Burning rate droplet

The burning rate of the droplet (kg/s), and its rate of change of radius ate related by ... 

Liquid mists of ethylene oxide will decompose explosively in the same manner as the vapor. Burning rate increases with decreased droplet size. 

The rate at which the droplet evaporates and bums is generally considered to be determined by the rate of heat transfer from the flame front to the fuel surface. Here, as in the case of gaseous diffusion flames, chemical processes are assumed to occur so rapidly that the burning rates are determined solely by mass and heat transfer rates. 

The previous developments also can be used to determine the burning rate, or evaporation coefficient, of a single droplet of fuel burning in a quiescent atmosphere. In this case, the mass fraction of the fuel, which is always considered to be the condensed phase, will be designated mr, and the mass fraction of the oxidizer ma. m0 is the oxidant mass fraction exclusive of inerts and i is... 

The form of Boq and Blq presented in Eq. (6.120) is based on the assumption that the fuel droplet has infinite thermal conductivity, that is, the temperature of the droplet is Ts throughout. But in an actual porous sphere experiment, the fuel enters the center of the sphere at some temperature 7) and reaches Ts at the sphere surface. For a large sphere, the enthalpy required to raise the cool entering liquid to the surface temperature is cpi(Ts — 7)) where cpi is the specific heat of the liquid fuel. To obtain an estimate of B that gives a conservative (lower) result of the burning rate for this type of condition, one could replace Lv by... 

It is now possible to calculate the burning rate of a droplet under the quasisteady conditions outlined and to estimate, as well, the flame temperature and position however, the only means to estimate the burning time of an actual droplet is to calculate the evaporation coefficient for burning, f3. From the mass burning results obtained, f3 may be readily determined. For a liquid droplet, the relation... 

For infinitely fast kinetics, then, the temperature profiles form a discontinuity at the infinitely thin reaction zone (see Fig. 6.11). Realizing that the mass burning rate must remain the same for either infinite or finite reaction rates, one must consider three aspects dictated by physical insight when the kinetics are finite first, the temperature gradient at r = rs must be the same in both cases second, the maximum temperature reached when the kinetics are finite must be less than that for the infinite kinetics case third, if the temperature is lower in the finite case, the maximum must be closer to the droplet in order to satisfy the first aspect. Lorell et al. [22] have shown analytically that these physical insights as depicted in Fig. 6.15 are correct. 

Current understanding of how particle clouds and sprays bum is still limited, despite numerous studies—both analytical and experimental—of burning droplet arrays. The main consideration in most studies has been the effect of droplet separation on the overall burning rate. It is questionable whether study of simple arrays will yield much insight into the burning of particle clouds or sprays. 

If, indeed, Eqs. (6.171) and (6.172) adequately predict the burning rate of a droplet in laminar convective flow, the droplet will follow a d3/2 burning rate law for a given relative velocity between the gas and the droplet. In this case (3 will be a function of the relative velocity as well as B and other physical parameters of the system. This result should be compared to the d2 law [Eq. (6.172)] for droplet burning in quiescent atmospheres. In turbulent flow, droplets will appear to follow a burning rate law in which the power of the diameter is close to 1. 

Finally, the burning rate of 8-(7 -norcaranylidene)-PCU (i.e., 5) has been studied. Compound 5 displays a rapid burning rate, i.e., 2.9 mm /s. The droplet explodes toward the end of the burn cycle, thereby indicating that a relatively large quantity of heat is released during the burning process. 

For vapour phase combustion, the burning rate of spherical droplets can be expressed as in equation (5.3) ... 

Ibid, pp 1075-79 Y) J.R. Richard et al, "Spontaneous Ignition and Combustion of Sodium Droplets in Various Oxidizing Atmospheres at Atmospheric Pressure , 12thSymp-Combstn, Poitiers, France, July 14-20, 1968 (Published in 1969), pp 39-48 Z) A. Ma ek J. McKenzie Semple, "Experimental Burning Rates and Combustion AA) F.J. Kosdon, "Combustion of Vertical Cellulosic Cylinders in Air , Ibid, pp 41-43 (8 refs) BB) Louis Viaud, Supersonic Combustion Research by ONERA , Ibid, pp 197-98 Note ONERA stands for "Office National... 

Injector design determines the physicochemical processes occurring in liquid propellant rocket engines. A complete quantitative description of the processes in liquid rockets is impossible because of our limited understanding of chemical reaction mechanisms and rates. The use of similarity principles simplifies the solution of theoretical combustion problems and is described for channel flow with chemical reactions and for diffusion flames over liquid droplets involving two coupled reaction steps. We find the new result that the observed burning rate of a liquid droplet is substantially independent of the relative rates of the coupled reactions. 

The use of the complete similarity relations for the specified 16 reaction steps appears excessively laborious in view of our lack of real knowledge concerning the dominant reaction paths. For this reason, we content ourselves with discussing the expected differences in estimated droplet burning rates when Reaction 20 is replaced by the following artificially concocted, highly simplified reaction scheme ... 

Thus, we find a remarkable lack of sensitivity for the calculated burning rates of an adiabatic droplet-burning process in which the reactions go to completion. This observed lack of sensitivity to reaction rates may well be related to the known successes (11,12, 22) of simplified diffusion-flame theories in theoretical predictions of droplet burning rates. 

The experimental techniques employed in the fundamental studies of the burning rate of a liquid droplet fall into three groups (a) The process of stationary, non-steady-statc combustion in which the combustion rate of a droplet suspended in a reacting medium is determined from the variation of droplet size with time (b) the process of stationary, steady-state combustion in which the geometric dimensions of a supported droplet are maintained constant during combustion and (c) the process of nonstation-ary, non-steady-state combustion in which a freely-moving droplet is allowed to come in contact with a gaseous reactant. 

EFFECT OF GAS TEMPERATURE ON BURNING RATE. It has been common practice in certain industrial applications to preheat the air before it enters the combustion region. The theoretical analysis of the droplet combustion process indicates that such an increased air temperature does not change materially the mass burning rate,... 

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