Propagation velocity thermal front

At places where the front is concave toward the unburnt gas, the heat flux is locally convergent. The local flame temperature increases and the local propagation velocity also increases, see the red arrows in Figure 5.1.5. The converse holds for portions of the front that are convex. The effect of thermal diffusion is to stabilize a wrinkled flame. 

Along with the methods of similarity theory, Ya.B. extensively used and enriched the important concept of self-similarity. Ya.B. discovered the property of self-similarity in many problems which he studied, beginning with his hydrodynamic papers in 1937 and his first papers on nitrogen oxidation (25, 26). Let us mention his joint work with A. S. Kompaneets [7] on selfsimilar solutions of nonlinear thermal conduction problems. A remarkable property of strong thermal waves before whose front the thermal conduction is zero was discovered here for the first time their finite propagation velocity. Independently, but somewhat later, similar results were obtained by G. I. Barenblatt in another physical problem, the filtration of gas and underground water. But these were classical self-similarities the exponents in the self-similar variables were obtained in these problems from dimensional analysis and the conservation laws. 

In connection with Kokochashvili s observations there arises an important fundamental question about the stability of normal propagation of a continuous plane flame front. We must analyze the influence of convexity and concavity of the flame front on the propagation velocity. In mixtures in which the diffusion coefficient is equal to or less than the thermal diffusivity, a convexity (in the direction of propagation) decreases and a concavity increases the flame velocity. The increase in the velocity is explained by the fact that the mixture, enveloped by the concave flame from all sides, heats up more rapidly.12... 

The propagation velocity of the TM does not exceed 85-87% of the theoretical detonation velocity DT. Calculation of DT is carried out under the assumption of a chemical reaction which runs after compression by the shock wave without any thermal or hydrodynamic losses. In the case of the TM, meanwhile, the very possibility of propagation of a fast flame with the velocity of the shock wave depends on a velocity redistribution as a result of braking of the layers adjacent to the wall. In constructing the equations for the motion as a whole, braking plays the role of a loss which reduces the velocity. In fact, the velocity will be even smaller than the value cited besides the losses in the hydrodynamic preparation zone (the zone of velocity redistribution between the shock wave front and the forward point of the flame front, zone I-II in Fig. 19) we must add the losses in the combustion zone (from the forward point of the flame front to the cross-section in which combustion has ended, zone II-III in Fig. 19). 

In the reaction zone, superposition of convective cooling and heat consumption through the endothermic reaction leads to an accelerated cooling of the fixed bed. The ratio of the propagation velocity of the reaction front (uw0) and the thermal front can be estimated as follows ... 

Using the experimental values for the width of the traveling wave front (portion be, Fig. 8), let us estimate the propagation velocity for the case of a thermal mechanism based on the Arrhenius law of heat evolution from the known relationship U = a/d, where a 10"2 cm2/s is the thermal conductivity determined by the conventional technique. We obtain 5 x 10"2 and 3 x 10-2cm/s for 77 and 4.2 K, respectively, which are below the experimental values by about 1.5-2 orders of magnitude. This result is further definite evidence for the nonthermal nature of the propagation mechanism of a low-temperature reaction initiated by brittle fracture of the irradiated reactant sample. 

Here T is the temperature x is the coordinate / is the thermal conductivity c and p are, respectively, the heat capacity and density of the solid mixture of reactants Q is the rate of reaction heat release, and V is the propagation velocity of the temperature wave front. 

Detonation is a chemical reaction given by an explosive substance in which produces a shock wave. High temperature and pressure gradients are generated in the wave front, so that the chemical reaction is initiated instantaneously. Detonation velocities lie in the approximate range of 1500 to 9000 m/s = 5000 to 30000 ft/s slower explosive reactions, which are propagated by thermal conduction and radiation, are known as -> Deflagration. 

In adiabatic or near-adiabatic systems, since the coefficients of the adsorption isotherm depend on the temperature, there will be an additional mass transfer zone which propagates at the velocity of the thermal front. Thus, one may... 

Consider a planar premixed flame front, such as that sketched in Figure 5.1.1. For the moment, we will be interested only in long length scales and we will treat the flame as an infinitely thin interface that transforms cold reactive gas, at temperature and density T p, into hot burnt gas at temperature and density T, A.-The flame front propagates at speed Sl into the xmbumt gas. We place ourselves in the reference frame of the front, so cold gas enters the front at speed = Su and because of thermal expansion, the hot gases leave the front at velocity 14 = Sl(Po/a)- The density ratio, Po/Pb, is roughly equal to the... 

From similar space-time high-speed camera studies of the shock initiation to detonation of NMe, Cook et al (Ref 9) observed a flasb-across phenomenon in which, an apparent wave of luminescence originated in the explosive behind the initial compression front and propagated at a reported velocity of 35 mm/ftsec to overtake the initial compression front. This "flash, across phenomenon was interpreted as a heat transfer wave caused by a sudden increase in the thermal conductivity of the shock-compressed NMe. The phenomenon was taken as a direct observation of the "heat pulse , which Cook et al had predicted in 1955 (Ref 2)... 

The slower autowave process is similar in some respects to classical combustion, despite the differences in their physical nature. The wave velocity shows the same dependence on thermal conductivity as in the case of flame propagation. Analogously to combustion, the reaction zone is near the maximum temperature Tm [it is near Tm that the critical gradient (dT/dx) switching on the reaction is realized], whereas the greater part of the front... 

The thermal explosion mode is entered with a small temperature gradient of 1.25 K/mm. The temporal developments of the fuel coneentration, gas velocity, pressure and temperature fields are shown in Fig. 7.21. The solutions show a uniform increase in pressure to be soon attained, with but low gas velocities, throughout the volume. The apparent speed of propagation of the reaction front away from the centre is higher than the acoustic velocity, a function solely of the initial temperature gradient away from the hot spot. 

---