these-beccantini
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these-beccantini

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A matrix free approach for multicomponent reactiveall-speed flows on complex and large geometriesThe use of Computational Fluids Dynamics (CFD) for industrial applications often impliesthe capability of dealing with geometries which are large with respect to the characteristic di-mensions oftheinvolved physical phenomena. Such situationariseswhen wewant todeterminepressure loads generated by a hydrogen-air combustion which might occur in a nuclear reactorcontainmentduringapostulatedLossofCoolantAccident. Indeed, ifweconsidertheEuropean3 3Pressurized Reactor, the free volume of the building is about 75000 m , i.e. (42m) . We arein similar situations when we want to determine pressure loads caused by a so-called VaporCloud Explosion which might occur in the case of accident in an hydrogen production plant(like the ones coupled with high temperature gas reactors [8]): even in this case, the domainof interest can have the dimension of hundreds of meters. Characteristic physical lengths aremuch smaller. To have an idea of the mesh dimension we need for the “direct simulation” offlame propagation and deflagration-to-detonation transition (DDT), see for instance [6].We can avoid the direct simulation if we consider the flame as infinitely thin, neglect thediffusion phenomena and model their effect, for instance, introducing phenomenological lawsfor the flame speed. Indeed, as explained in [5], pressure loads can be correctly predicted asthe flame speed is ...

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A matrix free approach for multicomponent reactive all-speed flows on complex and large geometries
The use of Computational Fluids Dynamics (CFD) for industrial applications often implies the capability of dealing with geometries which are large with respect to the characteristic di-mensions of the involved physical phenomena. Such situation arises when we want to determine pressure loads generated by a hydrogen-air combustion which might occur in a nuclear reactor containment during a postulated Loss of Coolant Accident. Indeed, if we consider the European Pressurized Reactor, the free volume of the building is about 75000 m3, i.e. (42m)3. We are in similar situations when we want to determine pressure loads caused by a so-called Vapor Cloud Explosion which might occur in the case of accident in an hydrogen production plant (like the ones coupled with high temperature gas reactors [8]): even in this case, the domain of interest can have the dimension of hundreds of meters. Characteristic physical lengths are much smaller. To have an idea of the mesh dimension we need for the “direct simulation” of flame propagation and deflagration-to-detonation transition (DDT), see for instance [6]. We can avoid the direct simulation if we consider the flame as infinitely thin, neglect the diffusion phenomena and model their effect, for instance, introducing phenomenological laws for the flame speed. Indeed, as explained in [5], pressure loads can be correctly predicted as the flame speed is. In the literature, there exist several other approaches which model flames as interfaces. Some of them need the solution of the reactive Riemann problem between the burnt and unburnt regions. In [1] an algorithm for the solution of the reactive Riemann problem for thermally perfect gases has been proposed. In [2] this algorithm has been used to design a “all shock” approximate Riemann solver which, used as an ingredient for the Discrete Equation Method [9], has been employed to compute high speed deflagrations and detonations. The algorithm has been implemented in the CEA code CAST3M and has been validated for compressible flows using analytical solutions in 1D and 2D (for instance, by computing 1D line-symmetric ”steady flames” [3]. As many other Riemann solvers, the “all shock” reactive solver cannot be used to compute flow at low Mach number speed. Thus, preconditioning of such solver is necessary [10]. At the same time, in order to get rid of a CFL conditions based on acoustic wave, implicitation in time is necessary. In [4], an free matrix method approach has been proposed for the solution of the compressible Euler and/or Navier Stokes equations for a mono-component flow at all speeds on unstructured meshes. In this approach, the matrices arising from the time-implicitation of the compressible equations are not stored and their inversion is performed using a point Jacobi technique which uses some properties of the preconditioning matrix to reduce the CPU cost per iterations. We emphasize that this approach can be easily implemented in a parallel fashion. The purposes of the thesis are the following ones. First, the preconditioning of the “all shock” reactive Riemann solver [1].
of the free matrix method proposed in [4] for mono-component flowsThen, the extension at all speed, to multi-component reacting flows at all speeds.
1
The validation of the approach will be performed first on analytical solutions available in the literature (for instance [3]) and on numerical experiments available in the Hysafe framework [7].
References
[1] A Beccantini, E Studer. The reactive Riemann problem for thermally perfect gases at all combustion regimes. Submitted to International Journal for Numerical Methods in Fluids. (2008)
[2] A Beccantini, E Studer. The reactive Riemann problem for thermally perfect gases at all combustion regimes. Part II. Numerical investigation. Submitted to International Journal for Numerical Methods in Fluids (2008).
[3] AL Kuhl, MM Kamel and AK Oppenheim. Pressure Waves Generated by Steady Flames. Fourteenth Symposium (International) on Combustion, The Combustion In-stitute, pages 1201– (1973).
[4] T Kloczko, C Corre , A Beccantini. Low-cost implicit schemes for all-speed flows on unstructured meshes. International Journal for Numerical Methods in Fluids, Volume 58 Issue 5, Pages 493-526 (2008)
[5] AA Efimenko and SB Dorofeev. CREBCOM code system for description of gaseous combustion. Journal of Loss Prevention in the Process Industries, Volume 14, Pages 575-581 (2001).
[6] VN Gamezo, T Ogawa and ES Oran. Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen-air mixture. Proceedings of the Com-bustion Institute, Volume 31, Pages 2463-2471 (2007).
[7] Hysafe web site. http://www.hysafe.net/. Visited in September 2008.
[8] Y Inaba, T Nishihara, MA Groethe, Y Nitta. Study on explosion characteristics of natural gas and methane in semi-open space for the HTTR hydrogen production system. Nuclear Engineering and Design, Volume 232, Pages 111-119 (2004).
[9]OLeM´etayer,JMassoni,RSaurel.ModellingevaporationfrontswithreactiveRiemann solvers. Journal of Computational Physics, Volume 205, Pages 567-610 (2005).
[10] E Turkel. Preconditioned methods for solving the incompressible and low Mach com-pressible equations. Journal of Computational Physics, Volume 72, Pages 277-298 (1987).