Model premixed laminar flame

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,... 

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... 

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)). 

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. 

The measurements of temperature and species concentrations profiles in premixed, laminar flames play a key role in the development of detailed models of hydrocarbon combustion. Systematic comparisons are given here between a recent laminar methane-air flame model and laser measurements of temperature and species concentrations. These results are obtained by both laser Raman spectroscopy and laser fluorescence. These laser probes provide nonintrusive measurements of combustion species for combustion processes that require high spatial resolution. The measurements reported here demonstrate that the comparison between a model and the measured concentrations of CH, O2,... 

The last two sections of this paper will discuss this interplay between detailed modelling and both theory and experiment. The third section describes how a model must be tested in various limits for physical consistency to insure its accuracy. The specific example chosen here is a comparison between an analytic solution and a detailed numerical simulation of a premixed laminar flame. The last section shows how a comparison between model results and experiments can be used to calibrate the model and to guide further experiments. The example chosen is a calculation of flow over an immersed object which is compared to both experimental and theoretical results. 

Valorani, M., Creta, F., Goussis, D., Lee, J., Najm, H. An automatic procedure for the simplification of chemical kinetic mechanisms based on CSP. Combust. Flame 146, 29-51 (2006) Van Oijen, J.A., de Goey, L.P.H. Modelling of premixed laminar flames using Flamelet Generated Manifolds. Combust. Sci. Technol. 161, 113-137 (2000)... 

The implicit numerical solution of the time-dependent conservation equations provides the most powerful general method of solving premixed laminar flame problems in systems of (in principle) arbitrary chemical complexity. Indeed, with the simultaneous development of improved diagnostic techniques for the measurement of flame profiles, the possibility of obtaining such solutions has opened the way to realistic studies of reaction mechanisms even in hydrocarbon flames. The choice of solution method and transport flux formulation involves compromise between precision and cost, which becomes a matter of considerable import when modeling hydrocarbon oxidation in flames, which may involve some 25 chemical species and 80 or so elementary reactions. 

Kee, R. J., Great, J. F., Smooke, M. D., and Miller, J. A., A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Report, SAND85-8240, (1985). 

Heimerl, J. M., and T. P. Coffee. 1980. The detailed modeling of premixed, laminar steady-state flames. 1. Ozone. Combustion Flame 39 301-15. 

As mentioned in the previous section, laminar, premixed, flat flames are used widely in the study of combustion chemistry. The left-hand panel of Fig. 1.1 shows a typical burner setup. The flames themselves are accessible to an array of physical and optical diagnostics, and the computational models can incorporate the details of elementary chemical reactions. 

The Detailed Modelling of Premixed, Laminar, Steady-State Flames. Results for Ozone... 

The flame structure is modeled by solving the conservation equations for a laminar premixed burner-stabilized flame with the experimental temperature profile determined in previous work using OH-LIF. Three different detailed chemical kinetic reaction mechanisms are compared in the present work. The first one, denoted in the following as Lindstedt mechanism, is identical to the one reported in Ref. 67 where it was applied to model NO formation and destruction in counterffow diffusion flames. This mechanism is based on earlier work of Lindstedt and coworkers and it has subsequently been updated to include more recent kinetic data. In addition, the GRI-Mech. 2.11 (Ref. 59) and the reaction mechanism of Warnatz are applied to model the present flame. 

An example The temperature field computed for a partially-premixed radi-ally-symmetric methane/air flame is shown in Fig. 15. This is the same 4> — 2.464 laminar flame simulated by Bennett et al. (2000). We used the same 217 reaction full chemistry model used by Bennett et al. (2000) to compute the temperature field shown on the left-hand side of Fig. 15. On the left-hand side is shown the temperature field computed using the full chemistry model everywhere. On the right-hand side is shown the temperature field computed by the Adaptive Chemistry method using 13 different reduced models ranging in size from zero reactions to 156 reactions. As guaranteed by the error control... 

R.J. Kee, J.F. Grcar. M.D, Smooke, and J.A. Miller, A Fortran Program for Modeling Steady, Laminar, One-Dimensional. Premixed Flames, Sandia Report SAND85-8240, Sandia National Laboratories. Albuquerque, NM, 1985. 

For flames that exhibit the parametric instability, the velocity at which the exponential growth of velocity fluctuations started for each experiment was noted. These critical velocities are shown in Fig. 7.5, normalized by the laminar-flame speeds reported in [13]. All points shown on this plot represent the ensemble average of measurements from five experiments, and the error bars indicate the standard deviation about the mean value. The other curve on this plot was calculated using the analytical model of a premixed flame under the influence of an oscillating gravitational field by Bychkov [17], ris described above. Each point represents the smallest normalized acoustic velocity at the most unstable reduced wave number that resulted in the parametric instability. The experimental results show the same trend as the theoretical model mixtures with an equivalence ratio of 0.9, which require the smallest normalized acoustic velocity to trigger the parametric instability while flames on either side require larger values. 

Various calculations of reacting flows, such as perfectly stirred reactors [12], laminar flames [13,14], turbulent flames [15,16], and hypersonic flows [17] have verified the approach presented above. Due to space limitation we shall only present one example, namely a premixed laminar flat flame calculation [13]. It provides a nice, simple test case for the verification of the model. The specific example is a syngas (40 Vol. % CO, 30 Vol. % H2, 30 Vol. % N2)-air system at p = 1 bar, and with a temperature of 290 K in the unburnt gas. The fuel/air ratio is 6/10. The influence of simplified transport models is described elsewhere [13]. Here, for the sake of simplicity, only systems with equal diffusivity shall be considered. In this case a three-dimensional manifold with enthalpy and two reaction progress variables as parameters has been calculated, i.e. the chemistry has been simpli-... 

Following the estimation of predicted output uncertainties, sensitivity studies can then be used to identify the kinetic and thermodynamic data that cause the highest uncertainty in the model simulation result. The contribution of the uncertainty of the parameters can be assessed using Sobol indices as discussed in Sect. 5.5.3. For example, as Fig. 5.22 shows, at stoichiometric equivalence ratio, in a premixed laminar methane-air flame, the uncertainties in the rate coefficients of reactions O2 -1- H = OH -1- O and H -1- CH3 = CH4 cause the highest uncertainty in the calculated laminar flame velocity. Knowing these rate coefficients with lower... 

Kee, R.J., Grcar, J.F., Smooke, M.D., Miller, J.A. PREMIX A FORTRAN program for modeling steady laminar one-dimensional premixed flames. Sandia National Laboratories (1985)... 

Many investigators use a flat flame model for their calculations. The best known flat flame calculation algorithm PREMIX [58] has been developed by SANDIA. A characteristic feature of this simulation is that the laminar flame velocity is found as a stationary problem solution. 

Lucassen A, Labbe N, Westmoreland PR, Kohse-Hoinghaus K. Combustion chemistry and fuel-nitrogen conversion in a laminar premixed flame of morpholine as a model biofuel. Combust Flame. 2011 158 1647-1666. 

Wang, H. and Frenklach, M., A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames. Combust. Flame, 110,173, 1997. 

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