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AMR Platform and Rapid Algorithms in Unsteady Combustion

Distribution de la pression acoustique
Fig. 1
Distribution of acoustic pressure.
Crossing of a spherical diffusion flame by a Gaussian shape acoustic wave.
a) diffracted wave, b) extremities of the incident wave, c) reflected waves.

Combining reasonable computation costs with detailed and realistic descriptions of the physical-chemical processes of reactive flows involving acoustics, turbulence, flame fronts, shock waves and other related phenomena is one of the objectives of Onera's research project CIM (Unsteady Single-Phase Combustion). To this end, we developed a 3-D calculation code based on a scheme that is accurate, robust and rapid and that integrates Navier-Stokes equations with variable transport coefficients and detailed chemical kinetics. The code can be used to carry out simulations (including direct numerical simulation) over a broad Mach number range and with rapid restitution times given the approach used.

This numerical tool has been validated and is now being integrated on an AMR platform (Adaptive Mesh Refinement) that can accept finite difference or finite volume solvers. It is used to study basic phenomena such as the interaction of acoustic waves with premixed or diffusion flames in low-speed flows. Figure 1 shows the spatial distribution, at a given instant, of the acoustic pressure when a Gaussian shape planar acoustic wave goes through a spherical diffusion flame. Only the low-intensity iso-surfaces

(-100 pa  pacous  100 pa) are drawn. It shows the development of the reflected waves and the diffracted wave.

The conservative form of the equations also allows to do simulations of flows in which shock waves may appear. For example, the behavior of a circular-section diffusion flame at the crossing of a shock is an interesting topic. Understanding the conditions under which the vortices forming after the interaction play a major role in the increase in flame surface and consequently in the reduction of complete combustion time remains an open question.

The temperature and the fuel concentration within the flame and the period of time between the moment when the reactions begin and the time when the flame goes through the shock have an influence on the combustion efficiency. We present a case in which these three parameters have the effect of counteracting the influence of the vortices, with the objective of increasing the flame surface. Finally, there is no increase in burning rate in this specific case. Figure 2 shows the temperature distribution when the flame has completely passed through the shock. The two counterrotating vortices completely wrap around part of the flame (white boxes); but as this region contains practically no oxygen, they do not manage to bring the fuel and the oxidizer into contact in proportions sufficiently close to the stoichiometric ratio and with a temperature sufficiently high to trigger the reactive processes.

Distribution de la température
Fig. 2
Temperature distribution after the crossing of a planar shock wave
in a circular diffusion flame.

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Last Update: 13 October 2006 - © ONERA 2009 - Terms of use