Burning rate equation

With T) = 1300 °C, Too = 25 °C and 7Fj0 = 1, we have two equations in two unknowns m" and nip for the extinction conditions. However, under only suppression of the burning rate, Equation (9.80) applies, giving a nearly linear result in terms of q" and m" as well as 02,oo. The nonlinearity of the blocking effect can be ignored as a first approximation, and the experimental results can be matched to this theory. By subtracting Equation (9.81a) from Equation (9.80), we express the critical mass loss flux as... 

Equation (3.54) is the simplified burning rate equation. If the reaction rates in the gas phase are known, the burning rate is given in terms of gas density (pressure), burning surface temperature, initial propellant temperature, and physical properties of the energetic material. 

When the logarithmic form of the burning rate equation given by Eq. (3.73) is differentiated with respect to the initial temperature of the energetic material at a constant pressure, the following is derived ... 

This burning rate equation with cross-flow is derived on the basis of experimental data and is known as the Lenoir-Robilard equation.I l... 

The constants "V and are dependent upon the chemical composition of the grains and their initial temperature. The burning rate equation (3.1) is based on the various empirical measurements and differs with the type of propellant. For one type of gunpowder the equation might be expressed as follows ... 

In fact, an area ratio equation such as (3.4) can be compared with the burning rate equation (3.2) by taking note of the fact that [or 0.24 in equation (3.2)] becomes 1— (or 0.76) in the area ratio equation. Therefore, equation (3.4) may be written. 

Burning rate equation R = Area ratio equation... 

The speed of burning of quickmatch is related to the chemical composition and the mass of the composition on the string. The linear burning rate equation enables a crude estimate of the speed of burning to be made. For example, a typical relationship already seen for gunpowder is given by equation (10.1),... 

This burning rate equation has been tested by McAlevy (58) with a so-called analog propellant. [The technique was first seriously exploited by Burger and van Tiggelen (17,96). ] In one form this propellant con-... 

Rastogi and Bisht (Ref 3a) made combustion studies on hybrid propints consisting of o-s m-and p-toluidine nitTates with aniline-formaldehyde polymer as solid fuels, and red fuming nitric acid as oxidizer. They found that the results fitted a burning rate equation of the type, = a (G)v, where a and v are constants and G is the mass velocity. The authors conclude that the heterogeneous combustion reaction is diffusion controlled, and its rate is dependent on particle size... 

Even when the reaction rate at the surface is effectively infinite, chemical kinetics in the gas can influence the carbon-burning rate. Equation (28) requires that residence times in the gas are short enough to prevent chemical depletion of O2 from occurring before oxygen reaches the solid surface. At sufficiently high temperatures—for example, above about 3500K—a substantial amount of dissociation of O2 may occur [39] O atoms are appreciably more reactive than O2 molecules on carbon surfaces... 

Equations (3.57) and (3.58) are substituted into Eq. (3.56) then, the burning rate equation for energetic materials propellant is given under the assumptions described above as... 

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