Premixed flame–wall interaction in a turbulent channel flow: budget for the flame surface density evolution equation and modelling

Turbulent premixed flame propagation in the vicinity of a wall is studied using a three-dimensional constant-density simulation of flames propagating in a channel. The influence of the walls is investigated in terms of the flamelet approach, where flamelet speed and flame surface density transport are used to describe the flame. The walls have constant temperature and lead to flamelet quenching for sufficiently small wall–flame distances. Starting from the exact evolution equation for the surface density of propagating interfaces (Trouvé & Poinsot 1994; Candel & Poinsot 1990; Pope 1988), a budget for the flame surface density equation is presented before, during, and after the interaction with the wall. Before the flame interacts with the wall, flame propagation is controlled by a balance between surface production and annihilation. During the interaction, high flame surface density gradients near the wall are responsible for the predominance of the transport terms. Closures of all terms of the flame surface density equation are proposed. These models are based on flamelet ideas and take into account wall effects. Enthalpy loss through the wall affects flamelet speed, flamelet annihilation and flame propagation. Decrease of turbulent scales near the wall affects turbulent diffusion and flame strain. This model is compared to DNS results using two types of tests: (i) a priori tests, where individual terms of the modelled flame surface density equation are compared to the terms of the exact interface density propagation equation, calculated with the DNS; (ii) a posteriori tests, where the final model is used to obtain total reaction rate, mean fuel mass fraction, heat flux at the wall and fuel mass fraction at the wall in the configuration used in the DNS. For both types of tests the model compares well with the DNS results.

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The evolution equation for the flame surface density in turbulent premixed combustion

Journal of Fluid Mechanics ◽

10.1017/s0022112094003599 ◽

1994 ◽

Vol 278 ◽

pp. 1-31 ◽

Cited By ~ 269

Author(s):

Arnaud Trouvé ◽

Thierry Poinsot

Keyword(s):

Evolution Equation ◽

Flame Propagation ◽

Surface Density ◽

Turbulent Flame ◽

Premixed Combustion ◽

Flame Surface ◽

Turbulent Premixed Combustion ◽

Flame Surface Density ◽

Propagation Effects ◽

Turbulent Premixed

One basic effect of turbulence in turbulent premixed combustion is for the fluctuating velocity field to wrinkle the flame and greatly increase its surface area. In the flamelet theory, this effect is described by the flame surface density. An exact evolution equation for the flame surface density, called the Σ-equation, may be written, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly. Direct numerical simulation (DNS) is used in this paper to estimate the different terms appearing in the Σ-equation. The numerical configuration corresponds to three-dimensional premixed flames in isotropic turbulent flow. The simulations are performed for various mixture Lewis numbers in order to modify the strength and nature of the flame-flow coupling. The DNS-based analysis provides much information relevant to flamelet models. In particular, the flame surface density, and the source and sink terms for the flame surface density, are resolved spatially across the turbulent flame brush. The geometry as well as the dynamics of the flame differ quite significantly from one end of the reaction zone to the other. For instance, contrary to the intuitive idea that flame propagation effects merely counteract the wrinkling due to the turbulence, the role of flame propagation is not constant across the turbulent brush and switches from flame surface production at the front to flame surface dissipation at the back. Direct comparisons with flamelet models are also performed. The Bray-Moss-Libby assumption that the flame surface density is proportional to the flamelet crossing frequency, a quantity that can be measured in experiments, is found to be valid. Major uncertainties remain, however, over an appropriate description of the flamelet crossing frequency. In comparison, the coherent flame model of Marble & Broadwell achieves closure at the level of the Σ-equation and provides a more promising physically based description of the flame surface dynamics. Some areas where the model needs improvement are identified.

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