Premixed flames laminar

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

Laminar Versus Turbulent Flames. Premixed and diffusion flames can be either laminar or turbulent gaseous flames. Laminar flames are those in which the gas flow is well behaved in the sense that the flow is unchanging in time at a given point (steady) and smooth without sudden disturbances. Laminar flow is often associated with slow flow from small diameter tubular burners. Turbulent flames are associated with highly time dependent flow patterns, often random, and are often associated with high velocity flows from large diameter tubular burners. Either type of flow—laminar or turbulent—can occur with both premixed and diffusion flames. 

Laminar flame speed is one of the fundamental properties characterizing the global combustion rate of a fuel/ oxidizer mixture. Therefore, it frequently serves as the reference quantity in the study of the phenomena involving premixed flames, such as flammability limits, flame stabilization, blowoff, blowout, extinction, and turbulent combustion. Furthermore, it contains the information on the reaction mechanism in the high-temperature regime, in the presence of diffusive transport. Hence, at the global level, laminar flame-speed data have been widely used to validate a proposed chemical reaction mechanism. 

Marra, F.S. and Continillo, G., Numerical study of premixed laminar flame propagation in a closed tube with a full Navier-Stokes approach, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 907-913,1996. 

Libby, R, Lihan, A., and Williams, R, Strained premixed laminar flames with nonunity Lewis numbers. Combust. Set. Technol, 34, 257, 1983. 

Darabiha, N., Candel, S., and Marble, R, The effect of strain rate on a premixed laminar flame. Combust. Flame, 64, 203, 1986. 

Giovangigli, V. and Smooke, M., Extinction of strained premixed laminar flames with complex chemistry. Combust. Sci. Technol., 53,23, 1987. 

Darrieus and Landau established that a planar laminar premixed flame is intrinsically unstable, and many studies have been devoted to this phenomenon, theoretically, numerically, and experimentally. The question is then whether a turbulent flame is the final state, saturated but continuously fluctuating, of an unstable laminar flame, similar to a turbulent inert flow, which is the product of loss of stability of a laminar flow. Indeed, should it exist, this kind of flame does constitute a clearly and simply well-posed problem, eventually free from any boundary conditions when the flame has been initiated in one point far from the walls. 

The modeling of steady-state problems in combustion and heat and mass transfer can often be reduced to the solution of a system of ordinary or partial differential equations. In many of these systems the governing equations are highly nonlinear and one must employ numerical methods to obtain approximate solutions. The solutions of these problems can also depend upon one or more physical/chemical parameters. For example, the parameters may include the strain rate or the equivalence ratio in a counterflow premixed laminar flame (1-2). In some cases the combustion scientist is interested in knowing how the system mil behave if one or more of these parameters is varied. This information can be obtained by applying a first-order sensitivity analysis to the physical system (3). In other cases, the researcher may want to know how the system actually behaves as the parameters are adjusted. As an example, in the counterflow premixed laminar flame problem, a solution could be obtained for a specified value of the strain... 

SMOOKE GIOVANGIGLI Counterflow Premixed Laminar Flames 405... 

Procedures enabling the calculation of bifurcation and limit points for systems of nonlinear equations have been discussed, for example, by Keller (13) Heinemann et al. (14-15) and Chan (16). In particular, in the work of Heineman et al., a version of Keller s pseudo-arclength continuation method was used to calculate the multiple steady-states of a model one-step, nonadiabatic, premixed laminar flame (Heinemann et al., (14)) a premixed, nonadiabatic, hydrogen-air system (Heinemann et al., (15)). 

A number of theoretical (5), (19-23). experimental (24-28) and computational (2), (23), (29-32). studies of premixed flames in a stagnation point flow have appeared recently in the literature. In many of these papers it was found that the Lewis number of the deficient reactant played an important role in the behavior of the flames near extinction. In particular, in the absence of downstream heat loss, it was shown that extinction of strained premixed laminar flames can be accomplished via one of the following two mechanisms. If the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity) of the deficient reactant is greater than a critical value, Lee > 1 then extinction can be achieved by flame stretch alone. In such flames (e.g., rich methane-air and lean propane-air flames) extinction occurs at a finite distance from the plane of symmetry. However, if the Lewis number of the deficient reactant is less than this value (e.g., lean hydrogen-air and lean methane-air flames), then extinction occurs from a combination of flame stretch and incomplete chemical reaction. Based upon these results we anticipate that the Lewis number of hydrogen will play an important role in the extinction process. 

Arc-length continuation, steady states of a model premixed laminar flame, 410 Architecture, between parallel machines, 348 Arithmetic control processor, ST-100, 125 Arithmetic floating point operations,... 

In Chapter 4 we examined the spread rate of a premixed flame and found that its speed, Su, depended on the rate of chemical energy release, m Ahc. Indeed, for a laminar flame, the idealized flame speed... 

This initial condition is rather idealized. In reality, one would expect to see partially premixed zones with f = fst and 7 = 0 which will move towards 7 = 1 along the stoichiometric line. The movement along lines of constant f corresponds to premixed combustion, and occurs at a rate that is controlled by the interaction between molecular diffusion and chemical reactions (i.e., the laminar flame speed). 

Results of the model for two parameters, i.e., the spatial temperature profile and the mass flux into the reaction zone as a function of gas mass flux are presented in Fig. 8.7. The temperature profile of the solid fuel flame (Fig. 8.7, left) is similar to that of a premixed laminar flame it consists of a preheat zone and a reaction zone. (The spatial profile of the reaction source term, which is not depicted here, further supports this conclusion.) The temperature in the burnt region (i.e., for large x) increases with the gas mass flux. The solid mass flux (Fig. 8.7, right) initially increases with an increase of the air flow, until a maximum is reached. For higher air flows, it decreases again until the flame is extinguished. 

Van Oijen, J. Flamelet-generated manifolds development and application to premixed laminar flames, PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, (2002). 

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