Comprehensive study of initial diameter effects and other observations on convection-free droplet combustion in the standard atmosphere for n-heptane, n-octane, and n-decane☆
Introduction
Droplet combustion is an important scientific problem as it relates to the earliest theoretical treatments of liquid combustion which assumed spherical symmetry [1], [2]. For this configuration, the droplet and flame are concentric and the gas flow is due entirely to evaporation. Figure 1a is a schematic of the combustion symmetry that results. If soot is produced during the burning process the aggregates will be trapped between the droplet and flame by a balance of the inwardly directed thermophoretic force and outwardly directed drag force due to evaporation of the fuel [3], [4]. The soot shell that results is porous spherical shell-like structure. An illustrative example of this for n-decane is shown in the photograph of Fig. 1b at one instant of its burning history.
The classical theory of droplet combustion leads to a scaling for the droplet diameter and time in the form where K is the “burning rate”,
Furthermore, the relative position of the droplet surface to the flame, or the flame “standoff” ratio (Df/D) is predicted to be a constant. These outcomes are not consistent with the reported measurements. Regarding soot, the theory assumes a single step reaction and, thus, has no capacity to predict formation of soot precursors or a soot shell, though it will be expected that soot forms on the fuel-rich side of the flame and that the relative position of the soot shell diameter to the droplet surface, or the soot standoff ratio (Ds/D), will track with the flame position.
Extensions to the spherically symmetric theory have incorporated a wide range of processes to explain some of the effects neglected by the classical theory, such as transient droplet heating, variable properties, non-luminous radiation, and detailed combustion chemistry [5], [6], [7], [8], [9], [10], [11]. The inclusion of detailed combustion chemistry is particularly significant because it provides the capability to address soot formation through prediction of its precursors (e.g., acetylene, polycyclic aromatic hydrocarbons, etc.) [3], [12], [13], [14], [15]. The results of these detailed numerical treatments show that the droplet burning process is inherently unsteady, with the burning rate exhibiting a time dependence that originates in liquid phase unsteadiness persisting throughout burning2 or flame extinction mechanisms that force the burning rate to decrease near the end of burning, with the flame standoff ratio continually increasing with time. Experimental observations confirm predictions of these effects from detailed numerical modeling [8], [9], [10], [11].
Though the burning rate is predicted to be constant and independent of time and droplet size, experiments show that the burning rate decreases as the initial droplet diameter increases and that it depends on time [3], [13], [14], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31]. This trend has not been fully explained, owing in part to the inability to model all of the important processes in droplet burning (i.e., unsteady transport, variable properties, soot formation, radiation, complex combustion chemistry). Scale analysis [32], [33] as applied to droplet burning offers capabilities to develop an understanding of the important variables involved. Appendix A discusses this approach. Three regimes of burning based on Do are identified as depicted in a schematic form in Fig. 2, based on heat transfer from the flame to the droplet and ambience in terms of radiation and conduction transport. A single burning rate for a given droplet history is an outcome of the theory, though in fact K is often time dependent owing to unsteady heating and various extinction mechanisms (e.g., diffusive and radiative mechanisms, and transitions to low temperature combustion (LTC) or “cool flame” regimes of burning) that may arise during the burning process.
Neglecting radiation (regime I in Fig. 2), the scale analysis presented in Appendix A leads to the burning rate being independent of Do. This trend is consistent with detailed numerical modeling that also predicts K to be independent of Do [8], [13]. This approximation would remain in effect for droplet sizes down to those found in sprays [33], [34], [35], [36]. The upper bound of droplet diameter for radiation to be unimportant is indicated as DoI in Fig. 2 where the soot shell will not form due to small residence times [3]. For large Do where radiative losses from the flame to the ambience are more important than diffusive transport (regime III) an energy balance (discussed in Appendix A) on the flame leads to an inverse power relationship, (n = 2/7 from the scaling analysis). Effects such as radiative extinction [9], [25], [36] and LTC phenomena as first postulated by Nayagam et al. in 2015 [37] and subsequently analyzed with detailed numerical modeling [38], [39], [40], [41] may also be important in this regime. An intermediate regime where both radiation and diffusive transport are important would bridge regimes I and III. Figure 3 summarizes the postulated influences of Do on K through various convoluted phenomena that may occur during a dynamic droplet burning process.
Scale analysis does not provide quantitative information about the boundaries for the various regimes in Fig. 2. Such information will come mainly from experiment and detailed numerical modeling. The limited data suggest that DoI ∼1 mm. The upper range (DoII) is unknown though probably in the range of 2 mm [33]. One of the purposes of the present investigation is to examine the droplet burning process over the widest range 0.5 mm < Do < 5 mm to elucidate various regimes of burning. Measurements made across such a large range of Do as reported in this study will also be valuable to test the ability of detailed ab initio numerical models of liquid fuel combustion that assume the base case of Fig. 1 [8], [9], [10], [11], [12], [15], [41], [42]. It is important to note that the motivation for studying the burning process of the large droplets at the upper end of this range in no way is meant to suggest the relevance of droplets for Do ∼ 5 mm to practical spray systems. To the contrary, typical Do values in spray flames are on the order of 100 µm or less, which would be most relevant to regime I in Fig. 2 which extends to about Do ∼1 mm. On the other hand, the physical processes that emerge to control burning as Do increases are very much relevant to combustion of spray systems even if the actual droplet diameters are not.
The virtue of examining the droplet burning process in the context of Fig. 1 is, therefore, to provide quantitative measurements over the widest possible range of Do with the available consistent experimental facilities. The understanding of processes known to exist in large (e.g., spray) systems can still be derived from observations on the scale of individual isolated droplets, where it is recognized that moving boundary, radiative and unsteady transport dynamics remain as the length scale of a spray is reduced to the base case of spherical symmetry [7].
The fuels employed in the present study are n-heptane, n-octane, and n-decane. A selected set of properties is given in Table 1. Their detailed combustion chemistry is relatively well-developed and they are representative of a chemical class that is prominent in real transportation fuels [43]. Being also in a series of straight chain hydrocarbons the results will facilitate an understanding of how hydrocarbons in such a series burn and respond to changes across the wide range Do investigated.
Section snippets
Promoting spherical symmetry for droplet burning
The droplet burning configuration of interest here is depicted in Fig. 1. Its development relies on reducing the relative velocity between the droplet and ambience, whether by forced convective or buoyancy flows. The relevant dynamic parameters are the Reynolds number, , and the Rayleigh number, . Both should be “small”. A small velocity Ur is achieved by ensuring that the test droplet experiences minimal drift during the combustion process. Two experimental designs
International space station
An experimental design was developed to form, deploy and ignite free-floating droplets in the low gravity environment of the ISS. The droplet combustion hardware (i.e., the Multi-user Droplet Combustion Apparatus (MDCA)) is housed within the “Combustion Integrated Rack” (CIR) of the ISS. An outline of the hardware and procedures are presented here. More details of the hardware design have been provided elsewhere [46], [47], [48].
The ISS instrumentation package includes video cameras to record
Results and discussions
Fig. 8, Fig. 9, Fig. 10 show a selected set of images of the burning histories of n-heptane, n-octane and n-decane, respectively. The Do values are indicated at the top of the figures. The vertical dotted line in Figs. 8–10 separates the GB experiments (Do < 1 mm) from the ISS experiments (Do > 1 mm). The scale factors are indicated at the bottom of the figures. The images along any column show the burning history of droplets for the indicated Do. The time stamps (on the left) correspond to the
Conclusions
The influence of initial droplet diameter, Do, on burning of single n-heptane, n-octane and n-decane droplets under micro-gravity conditions was examined to provide a better understanding for this dimension's effect on the combustion physics of spherically symmetric droplets. The effects of Do are largely attributed to the interplay of soot formation and radiative heat losses, with the extent depending on the size of the Do. The main findings in the present study are summarized as follows:
Acknowledgments
This work was supported by the National Administration of Space and Aeronautics (NASA) under Grants NNX08AI51G to Cornell University (where the ground-based experiments were carried out). The authors are pleased to acknowledge Drs. Vedha Nayagam and Daniel Dietrich of NASA-Glenn who offered insights regarding data analysis and combustion physics of some of the observed trends and assistance with some of the reported experiments. Messrs Jeff Rah, Koffi Trenou, Wei-Chih Kuo and Anthony Savas of
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Part of this paper is based on a presentation given at the 52nd Aerospace Sciences Meeting of the American Institute of Aeronautics and Astronautics, National Harbor, Md., January 13–17, 2014, as paper no. AIAA-2014-1019.
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Current address: Center for Combustion Energy, Tsinghua University, Beijing 100084, P.R. China.