Comparing Global Spray Combustion Characteristics and Local Shot-to-Shot Variations in a Reacting n-Heptane Spray

It is common to consider and describe reacting fuel sprays, like those found in diesel engines, in terms of average behavior. Parameters such as liquid length, liftoff length, and ignition delay time describe the result of an experiment for a given fuel, injected into some controlled ambient. Significant work has been done to develop methodologies and to compare between ensemble average spray behavior and various modeling approaches (e.g., Refs. [1] and [2]). Computational fluid dynamics (CFD) spray modeling using Reynolds-averaged Navier–Stokes (RANS) approaches was developed to simulate average/ensemble behavior of spray experiments. As computational power has increased, it has become possible to apply large eddy simulations (LES) with smaller grid scales, which are able to resolve the turbulent flow behavior in sprays [3,4] and relevant emission formation processes. Comparisons between LES and experiments are still largely based on global parameters, and qualitatively on local structures or properties, because a comprehensive direct replication of an experimental condition is not possible in simulation. In addition to exploring the physics of spray mixing and combustion processes, both RANS- and LES-based approaches are leveraged to enable reliable development of engine combustion control strategies.

To support development of these modeling approaches, researchers have created a variety of spray vessels with different features such as constant volume or pressure, and precombustion or electric heating (see Ref. [5] for description of some such systems). Regardless of the approach, the primary goal of these chambers is to enable controlled experimentation on fuel sprays at engine-relevant thermodynamic conditions. As the primary means by which features of the spray evolution can be quantified, these vessels are typically equipped with some combination of optical diagnostic techniques. In this work, an electrically heated constant-pressure flow rig (CPFR) is used in combination with rainbow Schlieren deflectometry (RSD), OH* Chemiluminescence (OH*), and two-color pyrometry (2CP) imaging to acquire measurements from 100 repeated injection experiments at nominally the same ambient conditions. While many studies report ensemble results or highly detailed investigations into measurements from a single injection, very few studies have explored shot-to-shot variations. In one example, Swantek et al. used X-ray imaging to generate statistical data on mass distributions from a single hole injector over 32 injections [6].

While RANS modeling is generally able to capture average behavior, and LES is able to capture single injection behavior, there remains the challenge in identifying which single injection to use to guide the design. It is critical to understand the bounds of shot-to-shot injection behavior that can be expected as combustion design efforts push the limits of combustion stability through hardware and control methods. It is often not economical to run large parametric sweeps (many realizations) of LES simulation to capture range of behavior, and thus this work aims to provide a new methodology and motivation for quantifying shot-to-shot variations.

Here, we will demonstrate how ensemble-averaged axisymmetric results can be obtained (and consider how many injections are required to achieve convergence) as well as present an analysis of different classifications of individual injection behavior. Single injection events that can be considered the most average or most unique (or other classifications in between)—identified using a statistical approach—will be considered alongside the ensemble results. Through this approach, this work will demonstrate how much variation can be observed in both global and local behavior even at nominally the same experimental conditions.

As an additional focus of this work, apparent turbulent flame speeds and their variations are extracted and discussed. Turbulent flame speed is a critical parameter for characterizing any turbulent combustion system, and one that is a challenge to measure and model. Many canonical experiments have been conducted to study the impact of geometry and conditions on turbulent flame speed and also provide data for model development. A recent work by Kolla et al. [7] presented validation of a turbulent flame speed model against experimental work from studies published between 1966 and 2006. They sampled this work in order to include results from a number of canonical flames such as V-shape, planar, and conical. The need to sample such a wide time span for validation data indicates that a relatively limited set of canonical results are available, let alone application-specific results such as for diesel fuel sprays. Despite the availability of turbulent flame speed models such as Refs. [7,8], it is typical to estimate the turbulent flame speed in spray modeling by extrapolating it from the laminar flame speed and the associated turbulent wrinkling of flame front [9]. While the complexity of the experiment is only compounded by the challenge of modeling, we present a method to measure the apparent turbulent flame speed via OH* chemiluminescence and RSD imaging; by spatially and temporally processing the vapor jet tip and the OH*-based liftoff length, and combining the associated velocities, the reaction front velocity can be determined.

The remaining sections describe the experimental setup, including test apparatus, diagnostics, and data processing, followed by results and conclusions. The results will first focus on demonstrating experimental repeatability in typical global parameters such as liquid length, vapor penetration, and liftoff length. Then, considering global repeatably, the local differences in shot-to-shot behavior will be considered for the RSD liquid and vapor penetration lengths, OH* reaction zones and intensity, and finally 2CP temperatures and soot concentrations. The major implication of the work is that despite repeatable global parameters, there are clear local differences in fuel–air mixing and subsequent ignition that would result in wide variations in emissions and overall combustion efficiency, especially important in cases when combustion stability is a concern.

The CPFR utilized in this study is shown in Fig. 1. This rig provides line-of-sight optical access to the nearly quiescent environment into which fuel is injected. Injections enter downward, in a counterflow arrangement as shown. Air velocity is approximately three orders of magnitude less than the fuel injection velocity, and thus, air can be considered as quiescent (this is also confirmed by RSD high-speed images). Electrically preheated, pressurized air enters the chamber at approximately 0.5 ms through a flow conditioner to produce a near-uniform inlet velocity distribution. The flow conditioner consists of six, 0.5 mm thick, 100 μm mesh elements, as well as a diffuser. The continuous upward air flow efficiently flushes repeated injections from the chamber, and thus, large datasets can be quickly generated (∼360 injections/h). Air exits the chamber through four, symmetrically placed, 3 mm diameter holes. The pressure of supplied air is controlled by a dome regulator (upstream), and the flowrate by a downstream control valve.

Fuel is supplied by a pneumatic pressure multiplying pump. The injector return flow, which increases with pressure (even when not injecting), results in pulsation as the pump repressurizes. In order to ensure repeatable injection pressures, the data acquisition and injection triggering systems are configured to automatically trigger on a rising edge of the pressure signal occurring within range of the desired injection pressure. Fuel is injected along the axis of the rig through a Bosch CRIN3-18 injector with a single 100 μm hole at the tip. The injector body and fuel temperatures are maintained by circulating coolant; specific test conditions are described below with details summarized in Table 1.

The layout of the three simultaneous optical diagnostics utilized in this study is shown in Fig. 2: RSD, chemiluminescence (or OH*), and two-color pyrometry (or 2CP). A summary of sampling rate and spatial resolution is provided in Table 2.

Rainbow Schlieren deflectometry is arranged perpendicular to the chamber windows in alignment with its light source; OH* chemiluminescence and 2CP signals are viewed at a slight, off-set angle. An Energetiq EQ-99X fiber coupled broadband light source is used for the RSD system (Energetiq Technology Inc., Wilmington, MA). This light is refocused by two 75 mm focal length, 50 mm diameter lenses onto a 3 mm × 100 μm rectangular aperture, located at the focal point of a 75 mm diameter, 250 mm focal length achromatic doublet lens. As shown in Fig. 2, the collimated light passes through the CPFR, and then it is decollimated (focused) by a matching achromatic doublet lens and focused onto a rainbow filter. The digitally designed and printed rainbow filter is a transparent strip with very fine (4 μm), linearly distributed hue (color) gradations, and it is placed at the lens imaging plane. Directly behind the filter plane is a Photron Nova S9 color camera, acquiring RSD images at 20 kHz with 4 μs exposure time and 512 × 784 pixel resolution (Photron USA Inc., San Diego, CA). A Nikon Nikkor 50 mm lens provides 90 μm/px spatial resolution. This camera was used to synchronize the two other cameras by generating a trigger pulse every other frame, resulting in acquisition rates of 10 kHz for OH* and 2CP high-speed cameras. OH* chemiluminescence from the reacting spray is reflected by a UV mirror through a 310 nm bandpass filter, a Nikon UV lens, an Invisible Vision UV intensifier (gate time 70 μs), and into a monochromatic Photron SA5 camera (Invisible Vision Ltd., Norwich, UK). The images are acquired over 896 × 848 pixels, with spatial resolution of 160 μm/px and framing rate of 10 kHz. Note that after experiments were completed, it became evident that the chemiluminescence camera was slightly out of focus. This results in a smoothing/blurring effect on the images, and thus while the OH* boundary detection and liftoff locations will be slightly affected, trendwise results and discussion are still valid.

The thermal radiation from soot, which dominates flame luminosity in the visible spectrum, is detected by the 2CP camera at two distinct wavelengths. Based on the calibrated apparent temperatures at the two wavelengths the actual soot temperature and concentration can be calculated [10,11]. A tungsten lamp (10 W UIS-LS, StellarNet Inc., Tampa, FL) with manufacturer's calibration was used to correlate camera intensity of each spectral image to a known radiance, from which apparent temperatures can be calculated [12]. The general layout of the 2CP collecting optics can be seen in Fig. 2. The flame luminosity passes through a 50/50 beamsplitter, which allows half of the light to be transmitted through and reflects the other half at a 90 deg angle. Band-pass filters of central wavelengths, 650 nm and 550 nm, each with 10 nm FWHM bandwidths, are attached to the outlets of the beamsplitter. Each spectral signal is reflected off of a turning mirror, toward a knife-edge prism mirror, and then along parallel paths to the camera. Both spectral signals follow paths of equal lengths and are imaged on the same camera sensor thereby avoiding the need for spatial resolution scaling or parallax errors induced by other designs. A spatial calibration target was used to determine the translation required to accurately map pixels between the two images. Further details of the intensity and spatial calibration procedures for this novel 2CP design can be found in Ref. [12]. A Nikon Nikkor 105 mm lens is used with a Phantom v7.3, 14-bit, monochromatic camera, giving spatial resolution of 242 μm/px (Vision Research Inc., Wayne, NJ). The 2CP system is triggered at 10 kHz framing rate.

Where possible, identical or similar programs analyzed images from each diagnostic for consistency of results; given the spatial differences, and the key fact the RSD images are derived from hue (color) while chemiluminescence and 2CP are intensity-based, this is not always feasible.

Determination of ignition delay is common to both OH* (chemiluminescence) and soot (2CP) signals. To calculate ignition delay, an intensity-signal background threshold was first established from mean and standard deviation of images before start of injection (bSOI), for each injection. The intensity signals recorded for the presence of OH*/soot vastly differentiate themselves from this threshold, so the program flagged the first frame to contain signals in statistical excess of this threshold as the ignition frame. Since the diagnostics were synchronized in time, the start of injection (SOI) was ascertained visually via captured RSD images. The known framerates were then used to convert frame number into ignition delay in milliseconds and to correct for the frames recorded bSOI. Figure 3 illustrates the synchronized nature of the multiple diagnostics, where time steps near ignition show the simultaneous acquisition by all three diagnostics and their spatial relationship with one another. Of course, while each diagnostic is applied for nearly the full field of view, Fig. 3 shows normalized RSD results up to the liftoff length and then shows a split view of the normalized 2CP (left) and OH* (right) raw signals. By processing each diagnostic as described, the time evolution of the spray mixing and reaction process has been analyzed in the Results section.

Liquid phase boundary detection is described in detail by Wanstall et al. [13]. Briefly, liquid phase is distinguished by extremely low intensity, or lack of signal, in RSD images due to light attenuation through scattering or absorption during interaction with the dense liquid. The vapor jet is easily distinguishable from the background by the conventional method of subtracting from each frame the value of the previous, thus removing any quiescent background structures and leaving only the spray region containing any significant signal. This differential signal can easily be processed to find the spray boundary using statistical threshold analysis, as shown in Fig. 3, where the spray region is visibly distinguishable from the background and the boundary is demarcated in white. For identifying and tracking reaction zones in OH* and 2CP images, the methodology uses a similar threshold analysis with signal intensity, rather than hue. The program detects regions where intensities are variants from the image background and determine the outer radial border at each axial location. OH* and 2CP signals from a single injection are shown in Fig. 3 with their corresponding boundaries. Furthermore, liftoff length is calculated for both OH* and 2CP, at each time-step after ignition. For each injection, a radial mean of OH* chemiluminescence and raw 2CP signals (at 650 nm) is referenced for each frame. Upstream (nonreacting) locations provide a threshold to determine the first downstream instance of statistically apparent signal, which is recorded as the liftoff length.

Having determined the vapor jet penetration and the liftoff length for OH* signal, local velocities are calculated from derivatives of the aforementioned lengths as a function of time. Note that the vapor/jet speed is determined with respect to the camera's stationary frame of reference, and likewise for the OH* signal speed, resulting in an value that is relative to the vapor/jet speed, since it represents reactions in the moving fuel–air mixture. Thus, an estimated local turbulent flame speed is identified when the flame appears stationary, indicating its equivalence with the jet velocity. The significance of this parameter is discussed further in the Results section.

A key focus of this study is to highlight the significant shot-to-shot variability observed in repeated experiments even when common global spray characteristics are nominally the same. To this end, and as the culmination of several processing techniques, a methodology was developed to identify, for comparison, the instantaneous data from the most superlative single injections from each diagnostic. The technique previously discussed to identify vapor phase penetration was used to demarcate two-dimensional boundary lines and was utilized across all diagnostic techniques to identify spray, OH*, or soot boundaries. This is shown on an instantaneous basis in Fig. 3, where boundaries (white outlines) are presented adjacent to their respective diagnostic data in a composite image. Maintaining shot-to-shot history of the boundary lines for the right and left sides of each injection, such lines were compared across all injections (of the same diagnostic) to establish a mean (μ) and standard deviation (σ) of injection boundaries. Consider that the boundaries and mean/standard deviation lines have radial (mm) values stored at each axial location; radial boundary values (x), from each injection, are then converted to a nondimensional standard score (also called z-score, $z=x−μσ$⁠). Thus, an injection's z-score is the difference between its own boundary and the mean value, in standard deviations, at a particular time and axial location.

The following process describes how z-scores, calculated for each injection at all axial locations and time steps, are used to identify superlative injections. After rejecting statistical outliers, z-scores from each side of the injection are averaged axially, and then averaged again in the time dimension to yield an average z-score (⁠$z¯$⁠) for both the left and right sides of each injection. Only frames between the start of injection and the end of reliable signal are considered in the temporal average. For RSD, this means prior to ignition, when the collimated light is the only source of light. OH* and 2CP intensities are reliably recorded at all times. Each injection is thereby described by a singular number (⁠$z¯$⁠), on both the right and left sides, representing how far away that injection's edges are, on average, both spatially and temporally, from a typical injection as it develops through time. Ascribing a physical meaning to this statistical parameter, it could be said that an injection of $z¯$ = 1.5 is best represented by the isoline of μ + 1.5σ as it develops. The right and left sides of the spray are maintained separately to support a wide range of superlative discovery. Consider that z > 0 indicates that the spray favors the positive radial direction; separate left/right values allow the determination of more than “rightmost” or “leftmost” injection because one side can be negated, in which case the greatest total z-score would represent the “widest,” and the least the “thinnest,” injections. The absolute value of both sides could be averaged to locate the “most representative” or “deviant” injections, regardless of directionality. Thus, the “widest,” “thinnest,” etc., injections are ascertained from each diagnostic and presented for comparison and discussion. Of course, any desired superlative or metric for identifying such can be used, and this study only serves to highlight the large difference among nominally the same injection events.

The global thermodynamic state of the CPFR was held constant for each injection experiment with values and ranges provided in Table 1. Ambient pressure and temperature were nominally 3 MPa and 800 K with a corresponding density of 13 kg/m³. n-heptane was injected for 2 ms with the fuel and injector body maintained at 90 °C. Finally, the injection pressure was set to 100 MPa. All actual measured values are shown in Table 1 with uncertainty indicating 95% confidence interval based on repeatability for any single injection over the 100 injection experiments included in the dataset for this study.

Given a very stable ambient and injection condition, it is expected that the subsequent spray mixing and ignition would be repeatable. The ignition delay results as determined from both OH* and 2CP imaging techniques are shown in Fig. 4. While the imaging rate (10 kHz) limits the ability to precisely identify the onset of ignition, it is clear from these results that the OH* signal precedes the first observations of soot signal by less than 0.1 ms on average. This corresponds to slightly less than 1 frame with an average ignition delay of 1.71 ± 0.16 ms from OH* and 1.79 ± 0.2 ms from 2CP—again with a 95% confidence interval for any individual injection. Another compounding consideration is that, as discussed above, the chemiluminescence system utilized a gate time of 70 μs, whereas the 2CP camera utilized the full exposure time of, nominally, 100 μs. Therefore, it is possible that the 2CP detected ignition after the chemiluminescence camera had ended its exposure, resulting in soot delay seemingly occurring earlier or simultaneously with OH*. An additional delay between OH* and 2CP signals is expected based on the extremely complex process by which soot particles are formed from conglomeration of carbon atoms. Many detailed soot formation and oxidation models of various complexities can be found in literature, such as Refs. [14–16].

The global thermodynamic condition, injection settings, and ignition delay are examples of properties generally considered as global parameters. It is expected then that for a given fuel, injected into a given ambient, the ignition delay will be a repeatable number. Global parameters such as this are often used to describe a spray or experiment and subsequently used to guide or generalize discussion. Of course, this type of spray combustion experiment is more complex than a premixed combustion system that might be modeled using detailed kinetics as a zero-dimensional homogeneous reactor, but the principle is similar. In this section, global parameters such as those already shown are considered for their repeatability across the 100-injection dataset. Figure 5 shows the average vapor and liquid penetration profiles as well as liftoff lengths as determined from both OH* and 2CP imaging techniques; all averages are bounded by single shot 95% confidence intervals.

Often liquid length and liftoff length are considered global parameters as well. Typically, they are quantified based on quasi-steady spray combustion results and thus allow a single scalar value to be used to characterize an experiment. In this study, the transient behavior of vapor, liquid, and liftoff length from the two diagnostics are considered based on Fig. 5. Note that the vapor penetration profile ends abruptly at 1.25 ms after start of injection (aSOI) as it leaves the Schlieren system field-of-view. The consistency of the vapor penetrations over repeated experiments is clear based on the approximately ±2 mm range observed even at 50 mm downstream of the injector tip. Further, the stability of liquid length in both time and across injections suggests the fuel and injector temperature control was effective.

The 2 ms injection duration can be visualized by the drop in liquid length right at that time. Relative to the OH*- and 2CP-based liftoff lengths, this end-of-injection timing clearly shows that a quasi-steady liftoff length was perhaps only just achieved at around 2.5 ms, before reaction zones are transported downstream by jet momentum after end-of-injection. While the average ignition delay is (1.71 ± 0.16 ms) from OH* and (1.79 ± 0.2 ms) from 2CP, a number of injections exhibit earlier ignition and thus an average liftoff length of the few injections, which ignite at 1.6 ms can be determined and accounts for the first instance of OH* and soot liftoff lengths in Fig. 5. After initial reaction at 1.6 ms takes place downstream, the relatively high turbulent flame speed causes the liftoff lengths of both OH* and 2CP to recess back toward the injector. The liftoff length eventually stabilizes only to begin increasing immediately at a location where the jet velocity and flame speed are momentarily equal. The liftoff lengths begin to increase again after 2.5 ms as they are swept downstream with the last of the fuel and the mixture becomes very lean as the entrainment wave passes [17].

The distinct phases of initial penetration, ignition, stabilization, and end-of-injection are clearly evident in this experiment. Note that it is possible, given a longer injection duration, that the quasi-steady liftoff lengths would be slightly shorter than those minimum values observed in this study. As may be expected based on the slightly longer delay before 2CP signal is detected compared to OH* (from Fig. 4), the liftoff length based on 2CP is longer than that from OH*. In the spatial frame of reference, later in time corresponds to further downstream from the injector. In this particular case, the relatively low ambient pressure, compared to those found in actual engines, results in a relatively long ignition delay. Such ambient conditions result in longer liftoff lengths as well; however, the trends and relative locations of both vapor, liquid, and liftoff lengths progress as expected. As a result of the relatively long ignition delay (again, compared to engine conditions) the differences in local fuel–air mixing from shot-to-shot seem to be causing a relatively high variation in the liftoff length measured by both OH* and 2CP techniques. This leads to the consideration that the relatively repeatable ignition delay results in Fig. 4 may actually represent substantial variations. The remaining results sections will explore this observation further.

While the field-of-view of the Schlieren system is limited, the vapor penetration can reasonably be expected to continue roughly proportional to the square-root of time. If one considers extrapolating the vapor penetration profile, it is clear that the OH* presence is first detected slightly behind the jet-head plume in time and space. The 2CP signal is first detected slightly closer to the leading edge of the jet, likely emanating from the rich core slightly after reactions begin as indicated by OH* signal. This discussion will be supplemented in the remainder of the results section, which includes images of the sprays for each diagnostic and discussion of apparent turbulent flame speeds based on these results in Fig. 5.

As described in the Data Processing section, a statistical approach for analyzing the boundaries of RSD, OH*, and 2CP results at each time-step was developed to identify superlative injections such as the “widest,” “thinnest,” and “most representative.” This analysis is cumulative over the entire injection event; however, the superlative description is suitable even at an instant in time. Figure 6 shows these superlative injections alongside the ensemble average results for RSD, OH*, and soot temperature and concentration from processed 2CP data. As the spray has moved beyond the RSD field of view before ignition, results for RSD are shown at 1 ms aSOI while for the other diagnostics results are shown at 2.5 ms aSOI when the average liftoff lengths are at a minimum as seen in Fig. 5. On each frame of Fig. 6, the specific injection number, time stamp, and boundary from the ensemble result are overlaid in white. For the RSD results, the average liquid boundary is also overlaid on the RSD superlatives and ensemble in black. The ensemble boundary gives context to the classification indicated at the top of the columns. Spatial scaling is uniform throughout all images and color bars are constant for each injection within a diagnostic parameter. Each diagnostic was considered separately when identifying superlative injections and thus the “widest” injection for RSD is not necessarily, and in fact is not, the same injection for OH* or 2CP*. The injection number stamp in each frame illustrates this identification. Of course, the choice could have been made to identify superlatives with one diagnostic and then compare the same injections for the other diagnostics.

First considering the RSD superlatives, the “widest” injection clearly stands out as being wider than the others while the thinnest is only marginally so compared to the most representative injection, and the differences are mostly obscured behind the overlaid average boundary. While the instantaneous RSD images do not appear to have much structure to their hue distributions, the ensemble-averaged image clearly shows the distinct hue distributions that enable RSD to be quantitative.

The OH* images show much more significant differences between the various superlative classifications. The ensemble result clearly shows a repeatable split reaction zone behavior with one peak at 50 mm and the other between 65 mm and 70 mm. Only the widest superlative injection shows this behavior; however, this structure must be common to many injections to be visible in the ensemble. The relative size of the thinnest injection is clearly the smallest overall reaction zone of the three while the shape of the most representative is slightly off from the ensemble. As with the RSD results, the behavior of an individual injection is only loosely connected with the ensemble result. In this case, the most representative injection does not have a split reaction zone, though it does have a slightly wider reaction zone further downstream from the injector. The magnitude of the ensemble is clearly reduced due to averaging (effectively filtering), though OH* magnitude is normalized and only used qualitatively in this case.

OH* location and magnitude primarily serve to mark regions where certain reactions in the overall-reaction kinetic-pathways are taking place; while OH* intensity is only loosely related to subsequent combustion and emissions formation, measurements of soot temperature and concentration from the 2CP system provide a direct measurement of soot formation processes and can be correlated with expected exhaust soot levels. It is important to note that while soot is clearly forming under the test conditions in this study, for this well-mixed spray condition, it is likely that very little net soot would be left in exhaust stream. After soot forms in the rich core of the spray, it can be expected that most of the soot is consumed through oxidation as it is transported through the primary stoichiometric reaction region at the jet head and edges. However, it is also possible that the high sooting regions in the edges of the jet may experience reduced heat release and thereby transport soot out of the reaction zone [18]. Based on the complexity of soot formation, oxidation, and transport processes, it is perhaps not surprising that 2CP results show the most dramatic shot-to-shot variations observed.

Considering either the soot temperature (T) or concentration (KL), it is apparent that between the widest, thinnest, and most representative injections, a wide range of local behavior is observed. As compared to the RSD and OH* results, the spatial size and temperature of the most representative injection actually closely resemble the average values, and yet due to the high sensitivity to temperature at low KL values [12], the instantaneous KL values are significantly different than the average values. The higher sensitivity of soot formation to local fuel air mixing is expected based on complexity of soot formation processes [15]. As with the OH* results, this averaging has a significant impact as it smooths the local peaks observed in single injection results. Despite only having a few millimeters different liftoff length, the total apparent soot concentration for the thinnest injection is significantly less than any of the other injections or ensemble results. It also has some of the highest peak temperatures suggesting better fuel–air mixing and perhaps near to stoichiometric reactions occurring and thereby avoiding soot formation altogether. On the other hand, the widest injection has the most cool soot regions, which result in higher concentrations. Note that a pyrometer optimized for a lower temperature range may in fact capture soot temperatures over a larger volume for the thinnest injection. Regardless, the trends and takeaways from the analysis in this work will be unchanged.

The larger reaction regions in both OH* and 2CP data can be correlated to the slightly wider initial RSD images but the actual mechanism is not so apparent. Typically, a wider jet would suggest more entrainment and better mixing. This is supported by the larger OH* reaction region indicating higher overall reactivity but is perhaps contradicted by the soot concentrations. Again, it is likely that all soot formed will be oxidized prior to end of combustion. Finally, while time histories of the results in Fig. 6 are not provided, time steps before and after those shown were investigated to determine if one or more of the instantaneous results were just a frame or so behind the others and would show similar structures a few tenths of a millisecond later. The relative differences remain clear for OH* and especially 2CP results even 0.5 ms earlier or later.

As demonstrated, the relatively repeatable global spray characteristics, such as those shown in Figs. 4 and 5, can give the impression that the local fuel–air mixing and ignition dynamics are repeatable as well. Even among the RSD results in Fig. 6, there are no dramatic differences between repeated injections. However, for OH* and 2CP results in Fig. 6, it is clear that local deviations from average mixing behavior exist, which result in significant differences in OH* and particularly 2CP results. While the shot-to-shot variation in the liftoff length for both OH* and 2CP is significantly higher than the variation in vapor penetration, this observation does not provide insight into why these differences are occurring. The question to ask is, how do local mixing differences between separate injections manifest with nominally similar global characteristics and produce substantially different local ignition and sooting behavior?

One such parameter that can be observed at a more global scale, but which is more closely linked with local fuel–air mixing, is the turbulent flame speed. As mentioned in the introduction, incorporating this parameter into models is a challenge still being addressed in both fundamental and applied research today. By comparing relative velocities of the OH*-based liftoff length at a given time-step and spatial location with corresponding values from the vapor jet tip penetration profile, some interesting and meaningful results can be obtained. Figure 7 shows the initial vapor jet tip penetration and OH* liftoff location velocities, both calculated as the derivative of position with time, plotted versus position (top) and time (bottom).

Though it obscures the changes with time, first consider the spatial results in the top frame of Fig. 7. It is clear that the reaction front initially recesses upstream (negative velocity) toward the injector. Then the reaction front is transported downstream slightly slower than the initial vapor jet due to the reduced momentum flux after end-of-injection. Note that there is no direct measurement of local velocities and they are only derived values based on vapor penetration and liftoff results in Fig. 5. At the point where the OH* liftoff location reaches zero velocity, it can be interpreted that the average turbulent flame speed along the reaction front can be approximated as the spray tip velocity at that axial position—in this case, about 42.5 m/s as illustrated.

This analysis is most appropriate under true quasi-steady conditions; however, the bottom frame of Fig. 7 actually illustrates that this case does not in fact have a quasi-steady period. While results are not available to confirm at this time, it can be expected that a truly quasi-steady condition would result in a sustained period of zero velocity OH* (and 2CP) liftoff lengths. This can be achieved by simply having a longer injection period or shorter ignition delay in future experiments. For the results shown here, while the liftoff length certainly seems to stabilize based on Fig. 5, the calculated liftoff location velocity only momentarily crosses zero from negative to positive as the front begins to be carried downstream after end-of-injection.

Consider the variation in the OH* liftoff location velocity illustrated as confidence interval bounds in the bottom frame of Fig. 7). This large variation offers insight into how the variability in local fuel–air mixing ultimately leads to the difference in the sooting behavior. During the reaction front recession (where velocity is negative), the variability is large compared to after it begins to be transported downstream after end-of-injection. While all injections ignite within ±0.2 ms of each other, the initial recession velocity varies from nearly 60 m/s (fast) to 10 m/s (slow). While individual liftoff location velocities are not shown, analysis shows that the widest injection from Fig. 6 has a correspondingly higher apparent flame speed and the most representative and thinnest have decreasing initial flame speeds. The initial flame speed correlates strongly with the subsequent size of the reaction zone as well as with the time it takes to reach zero velocity at the minimum liftoff length. Without further study, it can only be postulated that the faster initial reactions lead to a slightly shorter liftoff length, which can then lead to an overall richer reaction front. Based on simple jet modeling, it is clear that radial averaged equivalence ratio can be expected to increase rapidly closer to the injector [17]. This gives some support to the significant differences observed.

While this discussion does not directly explain how or why the local fuel–air mixing may be different from shot-to-shot, it does indicate that the average apparent turbulent flame speed, as determined in this work, could serve as an indicator for local reaction and sooting behavior. Future work will explore this approach further with comparisons to local fuel–air mixing and variance results from quantified rainbow Schlieren deflectometry.

The connection between experiments and modeling efforts in any field is a critical feedback loop, and one that evolves with advances in both areas. For models only able to capture average behaviors, it is often a challenge to perform enough experiments to ensure fully converged ensemble-averaged results. In contrast, capturing local details in an individual experiment is often possible and complex models capable of simulating these features are more and more prevalent. This introduces the new challenge for direct comparison, since subtle shot-to-shot differences are not sufficiently resolved in model configuration or experiment to precisely define initial conditions. As a result, multiple simulations or realizations based on uncertainty in initial conditions might be necessary to generate an average model prediction.

Expanding the understanding of shot-to-shot variations in high pressure diesel-like fuel sprays is a critical topic that needs exploration. This work provides a preliminary demonstration of a potential methodology for quantifying the variability between multiple injection experiments that exhibit nominally repeatable global characteristics. Bounding the shot-to-shot variation for these experiments may provide greater confidence to modeling efforts that will not require extensive parametric, multirealization campaigns to enable a direct comparison with experimental results. Results shown in this study demonstrate that under stable ambient and fuel injection test conditions, many of the global spray characterization parameters are repeatable and values converge neatly to an ensemble behavior. In particular, ignition delay, vapor and liquid penetrations, and liftoff lengths based on OH* and 2CP all show relatively repeatable behavior when averaging individual injection results or processing the ensemble average signal. Further, the distribution is well characterized by normal distribution standard deviation statistical approaches. However, when considering individual characteristic injections, there is clear deviation from average behavior for both OH* and especially 2CP soot concentration and temperature results.

By analyzing spatial and temporal vapor jet penetration velocity and liftoff length position, it is possible to assess the apparent average turbulent flame speed for a given injection experiment. Comparison of experiments with fast or slow initial reaction front velocities to a corresponding spray contour for both OH* and 2CP results shows a distinct connection. Fast initial reaction front velocity drives a larger reaction volume and slightly shorter liftoff length. This manifests as higher apparent soot concentrations, though total emission is not clear as total soot mass quantification is not part of this work. Despite this connection, it is still not clear what local fuel–air mixing differences are leading to high or low initial reaction speeds.

The methodology and observations made here may be further developed to enable more direct comparison with highly resolved spray simulations. Future work will expand the methodology to more thermodynamic conditions, fuels, and injection strategies to provide insight into the impact each may have on shot-to-shot variations. Additionally, with analysis of local fuel–air mixing and variance using RSD imaging, a more complete understanding of the spray combustion process can be observed. Complementing this work with other more detailed local measurement techniques is also desirable.

• U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE), Vehicle Technology Program (Award No. DE-EE0007980; Funder ID: 10.13039/100006134).