Combustion velocity

The output from each case produces a wealth of information, including distribution of pressure, combustion products, rates of combustion, velocity components, etc. The results of each case will be summarized by presenting the pressure time histories at the eight locations that were presented in Figure 2 together with the flame speed along some selected directions. Some contour plots will also be presented. 

The flame velocity—also called the burning velocity, normal combustion velocity, or laminar flame speed—is more precisely defined as the velocity at which unbumed gases move through the combustion wave in the direction normal to the wave surface. 

Some pyrotechnic formulations Ti/KDN/NC and Ti/CsDN/NC were formulated and tested for combustion velocity, sensitivity to impact, friction and electrostatic discharge etc. The data show that both formulations are extremely sensitive to impact (the sensitivity being in the range of pure HMX and PETN ). Further, it is also seen that the Ti/KDN/NC formulation is less sensitive [145] than Ti/ CsDN/NC. On the contrary, the formulations show a moderate sensitivity to friction and electrostatic discharge. The evaluation of such systems as components in ignition formulations appear to be very promising as this may allow replacement of the heavy metal primary explosives which are toxic in nature. 

One cannot help being impressed by the dominant character of the methyl group. It would seem that when the electron release of the methyl groups is balanced across the benzene nucleus the knock resistance is increased this indicates that the velocity of combustion is slowed down. On the other hand, when the electron releases of the methyl groups supplement each other, as in the case of the vicinal derivatives, knock resistance is decreased this indicates that the combustion velocity is increased. An accumulation of methyl groups either upon the side chain, as in ferf-butylbenzene, or upon the nucleus, as in isodurene, seems to increase the knock resistance. 

The double bond functions in a very analogous manner. It too interrupts effective chain length and determines the principal point of oxidative attack. In a manner quite analogous to the methyl group, through changes in the combustion velocity, the double bond also alters the octane number and critical compression ratio. 

Ch.A. Lebailiff, FrP 1429285(1966) St CA 65, 12058(1966) [A compn, whose combustion velocity can be controlled is obtd by mixing a combustible (gelled hydrocarbons), an oxidizer (such as Amm nitrates, chlorates or perchlorates) and of an aq soln of a gum. Amines as stabilizers are added]... 

F. Maslonlsa, Determination of the Laminar Combustion Velocity of Gas Mixtures from Values of Explosion Times Found in Determination of Explosion Characteristics , Petrochemia 18 (3), 99-103 (1978) CA 90,57473 (1979) [Good agreement between expti and calcd data is reported for vinyl ethylene using the equation 7 Ty — a constant, where 7 is the laminar combustion vel and Tv is the expln time (or time to expin )]... 

In unpublished experiments by the late P. Ya. Sadovnikov (Institute of Chemical Physics), the combustion velocities of explosive mixtures of carbon monoxide with air, diluted by the combustion products, were compared. The diluted mixtures were preheated so that their combustion temperatures did not differ from the combustion temperature of the undiluted mixture. These experiments confirmed with sufficient accuracy the relation required by the theory... 

Thus, considering the low accuracy of the calculations and the inexactness of experimental determination of concentration limits, the agreement must be deemed satisfactory. In evaluating the character of the agreement, it should be kept in mind that we calculate the concentration limits from completely independent data on the combustion velocity, gas radiation and thermo-chemical constants. Meanwhile, to date, calculations have not gone beyond determination of limits for mixtures of several fuels on the basis of the limits of the individual fuels (Le Chatelier s rule). 

We determine the magnitude of the combustion velocity u, i.e., the lower boundary of the spectrum of eigenvalues for problem (16), as a function of the source parameters TV, r. ... 

Mathematical Theory of a Steady Regime and the Combustion Velocity... 

Performing the integration with various values of the parameter u, we locate by trial and error the value at which the boundary conditions are satisfied, and this is in fact the true value of the combustion velocity. 

On the other hand, if the velocity of the heating wave is greater than the combustion velocity, a steady regime is impossible indeed, during combustion the surface of the liquid is heated to the temperature TB, however, at this temperature in the liquid a chemical reaction begins to run which heats the adjacent layers of the liquid before they are able to evaporate and burn. The temperature distribution in the liquid will turn out then to be non-steady. 

Thus we may foresee that when the heating wave velocity exceeds the combustion velocity, this leads to transition from combustion to detonation. 

The condition of transition from combustion to detonation may be calculated in advance on the basis of experimental data with minimal knowledge of the reaction mechanism. In doing so we use (1) the dependence of the combustion velocity on the pressure, measured in experiments as u = u1pm ... 

The difference between the combustion temperature and its steady value depends not only on the value

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We shall call the bold line the [/-curve since it shows the dependence of the combustion velocity on the temperature we shall call the fine lines T-lines since formula (5.6) describes the dependence of the temperature on the combustion velocity. In the natural sciences the concepts a depends on 6 and 6 depends on a are not equivalent, whereas in mathematics a = fy(b), b = /2(a) and /3(a, 6) = 0 have completely identical meanings. 

Let us compare the behavior of two possible regimes A and B corresponding to a single p. Let us imagine that regime A is realized. A small drop in the combustion velocity u will cause, in accordance with the Tb/... 

Thus, for a given p, of two possible combustion regimes of the gas the one which corresponds to the greater combustion velocity and higher combustion temperature is the one that always occurs. 

What behavior do we expect from the system in this case Let, us imagine that the conditions for steady combustion are fulfilled, especially the corresponding gradient tps. As we saw, the regime S is quite rapidly—within the small relaxation time of the gas—replaced by another regime D with the same tp — tps, but with a larger combustion velocity. In accord with the increased combustion velocity, slow growth of tp occurs, accompanied by movement from D to C. 

The condition of the limit of steady combustion is related to the temperature dependence of the combustion velocity. The last formula states that steady combustion is possible only at an initial temperature at which the combustion velocity is not less than 1/e, i.e., is not less than 37% of the combustion velocity of the c-phase heated completely to the temperature Tb. Above the limit the dependence of the steady velocity on the initial temperature does not undergo any changes. 

This example is particularly convincing because as the pressure is lowered the combustion temperature can only decrease, and the combustion velocity drops noticeably. Thermal losses to the outside, which are usually used to explain the limit, only grow it is difficult to find another explanation for the observed fact. 

Under given external conditions (tube diameter, etc.) the relative heat transfer, on which the velocity and possibility of combustion depend, increases as the combustion velocity decreases. The existence of a limit for the feasibility of combustion at low pressure, depending on the drop in the combustion velocity with decreased pressure, is therefore natural (together with the possibility of existence of an upper limit which depends on the increase in TB as the pressure is raised—see the example of nitroglycerin above). 

Finally, the considerations developed for the conditions of ignition and the feasibility of combustion may also be applied to the combustion of coal, liquid fuel, etc., due to oxygen in the surrounding medium. In these cases the temperature gradient in the c-phase (in coal or oil) also plays a role in the thermal balance. A number of substantial differences, particularly a different form of the combustion velocity curve as a function of the parameters, makes a special study, inappropriate here, essential. 

Together with the questions of ignition and the feasibility (limit) of combustion, the concepts developed here are important for the combustion of EM or powder under variable conditions, in particular, at non-constant pressure. Variable pressure is accompanied by a variable combustion velocity, and to each value of the combustion velocity corresponds a particular value of the gradient ip which is established in the steady regime. It is at precisely this value pressure variation the temperature distribution in the c-phase is not able to keep up with the change in pressure for a non-steady value of

different from the steady value. For rapid pressure variation the combustion velocity turns out to depend not only on the instantaneous pressure, but also on its variation curve, which distorts the classical law of combustion. 

We analyze a theory of steady combustion of condensed materials (secondary EM and powders) which determines the distributions of the temperature and concentrations and the combustion velocity. 

On the basis of the non-steady theory we predict the combustion limit which is attained when the combustion velocity falls to 37% of the combustion velocity at the boiling temperature. The limit depends on the internal instability of combustion, not on external thermal losses. 

In another paper Ya.B. considered2 the interaction between pressure pulsations in a powder-driven rocket chamber with supersonic flow of the combustion products and pulsations in the combustion velocity. It turned out that for small sizes of the combustion chamber self-generation of oscillations appears, leading to... 

In the diagram of Fig. 1 the detonation velocity may also take values from some minimum D to infinity, as the deflagration (slow combustion) velocity may vary from zero to some maximum D1. 

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