Burning-velocity calculations

It has been seen from the viewpoint of asymptotic analysis that when a one-step approximation is applicable for the chemical kinetics, the burning 

The problem in equation (83) is well-posed and solvable by matrix methods, with all eigenvalues being negative, and the derivatives dXi/dz at t = 1 are readily computed from equation (83). These derivatives provide linear relationships between and t in the reaction zone that enable the rates w,-there to be expressed explicitly in terms of t. A progress variable e for the effective one-step process may be defined, which changes from 0 to 1 across the reaction zone, and an equation of the form de/dz = Aoy(T) may be derived from equation (80), where A is inversely proportional to and cd(z) is known. Then 

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Before the size of the flammable portion of a vapor cloud can be calculated, the flammability limits of the fuel must be known. Flanunability limits of flammable gases and vapors in air have been published elsewhere, for example, Nabert and Schon (1963), Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985). A summary of results is presented in Table 3.1, which also presents autoignition temperatures and laminar burning velocities referred to during the discussion of the basic concepts of ignition and deflagration. 

The subject of flash fires is a highly underdeveloped area in the literature. Only one mathematical model describing the dynamics of a flash fire has been published. This model, which relates flame height to burning velocity, dependent on cloud depth and composition, is the basis for heat-radiation calculations. Consequently, the calculation of heat radiation from flash fires consists of determination of the flash-fire dynamics, then calculation of heat radiation. 

The cooling effect of the channel walls on flame parameters is effective for narrow channels. This influence is illustrated in Figure 6.1.3, in the form of the dead-space curve. When the walls are <4 mm apart, the dead space becomes rapidly wider. This is accompanied by falling laminar burning velocity and probably lowering of the local reaction temperature. For wider charmels, the propagation velocity w is proportional to the effective flame-front area, which can be readily calculated. On analysis of Figures 6.1.2b and 6.1.3, it is evident that the curvature of the flame is a function of... 

For Class D hazards, the company has defined the evaluation case event to be 8 x 106 Btu (8.4 x 106 kj) energy release as a hemispherical ground level explosion, unless a comprehensive analysis defines a lesser event as the evaluation case. For a VCE evaluation, this is further defined as the release and vaporization of 10,000 lb. (4,500 kg) of ordinary hydrocarbons, or the release and vaporization of 6,600 lb. (3,000 kg) of fast-burning materials [fundamental burning velocity >24 in/sec (>60 cm/sec)] within 5 minutes, when the largest connection to a tank or vessel is broken. [On a TNT basis, this is equivalent to a surface burst of approximately 2 tons (1,800 kg) TNT, calculated on the basis of 4% efficiency for ordinary hydrocarbons or 6.6% efficiency for fast-burning materials.]... 

As in the soap bubble method, only fast flames can be used because the adiabatic compression of the unbumed gases must be measured in order to calculate the flame speed. Also, the gas into which the flame is moving is always changing consequently, both the burning velocity and flame speed vary throughout the explosion. These features make the treatment complicated and, to a considerable extent, uncertain. 

Fig.13.8 Erosive burning model calculation and experimental data for erosive ratio as a function of gas flow velocity or mass flow velocity.

Use GRI-Mech (GRIM30. mec) and a laminar premixed flame code to calculate the burning velocity of a methane-air mixture at 1.0 atm. Repeat the calculation, replacing the nitrogen in the combustion air with helium. Compare flame speeds and adiabatic flame temperatures. 

Values of n are available for numerous gases and gas mixtures. Burning velocities have been measured on burner flames, and flame temperatures, Tb, can be computed thermodynamically. It is thus possible to put Equation 5 to a test by comparing experimental values of minimum spark-ignition energies with values calculated from data on quenching distances, burning velocities, heat conductivities, and flame temperatures. 

Results and Discussion. The burning velocity was calculated by the model described above for a number of different gas mixtures burning at stoichiometric conditions. Table 3 presents the compositions of the various gas mixtures studied. Each mixture is characterized by a mixture number MN and a mixture ratio R. 

Measurements of temperature and concentration in CO-H2-CH4 (or natural gas) flames were carried out. Rate profiles were developed for two excess air and two slightly fuel-rich flames as a function of temperature. Substitution of natural gas for methane does not bring about a marked change in the overall reactivity of these systems. Application of a modified theory analysis to these multiple-fuel flame mixtures allows one to satisfactorily correlate calculated values of the burning velocity with measured values. 

Figure 6. Correlation of calculated vs. measured burning velocities.

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