Burning-rate formulas

Burning Rate Coefficient, sometimes designated as Burning Rate Constant It is the interior baiiistics parameter "a in the soiid-propeiiant linear burning rate formula r= apn, where r is... 

A number of phenomena excluded by the assumptions given in Section 3.3.2 can modify the burning rate of a droplet. These phenomena often are too complex to be included in accurate theoretical burning-rate analyses and necessitate semiempirical methods in deriving burning-rate formulas. The most important of these additional phenomena will now be considered. 

Equation (6) is the required mass-burning-rate formula, which (under our present assumptions) determines m in terms of the interface temperature 7] and the properties of both the solid and the activated complex. 

The two-dimensional nature of the process initially forced semiempiricism upon theoretical descriptions of erosive burning. The first proposed empirical burning-rate formulas were of the form... 

In Section 5.3.6, activation-energy asymptotics have been applied to the adiabatic version of equation (9) for a particular rate function w burning-rate formulas are given in Section 5.3.6 for this rate function and in Section 5.3.7 for others. Here it is convenient to presume that for L = 0, the burning rate is known on the basis of these results and to employ the known adiabatic mass burning rate for the purpose of nondimensionalization. Thus, in analogy with equation (5-18), we introduce the nondimensional stream wise coordinate = m CpX/X and obtain the equation... 

Turbulent convective burning of vertical plate. An approximate solution matched to data was given by Ahmad and Faeth [11]. The average burning rate mp for a distance x measured from the start of the plate is given by the formula below ... 

From your formula, compute the initial burning rate in g/s for pure convective burning. 

PATR 2488(1958)(New formulas for rapid calcn of linear burning rates of solid proplnts) 32)J. Delacarte et al, MP 41, 223 65(1959)(Contribution to study of rates of burning and other props of composite proplnts) 33)J Taylor, "Solid Propellant and Exothermic Compositions , Interscience, NY(1959), 55-6 34)C.Napoly, MP 42, 229-46(1960)(4 refs)(Relations between linear rate of burning, apparent potential and pressures for proplnts consisting of only NC, NG and Centralite) 35)Anon, "Ordnance Proof Manual , Aberdeen Proving Ground, Md,7-24 36)L.Shulman et al, PATR FRL-TR 41(1961)... 

Any marked deviation from the last two formulas produces gunpowder which has a slower burning rate or which burns with less vigorous effect.10... 

Many approximate formulas for A have been developed on the basis of the physical idea that conditions in the vicinity of the hot boundary control the burning rate (for example, [8], [31]). One way to see how these formulas may be obtained is to follow the approach of von Karman [32]. Multiplying equation (42) by (1 — e) — (1 — t) and integrating from 0 to 1 yields... 

FIGURE 5.6. Dependence of the term y in the formula for the burning-rate eigenvalue, equation (76), on the reaction order n. 

Since the processes described above occur in series, the slowest processes may be expected to govern the overall burning rate. A number of different burning-velocity formulas may therefore be obtained, depending on which processes are dominant. We shall first discuss interface processes and then consider spatially distributed processes in different phases. 

Equations (45) and (46) are only two of many formulas that have been used to describe erosive burning [8]. Most of the formulas that have been suggested are based on physical concepts of influences of crossflow on propellant burning. Among these concepts is the idea that high external velocities produce a turbulent boundary layer (see Chapter 12) on the propellant surface and thereby effectively increase the thermal diffusivity of the gas, which in turn increases the rate of heat transfer to the propellant and hence the burning rate [99]. The idea that turbulent convective heat transfer from the hot combustion products outside the boundary layer provides an additive contribution to the heat flux reaching the propellant surface and,... 

Another aspect of nonlinearity is a change in the mean burning rate, which is of importance in producing secondary peaks of the mean pressure. It is easy to write formulas for this change if the response is assumed to be entirely quasisteady. For example, if equation (7-41) is taken to apply under conditions of oscillatory pressure, then with m = mo(l -f m ) and p — p(l -f p ), where mo is the value of m at p = 0 (so that m 0 at finite amplitude), we find through expansion to second order (by use of the average p = 0) that... 

This is obtained from the above formula of "Ammon red star brilliant" replacing strontium carbonate with ultramarine, NajSa.3NaAlSi04 ( ). Specific gravity=1.08 g/cc Burning rate =5.5 mm/sec... 

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