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Numerical Aspects of Laminar Flame Simulation

Bas van 't Hof

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numerical approximations: colorplots of temperature (left)
and methane concentrations (right) in a Bunsen flame.

Combustion plays an important role in many branches of science and engineering. Examples of combustion phenomena are laminar/ turbulent flames and detonation waves. At the Eindhoven University of Technology, research on combustion is carried out in the Faculty of Mechanical Engineering in cooperation with the Scientific Computing Group. This research is both experimental and numerical. In the Scientific Computing Group, research is done on the numerical simulation of laminar flames.

A laminar flame can be considered as the flow of a reacting gas mixture, consisting of N different chemical species. Therefore, in the theory of laminar flames both fluid dynamics and chemical kinetics play an important role. The governing equations describe conservation of mass, momentum and energy of the mixture as a whole and conservation of mass of each separate species. These conservation laws read:

The above set of equations has to be completed with the constitutive equations:

Numerical simulation of laminar flames involves discretization of the above conservation laws and iterative solution of the resulting algebraic equations. The finite volume method is employed for the discretization of this equation. Herewith, the domain is covered with control volumes, over which the conservation laws are integrated. In combination with a flux approximation scheme, this leads to a finite set of algebraic equations. An exponential scheme for the flux computation was developed which is second order accurate for both strongly diffusive and strongly convective flows. The resulting set of algebraic equations is finally solved using a multigrid scheme , accelerated with a Krylov-subspace method .

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