Mass burning velocity

The two-point boundary conditions for equation (42) are e = 0 at T = 0 and = 1 at T = 1. Three constants a, P and A, enter into equation (42). The first two of these constants are determined by the initial thermodynamic properties of the system, the total heat release, and the activation energy, all of which are presumed to be known. In addition to depending on known thermodynamic, kinetic, and transport properties, the third constant A depends on the mass burning velocity m, which, according to the discussion in Section 5.1, is an unknown parameter that is to be determined by the structure of the wave. Since equation (42) is a first-order equation with two boundary conditions, we may hope that a solution will exist only for a particular value of the constant A. Thus A is considered to be an eigenvalue of the nonlinear equation (42) with the boundary conditions stated above A is called the burning-rate eigenvalue. 

The linear burning velocity S is defined as the normal velocity of approach of the unbumt gas towards the flame front. Alternatively, the mass burning velocity M is the mass rate of consumption of reactant mixture per unit area of flame surface. By continuity, M is constant through a one-dimensional flame, and is given by... 

Kaskan, W. E. "The Dependence of Flame Temperatures on Mass Burning Velocity." Sixth Symposium (International) on Combustion, 134-43. Reinbold, NY, 1957. 

Kaskan, W. (1957). The Dependence of Flame Temperature on Mass Burning Velocity. Proc. Combust Inst, Vol. 6, pp. 134-143, ISSN 1540-7489... 

When the rate of accumulation dpjdt of all quantities in the system is zero, the condition is known as the steady state. All other systems are time dependent. Stationary flames supported on burners are steady-state phenomena, and so for a quasi-one-dimensional stationary flame d AMy)/dy = 0 and AMy = constant. In the hypothetical case of a true one-dimensional adiabatic flame the constant My is the adiabatic mass burning velocity. It is an eigenvalue solution of the physical problem, equal to the product of the density and linear velocity of the gas at any position in the flame. Thus... 

Turbulent mass burning rate versus the turbulent root-mean-square velocity by Karpov and Severin [18]. Here, nis the air excess coefficient that is the inverse of the equivalence ratio. (Reprinted from Abdel-Gayed, R., Bradley, D., and Lung, F.K.-K., Combustion regimes and the straining of turbulent premixed flames. Combust. Flame, 76, 213, 1989. With permission. Figure 2, p. 215, copyright Elsevier editions.)... 

If, in an infinite plane flame, the flame is regarded as stationary and a particular flow tube of gas is considered, the area of the flame enclosed by the tube does not depend on how the term flame surface or wave surface in which the area is measured is defined. The areas of all parallel surfaces are the same, whatever property (particularly temperature) is chosen to define the surface and these areas are all equal to each other and to that of the inner surface of the luminous part of the flame. The definition is more difficult in any other geometric system. Consider, for example, an experiment in which gas is supplied at the center of a sphere and flows radially outward in a laminar manner to a stationary spherical flame. The inward movement of the flame is balanced by the outward flow of gas. The experiment takes place in an infinite volume at constant pressure. The area of the surface of the wave will depend on where the surface is located. The area of the sphere for which T = 500°C will be less than that of one for which T = 1500°C. So if the burning velocity is defined as the volume of unbumed gas consumed per second divided by the surface area of the flame, the result obtained will depend on the particular surface selected. The only quantity that does remain constant in this system is the product u,fj,An where ur is the velocity of flow at the radius r, where the surface area is An and the gas density is (>,. This product equals mr, the mass flowing through the layer at r per unit time, and must be constant for all values of r. Thus, u, varies with r the distance from the center in the manner shown in Fig. 4.14. 

The total mass flux of A under the condition of the burning of a condensed phase, which imposes a bulk velocity developed from the mass burned, is then... 

Material Mass Burning Rate (kg/m s) Burning Velocity (mm/s)... 

Fig.13.8 Erosive burning model calculation and experimental data for erosive ratio as a function of gas flow velocity or mass flow velocity.

The combustion gas of an internal burning of a propellant flows along the port of the propellant If the nozzle attached to a rocket motor is removed, the pressure in the port becomes equal to atmospheric pressure and no sonic velocity is attained at the rear-end of the port. Then, no thrust is generated by the combustion of the propellant However, if the mass burning rate of the propellant is high enough to choke the flow at the rear-end of the port, the pressure in the port is increased and the flow reaches sonic velocity. The increased pressure in the port is converted into thrust. The thrust F is represented by... 

The assumption has been made that the pressure drop across a flame is so small that the momentum equation may be ignored. The steady-state restriction in the ordinary continuity equation ensures that the mass flux M is constant throughout. The mass flux is converted to the interesting parameter, burning velocity, by use of the cold gas density. 

Initial temperature affects maximum explosion pressure and rate of pressure rise. The maximum explosion pressure decreases when the starting temperature increases at the same starting pressure because of the lower density and thus smaller mass of material within a confined volume at higher temperatures. The maximum rate of pressure rise, (dp/dt)max, increases as the initial temperature rises because the burning velocity increases with an increase in initial temperature. 

The combustion velocities given in Table 13.4 show that the use of nano CuO is more of a factor towards high velocities than the Al when the Al is highly oxidized, and even slightly decreases performance when the velocity of pm-CuO / pm-A1 is compared to pm-CuO / nm-Al. The mass burning rate shows this even more starkly, as with a given particle size of CuO, the switch from micron to heavily oxidized nano aluminum decreases the mass burning rate. 

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... 

In the regime of heterogeneous propagation, the burning velocity may be estimated from equation (5-2) if w therein is approximated from results for droplet burning. If (1 4- v ) denotes the mass of the mixture reacted per unit mass of fuel burnt (where v is the stoichiometric fuel-gas ratio), then an estimate from equation (47), for example, is... 

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