Faculdade de Engenharia da Universidade do Porto
Numerical investigation of thermal
behaviour of core plates in core type
transformers
Pedro Miguel da Cunha Martins
Mestrado Integrado em Engenharia Mecânica
Supervisor at FEUP: Prof. José Manuel Laginha Mestre de Palma Supervisor at Efacec: Eng. Márcio Alexandre Magalhães Fraga Quintela
Numerical investigation of thermal behaviour of core
plates in core type transformers
Pedro Miguel da Cunha Martins
Mestrado Integrado em Engenharia Mecânica
Abstract
This dissertation was developed within the Integrated Master’s in Mechanical Engineering syllabus in the Thermal Energy branch of the same course, regarding the 5thgrade discipline Dissertation,
taught at the Faculty of Engineering of University of Porto (FEUP), in partnership with Efacec. The work was developed in the Power Transformers Research and Development (R&D) department, within the Thermal and Fluids team.
During the normal functioning of a power transformer, power is lost and converted into heat. These losses, in turn, lead to an increase in temperature that deteriorates components and reduces the equipment’s lifespan. A transformer contains different components that generate heat, from which windings, magnetic circuit, magnetic shunts, cables, bushings, tank and core plates are the most important. Core plates are integral components of the tightening structure of the magnetic circuit.
The main objective of this work was to numerically investigate the thermal behaviour of core plates. Computational fluid dynamics simulations were performed using Ansys Fluent software. A decision was made to conduct the simulation in Ansys Fluent while considering the potential effects of turbulent flow, by enabling the κ − ε turbulence model. The reasoning for this choice is that the flow at the outlet zones isn’t strictly laminar, with Reynolds values of ≈ 2800. However, since the main area of interest and where the heat transfer phenomenon occurs is within the core plate’s channel, where Re = 46.35, there’s a need to redo the simulation without considering the effects or turbulence.
An experimental and real scale 15MVA core-type three-phase power transformer has been built to perform R&D activities. Despite the studied power transformer being classified as oil directed (OD), having forced and directed circulation through cooling equipment, the oil within the magnetic core’s channel where core plates are placed is moved by buoyancy forces. This channel behaviour is closer to classified oil natural (ON) transformers. The obtained oil flow rate in the core plate channel was 0.097Kg/s at 7.5mm/s, from the total inlet flow rate of 1.871Kg/s.
The obtained average heat transfer coefficient, havg, was 62.77W/m2K. This result is coherent
with literature, which suggests roughly h = 70W/m2Kfor similar cases.
Experimental data ranging from 59 − 66ºC was provided from heat test runs, for the same conditions as the numerical model. The obtained hotspot temperature from the computational fluid dynamics simulation was above those results, at 110.4ºC. A 50mm deviation in sensor placement compared with the hotspot could cause a temperature drop of 10ºC, which could explain part of the difference.
Acknowledgements
I would like to acknowledge my supervisors on this work, Eng.º Márcio Alexandre Magalhães Fraga Quintela at the company Efacec and Prof. José Manuel Laginha Mestre de Palma at Faculdade de Engenharia da Universidade do Porto.
I would also like to thank the Thermal and Fluids team at Efacec, for all their support, their knowledge and patience given during the entire semester.
Finally, I would like to thank my friends, my family and my girlfriend. I will always be thankful to you.
Pedro
“Some men give up their designs when they have almost reached the goal, while others, on the contrary, obtain a victory by exerting, at the last moment, more vigorous efforts than ever before”
Herodotus
Contents
1 Introduction 1 1.1 Efacec . . . 1 1.2 Power transformers . . . 2 1.2.1 Main components . . . 4 1.3 Numerical methods . . . 81.3.1 Computational Fluid Dynamics . . . 8
1.3.2 Thermal Hydraulic Network Models . . . 10
1.4 Structure and Organisation . . . 10
2 Methodology 13 2.1 Formulation for heat transfer . . . 13
2.2 Formulation for turbulent flow . . . 14
2.3 Transformer data . . . 16
2.3.1 Dimensions . . . 16
2.3.2 Material properties . . . 16
2.3.3 Core plate losses . . . 18
2.4 Geometry . . . 19
2.4.1 Geometry considerations . . . 19
2.4.2 Simplified model . . . 20
2.4.3 New target geometry . . . 21
2.4.4 Final geometry . . . 22
3 Results 27 3.1 Mesh independence study . . . 27
3.2 Mesh . . . 29
3.3 Setting up Ansys Fluent . . . . 30
3.4 Results . . . 32
3.4.1 Core plate temperature profile . . . 32
3.4.2 Heat transfer coefficient . . . 32
3.5 Remaking the initial simplified model . . . 34
4 Analysis 41 4.1 Experiment . . . 41
4.2 Comparison and discussion . . . 41
5 Conclusions 43
6 Future work 45
viii CONTENTS
List of Figures
1.1 Example of a power transformer. . . 2
1.2 3D drawing of a magnetic core. . . 4
1.3 Hysteresis cycle of steel. . . 5
1.4 3D drawing of tightening structure around the magnetic core. . . 6
1.5 3D drawing of phases attached to tightening structure and magnetic core. . . 6
1.6 Core plate position. . . 9
1.7 Induced current in core plate. . . 10
1.8 Magnetic flux between windings and core plate. . . 11
2.1 Dimensions of magnetic core and core plate. . . 16
2.2 Properties of the selected mineral oil in function of temperature. . . 18
2.3 Losses of core plate along its height axis. . . 19
2.4 Initial target geometry. . . 20
2.5 Simplified model. . . 21
2.6 New model. . . 22
2.7 New model without the fluid. . . 22
2.8 New model with just the fluid. . . 23
2.9 New model with just the adiabatic parts. . . 23
2.10 New model without the tank and fluid. . . 24
2.11 3D CAD of the power transformer, used for comparison purposes. . . 24
2.12 Final geometric model. . . 25
2.13 Oil direction on inlet surfaces. . . 25
3.1 Simple 5mm mesh. . . 27
3.2 5mm mesh with inflation. . . 28
3.3 5mm mesh with inflation. . . 28
3.4 Model’s 3D 5mm mesh. . . 29
3.5 Model’s 3D mesh. . . 30
3.6 Model’s 3D mesh showing inflation layers. . . 30
3.7 Core plate’s temperature profile. . . 33
3.8 Oil temperature in contact with core plate. . . 35
3.9 Oil velocity across the core plate. . . 36
3.10 Velocity streamlines of the entire model. . . 37
3.11 Oil pressure across the core plate. . . 38
3.12 Side profile of pressure levels of the entire model. . . 39
3.13 Simplified initial model. . . 39
3.14 Top view of the new mesh. . . 40
4.1 Fiber optic sensor placement. . . 42
List of Tables
1.1 Four letter code to identify a transformer’s cooling state. (IEC,2011) . . . 7
2.1 Dimensions of magnetic core and core plate. . . 17
2.2 Properties of the relevant solid materials. . . 17
3.1 Results of simulations for the simplified model. Temperatures in Celsius. . . 29
3.2 Solution methods in Ansys Fluent settings . . . . 31
3.3 Courant number and relaxation factors in Ansys Fluent settings . . . . 31
3.4 Results of both simulations. Temperatures in Celsius . . . 32
4.1 Comparison between experiment, complete model and simplified model . . . 42
Nomenclature
Aht Area of heat transfer [m2]
cp Specific heat at constant pressure [J/(Kg.K)]
Dh Hydraulic diameter [m]
h Convective heat transfer coefficient [W /(m2.K)]
havg Average heat transfer coefficient [W /(m2.K)]
K Thermal conductivity [W /(m.K)] Ke f f Effective conductivity [W /(m.K)] Gr Grashoff number [−] Nu Nusselt number [−] R Thermal resistance [K/(W )] Ra Rayleigh number [−] Re Reynolds number [−] Sh Heat source [J] T Temperature [C] V Velocity [m/s] Greek α Thermal diffusivity [m2/s]
β Coefficient of volumetric thermal expansion [K−1]
κ Turbulent kinetic energy [m2/s2]
Gκ Generation of turbulent kinetic energy [m2/s2]
µ Dynamic viscosity [Pa.s)]
ν Kinematic viscosity [m2.s]
ρ Density [Kg/m3]
ε Turbulent kinetic energy dissipation rate [J/(Kg.K)] σκ Turbulent Prandtl number for kinetic energy [−]
σε Turbulent Prandtl number for dissipation rate [−]
Acronyms
2D Two Dimensional
3D Three Dimensional
CFD Computational Fluid Dynamics
OD Directed Oil
ON Natural Oil
HV High Voltage
LV Low Voltage
PT Power Transformer
R&D Research and Development
T HNM Thermal Hydraulic Network Model
Chapter 1
Introduction
This work aims to do a numerical investigation of the thermal behaviour of core plates in core type power transformers. Because they are subject to continuous heat generation, a cooling strategy must be developed.
This investigation is justified because core plates act as heat sources, so studying their ther-mal behaviour allows for the development of better cooling strategies, increasing efficiency and maximising heat transfer, which will impact the lifespan of the equipment.
In this thesis, a computational fluid dynamics (CFD) study using Ansys software is made with emphasis on the core plate, a structural component, predicting its thermal gradients. After this study the results are presented and compared to experimental data. Heat transfer coefficients for the core plates are extracted and then utilised to calibrate existing, specialised software tools, property of Efacec.
During the development of this work, a decision was made to collaborate with Efacec’s R&D engineer and PhD student Luis Braña. Braña’s expertise was extremely helpful to understand the losses phenomenon and how to determine them, providing the necessary values, and the acquired modeling skills during this work were useful for his CFD course, in which the simplified model mentioned in section2.4.2was used.
1.1 Efacec
Efacec is a Portuguese company whose history dates back to 1905, with the foundation of "A Moderna". In 1921, the now called "Electro-Moderna, Lda." had operations in the electrical field, cultivating the necessary skills to support the beginning of the Efacec brand, when "EFME - Empresa Fabril de Máquinas Eléctricas, SARL" was founded, in 1948. "ACEC-Ateliers de Constructions Électriques de Charleroi" would eventually become the largest shareholder of the group, consequently named in 1962, "EFACEC-Empresa Fabril de Máquinas Elétricas, SARL", before later selling its stake on the company.
2 Introduction Since the sixties, Efacec started restructuring processes and expanded its international presence. Nowadays, the company is present in over 65 countries, with business activity in the five continents and a focus on exportations, thus becoming one of the biggest Portuguese’s companies.
The group’s three main fields of operations are mobility, systems and power solutions, being in part powered by its more than 200 R&D employees. Within mobility, Efacec offers a full range of charging solutions to charge electrical vehicles, with systems that efficiently use the electrical grid infrastructure. The company’s systems field of operation focuses on energy, environment & industry, and transportation, while it’s power solutions activities are centered in servicing, automation and, between other things, transformers.
Efacec develops and manufactures power and distribution transformers. This work was de-veloped in the Power Transformers Research and Development department at Arroteia, within the Thermal and Fluids team. The team’s main work is centered around the thermal behaviour of the biggest heat generators inside power transformers; their windings, as well as developing appropriate cooling strategies with all components in mind.
Regarding power transformers, Efacec produces Core and Shell types, with different construc-tive aspects. Core type transformers have a vertical core arrangement, with approximately circular cross section. Their concentric windings are made up from cylindrical copper coils of small width and large surface, and insulation is guaranteed by pressboard and the oil itself (Efacec,2019).
“Empowering the future.”
1.2 Power transformers
Figure 1.1: Example of a power transformer.
Power transformers are static devices mainly used in a power grid to change voltage levels between circuits. As the power transformer gets energised, an alternating magnetic flux is gen-erated in the core, and by virtue of electromagnetic induction the current is transferred between windings at different voltages. This process has been the working principle of power transformers, with continuous work being done to improve and meet energy efficiency targets, reduce space requirements and manufacturing costs.
Transformers are the answer to economic viability of power transmission across long distances. After the development of reliable commercial transformers, power transmission did not require thick wires, and could be done even over long distances with lower losses than the direct current
1.2 Power transformers 3
(DC) based alternative. As shown in equations1.5and1.6, the rise in voltage level increases the efficiency of transfer of electrical power (Del Vecchio et al.,2017). Power transformers are then needed to change voltage levels to values compatible with the needs of end users.
Pip= Viv× I (1.1)
Where Piprepresents input power, V is input voltage and I is line current. Let’s assume that Vivand
I are in phase, which means real quantities.
R= ρ ×L
A (1.2)
Where R is resistance, ρ is electrical resistivity, L is line length and A is cross-sectional area.
Ptl= I2× R (1.3)
Where Ptl is the thermal loss, as described by the joule effect.
Vvd= I × R (1.4)
Where Vvd is voltage drop.
Dividing the thermal loss by the input power and the Voltage drop by the input voltage we get Thermal Loss Input Power = P× R V2 (1.5) and respectively, Voltage drop Input voltage= P× R V2 (1.6)
An ideal power transformer would have the same input and output power, respecting equation
1.1and only changing current levels in order to obtain the desired increase (step-up) or decrease (step-down) in voltage. Different final voltages can be achieved with tap-changers, providing extra versatility to the equipment. Since transformers have efficiency greater than 99% (Mora,2002), power may seen to barely change between input and output. However, since they work at great power levels1, these losses are significant, ranging from transmission losses in conductors, iron
losses thanks to the change in magnetic flux, and eddy losses in the tank walls and other metallic structures. All of these losses originate an increase in temperature inside the power transformer (Pavlik et al., 1993), which has an immediate financial impact and also affects mechanical and electric properties of different materials, negatively affecting its lifespan. As such, knowing at what temperatures power transformers should work is critical.
4 Introduction 1.2.1 Main components
Power transformers can be classified based on their structure. This work is focused on transform-ers with a magnetic circuit with approximately circular cross section, and vertically positioned laminated steel sheets. The mentioned structure is referred to as core type. Other characteristics include concentric windings formed by cylindrical coils with radial height of up to 100mm, and large surface. The tightening structure is designed in such way that it allows support for short circuit stresses while also aiding maintenance and transportation.
The main components of power transformers with regards to this work are:
• Magnetic Core — Approximately circular cross section and made from laminated steel sheets. Offers a continuous path to magnetic circuit flow, not letting the magnetic field disperse. In conjunction with windings, it forms the active part. A 3D drawing of a magnetic core is shown in figure1.2.
Figure 1.2: 3D drawing of a magnetic core.
As a consequence of its function the magnetic core must have a low magnetic reluctance in order to conduct the magnetic flux and a high electrical resistance to eddy losses. By changing the magnetic field in the conductor, loops of electrical current are induced, which causes heat and decreases the efficiency of the transformer. These Eddy Losses are responsible for 50% of core losses(Glotic et al.,2016). An increase in temperature could cause thermal energy to compete with the alignment and saturation energy of magnetisation of the core, with the saturation of magnetisation starting to fall until Curie’s point is reached and ferromagnetic properties disappear (Kulkarni and Khaparde,2016). Since the magnetic core does not reach temperatures above 140 Celsius, so the oil does not degrade, these effects can be ignored (Girgis et al., 2002). In most cases the difference between the core interior and surface temperatures is 20ºC (Kulkarni and Khaparde,2016).
1.2 Power transformers 5
In order to reduce unwanted losses, the magnetic core is usually ferromagnetic. The construc-tion itself is based on layers of thin, laminated sheets, insulated from each other with varnish or an oxide layer, with typical thickness range between 0.18 − 0.3mm and variable width. A cost saving measure includes forming steps with a number of equally sized laminated sheets instead of creating a perfectly circular cross section. The grain-oriented direction provides better magnetic permeability, and silicon makes the grain-orienting process easier, while increasing the resistivity of the steel. However, due to risk of increased brittleness, the material is usually made of only 3% silicon.
Other material options include iron-nickel alloys, that are used in high frequency scenarios, and amorphous materials, with low losses but expensive and brittle (Balci et al.,2017). High frequency scenarios might allow for smaller component sizes with lower losses (Hurley et al.,
1998).
Magnetic domains can be reticent in changing direction as the external magnetic field changes, and domain orientation in iron needs energy. This process causes what is known as hysteresis losses. The hysteresis cycle of steel is shown in figure1.3.
Figure 1.3: Hysteresis cycle of steel.
• Tightening structure — Also made from steel, allows support for possible stresses that the power transformer might face, while also aiding maintenance and pressing the core’s laminated steel sheets together. It is comprised by core plates and brackets and, in conjunction with some cardboard items, a 3D drawing is shared in figure1.4. These components are usually made of construction steel.
6 Introduction
Figure 1.4: 3D drawing of tightening structure around the magnetic core.
The tightening structure keeps these laminated sheets pressed together, so there is no space for movement during transportation or mechanical stresses due to high currents in windings. This could lead to partial discharges or short circuits and other losses, that would also generate heat.
• Phase — Comprises the windings and the rest of the electrical circuit. The specific power transformer used in this work is three-phase, with each phase having a high voltage (HV) and low voltage (LV) copper windings. 3D drawings are shown in figure1.5.
Figure 1.5: 3D drawing of phases attached to tightening structure and magnetic core. Each of the three phases has a pair of windings, the main conductors of the power transformer. In core-type transformers, the pair of windings is concentric, with the primary winding being the one where the feed is made, and the other being secondary. They are usually made from
1.2 Power transformers 7
copper discs, since copper has high conductivity and ductility, and the insulation is done by wrapping each disc and each winding in paper, a dielectric insulator. Channels between each disc and each winding allow fluid to flow through and act both as coolant and as insulator. There might be necessary to use washers in order to guarantee an uniform radial distribution of oil, so the average and maximum temperatures of copper discs are lowered. It’s widely common for the biggest losses and higher temperatures to happen in the first few and last few discs of a particular winding (Torriano et al.,2018).
• Cooling system — Internal cooling is done with the insulator fluid. The oil and possible air circulation can be forced or can be driven by buoyancy forces.
There are different cooling states used for the refrigeration of liquid-immersed power trans-formers, identified by a four letter code. the first two letters refer to the internal fluid and its circulation mechanism, while the last two letters are defined by the external cooling medium and its circulation mechanism, respectively, as shown in table1.1(IEC,2011).
Table 1.1: Four letter code to identify a transformer’s cooling state. (IEC,2011) Order Letter Meaning
First O Mineral oil or synthetic insulating liquid with fire point less or equal to 300ºC.
K Insulating liquid with fire point over 300ºC. L Insulating liquid with no measurable fire point. Second N Natural thermosiphon flow through cooling
equip-ment and in windings.
F Forced circulation through cooling equipment, ther-mosiphon flow in windings.
D Forced circulation through cooling equipment, di-rected from the cooling equipment into at least the main windings.
Third A Air
W Water
Fourth N Natural convection.
F Forced circulation (fans or pumps).
Besides providing better cooling capability than air, another reason to prefer oil as a cooling medium on transformers operating at higher voltages, is related with its capabilities as an electrical insulator, which are fundamental to prevent electrical discharges and other issues. Due to the low biodegradability of the standard mineral oil, there is an increasing need in finding alternatives with similar properties but biodegradable, like esters (Delgado et al.,
2013). High temperatures might also cause the oil to release gas. This gas can compromise some oil properties, like its ability to function as an insulator and, consequently, cause electrical discharges (Wang et al.,2007). Static can also be an issue. With an increase in
8 Introduction temperature, oil becomes charged and potentially charged, specially when in contact with rough surfaces or on a turbulent regimen. As such, it’s advised to reduce the oil flow rate during the heating process to avoid static related issues (Del Vecchio et al.,2017).
ONAN based systems are preferred. Oil circulates through radiators or coolers and exchanges heat with the external environment. Air is cheaper than water as an external medium, and since while operating in ONAN regimen there are not any moving components (like fans and pumps), reliability and efficiency are high. Usually natural convection is sufficient. Other cooling regimens, like ODAF, have advantages since with the use of wafers oil can be directed to otherwise hard to reach places, and increase thermal exchanges. Nevertheless, ODAF comes at a cost of increased local losses (Kim et al.,2013).
• Tank — Usually made of construction steel, protects all previously mentioned components. The core and windings are completely immersed in the tank, which also mitigates fire risks in case of malfunction and protects the oil from oxidation. Variations in oil volume due to variations in temperature must be accounted for, so a conservator tank is necessary.
• Exterior components — Some exterior components can be found in power transformers, like a conservator tank, which aids with the expansion of oil, and external radiators and fans, which aid the cooling. Bushings transmit the electric power in and out of the tank.
1.2.1.1 Core plates
This work is focused on structural components, namely core plates. Their relative position and geometry are shared in figure1.6. Between core plates and the magnetic core, there is pressboard, an insulating component. Around these components there are copper windings (orange colour).
During the normal operation of the power transformer, core plates act as heat sources due to eddy current losses, as seen in figure1.7. These losses have origin from the alternated magnetic flux that jumps from windings and end up impacting core plates, as seen in figure1.8.
In order to determine these ohmic losses, it’s necessary to know the effective current value, Irms. This process can be accomplished with the use of software that applies the finite element
method (FEM) and Maxwell’s equations to solve the current field, thus being able to calculate losses (Yan et al.,2015).
1.3 Numerical methods
1.3.1 Computational Fluid Dynamics
CFD provides an increasingly important approach to understand physical events such as fluid flow and heat transfer behaviour in geometries of interest. Regarding power transformers, windings have traditionally been the main focus of interest for these studies (Khandan et al.,2017).
1.3 Numerical methods 9
Figure 1.6: Core plate position.
The numerical methods applied in CFD involve the solving of partial differential equations that define flow, the Navier-Stokes equations for momentum, and the principles of mass and energy conservation (Torriano et al.,2018). CFD provides more detail regarding pressure, velocity and temperature, but is computationally more demanding and more expensive than other methods, such as thermal hydraulic network models (THNM) (Campelo et al.,2016). As a consequence, CFD is still necessary due to the shear complexity of these problems, but is preferred as a validation method or as an option to extract correlations for coefficients, like heat transfer coefficients or minor and major losses coefficients (Lomax et al.,2013).
The core’s thermal distribution can be a complex 3D problem due to the anisotropic properties of the material and uneven heat generation. In cases like this, CFD becomes a valuable tool (Kulkarni and Khaparde,2016). It’s possible to do CFD simulations and to obtain the convective coefficients. The finite element model has been successfully used when dealing with anisotropic materials and complex geometries (Tsili et al.,2012).
10 Introduction
Figure 1.7: Induced current in core plate.
In order to avoid result deviations, parameters like stability and convergence must be taken into consideration, otherwise the obtained results might not be realistic (Lomax et al.,2013).
1.3.2 Thermal Hydraulic Network Models
Thermal Hydraulic Network Models (THNMs) are an alternative to CFD that can use empirical and analytic expressions to calculate flux losses and convection coefficients. They use the same principles as CFD except the analysis is based on average values, which might result on less detailed, but faster to obtain, results (Campelo et al.,2016).
Hybrid solutions are flexible and fast (Tsili et al.,2009).
1.4 Structure and Organisation
This work is divided in 5 chapters.
Chapter1contextualises the scope of this thesis and presents Efacec. A typical core type power transformer is detailed, with explanations regarding the functions of relevant components to the understanding of this work, followed by a literature review on cooling power transformers.
In chapter2, the studied problem and the methodology used to perform and formulate CFD simulations are described, with details regarding the partnership with Efacec’s Luís Braña.
Chapter3includes the results and relevant data obtained from the simulations.
Chapter4presents the results analysis. A comparison is made with experimental data. In chapter5 the conclusion is presented, with a reflection of what was achieved, while in6
1.4 Structure and Organisation 11
Chapter 2
Methodology
For this work the chosen CFD tool was Ansys Fluent, a commercial code that focuses on the analyses of fluid flow with heat transfer. The mathematical models that rule physical events are partial differential equations. These equations are solved by Ansys Fluent by using the finite volumes method.
2.1 Formulation for heat transfer
Ansys Fluent uses the energy equation for determining heat transfer, as seen in equation2.1. ∂ ∂ t(ρE) + ∇[~v(ρE + ρ)] = ∇ " κe f f∇T −
∑
j hj − → Jj+ (τe f fv) # + Sh (2.1)Where E is defined by the equation2.2, E= h −p
ρ + v2
2 (2.2)
κe f f is the effective conductivity and the three first terms of the right side of the equation
represent heat transfer by conduction, diffusion and viscous dissipation, respectively. For the solid regions, as shown in equation2.3:
∂
∂ t(ρh) + ∇[~v(ρh)] = ∇(κ∇T ) + Sh (2.3) Where ρ is density, h is sensitive entalpy, κ is thermal conductivity and Shis volumetric heat
source.
For natural convection, Ansys Fluent relates Grashoff and Reynolds as shown in equation2.4: Gr
Re2 =
gβ ∆T L
v2 (2.4)
14 Methodology If this relation is close to or bigger than 1, buoyancy forces play a determinant role, that can be measured by the Rayleigh number, as shown in equation2.5.
Ra=gβ ∆T L
3ρ
µ α (2.5)
Where β is the thermal expansion coefficient and can be determined by equation2.6. β = −1 ρ ∂ ρ ∂ T p (2.6) And α is the thermal diffusivity, as determined by equation2.7.
α = κ
ρCp (2.7)
2.2 Formulation for turbulent flow
For an incompressible fluid, like mineral oil, the principle of mass conservation is given by equation
2.8.
∂ ρ
∂ t + ∇ · (ρU) = 0 (2.8)
Equation2.9verifies momentum conservation. The right side terms are pressure forces, viscous forces and buoyancy forces, respectively. Buoyancy forces are related with fluid density gradients.
∂ (ρU )
∂ t + ∇ · (ρU ×U) = −∇p + µ ∇
2U + g (ρ − ρ
re f) (2.9)
In this work it was used the κ − ε Standard turbulence model (Anderson et al.,2016). This is a semi-empiric model that is based on the model of transport equations for the kinetic turbulence energy(κ) and its dissipation rate (ε). In this model the fluid is treated as completely turbulent and the effects of molecular viscosity aren’t considered.
Utilising the transport equations2.10and2.11it’s possible to determine κ and ε. ∂ ∂ t(ρκ) + ∂ ∂ xi (ρκui) = ∂ ∂ xj µ + µt σκ ∂ κ ∂ xj + Gκ− ρε + sκ (2.10) ∂ ∂ t(ρε) + ∂ ∂ xi(ρεui) = ∂ ∂ xj h µ +µσt s ∂ ε ∂ xj i +C1sκε + (Gx+C3sGb) −C2sρε 2 κ + ss (2.11) C1ε, C2ε and C3ε are constants, σκ and σε are turbulent Prandtl numbers. All of their values were determined experimentally (Launder and Spalding, 1972): C1ε = 1.44; C2ε = 1.92; and
C3ε = 0.09; σκ= 1;σε = 1.3.
The term Gκrepresents the production of turbulence kinetic energy due to the average speed
gradient and can be determined with the equation2.12. Gκ= −ρu0ıu0j
∂ uj
2.2 Formulation for turbulent flow 15
The turbulent viscosity, µt is the result of the equation2.13.
µt = ρCµ
κ2
ε (2.13)
The calculations were based on the turbulence intensity, I, the hydraulic diameter DH and the
Reynolds number, Re, given by equations2.14,2.15and2.16, respectively. I= 0, 16 (ReDH) −1 8 (2.14) DH= 4A P (2.15) Re= ρ vDH µ (2.16)
The application of the turbulence model was deemed necessary because there are zones within the simulated model where the flow isn’t laminar. By applying the equation2.16 to the outlet zone of the model referenced in section2.4.4, where experimental data is available for velocity, temperature and, consequently, fluid properties, it’s possible to quickly estimate the Reynolds’s number:
1. Velocity v = 0.18m/s, obtained through experimental data;
2. Density ρ = 860Kg/m3and dynamic viscosity µ = 0.0055Pa.s for the fluid, both obtained
through the manufacturer’s data at outlet’s temperature of 328K, measured experimentally; 3. The outlet’s diameter D = 0.1m;
4. Thus, Re = 2814. The maximum Reynolds’s value for internal laminar flow is ≈ 2100. However, the heat transfer phenomenon doesn’t occur at the model’s outlet, but rather inside the core plate’s channel. With simulation data, it became possible to calculate Reynolds’s number inside the channel:
1. Perimeter P = 1.522m and the channel section area A ≈ 0.016m2, obtained through Ansys
Spaceclaim for the considered geometry;
2. The hydraulic diameter DH= 0.042m, obtained through equation2.15;
3. Density ρ = 860Kg/m3and dynamic viscosity µ = 0.0055Pa.s for the fluid, both obtained
for the same temperature of ≈ 328K. The temperature was determined as average area weighted for the channel’s section;
4. Velocity v = 0.0075m/s, directly obtained with CFD-Post for the channel’s section; 5. Thus, Re = 46.35.
16 Methodology The obtained Reynolds’s number proves that the flow inside the channel is laminar. Consequently, there’s a need to later redo the simulation without considering the effects of turbulence.
For a more detailed description of the mathematical model, the Ansys Fluent software manual should be consulted (ANSYS,2016).
2.3 Transformer data
For this study an experimental 15MVA ODAF Core-Type Three-Phase Power Transformer was selected. It was manufactured and tested at Efacec’s labs, with 50Hz frequency. The experimental transformer is equipped with a dedicated monitoring system to gather different parameters: the total oil flow rate of each winding is measured with independent flowmeters, the respective oil temperatures, bottom and top, are measured with RTD sensors, the average temperature of the windings are measured through winding resistance tests, and local winding temperatures are measured through seventy-two fiber optic sensors.
2.3.1 Dimensions
The most relevant dimensions are presented on figure2.1and table2.1.
Figure 2.1: Dimensions of magnetic core and core plate.
2.3.2 Material properties
The selected geometry has four main different materials: mineral oil, magnetic steel sheets, construction steel and insulation cardboard. In this study, the properties of solid materials are considered constant, while properties of the selected mineral oil, Nytro Taurus, are temperature dependent. Natural convection implies a variation of oil density with temperature.
2.3 Transformer data 17
Table 2.1: Dimensions of magnetic core and core plate.
Name Value (mm)
Diameter of magnetic core 420
Window height 1491
Window width 1190
Core plate height 2087
Core plate width 128
Core plate thickness 6
Table 2.2 shows the properties of the solid materials. Since the insulation pressboard has a thermal conductivity of just 0.08W/m.K, it can be considered adiabatic, which simplifies the geometry.
Table 2.2: Properties of the relevant solid materials.
Material Density Kg/m3 Thermal conductivity W/m.K Specific heat J/Kg.K
Magnetic sheets 7700 40 486
Construction steel 7850 52 460
Insulation pressboard 7150 0.08 5450
The selected mineral oil’s properties are directly acquired from the manufacturer’s catalogue. Figure2.2shows the oil’s properties in function of temperature. The results are then approximated to polynomial or exponential expressions and interpreted in Ansys Fluent as user defined functions (UDF). (Fluent,2013)
ρ = 1065.801 − 0.6585 × T (2.17)
Where ρ is the mineral’s oil density, and T its temperature.
κ = 0.1562308 − 8 × 10−5× T (2.18)
Where κ is the mineral’s oil conductivity, and T its temperature.
µ = 0.0379 × e−0.034T (2.19)
Where µ is the mineral’s oil dynamic viscosity, and T its temperature.
Cp= 3.455T + 1796.2 (2.20)
18 Methodology
Figure 2.2: Properties of the selected mineral oil in function of temperature.
2.3.3 Core plate losses
The determination of core plate losses was made by doing an electromagnetic simulation in Ansys
Maxwell, a commercial software habitually used by Efacec and part of the Ansys suite. The utilised
currents were 466Armsand 2638Armsfor high voltage and low voltage tests, respectively.
The results were exported to a spreadsheet in Microsoft Excel, and a graph was created detailing the losses along the core plate’s height, as shown in figure2.3. The highest losses are at the beginning and at the end of windings, as expected.
After studying how to create an UDF detailing heat sources, a .c file was created and inserted in Ansys Fluent as an interpreted UDF, with losses per height interval. The total loss per core plate is 566W.
Next, an UDF snippet is presented. The origin of the referential is exactly at half height of core plates. Their height is in the Y axis. The source’s units are W/m3.
Listing 2.1: UDF snippet of core plate losses DEFINE_SOURCE( h e a t _ s o u r _ u , c e l l , t h r e a d , ds , eqn ) {
/∗ D e f i n e s s o u r c e term
i n f u n c t i o n o f e l e m e n t ’ s c e n t r o i d c o o r d i n a t e s . coor_X =x [ 0 ] , coor_y =x [ 2 ] , coor_z =x [3 ] ∗/
r e a l x [ 2 ] ; r e a l s o u r ;
2.4 Geometry 19 i f ( x [ 2 ] >= −1.0435 && x [ 2 ] < −1.041413) s o u r = 1 6 5 . 6 2 9 1 8 9 ; i f ( x [ 2 ] >= −1.041413 && x [ 2 ] < −1.039326) s o u r = 1 6 4 . 6 7 4 1 2 6 ; i f ( x [ 2 ] >= −1.039326 && x [ 2 ] < −1.037239) s o u r = 1 6 1 . 5 0 7 3 8 9 ; i f ( x [ 2 ] >= −1.037239 && x [ 2 ] < −1.035152) s o u r = 1 5 7 . 0 7 0 7 8 0 ; . i f ( x [ 2 ] >= −0.002087 && x [ 2 ] < 0) s o u r = 2 0 8 . 3 3 7 6 4 5 ; i f ( x [ 2 ] >= 0 && x [ 2 ] < 0 . 0 0 2 0 8 6 ) s o u r = 1 8 7 . 8 1 3 1 1 7 ; . i f ( x [ 2 ] >= 1.037239 && x [ 2 ] < 1 . 0 3 9 3 2 6 ) s o u r = 1 6 . 8 1 5 3 6 5 ; i f ( x [ 2 ] >= 1.039326 && x [ 2 ] < 1 . 0 4 1 4 1 ) s o u r = 1 6 . 8 4 4 1 5 0 ; i f ( x [ 2 ] >= 1.041413 && x [ 2 ] <= 1 . 0 4 3 5 ) s o u r = 1 7 . 0 4 0 1 1 7 ; return s o u r ; }
Figure 2.3: Losses of core plate along its height axis.
2.4 Geometry
2.4.1 Geometry considerations
All geometries and characteristics that were deemed irrelevant from a heat transfer point of view were simplified. The model is comprised by the magnetic core, tightening structure, phases,
20 Methodology mineral oil and the tank and was made from the ground up in Ansys Spaceclaim, a CAD software from the Ansys suite.
In order to obtain a conformal mesh with shared topology, initial models had to be structured by breaking the geometry at each intersection with other bodies. This approach allows a lot of control over the mesh and results in hexahedral mesh elements, that can provide better results, but are computationally expensive when generating the mesh (Wang et al.,2004).
2.4.2 Simplified model
Initially, the target geometry for the model was supposed to be as shown in figure2.4. This would avoid an exaggerated computational cost with potential issues, and would allow a comprehensive and properly representative study of the thermal behaviour of core plates since it would take advantage of symmetry planes. It includes a leg of the magnetic core, the core plate, the insulating pressboard with adiabatic properties and all components are surrounded by mineral oil.
Figure 2.4: Initial target geometry.
The initial model is shown in figure2.5. The structured geometry allows the generation of a highly hexahedral mesh. However, due to a recent change in the internal oil distribution system, which is responsible for efficiently distributing oil within the tank, it became hard to predict the boundary conditions to apply to this simplified model. Values could be assumed, but a comparison
2.4 Geometry 21
with laboratory tests would become irrelevant. Consequently, a decision was made to collaborate with Efacec’s R&D engineer and PhD student Luis Braña, as mentioned in chapter1.
Figure 2.5: Simplified model.
2.4.3 New target geometry
The new target geometry has increased complexity. Approximations were made so the power transformer was considered symmetric. Since the goal became to take the whole fluid flow inside the power transformer into consideration, together with all solid bodies that generate heat (magnetic shunts, the tank, magnetic core, core plates and the rest of the tightening structure.), the complexity of new models grew exponentially. The new target geometry corresponds to one fourth of the power transformer.
Figure2.6shows the structured new model, with over fifty thousand bodies. Figure2.7shows the model without the oil, while figure2.8shows only the oil. The new inlet and outlets are visible. The elements that don’t generate heat are shown in2.9and can be considered irrelevant and don’t need to be sent for the mesher and solver softwares. Figure2.11shows a 3D CAD of the entire power transformer for comparison.
The sheer complexity of this model made the previous approach of breaking the geometry impossible to follow. Mesh generation, even when grouping the bodies into different components and not using shared topology, could take days, while using various processor cores. Structuring the geometry in a way that the generated mesh was conformal and with good quality was also an increasingly difficult task with each new body.
The global dimensions of the model also meant that refined meshes would have a prohibitive number of elements.
This whole approach continued for two months, and no simulation was successfully concluded, since Ansys Fluent would present a number of errors and other problems.
22 Methodology
Figure 2.6: New model.
Figure 2.7: New model without the fluid.
2.4.4 Final geometry
The problems that were faced with previous models opened the door for a different approach. After studying new methods it was concluded that, while the previous method of breaking and structure the geometry in order to get a good quality, hexahedral, mesh can work well for simpler models, the time and complexity it demands for more complex models is inefficient, since modern CFD software and computing hardware are lot more robust and sophisticated than they were years ago (Wang et al.,2004). By embracing tetrahedral mesh, enabling shared topology and post processing tools of Ansys Fluent, it is not necessary to break and structure the geometry to guarantee a conformal mesh and analyse areas of interest.
2.4 Geometry 23
Figure 2.8: New model with just the fluid.
Figure 2.9: New model with just the adiabatic parts.
Also, it was decided that since losses generated by other components besides the core plate were almost insignificant, only the core plate and mineral oil should be sent to Ansys Meshing and
Ansys Fluent. This consideration also affects the simplified model.
The end result of these simplifications is a much simpler geometric model, with only three bodies, as shown in figure2.12.
The model’s inlet is seen as surfaces on the fluid. They actually represent the fluid exits from the phase, that is omitted, into the tank. The real inlets of the power transformer aren’t represented. The outlets are longer tubes in order to avoid the phenomenon of reverse flow in CFD simulations. There are two symmetry axis, along the y and x directions, which represents the real physics
24 Methodology
Figure 2.10: New model without the tank and fluid.
Figure 2.11: 3D CAD of the power transformer, used for comparison purposes.
2.4 Geometry 25
Figure 2.12: Final geometric model.
Chapter 3
Results
As mentioned in chapter2, the selected domain is equivalent to one fourth of the power transformer. Only internal fluid and core plates are studied. Since the thermal behaviour of the transformer is largely driven by conductive and convective heat transfer, the effects as radiation as a heat transfer medium were not studied, as to lower the computational demand. Contact thermal resistances are also ignored.
3.1 Mesh independence study
Regarding element size, a mesh independence study was carried to determine what combination of element size and inflation techniques would provide accurate results without excessive use of computational resources. A coarse mesh might allow convergence and a solution, but results might not be realistic. On the other hand, an extremely refined mesh might provide precise results, but resource usage might be prohibitive.
Three mesh groups were selected:
• Elementary mesh with basic controls - Element sizes were 5mm, 2.5mm and 1.25mm.
Figure 3.1: Simple 5mm mesh.
• Mesh with inflation controls - Same three element sizes but with inflation controls. 27
28 Results
Figure 3.2: 5mm mesh with inflation.
• Even more refined mesh - Same three element sizes.
Figure 3.3: 5mm mesh with inflation.
Four results were needed for the mesh independence test: the average and maximum tempera-tures at the surface of the core plate, and the average and maximum temperatempera-tures at the volume of the same element. The simulation was validated by experimental testing. The results are shown on table3.1.
By analysing the simplified model’s results, it’s possible to conclude that there is a convergence tendency, and that coercer meshes with inflation techniques provide a good compromise of lower computational cost and good quality results.
3.2 Mesh 29
Table 3.1: Results of simulations for the simplified model. Temperatures in Celsius.
Type Name Tout Volume Tavg Volume Tmax Sup. Tavg Sup. Tmax Elements
Basic 5mm 41.7 116.3 280 125.1 279.6 133023 Basic 2.5mm 41.7 88.2 192.3 88.1 191.9 933530 Basic 1.25mm 41.8 71.4 136.2 71.3 135.7 7358020 Inflation 5mm 42.5 69.2 119.2 69.2 119.0 739024 Inflation 2.5mm 42.2 69.1 118.6 69.3 118.4 2186030 Inflation 1.25mm 41.9 68.9 115.6 69.1 115.1 10021670 More Inflation 5mm 44.4 70.0 110.4 69.8 109.8 2779700 More Inflation 2.5mm 44.0 69.8 111.2 69.8 110.6 6436180 More Inflation 1.25mm 43.4 69.6 112.6 69.6 112.6 18700660
3.2 Mesh
Due to the size difference in model volume and the implication on number of mesh elements, the main model will be meshed in Ansys Meshing with two different meshes: A simpler elementary mesh with no special mesh controls, with 5mm elements, and a 4mm mesh with inflation layers to increase element density where heat transfer happens between bodies.
As can be seen in figure3.4, the end result for the 5mm mesh is mostly tetrahedral elements with hexahedral elements on core plates. The final element count was 25 million. It should be noted that solid bodies could in theory have coercer meshes, but the difference in volume compared with the fluid body is so big that it wouldn’t make a relevant difference in the final number of elements.
Figure 3.4: Model’s 3D 5mm mesh.
The model’s 4mm mesh is composed mostly of tetrahedral elements, as can be seen in figure3.5. In this case, the final element count was 44.5 million. Figure3.6shows the inflation layers above the core plate’s surface, which shows hexahedral elements. It’s worth noting that these hexahedral elements connect to tetrahedral elements via pyramidal cells, which could affect overall mesh
30 Results quality. If skewness, orthogonal quality and aspect ratio of elements are deemed unacceptable,
Ansys Fluent won’t be able to solve and converge properly.
In this case, both are good quality meshes.
Figure 3.5: Model’s 3D mesh.
Figure 3.6: Model’s 3D mesh showing inflation layers.
3.3 Setting up Ansys Fluent
After importing each mesh onto Ansys Fluent, the program was set up with the following specifi-cations:
1. Ansys Fluent was set up in double precision, parallel processing with 12 cores; 2. The energy equation was activated in order to analyse heat transfer;
3. Gravity was activated and the value −9.81m/s2was inserted in the relevant Z axis;
4. The standard κ − ε turbulence model with enhanced wall treatment was activated with the default values;
3.3 Setting upAnsys Fluent 31 5. The mineral oil’s properties were set up with the use of an interpreted UDF, as mentioned
in2.3.2;
6. The core plate’s steel constant properties mentioned in table2.2were inserted;
7. As cell zone conditions, both core plates were set up with one heat source that was interpreted via UDF with their loss data, as mentioned in subsection2.3.3;
8. At the inlet, the velocity magnitude is set up to 0.041m/s and temperature is 328K. These values were calculated with data from the experimental task;
9. The outlet was set up as pressure outlet;
10. Residuals were changed from the default values of 10−3to 10−6.
11. The selected solution methods and solutions controls are shown in tables 3.2 and 3.3, respectively.
12. Solution monitors were set up for maximum and average temperatures of core plates, as well heat flux and inlet and outlet flow rates.
13. A hybrid initialisation was done.
Table 3.2: Solution methods in Ansys Fluent settings
Name Option
Pressure-Velocity Coupling Coupled scheme Gradient Least Squares Cell Based
Pressure Second Order
Momentum Second Order Upwind Turbulent Kinetic Energy First Order Upwind Turbulent Dissipation Rate First Order Upwind
Table 3.3: Courant number and relaxation factors in Ansys Fluent settings Name Initial Value Final Value
Courant number 200 20
Momentum 0.5 0.5
Body forces 1 0.8
Turbulent kinetic energy 0.8 0.8 Turbulent dissipation rate 0.8 0.6
Turbulent viscosity 1 1
32 Results
3.4 Results
During the simulation, relaxation factors were altered as needed in order to speed up convergence. The simulation reached residuals of 5 × 10−5 and the previously set up solution monitors were
closely observed. Since residuals were almost constant, and all the monitored parameters also were constant up to four decimal places for more than twenty iterations, the simulation was considered converged and finished.
Table 3.4 shows the final temperature results for the core plate for both simulations. As expected, the more refined mesh with smaller element size and inflation techniques is able to better capture heat transfer between the core plate and the fluid, showing Tmaxvalues up to 11ºC lower.
Only the results of the more refined mesh will be shared from now on.
Table 3.4: Results of both simulations. Temperatures in Celsius
Mesh Elements Volume Tavg Volume Tmax Sup. Tavg Sup. Tmax
5mmsimple 25million 74.16 122.2 74.05 121.75
4mminflation 44.5 million 77.78 110.93 77.77 110.4
3.4.1 Core plate temperature profile
Figure3.7shows the final results of the temperature profile for the core plate. From a qualitative point of view, the results are as expected. Initially, the temperature is the lowest and roughly the same as the inlet temperature of the mineral oil, 328K or 54.85ºC. With the increase in height the temperature increases to close to maximum levels, meeting the first winding disc, before dropping slightly and then increasing to a maximum of 384K or 110.9ºC. This hot spot was expected from literature (Girgis et al.,2002) and the losses profile in figure2.3.
3.4.2 Heat transfer coefficient
By utilising equation 3.1 it’s possible to determine the average heat transfer coefficient, havg=
62.77W /m2K.
Q= havg× Aht× (Tcpavg− Toilavg) (3.1) Where,
• Q is the core plate’s main surface heat flux. By applying Ansys Fluent’s "total heat transfer rate" to the surface of the core plate, it was possible to determine the desired value, 484.222W. As expected, it’s lower than the 566W mentioned in subsection2.3.3, since the side surfaces were not considered.
• Aht is the area of heat transfer, in this case the surface of the core plate, 2.087 × 0.128 =
3.4 Results 33
• Tcpavg is the average temperature of the surface of the core plate, presented in table 3.4,
77.77ºC.
• Toilavg is the average oil temperature. It’s determined by considering the oil temperature obtained experimentally at the real inlet1of the transformer, 42.06ºC, and the outlet
temper-ature, 54.85ºC, also obtained from experimental data.
Figure 3.7: Core plate’s temperature profile.
The gradient used in equation 3.1 corresponds to the thermal potential responsible for heat transfer. However, due to the transformer’s complex geometry, internal gradients are often deter-mined by using the bottom and top oil temperature.
3.4.2.1 Oil temperature profiles
Image3.8 shows the oil temperatures in three different points across the core plate’s height. It’s possible to observe that the temperature of oil in direct contact with the core plate increases with
34 Results the increase in z coordinate, as expected.
3.4.2.2 Pressure and velocity profiles
Image 3.9 shows the velocity of oil in three different points across the core plate’s height. It’s possible to observe that velocity increases only along the surface. The rest of the oil seems to be almost stagnated. Results for overall flow rate were 1.871Kg/s, but only 0.097Kg/s go through the interior channel, at 7.5mm/s where pressure and velocity profiles were measured.
Figure3.10shows the velocity streamlines. As expected, the outlet is where velocity is higher. Image3.11shows how the pressure is lower where velocity is higher, as expected.
Figure3.12shows the side profile of pressure levels. As expected, the lower half of the model shows higher pressure levels, since the oil moves a lot slower.
3.5 Remaking the initial simplified model
As proof of concept, the learned skills during the developing of this study were applied to simplified model.
As shown in figure3.13, the geometry was simplified, only ending with two bodies: half core plate and mineral oil.
For the mesh, and since the model is relatively small and the core plate only occupies a small volume, the general tetrahedral mesh element was set to 6mm, with flexibility, while a body sizing technique with mesh elements measuring 1mm was applied to the core plate. A patch conforming method was utilised and growth rate was set to 1.2. This approach gives the program flexibility, and the final conformal mesh has 11.5 million elements, very good quality, and is refined on the relevant heat transfer area, even the sides. The results can be seen in figure3.14.
The mesh was imported to the solver, with the same configuration and initial values. The solver converged to a solution in less than a hour, without the need to change any default relaxation value or Courant number, and the final results for maximum surface temperature and average surface temperature were lower by 20ºC and 10ºC, respectively, when compared with the previous most refined, 18.7 million element mesh.
3.5 Remaking the initial simplified model 35
36 Results
3.5 Remaking the initial simplified model 37
38 Results
3.5 Remaking the initial simplified model 39
Figure 3.12: Side profile of pressure levels of the entire model.
40 Results
Chapter 4
Analysis
From a qualitative perspective, the model appears to behave physically as expected, with hotter spots in the right places. General heat transfer also seems to be coherent with literature, where a convective coefficient of roughly 100W/m2K is considered a good starting point for core plate
studies in ODAF regimen. However, the studied model behaves more as an ON system, where OD effects aren’t felt by the core plate, and in this case a good suggested value for the convective coefficient is 70W/m2K (Del Vecchio et al., 2017). This suggestion is in agreement with the
obtained havg= 62.77W /m2K.
4.1 Experiment
Fiber optic sensors were strategically placed in what were predicted to be the core plate’s hottest spot, as seen in figure 4.1. The sensor is shaped like a coin and surrounded by pressboard. This should make the form factor of the sensor have an irrelevant impact on oil flow or heat exchange. Measurements were taken during the heat test runs, with the power transformer at thermal equilibrium.
A sensor was placed in three core plates. In total, there’s six measurements for the results to be compared against.
4.2 Comparison and discussion
The final results from this simulation and from experimental data are shown in table 4.1. For experimental data, the range of obtained measurements and the maximum equivalent temperature obtained at the core plate surface from this study are presented. Braña’s equivalent result is also presented.
While a degree of variation was to be expected due to the various simplifications made along this study, the differences between calculated and experimental data still appear to be very significant. While there were attempts to place the sensors on the right place, where temperature is highest, CFD data shows that deviations of 50mm along the core pate’s surface are enough to cause a
42 Analysis
Figure 4.1: Fiber optic sensor placement.
Table 4.1: Comparison between experiment, complete model and simplified model Experimental data Complete model Simplified model
59 - 66ºC 110.4ºC 112.6ºC
temperature drop of 10ºC. After placing the sensors, windings and other equipment still had to be put in place. Moreover, despite its coin-like shape and cardboard protection, it’s possible that the sensor is slightly affected by the coolant oil. This can be significant, since the opening for the fiber optic means that oil is in contact with the sensor, even if it should be stagnated.
Despite a different approach and different models, the end result was similar to another sim-ulation concerning the simplified model, and relevant initial values in the simplified model were carefully obtained from experimental values of past experiences.
Chapter 5
Conclusions
Transformers are vital devices in power grids, and their thermal-hydraulic behaviour directly impacts their lifespan. Some of their components demand CFD analysis, and in this work the thermal behaviour of core plates in core type power transformers was investigated.
The results seem to respect the physics of the model and the temperatures are within functioning range of power transformers. The hot spots are coherent with losses from windings.
The obtained result for average heat transfer coefficient, havg, was 62.77W/m2K. This result
is coherent with literature, with suggested values of 70W/m2K for ON transformers, which the
studied model can be compared to. Temperature result for the core plate’s surface was 110.4ºC, which differs from the 59 − 66ºC range of experimental data. CFD obtained data shows that deviations in sensor placement of 50mm, when compared to the hot spot are enough to cause a temperature drop of 10ºC. This could partially explain the difference between experimental and numerical data and as improvement more sensors across the plate could be used, providing detailed temperature information across more points.
The recent changes in the internal oil distribution system warranted a reformulation of this work´s objectives. The new objectives before simplifications proved to be extremely challenging regarding the modeling of the problem.
CFD provides more detail regarding pressure, velocity and temperature, but is computationally more demanding and more expensive than other methods, such as thermal hydraulic network models (THNM). As a consequence, CFD is still necessary due to the shear complexity of these problems, but is preferred as a validation method or as an option to extract correlations for coefficients, like heat transfer coefficients.
Chapter 6
Future work
In order to improve upon and keep developing this work, new simulations with more refined meshes should be carried out in an attempt to better capture the heat transfer phenomenon between core plate and fluid, which could improve the obtained solution by an unknown margin. Since Reynolds values of ≈ 2800 were only found in the outlet zone, where velocity is highest, the simulation should be redone considering only the effects of laminar flow. The reasoning is that the main area of interest is the core plate’s channel, where heat transfer occurs.
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