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Lagrangian properties of diffusion in the theory of turbulent combustion

DOI: 10.1615/ICHMT.2009.TurbulHeatMassTransf.1370
page 12

V. L. Zimont
CRS4 Research Centre, Science and Technological Park of Sardinia-Polaris, 09010 Pula(CA) Italy

G. Pagnini
CRS4, Polaris Bldg. 1, 09010 Pula (CA), Italy


In this paper we analyze two effects of the Lagrangian nature of turbulent transfer that are usually ignored in the theory of turbulent combustion. They are (i) nonequilibrium behavior of the turbulent diffusion coefficient, which is important for modeling of initial stage of combustion in the SI engine, and (ii) the existence of a traveling front of turbulent diffusion with finite speed, which controls the velocity of the steady state flame in strong turbulence. First we derive the parabolic diffusion equation with both the diffusion and chemical source terms expressed by Lagrangian characteristics of turbulence. We show that chemical transformation does not influence the turbulent diffusion coefficient and this result is important for combustion theories that relate the formation of the initial flame with the development of the diffusion coefficient. Second, an hyperbolic diffusion equation based on hydrodynamics is derived and we analyze relationship between velocities of the turbulent diffusion front and the speed of the steady state premixed flame. In particular, in the case of the flamelet combustion mechanism and strong turbulence, we state that the flame speed is very closed to the theoretical value of the diffusion front velocity, which is equal to the root mean square of turbulent velocity fluctuations.

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