Mathematical model and simulation of gas flow through a porous medium in high breaking capacity fuses

Rochette, David; Clain, Stéphane

doi:10.1016/j.ijheatfluidflow.2003.09.001

Cited by 19 publications

(17 citation statements)

References 15 publications

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“…The form of the momentum equation (2) follows that presented in various other works, for example De Ville (1996), Hsu and Cheng (1990), Jiang and Ren (2001) and Rochette and Clain (2004). The inclusion of the momentum flux gradient term, ∂ρu 2 /∂x, on the left-hand side of this equation is sometimes questioned (see, for example, Nield and Bejan (1999) for a discussion).…”

Section: Modelmentioning

confidence: 94%

“…Although this is a well-established approach we note that, unlike most other studies (e.g. Rochette and Clain, 2004), the model considered here involves a transport equation for the thermal, rather than the total, gas energy. Consequently our system does not take the usual form, and this has implications for the construction of the numerical flux approximations.…”

Section: Numerical Treatmentmentioning

confidence: 99%

“…None of the studies just mentioned address this question, and this aspect of thermal transport has, perhaps, received less attention. Previous studies in the area include the work by Spiga and Morini (1999), Abu-Hijleh et al (2004), Rochette and Clain (2004), Vafai and Sozen (1990). Spiga and Morini (1999) studied the development of temperature profiles in a semi-infinite porous media with a constant, uniform, unidirectional flow velocity and a time varying inlet fluid temperature.…”

Section: Introductionmentioning

confidence: 99%

“…The familiar longitudinal convection-diffusion equations with exchange coupling was studied numerically to assess the limitations of an assumption of local thermal equilibrium. Rochette and Clain (2004) considered transient heat transfer in gas flow through porous, high breaking capacity fuses. Their model for coupled mass, momentum and energy transport included mass and thermal energy source terms describing the effects of electrical energy input, which generates high temperatures and vaporization.…”

Section: Introductionmentioning

confidence: 99%

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Transient Heat Transport in Gas Flow Through Granular Porous Media

Swailes

Potts

2006

Transp Porous Med

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Models are developed to describe the time-evolution of gas and solid temperature profiles in a class of granular porous media; this time-dependence being the result of a heat source supplying energy uniformly to the gas as it flows into the medium. The solid-phase is treated as a fixed, axi-symmetric bed of randomly packed spheres of uniform size and material properties. An analytic expression for the locally averaged surface temperature of the solid phase is formulated in terms of the time history of the corresponding local gas temperature. This approach avoids the need to assume locally uniform temperatures within the solid phase, and provides a coupled model for the thermal energy transport in the system. A numerical scheme for treating the resulting transport equations is outlined, and results presented. A quasi-steady approximation is proposed, and this approximation is assessed by reference to numerical results obtained from the numerical scheme. One application of the work is to fixed-bed catalytic reactors and absorbers, and results are presented indicating how the regeneration times of such systems depend on operating parameters.

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Section: Modelmentioning

confidence: 94%

Section: Numerical Treatmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transient Heat Transport in Gas Flow Through Granular Porous Media

Swailes

Potts

2006

Transp Porous Med

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“…For example, in medium voltage switchgears, an internal arc fault generates an important overpressure in the cell and porous filters are employed to absorb the mechanical and thermal effects of the explosion (Gentils et al 2003, Rochette andClain 2004). The pressure wave generated by the electrical arc moves in the switchgear cell to reach the porous filter.…”

Section: Introductionmentioning

confidence: 99%

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

Rochette¹,

Clain²,

Buffard³

2005

International Journal of Computational Fluid Dynamics

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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.

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Contributions to numerical developments in shock waves attenuation in porous filters

Rochette

2007

Shock Waves

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International audienceThe paper deals with the numerical method of the compressible gas flow through a porous filter emphasizing the treatment of the interface between a pure gaseous phase and a solid phase. An incident shock wave is initiated in the gaseous phase interacting with a porous filter inducing a transmitted and a reflected wave. To take into account the discontinuity jump in the porosity between the gaseous phase and the porous filter, an approximate Riemann solver is used to compute homogeneous non-conservative Euler equations in porous media using ideal gas state law. The discretization of this problem is based on a finite volume method where the fluxes are evaluated by a “volumes finis Roe” (VFRoe) scheme. A stationary solution is determined with a continuous variable porosity in order to test the numerical scheme. Numerical results are compared with the two-phase shock tube experiments and simulations of a shock wave attenuation and gas filtration in porous filters are presented

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Mathematical model and simulation of gas flow through a porous medium in high breaking capacity fuses

Cited by 19 publications

References 15 publications

Transient Heat Transport in Gas Flow Through Granular Porous Media

Transient Heat Transport in Gas Flow Through Granular Porous Media

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

Contributions to numerical developments in shock waves attenuation in porous filters

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