Proper interpretation and overall accuracy of laminar flame speed measurements of single- and multi-component liquid fuels
Introduction
Kerosene-based fuels continue to be among the primary energy sources in the world. However, there are still numerous complications and uncertainties that must be properly addressed when studying these fuels in the laboratory, which are blends of hundreds to thousands of hydrocarbons, and are typically identified by an average molecule. However, the uncertainty, or standard deviation around that average, is frequently not reported or taken into account when determining uncertainty in overall equivalence ratio.
It is well known that these liquid fuels have a very low vapor pressure, and as such extreme care must be taken to ensure that they remain in the vapor phase throughout the experiment. This difficulty is another cause for concern in overall equivalence ratio, as the partial pressure method (which of course requires the fuel to be in gas phase), is often used to determine equivalence ratio in spherical flame experiments.
While the fuels that are the subject of the present paper have been investigated in the past with regard to laminar flame speeds, to the authors’ knowledge, there has never been a detailed uncertainty analysis of the chemical composition for these fuels. These uncertainties must be realistically quantified for the experimental results to be useful to the kinetics modeling community. This paper details the uncertainties that are always present and the ways to limit the experimental uncertainties when working with liquid fuels.
This paper begins with a discussion of differences and possible discrepancies in actual fuel compositions as reported in laminar flame speed studies from the literature for Jet-A. The next section provides a description of the current experimental setup, and Section 4 provides a methodical experimental uncertainty analysis using n-decane as the test fuel. Section 5 discusses laser absorption measurements for Jet-A as a means to independently check the mass of fuel in the vapor phase and to gauge repeatability of the methods used. Section 6 looks at the use of fuel mole fraction, XFUEL, as opposed to equivalence ratio as a way to normalize the results and reduce overall uncertainty.
Section snippets
Uncertainty in fuel composition
Traditionally, laminar flame speed experiments are dependent on accurately knowing the fuel-to-air equivalence ratio, as it is the parameter most often used as the primary, independent variable of laminar flame speed measurements. As such, laminar flame speed is often plotted versus equivalence ratio. However, calculating equivalence ratio for complex blends of liquid hydrocarbons is not always as straightforward as it would be for pure fuels. Because there is often uncertainty in the average
Experimental setup
New experiments were conducted in the high-temperature, high-pressure (HTHP), stainless steel, constant-volume vessel at Texas A&M University (TAMU). The design of this vessel is described in detail by Krejci et al. [9]. During the study herein, it was determined that injecting a known mass of fuel to determine equivalence ratio was necessary. To know the amount of fuel for a given equivalence ratio, it was required to have an accurate value for the vessel internal volume. To this end, the
Decane as a tool to determine experimental uncertainty
Decane is useful to study because it is one of the key components of kerosene-based fuels and has an average molecule similar to that of commercial jet fuels. With a known chemical formula, C10H22, not knowing precisely the average molecular formula as a cause for any uncertainty in the fuel's overall behavior was removed. Therefore, decane proved useful to quantify the uncertainty and repeatability in the setup and to improve the experimental methods. This approach helped to determine the
Laser absorption measurements
To help independently verify the vaporization of the fuel and the experimental procedures, an in-situ laser absorption technique was used to monitor directly the gas-phase fuel concentration within the vessel. To this end, a 3.39 µm HeNe laser in conjunction with Beer's Law was used to verify XFUEL, leading to the equivalence ratio. This procedure was described in detail by the authors in [10].
The 4.2% uncertainty in the absorption cross section for Jet-A reported by Klingbeil et al. [19]
Fuel mole fraction versus equivalence ratio
In typical laminar flame speed studies, data are presented as laminar flame speed versus equivalence ratio. While this approach is excellent for single-component fuels, or well-defined mixtures, it is arguably less useful when the fuel is defined by an average molecule that could change, sometimes significantly, from one production batch to the next. It is also less useful when there is some variance or even no information provided at all on the average molecule for a given fuel batch within
Conclusions
Understanding and limiting the uncertainty in the fuel-air mixture being tested (and hence equivalence ratio) was a large portion of this study. The uncertainty was found to be φ = ±0.03 stemming from a combination of instrumentation and fuel properties. The uncertainty in flame speed was likewise calculated to be on the order of ±2.79 cm/s. This value is primarily due to the repeatability of the experimental data.
The experimental results presented herein addressed several sources of
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The Jet-A used in this study was provided by Dr. Tim Edwards at the Air Force Research Laboratory in Dayton, OH. This research was funded partially by the Qatar National Research Fund through award NPRP8-1358-2-579. Additional funding came from a Veterans Research Supplement under National Science Foundation award number EEC-1560155.
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