## Abstract

New laminar flame speed experiments have been collected for some kerosene-based liquid fuels: Jet-A, RP-1, and diesel fuel #2. Accurately understanding the combustion characteristics of these, and all kerosene-based fuels in general, is an important step in developing new chemical kinetics mechanisms that can be applied to these fuels. It is well known that the precise composition of these fuels changes from one production batch to the next, leading to significant uncertainty in the mixture average properties. For example, uncertainty in a fuel blend's molecular weight can have a noticeable effect on defining an equivalence ratio for a typical fuel–air mixture, of the order of 15%. Because of these uncertainties, fuel mole fraction, XFUEL, is shown to be a more appropriate parameter for comparison between different batches of fuel. Additionally, a strong linear correlation was detected between the burned-gas Markstein length and the equivalence ratio. This correlation is shown to be useful in determining the acceptability and accuracy of individual data points. Spherically expanding flames were measured over a range of fuel mole fractions corresponding to equivalence ratios of φ = 0.7 to φ = 1.5, at initial conditions of 1 atm and 403 K in the high-temperature, high-pressure (HTHP) constant volume vessel at Texas A&M University. These new results are compared with the limited set of laminar flame speed data currently available in the literature for this fuel.

## Introduction

Kerosene-based fuels, such as Jet-A, RP-1, and diesel fuel #2, are some of the primary energy sources for the world. However, they are also notoriously difficult to use in precision, laboratory-scale flame experiments. As such, there is actually far less research than one might expect into these fuels.

This lack of experimental data sets is partly due to the fuels which are heavy, liquid hydrocarbons having a very low vapor pressure, which often requires heating of at least some portion of the experimental system to get the fuel into the vapor phase. As pointed out by Ji et al. [1], system preheating requires a careful balance of potential fuel condensation at cold spots and runs the risk of fuel cracking at hot spots in the experimental system. There have arguably been few well-defined techniques utilized to address such concerns in laminar flame speed experiments. As is seen in the literature review, precision instruments are typically used to measure the total amount of fuel in the system, by measuring partial pressure, liquid volume, or mass flow rate. However, no technique has previously been utilized to measure the total gaseous fuel–air mixture in flame speed experiments of the type of interest in this paper.

Accurate knowledge of the laminar flame speed is key to the development and validation of chemical kinetics mechanisms. However, the laminar flame speed of kerosene-based fuels is not well known, with arguably no consistent answers in the literature, making it difficult to accurately validate the chemical kinetics mechanisms and apply them to these fuels.

This paper begins with a discussion of the fuels—Jet-A, RP-1, and diesel fuel #2—investigated in this study. A brief literature review is then presented highlighting some of the previous studies into these fuels. Next, the current experimental setup is presented, followed by a presentation and discussion of the experimental results. Following the presentation of the results, the benefits of using fuel mole fraction are highlighted. The paper then moves into the final conclusions.

## Fuels

There were three fuels included in this study. These were typical kerosene-based fuels: Jet-A, RP-1, and diesel fuel #2. These fuels were sourced through the Air Force Research Laboratory (AFRL), and therefore included a POSF number identification. The use of the POSF number as described by Edwards [2] and discussed recently by the present authors in Ref. [3] is important as it allows researchers to know precisely what fuel each other is testing. A summary of some of the key properties of these fuels is shown in Table 1. These are the properties used to calculate equivalence ratio and fuel mole fraction throughout this study. However, for simplicity, the fuels are herein referred to by their common name (Jet-A, RP-1, etc.) unless they are being directly compared to data from a different study where identifying the POSF number, and therefore the batch of fuel, is necessary.

Table 1

Properties of fuels included in this study

FuelPOSF #Average moleculeMW (g/mol)
Jet-A10325C11.4H22.1159
RP-15235C12H24.1168
Diesel fuel #212758C13.1H24182
n-decaneC10H22142.29
FuelPOSF #Average moleculeMW (g/mol)
Jet-A10325C11.4H22.1159
RP-15235C12H24.1168
Diesel fuel #212758C13.1H24182
n-decaneC10H22142.29

Shown in Table 2 are the major class compositions of the three fuels included in the study, which were taken directly from the information provided by their source. These values are given as mass fractions and are rounded to the nearest hundredth of a percent, and thus may not add up to 100%.

Table 2

Major component classes of fuels investigated

% Weight
Molecular categoryJet-ARP-1Diesel fuel #2
Alkylbenzenes12.900.1514.41
Alkylnaphthalenes2.33
Cycloaromatics3.430.0410.61
Iso-paraffins29.4535.0722.10
n-Paraffins20.030.4612.77
Monocycloparaffins24.8740.4123.33
Dicycloparaffins6.7821.6611.52
Tricycloparaffins0.212.19<0.01
Diaromatics<0.014.92
Triaromatics0.35
% Weight
Molecular categoryJet-ARP-1Diesel fuel #2
Alkylbenzenes12.900.1514.41
Alkylnaphthalenes2.33
Cycloaromatics3.430.0410.61
Iso-paraffins29.4535.0722.10
n-Paraffins20.030.4612.77
Monocycloparaffins24.8740.4123.33
Dicycloparaffins6.7821.6611.52
Tricycloparaffins0.212.19<0.01
Diaromatics<0.014.92
Triaromatics0.35

As can be seen, even though these fuels have similar average molecules, their compositions are very different. Jet-A has just under 50% iso- and n-paraffins and about 30% cycloparaffins, whereas RP-1 is 64% cycloparaffins and only 36% iso- or n-paraffin.

For these fuels to enter and remain in the vapor phase throughout the experiment, their partial pressures must remain below the fuel vapor pressure at the experimental temperature. For example, the vapor pressure for Jet-A is reported to be ≈3.6 psia (182 Torr) at 403 K [2]. For the experiments included in this study, the partial pressure of Jet-A ranges from 6.5 Torr at φ = 0.7 to 13.9 Torr at φ = 1.5. Therefore, while there might be some uncertainty in the vapor pressure, the fuel should stay in vapor form for all conditions being tested provided the temperature is uniform and there are no cold spots in the system. This analysis is discussed in more detail later.

A conflicting concern was that the fuel would crack or break down into smaller parts due to the elevated temperature in the test vessel. Widegren and Bruno [4] investigated the decomposition kinetics of Jet-A. Based on this study, Jet-A should not decompose in our experimental timescale until the temperature exceeds 648 K. Hence, fuel cracking does not appear to become a concern at the current experimental temperature of 403 K. Similar results were seen for RP-1 by Andersen and Bruno [5].

## Literature Review

Previous fundamental combustion studies on liquid fuels typically fall into one of three categories. These categories are:

1. Purely experimental studies which compare new data to a surrogate fuel using a chemical kinetics mechanism already in existence.

2. Analytical studies focused on proposing new and potentially better surrogates for kerosene-based fuel properties. These studies typically also improved on or developed new chemical kinetics mechanisms.

3. Studies that conducted some combination of the previous two categories.

First, it is important to understand what a surrogate fuel actually is. Surrogate fuels are blends of a few hydrocarbons that are commonly used to model the complex mixtures of hundreds of hydrocarbons typically found in kerosene-based fuels. Basic guidelines on how to develop a good surrogate were proposed by Edwards and Maurice [6]. Surrogate formulas typically fall into one of two categories, physical surrogates or chemical surrogates. A physical surrogate is a mixture that typically has the same physical properties, such as density, viscosity, and thermal conductivity, as the actual fuel. A chemical surrogate is designed to have the same chemical-class composition and same average molecular weight as the actual fuel [6]. Some of the first surrogates proposed sometimes had upward of 15 components, while single-component surrogates such as n-decane or n-dodecane were also suggested. Most of the surrogates that have been proposed in recent years have contained between two and six components.

Purely experimental studies were conducted in Refs. [713], whereas surrogate development and kinetics modeling were conducted in Refs. [1426]. The study of Denman et al. [27] proposed two new surrogates and compared them to their own experimental data. A brief discussion follows for some of these key studies.

The experimental results of Ref. [7] were all conducted using a spherical combustion chamber heated via a custom oven. Both the partial pressure method and the measured liquid volume of the fuel were used to determine equivalence ratio. The fuel was injected into the vessel using a 24 in.-long needle that had a 1/16 in. diameter. Fuel condensation was not believed to be concern because the fuel was injected directly into the heated vessel. A 12-component surrogate with an average formula of C10.6H20.2 was used to calculate the properties of Jet-A. Overall, they found that the model overpredicted the available flame speed data for Jet-A by 10 to 15 cm/s with an experimental uncertainty of about 4.5% An updated version of the chemical kinetics mechanism called the “Poll Mi mech 2” was published by Ranzi et al. [16].

The work of Violi et al. [14] looked at finding a surrogate for JP-8, which is the U.S. military equivalent to Jet-A. Three surrogate blends were proposed, with only one labeled “Sur_1” showing up elsewhere in the literature. “Sur_1” was a six-component blend consisting of: 30% n-dodecane, 20% n-tetradecane, 10% iso-octane, 20% methylcyclohexane (MCH), 15% m-xylene, and 5% tetralin by volume. There is some confusion about the use of volume fraction. Most surrogates specifically say they are defined as mole fractions, which would be the same as volume fractions for purely gaseous mixtures. With liquid fuels this of course is not the case. However, it is assumed that they mean mole fraction in such cases. This assumption is based on two factors: when the surrogate was used as a comparison point in the work of Ref. [7] it was assumed that the fractions were mole fractions, and all other studies by the same research group discussed below specifically state mole fraction.

Three successive studies by the same research group [810] present flame speed results for Jet-A. The first of these, Kumar et al. [8], stated an experimental uncertainty in equivalence ratio of less than 2%. An unspecified, 12-component surrogate was used to calculate equivalence ratio for Jet-A. For the next two studies, Hui et al. [9,10], an average molecule based on the AFRL POSF number was provided and used to calculate equivalence ratio. In Ref. [10], an average molecular weight 142±20 g/mol was specified, which results in an uncertainty in the average molecule of around 14%. It should be noted that the results for each of the three studies [810] are all different, but this discrepancy is not addressed in any of the papers.

The recent study of Narayanaswamy et al. [24] combined three of their single-component mechanisms [2830] to develop a new chemical kinetics mechanism specifically tuned for their proposed surrogate Jet_A that consisted of 30.3% n-dodecane, 21.2% m-xylene, and 48.5% MCH by mole fraction. This study compared the experimental results from Refs. [1] and [79] to their mechanism.

While several groups have collected data for kerosene fuels, particularly Jet-A, there does not appear to be any consensus in the literature as to the baseline laminar flame speed. While the data do show a trend that is moving to a slower flame speed, there is still a lot of scatter between the experimental results. Different parameters are seen as key for developing a good surrogate model. Some of the more-recent chemical kinetics mechanisms are specifically tuned to run for a specific surrogate, which limits their usefulness when exploring new fuels. Unfortunately, the amount of experimental data used as comparison points for new models is not as extensive as it initially appears. Previous groups have quantified their uncertainty in mixture equivalence ratio, based solely on the accuracy of their instrumentation, and have not used any secondary diagnostic technique to verify the mixture equivalence ratio.

## Experimental Setup

The high-temperature, high-pressure (HTHP), stainless steel, constant-volume vessel at Texas A&M University was used for all experiments in this study. The overall design of this vessel is described in detail by Krejci et al. [31]. Briefly, the vessel has an internal diameter of 31.8 cm and an internal length of 28 cm, for an overall internal volume of 25.8 L±50 mL. The fused-quartz windows provide an optical aperture with a diameter of 12.7 cm.

Due to the nature of the low vapor pressure liquid fuel, the HTHP vessel was slowly heated from room temperature to the experimental temperature (usually 403 K) with a heating jacket. This procedure usually took about 3 to 4 days, raising the set temperature of the heating jacket 20 °C every 8 to 12 h to ensure constant heating throughout. This heating procedure was completed prior to any experiments being conducted. Once the vessel was heated, as many experiments as possible were conducted prior to the vessel being cooled for maintenance.

Images were collected using the Schlieren setup shown in Fig. 1. With this setup, the density gradient at the edge of the flame becomes visible and can therefore be tracked. These images were collected using a high-speed (Photron Fastcam SA1.1, San Diego, CA) camera. Because frames that are either ignition-affected near the beginning, or wall-affected near the end of the experiment need to be removed for proper analysis, the frame rate of the camera was set sufficiently high (10,000 fps) allowing for at least 100 images to be used for flame speed analysis.

Fig. 1
Fig. 1
Close modal
An internally developed matlab-based edge detection and analysis program, outlined in Sikes et al. [32], was used to extract the unburned, unstretched laminar flame speed from these raw images. A circle is fit to the leading edge of the flame, in these images, and from that the change in radius with respect to time is calculated. This program then applies the appropriate nonlinear method as outlined by Chen [33]. The method used is based on the Markstein length, Lb, of the flame. If the Markstein length is positive, then nonlinear method I (Eq. (1)) should be used. A negative Markstein length requires the use of nonlinear method II (Eq. (2)). This result is then divided by the density ratio (Eq. (3)) to achieve the unburned, unstretched laminar flame speed (Eq. (4))
$Sb=Sb0−Sb0Lb(2rf)$
(1)
$ln(Sb)=ln(Sb0)−Sb0Lb(2rfSb)$
(2)
$σ=ρuρb$
(3)
$SL,u0=Sb0σ$
(4)

The Markstein length is one of the key parameters commonly calculated and presented in laminar flame speed research. It is a very good indicator of the overall stability of the flame and can be linked to turbulent flame structures. In general, a flame with a larger, positive Markstein length will be more stable, whereas a flame with a smaller and potentially negative Markstein length will be less stable. Monteiro et al. [34] described the Markstein length as the slope of the Sb versus stretch plot, while Burke et al. [35] described it as an indication of the flame's response to the strain rate. Thus, for a positive Markstein length, the flame speed will decrease as stretch increases, whereas for a negative Markstein length, the flame speed will increase with stretch.

Figure 2 shows examples of two flames from this study. While the exact value of the Markstein length is not immediately evident, its positive or negative nature is usually very easy to quickly determine. On the left is a flame with a positive Markstein length. The flame appears to be very round with a clearly defined edge. In contrast, the flame on the right has a negative Markstein length. Cellular structures can be seen forming, especially near the bottom of the flame. The overall structure of the flame also no longer appears to be spherical.

Fig. 2
Fig. 2
Close modal

Nonetheless, the Markstein length is not always the easiest parameter to use for data analysis. As noted in Ref. [33], the results can vary by up to 300% among different groups. Part of this variation might be due to the overall small physical values for the Markstein length. For example, in the present dataset the Markstein length typically ranges from around 0.17 cm for a lean and stable mixture to around −0.06 cm at richer and less stable conditions.

### Laser Absorption Measurements.

To measure the overall concentration of the fuel in the vessel, an in situ laser absorption technique was implemented. This setup has previously been described by the authors in detail [3,36]. This concentration measurement was done in conjunction with the well-known Beer's Law. In general, the measurement is based on the known absorption cross section for Jet-A taken from Klingbeil et al. [37] and RP-1 taken from MacDonald [38]. The stated uncertainty in absorption cross section for Jet-A was 4.2%, which results in an uncertainty of about φ = ±0.05.

These data points were collected using the partial pressure method. The measured fuel concentrations agreed fairly well with the predicted values in literature [37,38], within 6% for Jet-A and within 2% for RP-1.

## Results

Laminar flame speed results for the three fuels are presented in this section. During this study, a method was developed to help identify good, questionable, or bad data points. This method was partially based on an analysis of the burned-gas Markstein length.

### n-Decane.

The single-component surrogate n-decane was tested to help refine and verify the experimental procedure and to determine the overall uncertainty. For partial pressure-based experiments, this uncertainty was largely due to the measurement of the fuel partial pressure. For experiments where a measured mass of fuel was injected into the vessel, the uncertainty was based on the volume of the vessel and the experimental temperature, which affect the total number of moles of an ideal gas the vessel can hold, and therefore the equivalence ratio. This process is described in detail by the authors in Ref. [36]. As such, the laminar flame speed results were similar to those available in literature and for brevity are not reproduced here.

However, an interesting trend was discovered while looking at the resultant burned-gas Markstein lengths during the n-decane study. While the Markstein length is frequently reported in laminar flame speed studies, these results are almost never the primary focus of the study. For most hydrocarbons in general, the Markstein length decreases at richer mixtures. So, a trend along these lines was to be expected. However, as seen in Fig. 3, a very strong linear trend was detected. It was determined that a linear fit to these results might be useful in helping to determine the acceptability of data points.

Fig. 3
Fig. 3
Close modal
The linear correlation of the burned-gas Markstein length as a function of equivalence ratio is shown in Eq. (5), with Lb in cm. This equation is a linear fit based on the stoichiometric and rich data because there appeared to be significantly more scattered in the data for lean mixtures.
$Lb=−0.28105φ+0.40227$
(5)

The dashed lines shown are based off of a ±0.04 uncertainty in φ. This value comes from the experimental uncertainty in equivalence ratio (based on the measured mass method). Data points falling outside the dashed lines are not automatically rejected. However, if the flame speed is found to be significantly outside what is expected or from the trend displayed in the entire dataset, these points would be rejected.

### Jet-A.

As discussed previously, the Jet-A used for all experiments in this study was identified as POSF 10325 with an average molecule of C11.4H22.1 and a molecular weight of 159 g/mol.

Three different sets of data were collected for Jet-A, each with more-refined level of precision to ensure the correct amount of fuel was injected into the vessel. The first of these utilized a 0–1000 Torr pressure transducer (Baratron MKS 631C) to measure the partial pressure of the fuel. The second set of data was collected using a 0–100 Torr pressure transducer (Baratron MKS 631D) to measure the partial pressure of the fuel. The final set of data calculated equivalence ratio by injecting a known mass of fuel into the vessel. For the graphs that follow, these data sets are identified by the precision with which the fuel was introduced into the vessel.

The results for all three data sets are shown in Fig. 4. For each study, the results are divided into three different categories: Good, Questionable, and Bad. These designations are discussed in more detail below. Overall, the results for all three curves show fairly good agreement. All three saw a peak flame speed around 55 cm/s at φ = 1.2. However, there was also some significant scatter in the results, such as a 10 cm/s difference in measured flame speed around φ = 1.0. The 0–1000 Torr data has the least-defined curve, and it also appears to have the most scatter. This poorer quality makes sense due to the less-accurate pressure gauge used to measure the partial pressure of the fuel.

Fig. 4
Fig. 4
Close modal

With the large amount of data collected, other trends sometimes become apparent, such as when the measured flame speed results do not appear reasonable. Examples of this would be the points labeled as “bad” in the 0–1000 Torr and measured-mass data sets located around φ = 1.2. Both of these points measured a laminar flame speed around 50 cm/s, which is about 9% below the expected data based on the other results.

To help determine the accuracy of the data, a Markstein length correlation, similar to the one discovered for n-decane, was used. The correlation for Jet-A is shown in Eq. (6). An uncertainty of φ = ±0.1 was applied to help determine if data points were acceptable or not
$Lb=−0.30688φ+0.43925$
(6)

As can be seen in Fig. 5, most of the data follow the same trend. However, there are some data points that are clear outliers, looking again at the two data points around φ = 1.2. Based on the correlation, the Markstein length should be around Lb = 0.070994 cm. The measured Markstein lengths for the two data points are Lb = −0.0189 cm for the 0–1000 Torr data point and Lb = 0.18 cm for the measured-mass data point. These Lb are both outside of the acceptable limits. Since neither the laminar flame speed nor the Markstein length are within reasonable limits, those points were rejected as bad data.

Fig. 5
Fig. 5
Close modal

In contrast, there were several data points that fell almost exactly on the correlation line. An example includes the measured-mass data point at φ = 1.075, which had a measured Markstein length of Lb = 0.1071 cm compared to the predicted value of Lb = 0.10954 cm. The flame speed of 50.25 cm/s is also within the acceptable range.

Overall, the Markstein length data look very good. The 0–1000 Torr data appear consistently to produce a slightly smaller Markstein length. The 0–100 Torr and the Measured Mass data show better agreement, with the results almost right on top of each other. The Markstein length remained positive for almost all mixtures investigated. A slightly negative value was only measured at the very richest conditions tested, and therefore nonlinear method I was used for analysis almost exclusively. This positive Markstein length trend also indicates that the flames remained very stable throughout all equivalence ratios tested.

After analyzing all of the data together, a final dataset was assembled including only data points determined to be acceptable. These data are compiled in Fig. 6. The dashed line shown is a trend line to help better visualize the overall shape of the curve. As before, the peak flame speed is around 56 cm/s near φ = 1.18. Error bars shown are based off of the overall uncertainty analysis for liquid fuels discussed in Ref. [36].

Fig. 6
Fig. 6
Close modal

### RP-1.

The RP-1 used for all experiments was identified as POSF 5235, with an average chemical formula of C12H24.1. The molecular weight for the fuel was listed as 168 g/mol.

The initial dataset for RP-1 was collected using the 0–100 Torr pressure transducer to measure the partial pressure of the fuel. The data were later repeated using the more-accurate measured mass method. The combined results are shown in Fig. 7. Overall, the flame speed trend looks good, with a peak value between φ = 1.1 and φ = 1.2. The peak flame speed was found to be 56.8 cm/s. As can be seen, the results were fairly repeatable as evidenced by the four points around φ = 1.1 that returned flame speeds within 1 cm/s of each other.

Fig. 7
Fig. 7
Close modal

There were far fewer “questionable” or “bad” data points for RP-1 when compared to the results for Jet-A. However two points from the Measured Mass dataset appear to have significant errors. The first of these at φ = 1.04 returned a flame speed of 48.57 cm/s. In the same dataset, the similar equivalence ratio of φ = 1.05 was repeated twice, with measured flame speeds of 52.27 cm/s and 52.17 cm/s. While this 7% difference could be within the acceptable scatter in the data, similar scatter was not seen at other equivalence ratios in the study, so therefore the point was rejected. The other data point collected at φ = 1.168 similarly reported a significantly slower, around 11%, laminar flame speed than expected.

It was hoped that the Markstein length correlation would help explain these points that were judged as outliers. As with decane and Jet-A, a strong linear correlation was also seen between the burned-gas Markstein length and the equivalence ratio. The correlation for RP-1 is shown in Eq. (7). Due to the stronger linear trend, the uncertainty limits were set at φ = ±0.05
$Lb= −0.3268φ+0.4678$
(7)

The burned-gas Markstein lengths for RP-1 are shown in Fig. 8. Most of the measured mass data points fall right on the predicted value. There appears to be slightly more scatter in the Markstein length for the 0–100 Torr data. Unfortunately, the Markstein analysis did not provide any clear indication of the problem points discussed above, as the Markstein lengths, while not on the predicted value line, are nonetheless very close to the dashed uncertainty lines. The leaner of the two points (φ = 1.04) is 1.5% outside the limits, whereas the other point (φ = 1.168) is 7.5% outside the limits. Similarly, there were points with reasonable flame speeds that had Markstein lengths that were well outside the predicted values (greater than 10%). These points were lean mixtures where the linear correlation has shown not to be as strong.

Fig. 8
Fig. 8
Close modal

The consolidated RP-1 data are shown in Fig. 9. As can be seen, the peak flame speed occurs around φ = 1.2 using the MW provided by the source. Overall, the results for this fuel appear to be more repeatable than Jet-A. The error bars shown are based on the same uncertainty that was seen for Jet-A.

Fig. 9
Fig. 9
Close modal

### Diesel Fuel #2.

The diesel fuel #2 used for all experiments was identified as POSF 12758, with an average molecular formula of C13.1H24. This average molecule results in a reported average molecular weight of 181.53 g/mol. Compared to the other fuels included in this study, the diesel fuel experiments were conducted at a higher temperature. The experimental temperature was initially raised to 413 K due to large amounts of condensation on the windows when attempting mixtures at 403 K.

The first set of data collected used the 0–100 Torr pressure sensor to calculate equivalence ratio; these data are referred to as “413 K PP.” The mass-based data were collected at increasing temperatures, and in the graphs that follow are labeled by the experimental temperature.

As seen in Fig. 10, the initial data produced reasonable results. The measured flame speeds were similar to those seen for Jet-A and RP-1 at the given equivalence ratios. Experiments were limited to lean, stoichiometric, and slightly rich mixtures due to obvious condensation on the windows when attempting richer mixtures. At the maximum equivalence ratio shown, φ = 1.161, only slight condensation was detected on the window. At the slightly richer condition, φ = 1.174, filling was aborted due to large amounts of condensation.

Fig. 10
Fig. 10
Close modal

When these experiments were attempted using the mass-based method, it was quickly noticed that there was something wrong. An initial mass loading of diesel fuel #2 of 1.52 g, which should have resulted in φ = 1.0, proved to be too lean to burn. Based on the corresponding partial pressure, 6.34 Torr, this should have resulted in φ = 0.765. Thus, it was understandable why it might have been too lean to burn. Based on these numbers, the back-calculated molecular weight was MW=240 g/mol, or 32.6% greater than expected.

These factors strongly indicated that fuel was pooling somewhere in the vessel and hence not entering or remaining in vapor form. To test this hypothesis, an extremely rich mixture, φ = 1.41, was tested with a fuel mass loading of 2.11 g. The data point, as seen in Fig. 11, shows where the loaded mass calculates the equivalence ratio, whereas the error bar extending to the left shows where the measured partial pressure calculates the equivalence ratio. As can be seen, if the partial pressure value was used, the resultant flame speed will be similar to what had been seen previously, thus verifying that fuel was pooling somewhere and not fully vaporizing. To get the measured partial pressure and mass-based methods results to agree in terms of the equivalence ratio, the temperature of the vessel needed to be raised.

Fig. 11
Fig. 11
Close modal

The temperature of the vessel was raised in 5 deg increments to control the leak rate of the vessel, while still finding a temperature that would allow the fuel to fully vaporize. As expected, as the temperature increased, the calculated molecular weight moved closer to the reported value, which resulted in the injected mass and measured partial pressure returning closer equivalence ratios. The increase in temperature also resulted in an increase in laminar flame speed. There was a 16 cm/s difference in flame speed at φ = 1.0 between 423 K and 448 K. At 448 K, the calculated molecular weight of diesel fuel #2 was 190.16 g/mol, a value 4.75% greater than the value reported by the supplier. However, there was little change in this value between 443 K and 448 K. Also at 448 K, a full curve was able to be collected with a peak value around φ = 1.2. Therefore, the temperature was not increased any further. Complete results are shown in Fig. 12.

Fig. 12
Fig. 12
Close modal
As with the previous fuels, an analysis of the measured burned-gas Markstein length was conducted. For this analysis, only the data collected at 448 K were used. Once again, a strong linear trend was seen. The correlation found for n-decane was adjusted in accordance with the previously described method. The current equation is shown as Eq. (8). Based on this analysis, the only point that could be considered questionable is the richest mixture tested, at φ = 1.425. The corresponding Markstein length results are shown in Fig. 13
$LB=−0.034633φ+0.4957$
(8)
Fig. 13
Fig. 13
Close modal

## Equivalence Ratio Versus Mole Fraction

Traditionally, equivalence ratio has always been used on the x-axis of flame speed plots. When dealing with these complex fuels, this way of presenting the data may not always be the best method. As has been shown by the authors previously [3,36], fuel mole fraction, XFUEL, is arguably a better parameter, especially when comparing different studies that used different average molecules or molecular weights to define their fuel (and hence equivalence ratio).

As seen in Table 3, there are significantly different average molecules that have been used to define Jet-A in the past. The average molecular weight of these fuels typically ranges from around 140 g/mol to 160 g/mol. This range is a difference of just over 14% difference. This variation is not reflected in true error bars ever reported around φ. Proposed surrogates are moving toward even smaller average molecular weights, like the recent surrogate proposed by [24], with an average molecular weight of 121.74 g/mol.

Table 3

Average molecules and molecular weights for various batches of Jet-A and identified surrogates

SourcePOSF #Avg. moleculeMW (g/mol)
Identified average molecules for Jet-A
Edwards [2]4658C11.7H22.6140.53
Dooley [22], Hui and co-workers [9,10], Kang [39]4658C10.17H19.91142.22
Edwards [2], Wang [40], Kang [39], TAMU (this study)10325C11.4H22.1159.12
Singh et al. [7]C10.6H20.2147.67
Denman et al. [27]C10.9H23154.07
Wu [13]C11.16H20.82155.02
Jet-A surrogate blends
Violi “Sur_1” [14]C10.3H20.5144.37
Narayanaswamy [24]C8.727H16.788121.74
SourcePOSF #Avg. moleculeMW (g/mol)
Identified average molecules for Jet-A
Edwards [2]4658C11.7H22.6140.53
Dooley [22], Hui and co-workers [9,10], Kang [39]4658C10.17H19.91142.22
Edwards [2], Wang [40], Kang [39], TAMU (this study)10325C11.4H22.1159.12
Singh et al. [7]C10.6H20.2147.67
Denman et al. [27]C10.9H23154.07
Wu [13]C11.16H20.82155.02
Jet-A surrogate blends
Violi “Sur_1” [14]C10.3H20.5144.37
Narayanaswamy [24]C8.727H16.788121.74

Unlike equivalence ratio, which is highly dependent on the average molecule used to calculate the stoichiometric ratio, fuel mole fraction is a straightforward description of the overall amount of fuel in the mixture. This way of presenting the data removes any confusion about what the fuel composition actually was and how much was present in the mixture.

When selecting the appropriate chemical kinetics mechanisms, there are several parameters that need to be taken into account. These include, but are not limited to: average chemical formula, H/C ratio, and chemical composition. The average formula of Jet-A, POSF 10325 is C11.4H22.1 with an H/C ratio of 1.938. As reported by the authors of Refs. [2,39], and [40], the chemical composition of POSF 10325 is 16.49% aromatics, 52.69% paraffins, and 30.83% naphthenes. Ideally, the more parameters that can be matched the better.

The recent, 3-component “Narayanaswamy surrogate” and accompanying chemical kinetics mechanism of Ref. [24] was specifically designed for Jet-A. This model was developed to use one hydrocarbon molecule from each of the major classes of hydrocarbons found in typical jet fuels and included: 30.3% dodecane, 21.2% m-xylene, and 48.5% MCH to represent paraffins, aromatics, and naphthenes, respectively. One of the drawbacks to this mechanism is the limited number of species included. For example, the mechanism does not contain n-decane, which is frequently used in other jet fuel surrogates. This drawback limits the number of surrogates that can be tested with the mechanism.

Another possible disadvantage of the “Narayanaswamy surrogate” is that it is actually not a very good match for the current batch of Jet-A. That is, the average chemical formula is C8.73H16.79 with an H/C ratio of 1.923. While this formula is a fairly close match in term of H/C ratio, with a 0.77% difference, there is actually a difference of almost three carbon atoms and five hydrogen atoms leading to a difference of 23.5% in the average molecular weight. As can be seen in Fig. 14, the chemical composition is not a perfect match either. While the same three major classes of hydrocarbons are present, the ratios are not the same. While paraffins, in this case n-dodecane, make up just under a third of the “Narayanaswamy surrogate,” they account for over 50% of the current Jet-A. Likewise, the naphthene species, MCH, accounts for just under half of the surrogate, while it measures a little under a third of the current batch of Jet-A.

Fig. 14
Fig. 14
Close modal

Similarly, the initial surrogate of Violi et al. [14], labeled “Sur_1” appears to be a better match to the current Jet-A. When the six components of the surrogate are divided into the three hydrocarbon classes discussed above, as seen in Fig. 14, the surrogate appears to be a much better match to POSF 10325 than the “Narayanaswamy surrogate.” The average molecule for the surrogate works out to be C10.3H20.5, which is not a perfect match for the current fuel, but it is closer.

As expected, because of the difference in average molecule, there is still a mismatch in the data peak when φ is used as the metric for comparison. These results are shown in Fig. 15. The peak flame speed for the surrogate is around φ = 1.08 compared to φ = 1.2 or around 11%, which is similar to the difference in the average molecular weight of the surrogate (144 g/mol) compared to POSF 10325 (159 g/mol).

Fig. 15
Fig. 15
Close modal

When the x-axis is switched to XFUEL, as seen in Fig. 16, the locations of the curves show excellent agreement. The peak flame speed for the surrogate (60.64 cm/s) does end up to be around 7.5% faster than the experimental data (56.38 cm/s).

Fig. 16
Fig. 16
Close modal

## Conclusions

New laminar flame speed data have been collected for three common, kerosene-based fuels: Jet-A, RP-1, and diesel fuel #2. An additional study was performed on n-decane to verify and improve the experimental procedure for working with these low vapor pressure fuels but is presented in depth elsewhere [36].

Overall, the fuels had very similar results. All fuels saw a flame speed that peaked between 56 and 60 cm/s between φ = 1.1 and φ = 1.25. While this is a richer peak equivalence ratio than expected, it is shown to be caused by the average molecule (as defined by the supplier) used to calculate the equivalence ratio. This observation is in part verified when switching to fuel mole fraction as the parameter to use when comparing results to the data (and models) available in the literature.

During the data analysis, a strong linear correlation was noticed for the burned-gas Markstein length for these fuels. This trend appears to be stronger for stoichiometric and rich mixtures. Fortunately, this correlation appears useful as a tool to help identify potentially inaccurate data points. More research should be conducted in this area to improve the correlation for lean mixtures and determine the application to other fuels.

When adjusted to XFUEL, direct comparisons to surrogates through chemical kinetics mechanisms and other experimental data are possible. The proposed surrogates also appear to be predicting slightly faster laminar flame speeds than the current experimental results suggest. However, many of these surrogates, such as the “Narayanaswamy Surrogate” [24], were all tuned using the experimental results from counterflow configurations [1,811]. As previously mentioned, the counterflow configuration is known to produce slightly faster results [41]. Therefore, the current spherical flame data should be used to develop and tune improved surrogates and chemical kinetics mechanisms.

However, experimentally, the largest source of uncertainty is with the fuel itself. With 15% uncertainty in the fuel average molecule, it becomes difficult to fully know with what chemical composition anyone is actually working. Surrogate mixtures are frequently used to model these real fuels, and they also have well-defined and known average molecules. However, when comparing the model results to experimental data, it is important to know if the surrogate has been chosen to match the fuel, or if the fuel composition has been artificially adjusted to match the surrogate.

For the liquid fuel community, it would be helpful if some standards were put into place to ease the comparison of results and facilitate future collaboration. Examples include things as simple as the way surrogates are defined. From the literature, the general trend is by mole fraction. However, there are still a few published surrogates that are defined by mass fraction or liquid volume. While good attention to detail will catch this, and adjust accordingly for it, it may still lead to additional confusion for future researchers and users. While XFUEL is shown to be a better parameter to use when comparing different data sets, tradition favors the continued use of φ. If this preference is to continue, then there should be an agreed upon standard average molecule for Jet-A and other kerosene-based fuels that needs to be used.

## Acknowledgment

The kerosene-based fuels used in this study were 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 No. NPRP8-1358-2-579. Additional funding came from a Veterans Research Supplement under National Science Foundation Award No. EEC-1560155.

## Funding Data

• National Science Foundation (Award No. EEC-1560155; Funder ID: 10.13039/100000001).

• Qatar National Research Fund (Award No. NPRP8-1358-2-579; Funder ID: 10.13039/100008982).

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