Premixed Flame Structure

The fuel and oxygen are consumed primarily by a sequence of chain-branching reactions that yield a net production of active free radicals  

Beyond a distance of approximately 0.9 mm, the chain-branching reactions achieve a partial-equilibrium condition, in which the forward and reverse rates are essentially equal. At this point the slower three-body recombination reactions can begin to dominate the chemistry, since the fast reactions are nearly equilibrated. 

The recombination reactions consume free radicals to create stable species, resulting in a net reduction of radicals. Since these recombination reactions are very exothermic, they cause the temperature to increase. The lower panel of Fig. 16.11 shows the contribution of various reactions to the temperature rise. Specifically, it shows the contribution of each reaction i to the heat-of-reaction term in the thermal-energy equation (Eq. 16.98)  

This expression, of course, accounts only for the chemical contributions to thermal energy and neglects the diffusive-transport terms. It is apparent from Fig. 16.11 that recombination reactions play a dominant role in releasing the thermal energy that causes temperature rise in the flame. 

Hydrogen atoms readily diffuse upstream of the flame front into the cooler unbumed region. At temperatures below about 750 K, the production of H02 dominates, but at the higher temperatures in the flame front, the chain-branching dominates. As the temperatures continue to rise, the chain-branching reaction equilibrates and the three-body reaction can 

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This recent attempt differs from the previous classification where the wrinkled flamelet regime has been considered up to rj = (5l- Chen and Bilger have proposed to tentatively classify the different turbulent premixed flame structures they observed among four different regimes ... 

With these identifications, according to Borghi [6], one obtains a diagram with almost identical regions as for premixed combustion. In Fig. 13.1, the non-premixed regions are identified with the letter N. Note that the basic turbulence-chemistry interactions which define these regions, that is Ret =, Da = 1, and Ka = I, also define the different regions for the non-premixed flame structures. 

The chronology of the most remarkable contributions to combustion in the early stages of its development is as follows. In 1815, Sir Humphry Davy developed the miner s safety lamp. In 1826, Michael Faraday gave a series of lectures and wrote The Chemical History of Candle. In 1855, Robert Bunsen developed his premixed gas burner and measured flame temperatures and flame speed. Francois-Ernest Mallard and Emile Le Chatelier studied flame propagation and proposed the first flame structure theory in 1883. At the same time, the first evidence of detonation was discovered in 1879-1881 by Marcellin Berthelot and Paul Vieille this was immediately confirmed in 1881 by Mallard and Le Chatelier. In 1899-1905, David Chapman and Emile Jouguet developed the theory of deflagration and detonation and calculated the speed of detonation. In 1900, Paul Vieille provided the physical explanation of detonation... 

Chao, B.H., Egolfopoulos, F.N., and Law, C.K., Structure and propagation of premixed flame in nozzle-generated counterflow. Combust. Flame, 109,620,1997. 

As the concentration gradient further increases (regime C), the radius of curvafure of premixed wings l cur decreases. When if becomes comparable wifh, for example, the preheat zone thickness Sj, typically O (1mm), one or both of fhe premixed flame wings can be merged to the trailing diffusion flame by having a bibrachial or cotton-bud shaped structure. 

S. H. Chung and C. K. Law, An integral analysis of the structure and propagation of stretched premixed flames. Combust. Flame 72 325-336,1988. 

Real-life premixed flame fronts are rarely planar. Of course, if the flow is turbulent, gas motion will continuously deform and modify the geometry of the flame front, see Chapter 7. However, even when a flame propagates in a quiescent mixture, the front rapidly becomes structured. In this chapter, we will discuss hydrodynamic flame instability, thermo-diffusive instability, and thermo-acoushc instability. 

P. Clavin and F.A. Williams. Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. Journal of Fluid Mechanics, 116 251-282,1982. 

J. Quinard, G. Searby, and L. Boyer. Stability limits and critical size of structures in premixed flames. Progress in Astronautics and Aeronautics, 95 129-141, 1985. 

Y. Huang and V. Yang. Bifurcation of flame structure in a lean-premixed swirl-stabilized combustor Transition from stable to unstable flame. Combust. Flame, 136(3) 383-389, 2004. 

Nevertheless, despite all these remarkable achievements, some open questions still remain. Among them is the influence of the molecular transport properties, in particular Lewis number effects, on the structure of turbulent premixed flames. Additional work is also needed to quantify the flame-generated turbulence phenomena and its relationship with the Darrieus-Landau instability. Another question is what are exactly the conditions for turbulent scalar transport to occur in a coimter-gradient mode Finally, is it realistic to expect that a turbulent premixed flame reaches an asymptotic steady-state of propagation, and if so, is it possible, in the future, to devise an experiment demonstrating it ... 

B. Renou, M. Boukhalfa, D. Puechberty, and M. Trinite 2000, Local flame structure of freely propagating premixed turbulent flames at various Lewis number. Combust. Flame 123 107-115. 

B. Renou, A. Mura, E. Samson, and M. Boukhalfa 2002, Characterization of the local flame structure and the flame surface density for freely propagating premixed flames at various Lewis number. Combust. Sci. Technol. 174 143-179. 

Y.C. Chen, N. Peters, G.A. Schneemarm, N. Wruck, U. Renz, and M.S. Mansour 1996, The detailed flame structure of highly stretched turbulent premixed methane-air flames. Combust. Flame 107 223-244. 

Y.C. Chen and R. Bilger 2001, Simultaneous 2-D imaging measurements of reaction progress variable and OF radical concentration in turbulent premixed flames Instantaneous flame front structure. Combust. Sci. Tech. 167 187-222 (more informations through www.infor-maworld.com). 

R. Borghi 1985, On the structure and morphology of turbulent premixed flames, in C. Bruno and S. Casci (Eds.), Recent Advances in the Aerospace Sciences, Plenum Press, New York, pp. 117-138. 

J. Abraham, RA. Williams, and RV. Bracco 1985, A discussion of turbulent flame structure in premixed charge, SAE Paper 850343, in Engine Combustion Analysis New Approaches, p. 156. 

Abraham, J., FA. Williams, and F.V. Bracco, A Discussion of Turbulent Flame Structures in Premixed Charges. SAE, 850345, 1985. 

The system of equations is a boundary value problem, and we solve it by a method that we have developed to compute the structure of premixed flames. 

Consider Equations (6-10) that represent the CVD reactor problem. This is a boundary value problem in which the dependent variables are velocities (u,V,W), temperature T, and mass fractions Y. The mathematical software is a stand-alone boundary value solver whose first application was to compute the structure of premixed flames.Subsequently, we have applied it to the simulation of well stirred reactors,and now chemical vapor deposition reactors. The user interface to the mathematical software requires that, given an estimate of the dependent variable vector, the user can return the residuals of the governing equations. That is, for arbitrary values of velocity, temperature, and mass fraction, by how much do the left hand sides of Equations (6-10) differ from zero ... 

In flame extinction studies the maximum temperature is used often as the ordinate in bifurcation curves. In the counterflowing premixed flames we consider here, the maximum temperature is attained at the symmetry plane y = 0. Hence, it is natural to introduce the temperature at the first grid point along with the reciprocal of the strain rate or the equivalence ratio as the dependent variables in the normalization condition. In this way the block tridiagonal structure of the Jacobian can be maintained. The flnal form of the governing equations we solve is given by (2.8)-(2.18), (4.6) and the normalization condition... 

Recall that we are assuming faem "C faff (°r fax, if turbulent flow). Anyone who has carefully observed a laminar diffusion flame - preferably one with little soot, e.g. burning a small amount of alcohol, say, in a whiskey glass of Sambucca - can perceive of a thin flame (sheet) of blue incandescence from CH radicals or some yellow from heated soot in the reaction zone. As in the premixed flame (laminar deflagration), this flame is of the order of 1 mm in thickness. A quenched candle flame produced by the insertion of a metal screen would also reveal this thin yellow (soot) luminous cup-shaped sheet of flame. Although wind or turbulence would distort and convolute this flame sheet, locally its structure would be preserved provided that faem fax. As a consequence of the fast chemical kinetics time, we can idealize the flame sheet as an infinitessimal sheet. The reaction then occurs at y = yf in our one dimensional model. 

Recall that there are length scales associated with laminar flame structures in reacting flows. One is the characteristic thickness of a premixed flame, <5L, given by... 

Since diffusion rates vary with pressure and the rate of overall combustion reactions varies approximately with the pressure squared, at very low pressures the flame formed will exhibit premixed combustion characteristics even though the fuel and oxidizer may be separate concentric gaseous streams. Figure 6.1 details how the flame structure varies with pressure for such a configuration where the fuel is a simple higher-order hydrocarbon [1], Normally, the concentric fuel-oxidizer configuration is typical of diffusion flame processes. 

As the important effect of temperature on NO formation is discussed in the following sections, it is useful to remember that flame structure can play a most significant role in determining the overall NOx emitted. For premixed systems like those obtained on Bunsen and flat flame burners and almost obtained in carbureted spark-ignition engines, the temperature, and hence the mixture ratio, is the prime parameter in determining the quantities of NOx formed. Ideally, as in equilibrium systems, the NO formation should peak at the stoichiometric value and decline on both the fuel-rich and fuel-lean sides, just as the temperature does. Actually, because of kinetic (nonequilibrium) effects, the peak is found somewhat on the lean (oxygen-rich) side of stoichiometric. 

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