Burning-rate response

The ratio /t often is termed the response function, or the burning-rate response, and combustion-zone analyses typically provide magnitudes of order unity for it. Therefore, equation (52) indicates that y is of the same order of magnitude as the Mach number of mean flow of the burnt gas. This observation enables the order of magnitude of the growth or decay rate to be estimated directly from equation (30). More accurate computations necessitate calculating Re /x. The many different possibilities for steady-state structures of the combustion zone indicated in Chapter 7 imply that many different analyses can be relevant to the calculation of /i. Here we shall outline only two and comment on other approaches. 

FIGURE 9.4. Representative burning-rate response curves obtained from equation (66), showing a nondimensional measure of the amplification rate as a function of the nondimensional frequency for various values of the nondimensional activation energy for gasification, A, with A = IB. 

Figure 20 shows the time-domain burning rate response to a sinusoidal variation in pressure with 1% amplitude. This amplitude is small enough that the linear approximation is reasonably valid, i.e., output is proportional to input. 

Fig. 20 Small amplitude (linear) burning rate response (dyn) to sine wave variation in pressure with 1% amplitude. Mean input parameters are nominally those of non-dimensional case (Eg...

Fig. 22 which shows both magnitude and phase of the burning rate response as a function of non-dimensional frequency. 

Fig. 23 Large-amplitude (nonlinear) burning rate response to sine wave variation in pressure...

FIRE SIMULATOR predicts the effects of fire growth in a 1-room, 2-vent compartment with sprinkler and detector. It predicts temperature and smoke properties (Oj/CO/COj concentrations and optical densities), heat transfer through room walls and ceilings, sprinkler/heat and smoke detector activation time, heating history of sprinkler/heat detector links, smoke detector response, sprinkler activation, ceiling jet temperature and velocity history (at specified radius from the flre i, sprinkler suppression rate of fire, time to flashover, post-flashover burning rates and duration, doors and windows which open and close, forced ventilation, post-flashover ventilation-limited combustion, lower flammability limit, smoke emissivity, and generation rates of CO/CO, pro iri i post-flashover. 

Friedly (F4) expanded the theoretical analysis of Hart and McClure and included second-order perturbation terms. His analysis shows that the linear response of the combustion zone (i.e., the acoustic admittance) is not sign-ficantly altered by the incorporation of second-order perturbation terms. However, the second-order perturbation terms predict changes in the propellant burning rate (i.e., transition from the linear to nonlinear behavior) consistent with experimental observation. The analysis including second-order terms also shows that second-harmonic frequency oscillations of the combustion chamber can become important. 

A.C. McIntosh. The linearised response of the mass burning rate of a premixed flame to rapid pressure changes. Combustion Science and Technology, 91 329-346, 1993. 

This heat flux is responsible for the burning rate given by Eq. (3.71) in the low-pressure zone, as shown graphically in Fig. 7.7. 

The main species responsible for the blue flame from such a composition is cuprous chloride, CuCI hence the use of this salt together with the chlorine producer (hexachloroethane) and a source of extra copper (pyrotechnic copper powder). The cellulose dust acts as a moderator to control the burning rate of the pressed composition. 

The mere presence of the ash seems responsible for the ability of the LP3—AP propellant to undergo self-sustained combustion to pressures as low as 0.005 atm., an order of magnitude less than PBAA-AP and PB(CT)-AP propellants, and to maintain a relatively high burning rate at such low pressures. Two questions are of interest why does it form, and how does it sustain the burning rate It is not clear why the ash forms. It may be related to Bircumshaw and Newman s (14,15) discovery that only 30% of the original AP decomposes when the temperature is below ca. 350 °C. and that the remaining 70% is unreacted solid AP, and to the fact that the surface temperature and the temperature in the ash were measured by Most (60) as 250° 300°C. (The GDF theory with a collapsed A/PA flame indeed predicts a low surface temperature, ca. 400°C. below 0.01 atm.)... 

Nonlinear phenomena, usually associated with high amplitudes of the acoustic field, can introduce many interesting effects into acoustic instability [76]. Here we shall discuss only three topics involving nonlinearity the response of the combustion zone to transverse velocity oscillations (conventionally termed velocity coupling), changes in the mean burning rate of the propellant in the presence of an acoustic field, and instabilities that involve the propagation of steep-fronted waves (identified in the introduction as shock instabilities). 

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