外文文獻(xiàn)和翻譯---在多元液體氣化中改變液相大規(guī)模擴散的暫時性影響

南京工業(yè)大學(xué) 化學(xué)工程與工藝 專業(yè) 本科畢業(yè)論文 (設(shè)計 ) 外文資料翻譯 原文名稱 Effects of temporally varying liquid-phase mass diffusivity in multicomponent droplet gasification 原文作者 Huiqiang Zhang, Chung K. Law 原文出版 Combustion an Flame 翻 譯內(nèi)容頁碼 全文 中文名稱 在多元液體氣化中改變液相大規(guī)模擴散的 暫 時性影響 學(xué)生姓名 唐柯楠 專業(yè) 化學(xué)工程與工藝 班級學(xué)號 040126 指導(dǎo)教師 （簽字） 對譯文的評價 技術(shù) 學(xué)院 2008 年 6 月 1 Effects of temporally varying liquid-phase mass diffusivity in multicomponent droplet gasification Abstract The relative roles of liquid-phase diffusional resistance and volatility differential in multicomponent droplet gasification are revisited, recognizing that liquid-phase mass diffusivities can be substantially increased as the droplet is progressively heated upon initiation of gasification, leading to a corresponding substantial weakening of the diffusional resistance. Calculations performed using realistic and temperature-dependent thermal and mass diffusivities indeed substantiate this influence. In particular, the calculated results agree with the literature experimental data, indicating that the gasification mechanism of multicomponent fuels is intermediate between diffusion and distillation limits. Investigation was also performed on gasification at elevated pressures, recognizing that the liquid boiling point and hence the attainable droplet temperature would increase with increasing pressure, causing further weakening of the liquid-phase diffusional resistance. This possibility was again verified through calculated results, suggesting further departure from diffusion limit toward distillation limit behavior for gasification at high pressures. The study also found that diffusional resistance is stronger for the lighter, gasoline-like fuels as compared to the heavier, diesel-like fuels because the former have overall lower boiling points, lower attainable droplet temperatures, and hence lower mass diffusivities in spite of their lower molecular weights. 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Multicomponent droplet; Liquid mass diffusivity; Distillation 1. Introduction It is well established that the gasification mechanism of a multicomponent droplet is controlled by three competing factors, namely the volatility differentials, the liquid-phase mass diffusivity, and the droplet surface regression rate 17. Consequently, for slow surface regression relative to mass diffusion, as in the case of vaporization in a low-temperature environment, the droplet composition tends to be perpetually uniformized and the fractional gasification rates would be closely controlled by the volatility 2 differentials between the constituents. This leads to a gasification mode that is largely independent of liquid-phase mass diffusion, and as such resembles that of batch distillation 8. This is the formulation adopted in early studies of multicomponent droplet gasification. On the other hand, in the limit of very fast gasification relative to mass diffusion, the composition of the droplet is effectively frozen, so that the fractional gasification rates of the individual constituents are equal to their respective fractions in the original liquid composition. This leads to an onionskin mode of gasification, which is independent of the volatility differentials and as such is similar to the gasification of a solid. Since mass diffusion does occur in the liquid, even for situations of slow diffusion and rapid gasification, the gasification mechanism that has emerged for such mass-diffusion-limited gasification is one that consists of three periods 3,4. Specifically, after initiation of gasification, most of the volatile components in the surface layer are preferentially gasified, leaving this layer with a higher concentration of the less volatile, higher-boiling-point components. The droplet temperature subsequently increases, being largely dependent on the boiling points of the less volatile components. After the concentration layer is established, the supply of species from the droplet interior to the surface is controlled by the slow diffusion and droplet surface regression, resulting in a prolonged period of steady-state gasification, with the diffusion rate balancing the surface regression rate. Finally, toward the end of the droplet lifetime, mass diffusion becomes efficient again, resulting in a brief period during which the more volatile components are rapidly depleted from the droplet interior, with the concomitant increase of the droplet temperature to approach the effective boiling point of the less volatile components. Thus the characteristic of mass-diffusion limited gasification is the attainment of a fairly steady state of gasification resembling the onionskin mode, except for the presence of the thin transition concentration layer at the surface. Experiments were conducted 9 in which freely falling bicomponent droplets undergoing either pure vaporization or burning were abstracted at various stages of their lifetime, and the spatially averaged composition was subsequently analyzed. Results show that, except for mixtures whose volatility differential is minimal, the average molar fraction of the volatile component steadily decreases quite substantially, implying that a 3 steady mode of gasification is not attained. Furthermore, since the gasification sequence also does not appear to conform to that of batch distillation, the experimental results seem to indicate mixed-mode behavior. The primary objective of the present study is to gain further understanding, particularly quantitatively, on the gasification mechanism of multicomponent droplets, with the following focuses. First, recognizing that diffusion-limited gasification is favored for rapid gasification rates and components with large volatility differentials, while distillationlike gasification is favored otherwise, we shall extend previous studies 4,7 to systematically demonstrate these distinguishing influences. Second, it is also recognized that liquid-phase mass diffusivity is a sensitive function of temperature. Consequently it is reasonable to expect that the diffusivity could become progressively larger as the droplet is heated up upon the initiation of gasification, hence weakening the diffusional resistance responsible for the quasi-steady behavior. The extent of this sensitivity needs to be assessed. Third, as a corollary to the temperature sensitivity, and recognizing that the droplet temperature would increase with ambient pressure because of the corresponding increase of the liquid boiling point, it is also of interest to assess the extent to which diffusional resistance is further weakened as the ambient pressure is increased. This issue is of practical relevance because most internal combustion engines operate at elevated pressures. Fourth, we shall study mixtures that are representative of both diesel and gasoline fuels, noting that while the former have smaller diffusivities because of their higher molecular weights, the diffusivities can be enhanced to a greater extent because the droplet can attain higher temperatures on account of the higher boiling points of these fuels. In contrast, gasoline fuels have low molecular weights but also lower boiling points. It is therefore not clear a priori what are the relative gasification modes of diesel vs gasoline fuels. The structure of the paper is as follows. Since a satisfactory resolution of the above questions would require quantitatively realistic assessments, particularly in light of the sensitivity of the liquid-phase mass diffusivity with temperature and the mixture 4 constituents, we shall first extend, in Section 2, the constant (liquid-phase) property model 4 to variable properties. In Section 3 we shall study the response of bicomponent, diesel-like mixtures with a large volatility differential undergoing vaporization at moderate temperatures. The investigation, however, will still be performed in the context of constant liquidphase diffusivities in order to clearly bring out some of the underlying physics. In Section 4 we validate our variable property formulation by comparing the calculated results with literature experimental data, and subsequently we present, in Section 5, results and understanding gained on the various aspects of the gasification response discussed earlier. 2. Variable property formulation The problem of interest is the spherically symmetric gasification of a droplet, initially of radius and temperature and consisting of constituents having similar liquid densities and characterized by their respective diffusive and thermodynamic properties. At time this droplet is introduced, and ignited in the case of combustion, in a stagnant, unbounded atmosphere. The atmosphere is characterized by its temperature its pressure and the concentrations of its species consisting of the gasifying species, the oxidizer gas and a noncomdensible inert species such as nitrogen. In addition to the usual droplet combustion responses such as the droplet burning rate, the flame temperature, and the flame radius, we are also interested in determining the temporal variations of the temperature and composition profiles within the droplet, and the fractional gasification rates of the individual components. The detailed formulation, including the numerical scheme for the solutions and its accuracy, is given in 4. Briefly, the formulation consists of the quasi-steady description of the gas-phase transport, with or without flame-sheet burning, which is supported by the release of the fuel species with different gasification rates. The gas-phase solution is coupled to an unsteady analysis of the heat and mass transport processes within the quiescent droplet interior that is bounded by the regressing droplet surface, being governed by 5 subject to the initial and boundary conditions where is the droplet temperature, the liquid mass fraction of species the radial coordinate, and the droplet radius. Furthermore, and are the nondimensional expressions for the total and fractional mass vaporization rates, respectively, and are the nondimensional heat transfer to the droplet from the gas and the latent heat of vaporization, respectively, and and where is the thermal conductivity, the specific heat, and the subscripts and respectively designate the gas and liquid phases. Expressions for some of these parameters are given in 4. It is also noted that the use of Ficks law of diffusion for the mass fractions instead of the molar fraction, holds rigorously for a bicomponent mixture, which is the case studied in the rest of this paper, and approximately for components with similar molecular weights. The above equations can be readily solved numerically, given the gas-phase conditions or solutions. The gas-phase properties are treated as constants while the liquid-phase properties are treated as variables. This is a reasonable approximation because the transient nature of the present problem is driven by the corresponding transient variation of the liquid-phase diffusivity. The gas-phase properties, while spatially varying, are not expected to be temporally varying to any great extent. 6 It is also noted that this is a moving boundary problem because of the regressing droplet surface. In particular, although Eqs. (1) and (2) are the standard heat diffusion equations consisting of the transient and diffusion terms, the regressing surface imparts a convective influence to the transport processes within the droplet. The constituents of the mixtures studied are alkanes. In Appendix A we list the relations used in the evaluation of the various liquid-phase properties of these constituents and their mixtures. 3. Constant-property results It is useful to first specialize the variable liquidphase property formulation to that of constant properties in order to investigate the roles of volatility differential and surface regression rate in the gasification process. Two cases are considered: an equimolar hexadecanetetradecane droplet burning in 1300-K, 1-atm air, and an equimolar hexadecane decane droplet undergoing vaporization in 1020-K, 1-atm air. The former tends to promote quasi-steady diffusion-limited gasification behavior because of the small volatility differential and the high surface regression rate, while this tendency is weakened for the latter as the volatility differential is widened and the surface gasification rate decreases. The effects of liquid-phase diffusional resistance are represented by a constant liquid-phase Lewis number, Le, defined as the ratio of a thermal diffusivity to a mass diffusivity. Various Lewis numbers are used to simulate the influence of liquid-phase diffusional resistance: the larger the Le, the stronger the resistance. Since liquid-phase mass diffusivity is usually much smaller than thermal diffusivity, Le is a large number and we have adopted the value of 30, used in 4, to investigate the effects of strong diffusional resistance. In addition, we have also used the values of 5, 1, and 0.1 to characterize situations of weakened diffusional resistance. The cases Le =1 and 0.1 are both artificial, simulating the batch distillation mode of gasification, with the latter exaggerating the influence of mass diffusion. Fig. 1 shows the surface and center values of the molar fraction of the more volatile component, tetradecane, in the hexadecanetetradecane droplet. The time used here is a 7 nondimensional time, which is a normalized physical time when the holds rigorously. Results for the Le =30 case demonstrate that the gasification process basically follows diffusion-limited behavior in the development of a surface concentration boundary layer that persists until almost the end of the droplet lifetime, as shown previously 4. On the other hand, for Le =1 and 0.1， the facilitated diffusion renders the droplet composition fairly uniform throughout the droplet lifetime, with the volatile component steadily decreasing. This steady, instead of fairly rapid, reduction of the more volatile component is due to the small volatility differential between the two components. Thus the less volatile component, hexadecane, is gasified fairly efficiently even in the batch distillation limit. Fig. 2 shows the corresponding plot for the hexadecane decane droplet undergoing vaporization. It is seen that, for the Le =30 case, the strength of the diffusional resistance is mostly maintained, except that the diffusion wave does reach the droplet center earlier, hence slightly changing the composition there. The larger volatility differential also leads to a smaller volatile concentration at the surface, as compared to the tetradecane concentration in Fig. 1. For Le =1 and 0.1, the larger volatility differential leads to a fairly 8 rapid reduction of the volatile concentration, such that about 90% of its initial content is depleted at 30% of the droplet mass lifetime. The above results therefore indicate that liquid-phase mass diffusivity, as represented by Le, is perhaps the single most important parameter in controlling the gasification behavior, even for mixtures with large volatility differentials and as long as the gasification rate is not too low. Fig. 3 compares the experimental 9 and calculated temporal variations of the spatially averaged molar fraction of decane for a hexadecanedecane droplet; note that the initial concentration of the droplet used in the computation is the experimental value. It is seen that during the initial stage, when the calculated values obtained by assuming the two extreme limits of diffusion, Le =30 and 0.1, agree well not only with each other but also with the experimental value. The result for the Le =1 case is similar to that for Le =0.1 and hence is not shown. Fig. 2 shows that this is the same period during which the concentration boundary layer is established, for Le =30 The result is therefore reasonable and selfconsistent in that mass diffusion is efficient through the relatively thin concentration layer at the surface during the period when it is established, regardless of the assumed Le. Furthermore, the surface layer consists of a substantial amount of the mass of the droplet due to the volume, effect. Consequently the averaged amount is strongly 9 affected by the amount in the surface layer. Subsequent to this initial period of adjustment, the calculated result for the Le =30 curve gradually levels off while that for the Le =0.1 curve decreases rapidly. The experimental result is situated somewhere in between these two limiting modes of gasification, indicating that the gasification mechanism is a mixed one. In order to understand the cause for the observed mixed mode behavior, we have reevaluated the temporal and spatial variations of Le based on the calculated local composition and temperature for the Le =30 case. Fig. 4 shows that there is significant variation in Le, especially during the initial, transient period when the concentration boundary layer is established and the droplet is rapidly heated. After this period, the surface and center values not only progressively approach each other, but also appear to attain a fairly constant value that is substantially smaller than the originally assigned value of 30. Thus by using a constant Le =30 we have underestimated the correct Le initially, but overestimated it subsequently. The cause for this substantial and rapid reduction of Le is the equally substantial and rapid increase in the droplet temperature and the sensitivity with which liquid-phase mass diffusivity varies with temperature. To appreciate this influence, we also plot in Fig. 4 the temporal variation of the droplet temperature profile. It is then seen that the entire droplet 10 temperature, from the center to