Thickness of the combustion wave

The creation of eddies in a combustion zone is dependent on the nature of the flow of the unburned gas, i. e., the Reynolds number. If the upstream flow is turbulent, the combustion zone tends to be turbulent. However, since the transport properties, such as viscosity, density, and heat conductivity, are changed by the increased temperature and the force acting on the combustion zone, a laminar upstream flow tends to generate eddies in the combustion zone and here again the flame becomes a turbulent one. Furthermore, in some cases, a turbulent flame accompanied by large-scale eddies that exceed the thickness of the combustion wave is formed. Though the local combustion zone seems to be laminar and one-dimensional in nature, the overall characteristics of the flame are not those of a laminar flame. 

The thermal structure of the combustion wave of a double-base propellant is revealed by its temperature profile trace. In the solid-phase reaction zone, the temperature increases rapidly from the initial temperature in the heat conduction zone, Tq, to the onset temperature of the solid-phase reaction, T , which is just below the burning surface temperature, T. The temperature continues to increase rapidly from T to the temperature at the end of the fizz zone, T, which is equal to the temperature at the beginning of the dark zone. In the dark zone, the temperature increases relatively slowly and the thickness of the dark zone is much greater than that of the solid-phase reaction zone or the fizz zone. Between the dark zone and the flame zone, the temperature increases rapidly once more and reaches the maximum flame temperature in the flame zone, i. e., the adiabatic flame temperature, Tg. 

Thus, the combustion wave structure of double-base propellants appears to showa two-stage gas-phase reaction, taking place in the fizz zone and the dark zone. The thickness of the fizz zone is actually dependent on the chemical kinetics of the... 

In order to clarify the combustion wave structure of AP composite propellants, photographic observations of the gas phase at low pressure are very informative. The reaction rate is lowered and the thickness of the reaction zone is increased at low pressure. Fig. 7.3 shows the reduced burning rates of three AP-HTPB composite propellants at low pressures below 0.1 MPa.FI The chemical compositions of the propellants are shown in Table 7.1. The burning rate of the propellant with the composition ap(0-86) is higher than that of the one with ap(0-80) at constant pressure. However, the pressure exponents are 0.62 and 0.65 for the ap(0-86) and Iap(0.80) propellants, respectively that is, the burning rate is represented by r for the p(0.86) propellant and by r for the p(0.80) propellant. 

Combustion models which consider the thickness of the reaction zone usually accentuate cither heat conduction mechanisms (thermal theory) or the diffusion mechanisms (diffusion theory) and the models are of necessity of limited value. Simpler models in which the reaction zone or flame front is considered to be an infinitesimally thin discontinuity in the flow, while not simulating exactly the observed conditions, allow the model to be of more general utility and many combustion phenomena become easier to understand because of this simplification. It is the latter approach which is discussed first in this paper—i.e., the combustion process is regarded as a wave phenomenon. 

While providing a simple method for analyzing the redistribution of energy in the combustion wave, the models discussed in the previous section do not account for the local structural features of the reaction medium. Microstructural models account for details such as reactant particle size and distribution, product layer thickness, etc., and correlate them with the characteristics of combustion (e.g., U,T,). 

The second model (Fig. 20c) assumes that upon melting of reactant A, a layer of initial product forms on the solid reactant surface. The reaction proceeds by diffusion of reactant B through this layer, whose thickness is assumed to remain constant during the reaction (Aleksandrov et al., 1987 Aleksandrov and Korchagin, 1988). The final product crystallizes (C) in the volume of the melt after saturation. Based on this model, Kanury (1992) has developed a kinetic expression for the diffusion-controlled rate. Using this rate equation, an analytical expression for the combustion wave velocity has been reported (Cao and Varma, 1994)... 

Nine compositions with the diamond concentration of 3, 5, 7, 9, 10, 12, 15, 20, 25 mass % were mixed with the charge Ti-C-Mo to produce multi-layered semi-products. The ready mixtures were placed layer-by-layer into a pressform in the following order diamondless layer weighing 25,5 g 3 mass % diamond layer, weighing 10 g 5 % layer -10 g 7 % layer - 10 g 9 % layer - 9,9 g 12 % layer - 9,9 g. After densification pellets were obtained 48 mm in diameter with the thickness of the layers 5.0, 2.0, 2.0, 2.0, 2.0, 2.0 mm correspondently. Multilayered pellets with the diamond concentration from layer to layer as much as 0, 5, 10, 15, 20, 25 % mass were prepared similarly. The final pellet was placed into a reactional mold. An SHS reaction was initiated from the lateral face of the cylindrical pellet by a tungsten spiral. After accomplishment of the combustion reaction and propagation of the combustion synthesis wave, the hot SHS-products were compacted in a hydraulic press at P > 400 MPa for no more than 10 s. The time of exposure to pressure was chosen dependent on the combustion temperature and reology of the products, e.g., on their plasticity and the amount of the liquid phase formed. Usually this time is 0.5 -4 2 sec. SHS-products were cooled at the room temperature. 

MAF 24, 443-50(1950) CA 45, 8772(1951) (Present state and value of the hydrothermo-dynamic theory of explosions and shocks, I. The plane shock waves compressibility by shock without combustion) 17) Ibid 25, 421-624 923-1006(1951) (Thickness of shock waves and mechanism of inflammation in combustion waves) 18) T. VonKarmdn, Termotecnica (Milan) 5(2),... 

Fig, XIV.7. Pressure profile of a one-dimensional detonation wave. = the velocity of the shock front relative to the unburned gases Vb(burned gases relative to the unburncd gases 5/ = thickness of combustion zone. 

The burning velocity Vq can be related to this wave thickness as follows. The mass of combustible material per unit area per second flowing into the wave is PqVq, where po is the density of the initial combustible gas mixture. The deflagration wave consumes these reactants at a rate wd (mass per unit area per second). Hence mass conservation implies that PqVq = wd, which, in conjunction with equation (1), yields... 

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