**7. References**

Blume, W. (1986). *Computer Circuit Simulation*, BYTE, July 1986

Bucatariu, I. & Surianu, F. (2009). Optimal Placement of Fixed Series Capacitor in Distribution Networks, *Proceedings of the 9thWSEA/IASMES International Conference on*  *Electric Power Systems High Voltages, Electric Machines Control & Signal Processing,*  Genova, Italy, October 17-19, 2009, pp.65-70

Chuco, B. (2005). Electrical Software Tools Overview *in* SINATEC-IEEE

498 Numerical Simulation – From Theory to Industry

(Rt > 100Ω).

equipments.

values of zero sequence component, obtained by the two methods, are quite acceptable from

The resistance of the broken conductor to ground is extremely important, small values of Rt implying long damping periods. If this undesirable condition happens the currents might have high values, as well as important values of the over voltages leading to important supplementary mechanical stress and damages of the insulating devices and, eventually a

For small values of the grounding resistance at the fault location (Rt < 10Ω) difference between measured and simulated values is a litle higher than in the case of greater values

The model is very useful by giving the values of the voltages on the healthy lines (over voltages that might jeopardize the insulation) and zero sequence currents of the faulty lines

Using the conclusions of the simulation of a MVN for the values of the currents and voltages during different types of faults it is possible to adjust the prescribed values of the protection. Simulation of the broken conductor fault, either connected to the ground or not, shows that resonance might occur, over voltages due to this resonances being dangerous to the

When double phase to ground fault was simulated the values of the voltages showed

The numerical simulator has the advantage of analyzing rapidly several variants as models

The simulator is flexible and all kinds of faults can be simulated for different MVN, just by making the proper modification in the parameters of the simulator. These modifications are

The precision of the results obtained by simulation depends essentially on the accuracy of

Bucatariu, I. & Surianu, F. (2009). Optimal Placement of Fixed Series Capacitor in Distribution Networks, *Proceedings of the 9thWSEA/IASMES International Conference on* 

Either using PSPICE or Mathlab-Simulink the accuracy of the analysis is similarly good.

slightly easier to be performed when PSPICE simulating model is used.

a technical point of view and this concordance validates the model.

(fixing the condition of the fault detection by protection devices).

simple fault can turn to a multiple fault situation.

dangerous voltages for step or touch voltage.

Dumitru Toader, Stefan Haragus and Constantin Blaj

Blume, W. (1986). *Computer Circuit Simulation*, BYTE, July 1986

*"Politehnica" University of Timisoara, Romania* 

of different possible situations.

the MVN parameters.

**Author details** 

**7. References** 


Vladimirescu, A. (1999). *SPICE*, Ed.Tehnica, Bucuresti Vladimirescu, A. (1997) SIMULINK ; *Dynamic System Simulation for MATLAB, User's Guide, version 2.1*, MathWorks Inc.

**Chapter 0**

**Chapter 21**

**Multidimensional Numerical**

**of TiC Combustion Synthesis**

Additional information is available at the end of the chapter

A. Aoufi and G. Damamme

http://dx.doi.org/10.5772/48441

**2. Mathematical modelling**

properly cited.

**1. Introduction**

**Simulation of Ignition and Propagation**

The purpose of this book chapter is to analyze from a numerical point of view a reaction diffusion mathematical modelling of titanium carbide combustion synthesis from a mixture of titanium and carbide reactive powders thanks to self-propagating high temperature synthesis process. This modelling results in the coupling between a nonlinear parabolic equation expressing the enthalpy balance of the system with radiative boundary conditions and a nonlinear differential equation describing the exothermic chemical reaction in the system. An another multiphysics coupling was analyzed in [3]. This Self-propagating High temperature Synthesis (SHS) process was discovered in 1965 by Merzhanov [7], [8] and uses the energy released by the exothermic reaction itself to ensure its self-propagation inside the material after a localized heat supply has been performed for several seconds on the surface of the solid mixture. The stoichiometric solid mixture is made of several kinds of reactive powders. We analyze in this book chapter, the influence of radiative boundary conditions *related to the heat supply* over the ignition and eventual propagation of a combustion front inside the material. Four sections are used to present our numerical simulation work. Section two presents the governing equations of the modelling. Section three outline the main aspects of the numerical scheme. Section four analyzes and discusses the main numerical simulation results of the combustion synthesis process. A conclusion summarizes the results that were obtained.

This section describes the main features of the modelling which expresses the coupling between a reaction-diffusion written for the enthalpy balance and a differential equation written for the exothermic chemical kinetics. SHS (Self-propagation High-temperature Synthesis) process is a condensed phase process which converts a mixture of powders into an end product. In this paper we consider the synthesis of titanium carbide in solid phase

and reproduction in any medium, provided the original work is properly cited.

©2012 Aoufi and Damamme, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,
