Laminar flames dynamics

Flame dynamics is intimately related to combustion instability and noise radiation. In this chapter, relationships between these different processes are described by making use of systematic experiments in which laminar flames respond to incident perturbations. The response to incoming disturbances is examined and expressions of the radiated pressure are compared with the measurements of heat release rate in the flame. The data indicate that flame dynamics determines the radiation of sound from flames. Links between combustion noise and combustion instabilities are drawn on this basis. These two aspects, usually treated separately, appear as manifestations of the same dynamical process. 

Since the concern here is with the destruction of a contiguous laminar flame in a turbulent field, consideration must also be given to certain inherent instabilities in laminar flames themselves. There is a fundamental hydro-dynamic instability as well as an instability arising from the fact that mass and heat can diffuse at different rates that is, the Lewis number (Le) is nonunity. In the latter mechanism, a flame instability can occur when the Le number (oJD) is less than 1. 

The characteristics of a reactive gas (a premixed gas) are dependent not only on the type of reactants, pressure, and temperature, but also on the flow conditions. When the flame front of a combustion wave is flat and one-dimensional in shape, the flame is said to be a laminar flame. When the flame front is composed of a large number of eddies, which are three-dimensional in shape, the flame is said to be a turbulent flame. In contrast to a laminar flame, the combustion wave of a turbulent flame is no longer one-dimensional and the reaction surface of the combustion wave is significantly increased by the eddies induced by the dynamics of the fluid flow. 

The difference between RANS and LES is depicted in Figure 20.1, which shows the temperature fields of a pool fire flame. While the RANS result shows smooth variations and looks like a laminar flame, the LES result clearly illustrates the large-scale eddies. Both results are the correct solutions of the corresponding equations. However, the time accuracy of LES is also essential for the quantitative accuracy of the buoyancy-driven flows. As Rehm and Baum have shown [10], the dynamic motions or eddies are responsible for most of the air entrainment into the fire plumes. Because these motions cannot be captured by RANS, LES is usually better suited for fire-driven flow. LES typically requires a finer spatial resolution than RANS. Examples of RANS-based fire CFD models are JASMINE, KAMELEON [11], SMARTFIRE [12], SOFIE [13], ISIS [14], and ISIS-3D [15]. Examples of LES models are the FDS [4,5] and SMAFS [16], developed at Lund University. Fire simulations using LES have also been performed by Cheung et al. [17] and Gao et al. [18],... 

Recently some progress has been made along these lines (N. Peters and F. A. Williams, Effects of Chemical Equilibrium on the Structure and Extinction of Laminar Diffusion Flames, Dynamics of Flames and Reactive Systems, J. R. Bowen, N, Manson, A. K. Oppenheim and R. 1. Soloukhin, eds. vol. 95 of Progress in Astronautics and Aeronautics, New York American Institute of Aeronautics and Astronautics, 1984, 37-60). 

In the reaction-sheet regime, the structure of the turbulent flame is determined by the dynamics of wrinkled laminar flames. Thus the thickness of the turbulent flame (if it is large compared with that of the laminar flame) is controlled by the distance to which fluctuations in the laminar-flame position may extend. Statistical aspects of distributions of temperature and of species concentrations in the turbulent flame can be expressed entirely in terms of statistics of the laminar-flame position (through /), orientation (through V //1V / ), and structure (through k). The simplest example is... 

With representative values for A, Cp, and po> and with Vq 50 cm/s, equation (4) gives d 10" cm. Therefore 5 is large compared with a molecular mean free path (about 10 cm), and the continum equations of fluid dynamics are valid within the deflagration wave but 6 is small compared with typical dimensions of experimental equipment (for example, the diameter of the burner mouth, and hence the radius of curvature of the flame cone, for experiments with Bunsen-type burners), and laminar deflagration waves may be approximated as discontinuities in many experiments. Since equations (3) and (4) imply that b at constant temperature, experimental studies of the interiors of laminar flames are often performed at subatmo-spheric pressures. 

Kazakov, A. Frenklach, M. 1998 Dynamic modelling of soot particle coagulation and aggregation implementation with the method of moments and application to high-pressure laminar premixed flames. Combustion and Elame 114, 484-501. 

Here we are interested in mechanisms of the transition process. Some of the basic questions we must address are fluid dynamics questions how do laminar flows transition to turbulent flows and what are the mechanisms of vorticity generation. Then we ask how the presence of chemical reactions and energy release alter these situations or generate additional mechanisms through coupling interactions. This involves questions such as how do flames stretch and increase their surface area, and thereby increase the burn rate and flame velocity. 

Egolfopoulos FN Dynamics and structure of unsteady, strained, laminar premixed flames, Proc Combust Inst 25 1365—1373, 1994. 

P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Prog. Energy Combust. Sci. 11, 1-59 (1985)... 

---