr. Power Appl., 2017, Vol. 11, Iss. 4, pp. 664–673 & The Institution of Engineering and Technology 2017
Fig. 4 3D models with a cut plane along with flow rate and temperature distributions a 3D model with a cut plane with R = 0.6, 0.7 and 0.8, respectively [24] b Flow rate distribution in % relative flow against the height of the duct (in mm) c Temperature distribution (°K) of transformer oil in cooling ducts of constant width (in mm)
4
Model validation
Usually the domain of 2D geometry encountered in a practical fluid flow and heat transfer problem has an irregular shape. For discretisation of such an irregular domain, using rectangle, as a basic finite element is obviously the simplest but not the most appropriate choice because they cannot accurately represent the arbitrary geometrical shape of the domain. Thus for a given element size, the triangular element is preferred to rectangular element for discretisation of 2D domain as in that case the discretisation error would be negligibly small. This is illustrated graphically in Fig. 2a. On the other hand, for meshing in 3D domain, the tetrahedral (tets) are the default element type used in most physics based model within COMSOL Multiphysics, and the other three elements are, hexhedra (bricks), triangular prismatics (prism), and pyramid elements. Unlike the later three, any 3D geometry, regardless of the shape or topology, can be meshed with tetrahedral element, and furthermore, they are the only kind of elements that can be used with adaptive mesh refinement, and for these reasons, tetrahedral element is preferred for discretisation of 3D domain in this study. Fig. 2b shows spatial discretisation of the computational domain (oil ducts), and to resolve phenomena near the wall regions the default boundary layer meshing was employed to solve the variations in the flow rate normal to the duct wall, while reducing the number of grid points in the direction tangential to the wall, and thus help to avoid any convergence instability. A mesh convergence analysis was performed with the objective of saving computational time and at the same time, to ensure that the
IET Electr. Power Appl., 2017, Vol. 11, Iss. 4, pp. 664–673 & The Institution of Engineering and Technology 2017
solutions obtained were not mesh dependent. Fig. 2c illustrates the variations of maximum temperature (°K) with the number of mesh elements. From the results summarised in Table 2, it can be seen that the variations 8952. Similarly, the convergence analysis extended to 3D model showed a variation of
