Inverse burning rate

The linear burning rate which is generally expressed in cm per second is determined using the lead fuse method [71]. However, it is the usual practice in pyrotechnics to report burning rate as inverse burning rate (IBR), expressed in seconds per cm. The method in brief is as follows ... 

White ammonium nitrate furnishes the slowest burning propellant-type mixtures, the use of catalysts and fuels decreases the burning time (inverse burning rate, used here for easier comparison with strictly pyrotechnical performance) to 2—5 sec/in. at a pressure of 1000 Ib/in. ... 

Burning rate BR)j Burning time (BT)—The linear regression of the reaction zone measured in in./sec or in other units is the burning rate the reciprocal term sec/in. should not be called burning rate but rather burning time or inverse burning rate. Rate is common for propellants, time for pyrotechnics such as flares and delay columns,... 

Turbulent mass burning rate versus the turbulent root-mean-square velocity by Karpov and Severin [18]. Here, nis the air excess coefficient that is the inverse of the equivalence ratio. (Reprinted from Abdel-Gayed, R., Bradley, D., and Lung, F.K.-K., Combustion regimes and the straining of turbulent premixed flames. Combust. Flame, 76, 213, 1989. With permission. Figure 2, p. 215, copyright Elsevier editions.)... 

Thus, th in a kinetically controlled regime is described by a dl law. Furthermore, th is found to be inversely proportional to pressure (for a first-order reaction) under kinetically controlled combustion, and in contrast, independent of pressure under diffusionally controlled combustion (since D P-1). In the kinetically controlled regime, the burning rate depends exponentially upon temperature. 

If Da = 1 is defined as the transition between diffusionally controlled and kinetically controlled regimes, an inverse relationship is observed between the particle diameter and the system pressure and temperature for a fixed Da. Thus, for a system to be kinetically controlled, combustion temperatures need to be low (or the particle size has to be very small, so that the diffusive time scales are short relative to the kinetic time scale). Often for small particle diameters, the particle loses so much heat, so rapidly, that extinction occurs. Thus, the particle temperature is nearly the same as the gas temperature and to maintain a steady-state burning rate in the kinetically controlled regime, the ambient temperatures need to be high enough to sustain reaction. The above equation also shows that large particles at high pressure likely experience diffusion-controlled combustion, and small particles at low pressures often lead to kinetically controlled combustion. 

The burning rate of a pressed strand of AP as a function of pressure has been dealt with by Ardenlil and by Levy and Friedman.PI The lower pressure limit of AP burning is about 2.7 MPa and the burning rate increases as the pressure is increased above this lower limit. The thickness of the gas-phase reaction of NH3/ HCIO4 is less than 100 pm at 10 MPa and decreases as the pressure is increased, and the reaction time is inversely proportional to the pressure (MPa) represented by 6.5 X 10 /p seconds.[ 1... 

The heat flux transferred back from the gas phase to the burning surface is dependent on the temperature gradient in the gas phase, which is inversely proportional to the thickness of the reaction zone in the gas phase. Since the reaction in the gas phase is complete at the upper end of the bluish flame, the heat flux defined by Am conforms to the proportionality relationship Am l/6g p0- . The observed pressure dependence of the burning rate, is caused by the pressure depend-... 

It is not surprising that the oxygen flux decreases or that the consumption of fuel decreases with time as the ash thickness increases. What one obtains, however, is an inverse square root dependence with time and a square root dependence with concentration. Thus for an ash-forming fuel in which ash remains Arm throughout the combustion process, the burning rate is proportional to the square root of the oxygen concentration and is independent of the convective nature of the oxidizer stream. 

The KDIE value normally is expressed as a ratio between reaction rate constants of the normal C—H compound and its C—D labeled analogue. While kh/ka rate constants are most often used, inverse induction period times ta/th > critical temperature Tch/Tca burn rates rbh/rbd, s id impact sensitivity Va/Vh > can be used since they all are dependent upon the global decomposition rate of the given energetic compound. This is especially important in chemical reactions or processes when one cannot directly obtain an experimental rate constant (k).5,7-10 There are three characteristics regarding the KDIE which one must remember, especially as it might apply to the complex thermochemical decomposition process of an energetic material ... 

Table 10.12 nicely shows the inverse relationship often encountered with spectral efficiency and burn rate. Even though mixing is far less ideal with all-coarse components, slower reaction allows better consumption than with very fast burning mixes. 

X 20 cm, 2.5 x 5 cm, 1.3 x 0.6 cm, etc, or even narrower ranges, are more conducive to uniform calcination. As an example, if the size ranges between 1.25—15 cm, the small size would tend to be severely over-burned, or the large size would be incompletely calcined if the small size was properly burned. At constant temperature, the rate of calcination varies inversely with the size of the stone, increasing with smaller fractions. 

The decrease in film burn-out heat flux with increasing mass velocity of flow at constant quality has been explained by Lacey et al. in the following way. At constant quality, increasing total mass flow rate means increasing mass flow of vapor as well as liquid. It has been shown that above certain vapor rates increased liquid rates do not mean thicker liquid layers, because the increased flow is carried as entrained spray in the vapor. In fact, the higher vapor velocity, combined with a heat flux, might be expected to lead to easy disruption of the film with consequent burn-out, which seems to be what actually occurs at a constant steam mass velocity over very wide ranges of conditions—that is, the critical burn-out steam quality is inversely proportional to the total mass flow rate. 

ATMOLYSIS. The separation of a mixture of gases by means of their relative diffusibility through a porous partition, as burned clay. The rates of diffusion are inversely proportional to the square roots of the densities of the gases. Hydrogen, thus, is the most diffusible gas. 

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