David Rochette

Numerical study of the short pre-arcing time in high breaking capacity fuses via an enthalpy formulation

In order to study the short pre-arcing time in high breaking capacity (HBC) fuses, we use a mathematical model including the phase change of the fuse-element heating coupled with the Laplace equation for the potential and Ohms law. The thermal model is based on the enthalpy formulation of the heat equation with a source term representing the Joule heating. For the time range considered (up to 10 ms), we assume no heat transfer between the fuse-element and the surrounding sand. To solve numerically the governing equations, we employ a semi-implicit scheme for time integration and a finite element method for space discretization. Using electrical and thermal properties of the silver fuse-element, we present pre-arcing characteristics (temperature, current density, potential) for a fuse-element used in industrial protection circuits.

First- and second-order finite volume methods for the one-dimensional nonconservative Euler system

Gas flow in porous media with a nonconstant porosity function provides a nonconservative Euler system. We propose a new class of schemes for such a system for the one-dimensional situations based on nonconservative fluxes preserving the steady-state solutions. We derive a second-order scheme using a splitting of the porosity function into a discontinuous and a regular part where the regular part is treated as a source term while the discontinuous part is treated with the nonconservative fluxes. We then present a classification of all the configurations for the Riemann problem solutions. In particularly, we carefully study the resonant situations when two eigenvalues are superposed. Based on the classification, we deal with the inverse Riemann problem and present algorithms to compute the exact solutions. We finally propose new Sod problems to test the schemes for the resonant situations where numerical simulations are performed to compare with the theoretical solutions. The schemes accuracy (first- and second-order) is evaluated comparing with a nontrivial steady-state solution with the numerical approximation and convergence curves are established.

Numerical Investigations on the Pressure Wave Absorption and the Gas Cooling Interacting in a Porous Filter, During an Internal arc Fault in a Medium-Voltage Cell

A mathematical model and a numerical method have been developed to simulate the mechanical and the thermal physical phenomena in a energy absorber like a porous filter, during an internal arc fault in a medium-voltage apparatus. A 1D gas flow model in porous medium with variable porosity is described. The main point is the introduction of a new numerical scheme to take accurately into account discontinuous variations of the porosity and correctly simulate the creation of the transmitted and reflected waves. Numerical simulations are compared to experimental measurements performed on apparatus specially adapted for tests to provide a better understanding of the physical phenomena involved, for instance, the gas cooling and the shock wave absorption by the porous medium of the filter.

A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for axisymmetric swirling flows

A finite volume method for the numerical solution of axisymmetric inviscid swirling flows is presented. The governing equations of the flow are the axisymmetric compressible Euler equations including swirl (or tangential) velocity. A first-order scheme is introduced where the convective fluxes at cell interfaces are evaluated by the Rusanov or the HLLC numerical flux while the geometric source terms are discretizated to provide a well-balanced scheme i.e. the steady-state solutions with null velocity are preserved. Extension to the second-order space approximation using a multislope MUSCL method is then derived. To test the numerical scheme, a stationary solution of the fluid flow following the radial direction has been established with a zero and nonzero tangential velocity. Numerical and exact solutions are compared for classical Riemann problems where we employ different limiters and effectiveness of the multislope MUSCL scheme is demonstrated for strongly shocked axially symmetric flows like in spherical bubble compression problem. Two other tests with axisymmetric geometries are performed: the supersonic flow in a tube with a cone and the axisymmetric blunt body with a free stream.

Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump

A finite volume method based on a VFRoe solver to simulate the flow of compressible gas in a variable porous medium for two-dimensional geometries is proposed. The modeling is based on the Euler system where a non-conservative term is added to take the porosity variation into account. A detailed presentation of the scheme is given, the main point is the construction of non-conservative fluxes to reproduce the non-conservation aspect of the problem. We compare the numerical method with an exact solution of the Riemann problem and we check that the method preserves steady-state situations even if we use a discontinuous jump for the porosity. Finally, we present two simulations involving a two-dimensional gas flow.

Porous Filter Optimization to Improve the Safety of the Medium-Voltage Electrical Installations During an Internal Arc Fault

Electrical power distribution equipment, such as medium-voltage (MV) switchgear, must be designed to withstand the pressures and temperatures of gases resulting from an internal arcing fault. An original way to limit the external effects of the arc consists in channeling downward the gas flow across a filter composed of a granular porous medium in order to absorb the abrupt pressure wave and to cool the hot gas flow. In this paper, we propose an optimization of the MV switchgear configuration to enhance the porous filter efficiency where we manage to strongly reduce the external manifestations of the arc fault. On one hand, we employ the numerical simulation tool lying on a physical model where the major events are taken into account. On the other hand, real experimental tests have been performed according to the IEC standards and pressure and temperature histories obtained by numerical simulation are compared with the experimental measurements.

Numerical scheme to complete a compressible gas flow in variable porosity media

We present an approximate Riemann solver coupled with a finite volume method to compute non conservative Euler equations in variable porosity media using ideal gas state law. The non conservative term is numerically taken into account from an original idea of LeRoux (1998) but here Riemann problems at each interface of the mesh are linearized using a VFRoe approach. The main goal is the resolution of the non conservative system even if the porosity is discontinuous. Stationary solutions are determined with continuous and discontinuous porosity in order to test the numerical scheme and computations of gas shock subsonic wave moving in a non continuous porosity medium are presented.

Two-dimensional modelling of internal arc effects in an enclosed MV cell provided with a protection porous filter

Medium voltage (MV) cells have to respect standards (for example IEC ones (IEC TC 17C 2003 IEC 62271-200 High Voltage Switchgear and Controlgear—Part 200 1st edn)) that define security levels against internal arc faults such as an accidental electrical arc occurring in the apparatus. New protection filters based on porous materials are developed to provide better energy absorption properties and a higher protection level for people. To study the filter behaviour during a major electrical accident, a two-dimensional model is proposed. The main point is the use of a dedicated numerical scheme for a non-conservative hyperbolic problem. We present a numerical simulation of the process during the first 0.2 s when the safety valve bursts and we compare the numerical results with tests carried out in a high power test laboratory on real electrical apparatus.

Numerical method for pre-arcing times: Application in HBC fuses with heavy fault-currents

This works deals with calculations of pre-arcing time prediction for fuse links used in industrial protection circuits in case of heavy faults-currents. An enthalpy method to solve heat-transfer equation included two phase-changes is presented. The mathematical model couples thermal and electrical equations based on the principle of energy conservation and the Ohms law respectively. In order to determine current density and temperature evolution in the fuses, three typical fuse links have been chosen for the calculations with circular, rectangular and trapezoidal reduced sections at their centre. Silver physical properties, mathematical equations and the numerical method are reported. Calculations results show that for the fuse link with rectangular reduced section a major heat-transfer mechanism took place compared to the other ones.

Pressure evolution during HBC fuse operation

The purpose of this paper is to describe the influence of the silica sand grains on pressure during the energy release in a high breaking capacity (HBC) fuse. During the HBC fuse operation, the pressure evolution is the result of two opposite trends: the pressure increase due to the interaction of the silica plasma with the surrounding granular sand, and the pressure decrease due to the propagation of the pressure waves toward the porous medium. Due to the complex phenomena occurring during the current extinction by a fuse, two kinds of pressure are distinguished: the pressure inside the silica plasma and the pressure in the silica sand. From the simulations we show that the Forchheimer flow resistance is stronger than the Darcy flow resistance once the electric power is over 30% of the maximum value. A comparison of the calculated and measured pressures is made at various positions from the fuse element axis. Two different pressures are obtained experimentally: the pressure PSAND exerted on the sand grains due to the plasma pressure, and the pressure PGAS of the gas flowing through the interstices of the silica sand. We show that the experimental and calculated trends are similar and they both depend on the electric power level and the silica sand mean granulometry. The maximum pressures are observed at the same time as the maximum electric power levels. The ratio PSAND/PGAS is about 8 with PGAS values not exceeding 1.5 × 105 Pa.