Laminar Flame Velocity

Si is the laminar flame velocity, the function Z(co) is the heat response function Equation 5.1.16, whose real part is plotted in Figure 5.1.10. The function f(r, giJ is a dimensionless acoustic structure factor that depends only on the resonant frequency, a , the relative position, r, of the flame, and the density ratio Pb/Po-... 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

FIGURE 4.23 Methane laminar flame velocities in various inert gas-oxygen mixtures (after Clingman et al. [27]). 

Early theoretical treatments of bluff-body stabilized flame spreading have been based, in general, on the assumption that the flame is a discontinuous surface separating gas streams of different densities and temperatures [1, 15-17]. These theories neglect the finite thickness of turbulent flame zone and predict the increase of the spreading rate both with the density ratio across the flame, and with the increase in the laminar flame velocity of fuel-air mixture. This does not correspond to experimental observations (e.g., [8, 10]). 

In Fig. 15.4, the measured turbulent flame speeds, normalized with mixture-specific laminar flame velocities obtained recently by Vagelopoulos et al. [14], are compared with experimental and theoretical results obtained in earlier studies. Also shown in the figure are the measurements made by Abdel-Gayed et al. [3] for methane-air mixtures with = 0.9 and = 1 a correlation of measured turbulent flame speeds with intensity obtained by Cheng and Shepherd [1] for rod-stabilized v-flames, tube-stabilized conical flames, and stagnation-flow stabilized flames, Ut/Ul = l + i.2 u /U ) a correlation of measured turbulent flame... 

The steady-state approximation is often used for the atomic and free radical intermediates occurring in combustion processes. The validity of this approximation has been examined in connection with the theoretical calculation of laminar flame velocities (3, 20, 21) in premixed gaseous systems. The steady-state approximation is occasionally useful for obtaining first-order estimates for flame-propagation velocities but should probably not be used in estimating concentration profiles for reaction intermediates. Some additional observations on the steady-state approximation are contained in Appendix I. 

A similar flat flame technique—one that does not require a heat loss correction—is the so-called opposed jet system. This approach to measuring flame speeds was introduced to determine the effect of flame stretch on the measured laminar flame velocity. The concept of stretch was introduced in attempts to understand the effects of turbulence on the mass burning rate of premixed systems. (This subject is considered in more detail in Section 4.E.) The technique uses two... 

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... 

Fig. 5.23 Local sensitivity coefficients of the laminar flame velocity of a stoichiometric methane-air flame. Grey stripes refer to the local sensitivity coefficients at the nominal parameter set During the Monte Carlo analysis, the local sensitivity coefficients were calculated for each parameter set, which allowed the calculation of the standard deviation of the sensitivity coefficients small bars interconnected with a horizontal line) and the attainable minimum and maximum sensitivity coefficients at any parameter set within the uncertainty limits of parameters (outer larger bars). Adapted with permission from Z or et al. (2005b). Copyright (2005) American Chemical Society...

A laminar flame velocity is one of the fundamental characteristics of premixed combustible gas reactivity. It specifies an amount of mixture reacting across a unit flame front area per unit time. According to the classical definition, a laminar flame (combustion) velocity is the expansion rate of a flat one-dimensional flame front in the direction normal to the wave surface with respect to the unburned gas [1]. 

The characteristic dimensional parameter Lm takes into account the flame curvature effect on the burning velocity. The higher its absolute value, the stronger the curvature effect is. The Markstein length relation to the laminar flame thickness S = dSu, where - the laminar flame velocity, is known as the Markstein number Ma = Lyild. Table 1.1 [15] presents the Markstein length for hydrogen-air mixtures at 298 K and 0.1 MPa... 

The flame stretch-effect influences a laminar flame velocity due to the thermal and mass selective diffusion [7-12]. This effect may cause a flame front instability depending on the sign of the Markstein length. When a Markstein length is negative, the flame laminar velocity increases with the stretch growth. 

In the region 1, where the pulsation velocity does not exceed the laminar flame velocity, the turbulent flame possesses a curved front of thickness similar to that of the laminar front. With the pulsation velocity growth, the level of curvature increases and the flame can lose its continuity. 

Quantitative investigations of gaseous mixture combustion have been developed and upgraded since the first studies in the nineteenth century. The theoretical concepts of laminar flame velocity measurements have been developed by Gui and Michelson [9]. Michelson was the first who measured a flame velocity in a hydrogen + air mixture at atmospheric pressure and room temperature on the inner surface of a cone Bunsen flame [10]. Those unique and little known results were obtained for a wide range of hydrogen concentrations (from 15.3% to 74.6% of the mixture volume). 

Table 2.1 Laminar flame velocity (cm/s) in hydrogen-air mixtures at the atmospheric pressure and the room temperature...

This method is applied at the initial stage of a spherical flame development, when the flame radius does not exceed one-half of a vessel radius. The measuring techniques for spherical laminar flame velocities have been considered in the literature [1, 3, 5, 21, 24, 27, 31-33, 38-43]. 

Fig. 2.4 The comparison of laminar flame velocities measnred by varions techniqnes in H2 + air mixtures at atmospheric pressure and room temperature 1 - Michelson [10] 2 - Kozachenko [ 13] 3 - Manton and Milliken [21] 4 - Grumer [24] 5 - Andrews and Bredley [2] 6 - hjima and Takeno [26] 7 - Liu and MacFarlane [19] S - Dowdy and co-authors [27]. The short strokes - Liu and MacFarlane correlated curvature. The long strokes - calculation performed by IChPh RAS (spherical flame). The solid curves - calculation performed by IChPh RAS (flat flame)...

Figure 2.3 presents the values of visible velocity Sh of a single spherical source [2] and laminar flame velocity [27] for hydrogen-air mixtures. Later on, the double ignition method was used in [20] for measuring combustion velocities of both laminar and turbulent flames in lean hydrogen-air mixtures. 

Figure 2.4 presents the laminar flame velocities measured by various techniques in H2 + air mixtures. The results obtained by Liu and MacFarlane [19] noticeably differ from those obtained for a spherical flame and in a Bunsen burner, which is explained by the stretch effect. In [19] they used a small nozzle with a 3-mm diameter it resulted in overrated combustion velocity values. Figure 2.5 presents... 

Data obtained for a smooth undisturbed flame by the spherical container method agree with the numerical simulation results of a spherical laminar flame propagation provided that an up-to-date detailed kinetic scheme with hydrogen oxidation and transport coefficients for describing multi-component diffusion of mass and heat are taken into account [27, 30, 43]. In some cases, when the agreement is not observed, it is necessary to analyze the arrangement of laminar flame velocity measurements. 

In practice, not all these conditions are met. It is the reason for a significant discrepancy in values of laminar flame velocity measured by various techniques and observed in some cases. For example, the difference in published values of the hydrogen-air flame combustion velocity in lean mixtures (15% H2 and less) runs up to 2.5 times. 

Development of Laminar Flame Velocity Measuring Techniques... 

Measurement of laminar flame velocities is complicated in quick-burning H2 + O2 mixtures, and the data published are conflicting. It specifically relates to a high pressure combustion. 

Fig. 2.7 The laminar flame velocities S in H2 + O2 mixtures at atmospheric pressure and 298 K temperature. The measured results [11] - i and [25] - 2 at Bunsen burner [53] - 3 at nozzle burner. The curve - calculated data taking into account detailed kinetics...

Currently, numerical simulations of flame propagation accounting for qualitative mixture compositions and multi-component transports have been widely performed. For example, calculation data of the laminar flame velocity in premixed H2 + air mixtures at atmospheric pressure and room temperature have been published in [27, 38, 54-57]. 

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. 

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