Oil filled transformer explosions and their prevention is a complex industrial issue. Experimental tests showed that when an electrical fault occurs in a transformer, it generates dynamic pressure waves that propagate in the oil. Reflections of these waves on the walls build up high static pressure which transformer tanks cannot withstand.

The tank’s ability to withstand this pressure is one of the key parameters in transformer explosion prevention, and a numerical tool was developed to simulate the phenomena highlighted experimentally, especially the pressure wave propagation. Our aim is to complete this numerical tool so that the mechanical behavior of the tank can be accurately studied. The hydrodynamic numerical tool was subsequently coupled with a dynamic structure analysis package: the open source software Code_ASTER. A weak coupling strategy was first developed by applying the simulated pressures to the structure geometry in order to evaluate stresses and deformations. This strategy evolved with the development of a strong coupling strategy which required establishing a moving mesh technique for the hydrodynamic code to accept displacement data from the structure code and complete the exchange between hydrodynamic and structure codes. Our first encouraging results are shown

**I. INTRODUCTION**

**A. APPLICATION FIELD**

Electricity markets have become increasingly competitive over the last few years. To limit costs, electricity companies are often forced to reduce their investments by using aging equipment and by overloading their power transformers. Nevertheless, these transformers are among the most dangerous electrical equipment because of the large quantity of oil they contain in direct contact with high voltage elements. Oil-filled transformer explosions are increasingly frequent. They result in dangerous fires, with expensive damages and possible environmental pollution. Therefore, transformer explosions and their prevention are a critical industrial challenge.

**B. CHRONOLOGY OF THE EVENTS**

When transformer oil loses its dielectric properties (because of age, design errors, oil pollution, overloading, lack of maintenance…) **(1) **electrical arcs can occur inside the transformer tank; **(2) **Oil is then vaporized, and **(3) **the generated gas is quickly pressurized because the liquid inertia prevents its expansion; **(4) **The pressure difference between the gas bubbles and the surrounding liquid oil generates a dynamic pressure peak which propagates and interacts with the tank structure; **(5) **The average pressure in the transformer then rises, and **(6) **the static overpressure leads to the tank explosion and possible fire, resulting in very expensive damages for electricity facilities.

**C. EXPERIMENTS AND MAIN CONCLUSIONS**

Because of the risks such a catastrophic event may represent, many studies have been performed to analyze the explosion process and to propose prevention strategies. A series of experimental campaigns were carried out [10][11][13], most of them involving small size transformers [6][7][8]. More recently internal arcing tests were performed on industrial size oil-filled transformers *(5.3m*x*3.8m*x*2.3m) *fully equipped with their inner structure (windings, magnetic core, etc.).

These tests enabled studying the physical phenomena after the arc appearance as well as the efficiency of a fast-direct- depressurization-based method which is fully described in reference [15]. The test campaign emphasized two points:

**The pressure wave propagation:**The larger scale experiments showed**(1)**pressure increase and variations are not spatially uniform in the tank, and**(2)**pressure waves, generated after the arc appearance, propagate at a finite speed within the liquid oil, progressively interacting with the tank structure;**Tank withstand to high dynamic pressure:**Pressure peaks up to*14 bars (abs.)*were locally experienced during that test campaign. No tank rupture was noticed: due to the quick protection operation the tank was subjected to localized pressure peaks for only a very short period of time. If oil evacuation through a protector set is activated within milliseconds by the first dynamic pressure peak of the shock wave, the transformer avoids explosions before static pressure increases.

**D. NEEDS FOR NUMERICAL SIMULATION TOOLS**

Nevertheless performing such experiments on large transformers is expensive and may be dangerous. Moreover, all physical and all on-site configurations cannot be experimentally tested. In order to easily and efficiently evaluate protection strategies it becomes necessary to study transformer explosions and depressurization technologies using computational simulations.

For this purpose, a complete numerical tool has been developed. This tool can simulate unsteady compressible two- phase flows, allowing for additional physical effects (arc energy influence, viscous, gravity effects) in an unstructured 3D framework which can account for complex transformer geometries. The detailed model is presented in [5].

**E. TANK STRUCTURE INTEGRITY**

The description of the pressure wave interaction with the structure is a challenge. Estimating the inner local overpressure is important to check if the transformer tank walls can withstand the stresses to which they are subjected.

Global evaluation of those stresses was implemented. However, complex transformer geometries combined with 3D unstructured mesh data structures and the level of detail required to describe bolted and welded assemblies led to consideration of more advanced ways to compute the effects of inner pressure waves onto the tank structure.

Simultaneously, the need to more accurately describe external transformer features rose. Indeed, the influence of external reinforcement beams or other specific features might not be negligible in the overall tank dynamic structural behavior and therefore must be included in the modeling.

**F. EMERGENCE OF A NEED FOR IMPROVING TRANSFORMER TANK MECHANICAL BEHAVIOR DESCRIPTION**

All the previous issues may be resolved by the development of a Fluid/Structure Interaction **(FSI) **strategy based on the coupling of an in-house developed hydrodynamic code called HYCTEP (**HY**drodynamic **C**ode for **T**ransformer **E**xplosion **P**revention) with a structure code that will ensure the accurate computation of the stresses and tank wall displacements.

Our aim is to present the first steps undertaken towards this goal. The next section will briefly describe HYCTEP and some requirements providing motivation for the structure code. The Fluid/Structure strategy as well as the different coupling options will then be discussed. Specific problems and their solutions are addressed. Finally, preliminary results will illustrate the abilities of the developed strategy.

**II. IMPLEMENTATION OF THE FSI STRATEGY**

** ****DESCRIPTION OF HYCTEP - ****Mesh Data Structure Creation - GMSH**

Before undertaking any computation with HYCTEP, geometry and mesh must be created with GMSH. This 3D unstructured mesh generator is convenient because **(1) **its use is intuitive and **(2) **it combines the creation of geometry and associated mesh in one tool. More details can be found in [9]. Choosing GMSH to generate HYCTEP data requires the choice of a structure code to be GMSH compatible.

**2. Modeling**

Two-phase flow models used in a compressible framework can be found in the literature, largely in the detonation field where materials are subjected to extreme pressures. Such an approach was first used by Baer & Nunziato [3] who derived the basis of a very general compressible two-phase flow model where every phase has its own pressure and velocity to depict explosions and detonations. Their work was adapted and improved to take into account relaxation terms in order to get back instantaneously to mechanical equilibrium and handle flows with interfaces [17]. Based on that work, an asymptotic analysis was applied to simplify the general model under the assumption that the mechanical equilibrium must be fulfilled instantaneously between phases in contact [12]. This model was further improved to describe flows with gas/liquid interfaces, and proof was given for its ability to accurately describe pressure wave propagation within two-phase flows [1][14]. The model can depict pressure wave propagation inside liquids and gases [1] [14]. Other physical effects (gravity, energy transfers) are accounted for [5]. Each fluid is described by its own Equation Of State **(EOS)**. The Stiffened Gas EOS is used for gases and liquids. The model is closed by an isobaric mixture EOS that enables describing the artificial mixture zones which appear at the smeared interfaces between oil and gas because of the method’s numerical diffusion.

**3. Numerical Method**

A Finite Volume method has been adopted to numerically solve the PDE (Partial Differential Equation) system specified in [5]. Numerical fluxes are evaluated at each cell surface boundary thanks to a Riemann Problem that is solved to determine all flow variables at the surface boundary. The unstructured 3D mesh is made of tetrahedra. Such a description allows for a precise description of complex geometries such as power transformer tanks. Model and method have been thoroughly described in several references [1][14] and their application to the transformer explosion prevention field has been addressed in [5].

**B. CHOICE OF A STRUCTURE CODE**

**Choice of Code_ASTER - ****Brief Presentation**

Code_ASTER development has been initiated by the French national electricity utility, EDF, Electricite de France, and its maintenance involves many high level research laboratories specialized in structure analysis. Code_ASTER is based on a Finite Element method that can describe the mechanical behavior of a structure in different configurations. More information can be found on the official website of the project, including all validation tests [2]. In the following sections Code_ASTER will be referred to as ASTER.

**b) Why ASTER?**

ASTER has been chosen because **(1) **this Open Source GNU Licensed program is actively maintained by laboratories dedicated to structural analysis; **(2) **many validation tests have been carried out; **(3) **dynamic and static computations can be run in both elastic and plastic regimes; **(4) **it can be run by batch file, which ensures that a full automation of the coupling strategy is feasible; **(5) **it is GMSH, and therefore HYCTEP, compatible; and finally **(6) **a similar coupling strategy has already been attempted by EDF when coupling their in-house developed incompressible flow solver, Code_SATURNE, with Code_ASTER [4], and **(7) **ASTER is able to describe bolted assemblies with rigid body elements using hull theory.

**C. FSI COUPLING STRATEGIES**

**Coupling basics - ****Assumptions and ASTER Options**

The width and height of the tank walls are much larger than wall thicknesses. Therefore, instead of describing in detail the transformer tank walls and meshing them, we use hull theory to parameterize ASTER.

The FSI strategy is to evaluate qualitatively and quantitatively the mechanical response of the tank walls when subjected to highly dynamic pressure waves. Time and space evolution of the mechanical stresses and of the local tank walls’ deflections is solved through time-dependent simulations in the elastic-plastic regime.

**b) Problems Faced and Solution Found**

To implement Fluid/Structure Interaction by coupling two different codes, we modified HYCTEP to cope with ASTER requirements, customized ASTER to describe the structure, and created a wrapper that manages the communication between the two programs. Specific problems were addressed:

**· Problems with adapting the fluid simulations**

To account for the external beams on the tank, HYCTEP was modified so that the extra structure-related geometrical elements are accounted for in the data structure but not in the hydrodynamic computation itself; line boundaries were included in the mesh reader to facilitate fixed edge conditions in structure computation. Normal vectors in each point are now extracted to be used while applying pressures. Several subroutines were added or modified to account for mesh displacements.

**· Problems with adapting the structure simulation**

The first issue was to extract the structure geometry from the initial “.geo-format” file that describes the hydrodynamic geometry. The volume mesh is exported to HYCTEP, while the surface mesh is exported to ASTER. This was achieved by defining appropriate physical groups in GMSH while setting up the geometry. The format of ASTER launch file had to be determined without using the built-in user interface. We ensured that the normal vectors to the hull are in the right direction by the direct use of HYCTEP outputs. The management material descriptions for multi-material computation were accounted for by the creation of a repository for material data, allowing users to choose any material or create new materials by entering constitutive constants.

**· Problems with creating the coupling**

The coupling is an automated script that transfers information from HYCTEP and ASTER. The coupling has been designed to use either of two modes of operation. In the one-way coupling, HYCTEP first calculates the pressures which are then supplied to ASTER to calculate the displacements and stresses. The two-way coupling has HYCTEP calculate the pressures which are then supplied to ASTER calculating the displacements and stresses and transferring the displacements back into HYCTEP affecting the next set of pressures by altering the volume. Both coupling modes then repeat this process wherein HYCTEP waits until the end of each ASTER simulation before proceeding.

**c) Automating the Coupling**

We wrote a coupling program to accurately control the tandem timing of the two calculations, and to automate the exchange of physical data.

ASTER calculations are controlled by a command file. Upon launching, ASTER will read the command file, the mesh file, and any other file as instructed. For similar simulations only small changes are needed in the command file and different calculations can be performed. By adopting some conventions in the mesh creation, even if the mesh geometry is quite different, the commands will remain the same. These similarities make it reasonable to automate the changes to the command file, allowing the ASTER calculation to be automated.

The output from HYCTEP of pressures calculated at the exterior element faces are input into ASTER. The ASTER command to set this condition will not accept a list of matched data. It only accepts the same pressure to a group of entries or single entry pressure to single element. Therefore a function was necessary to write the command joining the individual pressures to their respective mesh elements.

Additional functions were added to the command file generation to allow for sectioning of the deformable walls and differing materials. These additions require minimal user input due to assumptions about which mesh groups should be used with each command. These conventions are flexible enough to allow for great variances in geometries.

**2. Weak Coupling Procedure**

The weak coupling strategy uses the pressure data computed by the hydrodynamic code as input mechanical loads onto the structure (see FIGURE 1). The challenge is to set a structure time step, D*t**structure *, for the structure to locally reach its equilibrium state. During this interval, several hydrodynamic iterations are calculated to evaluate the pressure applied onto the inner tank walls; the hydrodynamic time step, D*t**hydro *, is a fraction of the structure time step. After the structure time

step is reached by the hydrodynamic computation, the pressure map is exported from HYCTEP to ASTER where pressure values are used as external mechanical loads. ASTER can then estimate the local mechanical stresses and structure displacements. Rupture criteria are applied to determine if and where the rupture occurs.

**3. Strong Coupling**

**Procedure**

With weak coupling the pressure data extracted from HYCTEP were used to evaluate the mechanical stresses and the structure deformations. With the strong coupling, these deformations are injected back into the hydrodynamic code after the structure computation in order to account for the deformations’ influence on the local pressure (see FIGURE 2).

**b) Modifications Compared to the Weak Coupling**

To achieve a stronger coupling between the hydrodynamic code HYCTEP and the structure code ASTER, we explicitly account for the effects of the mesh displacements on the local pressure values. When a plate or a wall is impacted by a pressure wave the local pressure rises and leads to local deformations of the structure. As the Fluid/Structure Interaction continues, these deformations may induce a very local pressure drop. In order to allow for these effects in HYCTEP, a moving mesh strategy was implemented. The work detailed in [16] that was exclusively developed for the conservative PDEs, has been extended to non conservative sets of equations. As in the conservative case, a flux due to surface boundary velocity is added into the expressions of the conservative fluxes. Time averaged normal vectors to the cell boundary surface are used to evaluate the non conservative terms due to the volume fraction equation. This new framework has then been validated on two-phase shock tubes.

**4. Parallelization**

In addition to the sequential version of HYCTEP, a parallelized version was developed to **(1) **better describe complex transformer geometries, and **(2) **shorten the computation time when accounting for real industrial configurations. The

framework used for the parallel computations has completely been automated from the mesh partition to the simultaneous launch of the structure and hydrodynamic computations on several distant computers.

**III. RESULTS**

**OLTC COMPUTATIONS**

**1. Motivation**

In this study we estimate the influence of reducing the OLTC protection size on the depressurization process. Two OLTC configurations were examined using our weak coupling strategy **(1) **a test where the OLTC is protected with a 6 inch Depressurization Set (DS) with a 5 bar calibrated burst pressure, the ‘standard’ test and **(2) **a test with a reduced diameter (5 inch) for the DS. The stress threshold is 450MPa.

**2. Description**

The arcing conditions used for each of the simulations in this report are the following: (1) Arc location: middle of the tank just off the axis, (2) Arc duration: 90ms, (3) Arc voltage: 20 kV, and (4) Arc current: 12.366 kA.

3**. OLTC Incident Protected with Standard DS Design**

In the following simulation, the OLTC is protected by a 6 inch diameter, 5 bar burst pressure calibrated fastdepressurization system. The arc was activated and leads to the appearance of an internal overpressure. The pressure maps can be seen in FIGURE 4. The protection is fully open by 10 ms and the pressure is already being relieved with average values about 16 bars. The pressure continues to be relieved and then returns to safe pressure levels (below 5 bars) within 29 ms. Stresses concentrate between the bolt holes on the cover of the tank, shown in FIGURE 5.

**4. OLTC Incident with a Reduced DS Cross-Section**

This configuration has been simulated in order to evaluate the effects of reducing the cross-section of the DS by reducing the diameter from the standard 6 inches to 5 inches. FIGURE 6 and FIGURE 7 display the pressure distribution. Due to the reduced size of the DS, the depressurization of the tank takes longer, and the pressures experienced by the tank are higher than in the standard case. Safe pressure levels in the case of the reduced cross section occur only after 38 ms, a 31% increase in the depressurization time. B. LIQUID OIL JET IMPACTING A STEEL PLATE 1. Reasons of Such a Test This test case was considered to verify calculated deformations due to pressures from oil movement. This simulation uses the strong coupling strategy

**Description**

The steel plate is a square two meters on a side that is held fixed along its edges. The plate is defined as a deformable wall section. The inlet condition is set to simulate oil spraying at two hundred meters per second. All other surfaces of the volume used by HYCTEP are set for outlets.

**Results**

The spray onto the plate causes bowed deflection as expected. Oil jet impacts the plate and the high pressure causes a deformation, but as the plate deforms the pressures at the plate are reduced. As the displacements slows the pressure increases again. The final pressures are shown in FIGURE 8. No stress withstand limit was used in this test so the simulation continues to deform the plate well beyond the point of failure of an actual steel plate.

However, this test shows **(1) **the adaptation of the moving mesh strategy to this new set of equations is effective and **(2)**

the advanced communication protocol between the hydrodynamic and structure codes is operational.

**CONCLUSIONS & PERSPECTIVES**

Transformer explosion prevention is an important industrial issue for electricity companies. To understand the phenomena involved and to set up efficient prevention strategies [15] experiments have been carried out. Numerical simulation tools have been developed to study any kind of physical configuration. A hydrodynamic model has been adapted to this new application. This framework allows for the description of liquids and gases as compressible media, which enables accurately describing the propagation of the pressure waves that are generated after the appearance of an electrical arc in the oil.

A need for a better description of the mechanical behavior of 3D complex geometries has risen and a Fluid/Structure Interaction strategy has been developed by coupling the in-house developed compressible two-phase flow hydrodynamic

code, HYCTEP, to the structure analysis code, Code_ASTER. The present paper thus gave an insight into the different problems faced and solved in order to achieve this goal:

- A wrapper manages the inputs, outputs and automatic launch of each program, thus ensuring the communication between them both;
- Local mechanical stress evaluation and local structure displacements are computed such that local mechanical behavior of the structure can be better assessed;
- A moving mesh strategy has also been set in order to account for the influence of mesh displacements computed by ASTER on the local pressure.

The global strategy has been illustrated and tested on several configurations. These first encouraging results show that the procedure is appropriate to deal with more complex industrial problems. We may use this strategy to model transformer arcing events, and means to mitigate tank explosions.

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