Mass Vaporization Rate Research Articles

Calculation of sublimation with allowance for impurity diffusion

We have calculated the impurity distribution in a spherical material during sublimation. The solutions found depend on two dimensionless parameters: separation factor β and diffusional Peclet number Pe = wR 0/(ρ1 D), where w is the mass vaporization rate, R 0 is the initial sphere radius, ρ1 is the density of the material, and D is the impurity diffusion coefficient. For the limiting cases Pe ≫ 1 and Pe < 1, we derived analytical expressions for the impurity distribution in the subliming material and for the average impurity concentrations in the residue and condensate as functions of time t or the degree of sublimation g(t). The present results can be used to optimize the dimensions of subliming materials and sublimation conditions.

Influence of droplet concentration on evaporation in a high-temperature gas

This paper presents the study of the evaporation of water droplets with initial sizes from 100μm to 300μm. The spray is falling down in high temperature gas counter flow with velocity of about 1.5m/s at temperature of about 1100K. The gas in this study is a mixture of air and combustion products of kerosene. The concentration of droplets in the gas flow varied in the range 0.2·10−4–1.2·10−4m3 of water/m3 of gas. This concentration corresponds to wide group of high-temperature gas–vapor droplets applications (e.g., firefighting by water mist, fog and dropping veil; thermal treatment of liquids; using the flows of flue gases, droplets and water vapor to transport heat). With the use of cross-correlation and high-speed video cameras, panoramic optical flow visualization techniques (PIV, Stereo PIV, PTV, IPI, SP) and Tema Automotive software the main parameters of the droplets evaporation process were measured, allowing to calculate the mass vaporization rates. The obtained laws allow predicting the conditions and characteristics of evaporation in a wide range of different droplets concentrations in a gaseous medium. It is demonstrated that increasing the number of droplets per unit volume may reduce the evaporation rate.

Transient gas phase interaction effects during droplet-stream combustion

Gas-phase transient effects during the combustion of an infinite linear array of droplets are studied in the limit of infinite Damkoler number and in the absence of surrounding convective effects. The present study stems from the quantification of truncation-distance effects on the droplet mass vaporization rate, flame position and flame shape in quasi-steady numerical simulations. The solution domain is initially split into near and far-field subdomains. Within each subdomain, analytical grid generation techniques are applied allowing the development of appropriate finite-difference expressions, the control of grid point distribution and the treatment of outflow boundary conditions. The interdroplet distance effect is studied and results for the droplet mass vaporization rate and flame behavior are presented. The results show the existence of different flame regimes ranging from isolated to merged flame conditions and similar vaporization rate evolution for different interdroplet distances.

Flame and droplet interaction effects during droplet-stream combustion at zero reynolds number

This work presents a numerical analysis of the quasi-steady combustion of an infinite stream of droplets in the limit of infinite Damköhler number and stagnant ambient conditions. The small and large length-scale phenomena associated with the process are addressed by splitting the physical domain into near- and far-field subdomains. Within the inner subdomain, validated expressions are used during the grid generation procedure, allowing the development of appropriate finite-difference expressions and control of the distribution of points. Analytical transformations are developed and applied to the outer subdomain coordinate system in order to match the inner and outer grids along the domain interface and to properly address the outflow boundary conditions using a regularly spaced grid. A system of transformed governing equations is obtained and discretized into a coupled system of algebraic equations, which are solved by standard scientific subroutines, incorporating automatic control of error. The developed transformations are inverted and the solutions within the physical domain are obtained. Interdroplet interaction effects are presented in terms of droplet mass vaporization rate, droplet lifetime, and flame-sheet shape and position for different droplet spacings and fuels. The results indicate interaction effects present over a broad range of interdroplet spacings and are compared with theoretical and experimental ones available in the literature.

Analysis of transient combustion of a multicomponent liquid fuel droplet

The transient combustion of a multicomponent liquid fuel droplet has been studied. The unsteady effects caused by the liquid- and gas-phase processes are considered. The numerical results demonstrate that due to the process of fuel vapor accumulation within the inner region to the flame and to the high liquid-phase mass diffusional resistance, a situation is reached where the concentration of fuel vapor in the inner zone of the flame or in the immediate vicinity of the droplet surface exceeds that at the droplet surface for certain values of the liquid-phase Lewis number. This results in a suppression of the mass vaporization rate (i.e., negative vaporization rate) without any indication of flame extinction. The results also indicate that with the increase in the volatility differentials between the mixture constituents vaporization is suppressed earlier in the droplet lifetime. However, by decreasing the liquid Lewis number, this phenomenon can be eliminated and the complete droplet lifetime can be computed. For example, the numerical results show that for a 50-50 by mass heptane-decane droplet, a liquid-phase Lewis number larger than three results in suppression of vaporization.

Unsteady vaporization of fuel droplets in a convective environment with varying ambient conditions

In the present work, a comparison of an integral and the two-dimensional boundary layer solution for the unsteady droplet vaporization problem has been made. The quasi-steady two-dimensional conservation equations (uncoupled from the liquid-phase) for the axisymmetric gas-phase boundary layer have been solved for both the circulating and the non-circulating droplets. The integral approach developed earlier (S. Prakash and W. A. Sirignano, Int. J. Heat Mass Transfer 23, 253–268 (1980)) for the gas-phase analysis of the droplet vaporization problem has been modified and extended for time-dependent ambient conditions, namely temperature, pressure, fuel mass fraction and free stream velocity. The effect of variation of these ambient parameters on the droplet vaporization has also been studied. It is found that the integral approach is reasonably good in predicting the heat and mass fluxes as well as the velocity temperature and the fuel mass fraction profiles across the boundary layer. Also the droplet lifetime is predicted reasonably well by the integral approach. The difference of fuel mass fraction at the droplet surface and in the ambience, ( Y Fs − Y Fe ), through its effect on droplet surface temperatures affects the droplet lifetime, though not significantly. Also, the rate of droplet heating during the earlier part of the droplet lifetime has a significant effect on the vaporization rate and the droplet lifetime. The lower values of ambient pressure during the earlier part of the droplet lifetime result in higher vaporization rates. As expected, the mass vaporization rates are reduced and the droplet lifetime is increased because of drag.

Convective droplet vaporization with transient non-convective liquid-phase heating

The vaporization of a liquid droplet in a hot convective gaseous environment when the internal liquid-phase motion is completely inhibited has been analyzed. A two-dimensional analysis of the droplet heating is employed in the present model. The liquid-phase heating is solved by an ADI method and is coupled to the gas-phase equations which are solved using an integral approach. The contribution of the wake region has also been included in a simplified manner. Transient mass vaporization rates and transient temperature fields within the droplet have been obtained for n -hexane, n -decane and n -hexadecane, and compared with those of droplet vaporization including liquid-phase circulation. The results indicate that droplet core heating is slow, whereas the rise in the surface temperature is initially fast, but persists throughout. The results further indicate that the droplet life-time is not affected very much by the absence or the presence of liquid-phase convections, although the temperature fields within the droplet are quite different. In the absence of liquid-phase circulation, the lifetime of the n -hexadecane (a less volatile fuel) droplet is reduced by about 10 percent. A one-dimensional model of droplet heating is also proposed.

Reduction of NO x and solids emissions by stagedcombustion of coal liquid fuels

Results are reported of experiments on the amenability of SRC-II coal-derived liquid fuels to combustion process modification by air staging for NO x and solids emission control. Two experimental systems were used: 1) a laboratory laminar flow reactor for determining rates of evolution of fuel-bound nitrogen from pyrolyzing arrays of 150 μm SRC-II fuel droplets, and 2) a pilot plant scale furnace for determining the effects of combustion air staging, air preheat, quality of atomization and fuel type on the conversion of fuel-nitrogen to NO x . These latter experiments were guided by computations of the conversion of fuel-nitrogen as a function of fuel equivalence ratio, temperature and residence time in the fuel-rich stage of the flame. Three SRC-II fuel types were considered in the studies: a medium distillate (450–500 K boiling range), a heavy distillate (560–728 K boiling range), and a 2.9/1 blend of medium to heavy distillate. Results of the droplet array pyrolysis studies show that, in general nitrogen evolution ratesare trailing mass vaporization rates at the beginning of droplet vaporization but that the two rates are comparable after a mass loss of 10 to 20%. For the heavy distillate and for the case of high rates of vaporization, nitrogen evolution rates exceed those of vaporization due to departures from equilibrium distillation conditions. Results of the combustion experiments show that there is a significant potential for controlling NO x and particulate matter emissions in coal-derived liquid fuel flames by combustion modifications; NO x emission levels were reduced from 550 ppm (at 3% O 2 ) measured in fast mixing single stage flames to less than 100 ppm (at 3% O 2 ) under optimized staged combustion conditions with particulate emission levels below 5.5×10 −6 kg/m 3 (300 K, 100 kPa). The overall excess air was maintained at ∼10% in the experiments.

On the role of oxygen in the horizontal flame spread of polypropylene

AbstractThe horizontal flame‐spreading behavior of slabs of uninhibited polypropylene (PP) and commercial polymethylmethacrylate (PMMA) is described, and the flame spread and mass vaporization rates are discussed. The quantities of peroxide and carbonyl moieties formed on the surface of PP beneath the flame front, determined by an iodometric procedure and by reaction with 2,4‐dinitrophenylhydrazine, are presented. A statistical analysis was performed to ascertain the significance of these quantities formed in four combustion environments, each differing in oxygen concentration. Flame and surface temperatures of the PP samples at each oxygen concentration as well as flame and surface temperatures of samples burned in 23% oxygen with an added external radiant heat source are presented. The data support the concept that surface oxidative reactions occur in the combustion of PP, that the quantity of oxidative products is related to the concentration of oxygen in the combustion environment, and the possible importance of these reactions in producing heat to propagate the flame is indicated. Comparison of PP and PMMA show that the two are quite dissimilar in flame‐spreading behavior.

Theory of quasi-steady one-dimensional diffusional combustion with variable properties including distinct binary diffusion coefficients

A previously formulated variable-property theory for a class of heat and mass transfer problems, exemplified by droplet vaporization and combustion, is generalized herein such that in addition to the previous features that the specific heats C, the thermal conductivity k, and the binary diffusion coefficient D ij are temperature dependent whereas C and k are further concentration-weighted, in the present formulation the D ij 's are also distinct for all species pairs. Explicit expressions are derived for the temperature and species profiles, the mass vaporization rate, and the flame-front standoff ratio. It is shown that oxidizer mass diffusion in the outer region and heat transport in the inner region are the dominant transport processes. A simplified model is recommended to obtain estimates of the various vaporization characteristics.

Surface Temperature and Disposition of Beam Energy for a Laser-Heated Target

An analysis has been carried out of an experiment in which a laser-produced plasma is probed with an electron beam. The target surface temperature as a function of time is obtained. The mass vaporization rate is obtained. The disposition of laser beam energy and of the target recoil momentum are given at three different times after laser pulse initiation. The results are discussed and compared with those of other experiments.

Calculations of steady state droplet vaporization at high ambient pressures

A mathematical model of a spherically symmetric quiescent droplet undergoing quasi-steady vaporization in the region of its thermodynamic critical point was investigated. By steady state it is implied that all the energy arriving at the droplet surface is carried away entirely by the mass transfer. Calculated steady state temperatures and rates of vaporization of a liquid carbon dioxide droplet vaporizing in a nitrogen atmosphere are reported for ambient temperatures of 500–1600°K and pressures of 70–120 atm. The calculations include the effects of non-ideal mixtures, solubility of nitrogen in the carbon dioxide liquid, variation of the properties through the boundary layer, the effect of total pressure on vapor pressure, and the non-ideality of the enthalpy of vaporization. All of these effects were found to be important. The theory indicates that at sufficiently high pressures, steady state conditions cannot be attained. This implies that the droplet vaporizes unsteadily from its injection conditions until complete vaporization takes place. At a fixed pressure, the thermal boundary layer increases with increasing ambient temperature and at a fixed droplet temperature decreases with increasing total pressure. The steady state mass vaporization rate increases with increased pressure and/or increased ambient temperature. The droplet temperature increases slowly with ambient temperature, the rate of increase being slowest in the region near the critical pressure.