Abstract

The present work explores a novel flow-independent liquid injection scheme, incorporating solid obstructions to alter the key mechanisms controlling the liquid breakup and trajectory. These obstructions, designated pintiles, minimize the variability of fuel injection dynamics over a range of operational conditions. To better understand these mechanisms, a variety of solid pintile obstructions are designed and incorporated into a liquid jet in crossflow experiment. The design parameters of interest include the fraction of the liquid jet orifice blocked by the pintile (orifice coverage), the vertical height of the pintile in the liquid stream, and the angle of the obstruction with respect to the injection plate. All pintiles are tested at non-reacting ambient temperature and pressure conditions over a range of engine relevant Reynolds numbers (Re = 171,500–343,000), momentum flux ratios (Q = 4–45), and Weber numbers (We = 20–80) to understand the leading order effects the solid–liquid–gas interaction has on the liquid breakup and trajectory control. The results demonstrate that the most consistent jet trajectories are achieved with pintiles with a high orifice coverage, a large height, and an angle of 45 deg. Other parameters, such as the transverse spread of the liquid jet and droplet size distributions, are quantified to ensure that consistent jet trajectories can be achieved without imparting adverse effects on other relevant combustion characteristics. The results provide a foundational, first-order understanding on how to minimize variability of liquid injection across engine relevant Reynolds numbers, Weber numbers, and momentum flux ratios.

1 Introduction

Liquid fuel injection is one of the most important processes for aircraft propulsion combustion systems due to its influence on engine performance, efficiency, and emissions. While they are used in many of aircraft propulsion engines, liquid jet in crossflow (LJIC) systems are highly complex and can experience large variations in injection behaviors with operating conditions. Universally, the atomization, breakup, and trajectory of the liquid fuel are strongly dependent on engine flow parameters, such as Reynolds number, Weber number, and the momentum flux ratio. As such, fuel injectors must be designed to provide the necessary breakup and mixing properties to support flame stabilization over a large operational range. Fuel-injector properties of interest include the trajectory of the liquid stream, the penetration height, plume size, and concentration profiles [1], which will subsequently impact ignition, flame stabilization, and engine efficiency. It is also preferable to design fuel injectors with geometric simplicity that minimize stagnation pressure losses and entropy gain [1]. Consequently, many fuel-injector designs have been proposed for both subsonic [25] and supersonic flow regimes and combustors [6,7] and the jet in crossflow technique is used for both gaseous [8,9] and liquid flows. However, there remains continued interest in novel fuel injection schemes which can provide uniform spray properties and stable combustion over a wide range of inflow conditions [1].

Liquid jets in crossflow are commonly used to obtain all the desired properties of a fuel injection system with an easily manufactured and lightweight system. As a result, the performance of fuel injectors is commonly studied. The key characteristics of LJICs, including breakup modes and trajectory, have been well characterized and vary greatly depending on the flow conditions into which the jet is injected, e.g., the Reynolds number, Weber number, and momentum flux ratio. To describe the effects of Reynolds number and Weber number on liquid jet trajectories, Ingebo [10] developed the following correlation to describe the maximum penetration of the jet:
(1)
where the velocities and densities of both the jet and the crossflow are considered. More sophisticated correlations use the momentum flux ratio to characterize the trajectory, rather than only the maximum penetration of the jet into the crossflow. One such example of a trajectory correlation is from Wotel et al. [11] stating that
(2)

An abundance of similar correlations has been presented throughout the literature [1221], with a comprehensive review of LJIC trajectory correlations presented in Ref. [22]. Computational models have also been developed to aid in the prediction of both breakup and trajectory of LJIC systems, in both subsonic [23] and supersonic conditions [24,25], and experimental observations have been made to characterize their three-dimensional (3D) structures [26].

The breakup of the jet, as described by Wu et al. [27], is determined primarily by the Weber number (We). At low Weber numbers, typically below 10, the column breaks up in an enhanced capillary mode, in which the natural capillary breakup of the jet is accelerated by the crossflow. At higher Weber numbers (∼10–30) aerodynamic forces cause the liquid column to form bags, which subsequently break off to form ligaments, in a breakup regime referred to as bag breakup. For Weber numbers between 30 and 100, the breakup is multimode, in which both bag breakup and shear breakup mechanisms are present. When Weber numbers exceed 100, the breakup of the jet is primarily due to shearing droplets from the surface of the jet, in a regime known as a shear breakup. In most cases, the breakup of the jet is largely independent of the trajectory [12,22,2830]; however, it remains crucial that the breakup of the jet is not greatly reduced, or combustion efficiency will suffer [31].

The research presented above shows that the characteristics of the liquid jet are highly nonuniform between flow conditions. Practical air-breathing combustors will experience a myriad of operating conditions over a wide range of Reynolds numbers, Weber numbers, and momentum flux conditions, which may lead to unwanted variabilities in liquid fuel injection and flame-flow behavior [32], and even simple changes in injector designs can have significant impacts on combustion performance [33,34] and emissions [34,35]. The present research seeks to address this challenge and reduce the performance variability of the LJIC by the introduction of a solid obstruction (pintile) to the liquid jet. The pintiles seek to reduce the dependence of both the breakup and the trajectory of the jet, primarily by influencing the interaction of the injected liquid in ways that do not scale between flow conditions, resulting in flow patterns, which are more similar across flow conditions than a bare jet in crossflow.

The present work investigates a variety of cylindrical pintile injector configurations in an LJIC experiment to explore how solid–liquid–gas interactions can provide uniform jet trajectories, spread, and droplet characteristics across a range of Reynolds numbers, Weber numbers, and momentum flux ratios. The varied pintile parameters include the liquid jet orifice coverage, obstruction angle, and obstruction height. For each pintile injector, the LJIC trajectory and spread are analyzed using high-speed Mie scattering techniques from multiple viewpoints, and liquid droplet size distributions are quantified with phase doppler interferometry (PDI) measurements. The measurements reveal the fluidic mechanisms that control the trajectory and breakup processes are used to identify the optimal spray/splash characteristics that provide uniform properties across flow conditions, equivalently defined here as flow independence. The mechanisms discussed here are known factors that will influence the combustion process in reacting engine environments [31]. Thus, a better understanding of these mechanisms will help catalyze the design of flow-independent fuel injectors to decrease performance variability in aerospace and propulsion technologies.

2 Experimental Methods

2.1 Experimental Facility and Instrumentation.

The experiment was conducted in a wind tunnel facility, shown in Fig. 1. The facility consists of a flow-conditioning plenum, a converging nozzle, and an optically accessible test section, which exhausts to atmospheric conditions. The optical test section has a rectangular cross section and measures 127.5 mm × 45 mm (depth × height). Air velocity through the test section was controlled by a JFlow electro-pneumatically positioned ball valve, downstream of a high-pressure regulator and air source. The main air was regulated to 300 psi upstream of the ball valve, and the mass flowrate was measured downstream of the ball valve by a venturi flowmeter coupled with a Dwyer Instruments differential pressure transmitter (model 629C-02-CH-P2-E5-S3), resulting in uncertainty in air flowrate of 3.5%. JFlow electro-pneumatic ball valve was then actuated using a LABVIEW control program to obtain the target test section velocity.

Fig. 1
LJIC experimental facility and flow control schematic
Fig. 1
LJIC experimental facility and flow control schematic
Close modal

Water was injected from a pressurized tank into the top plate of the test section through a 1/32″ (0.79 mm) circular orifice, which is located 181 mm upstream of the test section outlet. The water jet flow is driven from a pressurized air source, where the liquid flowrate is calibrated by regulating the gaseous pressure. The calibration was accomplished by measuring the volumetric flowrate through the jet orifice for a given reservoir pressure. The gas pressure in the reservoir tank was measured using an analogue pressure gage with an error of ± 0.1 psi and metered using a pressure regulator. The uncertainty in the liquid flowrate resulting from the calibration process is then 2.12%. This calibration, together with the wind tunnel measurements, allowed for the calculation of the momentum flux ratio and Weber number.

Figure 2 shows the optical setup used in the experiment. High-speed Mie scattering data were captured using two Photron SA1.1 cameras, each at a framerate of 10,000 frames per second, with a shutter speed of 1/50,000 s and at a resolution of 1024 × 512 pixels (150 µm/pix). Images were captured for a duration of 1 s during steady-state operation, resulting in a set of 10,000 images per test. An additional PCO 1600 camera was used to capture images at a higher spatial resolution (116 µm/pix) in the x–y plane at 30 frames per second, with a shutter speed of 0.1 ms. The cameras capturing data in the x–y plane were focused on the centerline of the injection orifice. In the x–z plane, the camera was focused on the centerline of the test section, keeping a wide depth of field to allow the entire section to remain in focus. Additionally, PDI measurements were acquired with an Artium PDI (model 1D-PDI) to capture centerline particle distribution, recording data for droplet size (±0.5 µm), count, and velocity (±0.1%) for 2 s during the steady-state operation of the test.

Fig. 2
Imaging setup and coordinate axes for LJIC experiments
Fig. 2
Imaging setup and coordinate axes for LJIC experiments
Close modal

2.2 Test Conditions.

To quantify flow independence, each pintile was subjected to five different flow conditions, which are detailed in Table 1. All tests were conducted at ambient pressures and temperatures to evaluate the breakup and trajectory of the liquid injector. The remaining flow conditions (We, Re, and Q), were selected in collaboration with industry partners to ensure that the solid–liquid–gas interaction dynamics are applicable to propulsion engines. The Weber number of the crossflow was varied between 21 and 85, with the momentum flux ratios varying between 5 and 45. The five flow conditions were first tested in a baseline configuration with no pintile. The same five conditions were repeated for each of 11 different pintile designs (as discussed in the subsequent section) for a total of 60 experimental trials.

Table 1

Experimental flow conditions

Test caseWeQvj (m/s)Rejet = (ρvd/µ)jetv (m/s)Re = (ρvd/µ)
A2151.91,69040171,500
B218.33.83,37040171,500
C21338.87,81040171,500
D855.426.55,77080343,000
E854518.716,59080343,000
Test caseWeQvj (m/s)Rejet = (ρvd/µ)jetv (m/s)Re = (ρvd/µ)
A2151.91,69040171,500
B218.33.83,37040171,500
C21338.87,81040171,500
D855.426.55,77080343,000
E854518.716,59080343,000

2.3 Pintile Designs.

Eleven distinct pintile configurations were tested in the LJIC experiment. A summary of pintile variations and associated specimen names are listed in Table 2. The different pintiles were developed by varying three parameters: the jet orifice coverage (l), the height of the pintile from the plate surface (H), and pintile angle (θ), as illustrated in Fig. 3. Each of these parameters is expected to alter liquid jet trajectory and breakup processes. The jet orifice coverage was varied as l/dj = 50, 75, and 100%. The pintile heights investigated here are H/djet = 1.6, 3.2, and 4.8. Each combination of pintile height and orifice coverage was evaluated, for a total of 9 test specimens, all designed with a 45-deg angle. The 1.6djet height pintile at an orifice penetration of 75% was also tested in additional configurations of 30 deg and 60 deg. All test pintiles had a cylinder diameter of 1/16″, twice the diameter of the injection orifice.

Fig. 3
Schematic of pintile geometry, key design variables, and position within the test section
Fig. 3
Schematic of pintile geometry, key design variables, and position within the test section
Close modal
Table 2

Pintiles used in experimentation

Pintile numberHeight (H/djet)Orifice coverage (l/djet)Pintile angle (θ, in deg)
11.650%45
21.675%30
31.675%45
41.675%60
51.6100%45
63.250%45
73.275%45
83.2100%45
94.850%45
104.875%45
114.8100%45
Baseline
Pintile numberHeight (H/djet)Orifice coverage (l/djet)Pintile angle (θ, in deg)
11.650%45
21.675%30
31.675%45
41.675%60
51.6100%45
63.250%45
73.275%45
83.2100%45
94.850%45
104.875%45
114.8100%45
Baseline

Each pintile was 3D printed on an Anycubic Photon S SLA resin printer, with a print resolution of 47 µm. The resin used was LiqCreate StrongX 405 nm Photosensitive resin. The specimens were then cured under a 405-nm ultraviolet (UV) light to ensure maximum strength of the print and ensure minimal flexure during the experiment. An image of the pintile height and orifice coverage variants is shown in Fig. 4. The pintiles were slotted into an injection holder and clamped into place. The orientation of the pintile is depicted in Fig. 3, where the base of the pintile is flush with the wall and the protrusion extends over the liquid jet.

Fig. 4
Pintile variations: (a) computer-aided design (CAD) and (b) 3D printed pintiles
Fig. 4
Pintile variations: (a) computer-aided design (CAD) and (b) 3D printed pintiles
Close modal

2.4 Image Processing.

A standardized procedure was developed to process the LJIC images and extract the time average windward edge trajectory and the jet spread. The data processing is summarized in Fig. 5. For each data set, background subtraction is first performed on the sequence of images. The time-averaged jet trajectory was determined using an edge-finding binarization algorithm. The images were binarized using a global threshold determined by a minimum cross-entropy (Li’s) method [36]. This method accounts for the variability in overall image brightness due to variation in flowrates across test cases while maintaining an objective binarization threshold between image sets. A narrow disk filter (4 pixels in radius) was then applied to remove any noise in the image. The windward edge of the binarized jet was then taken as the jet trajectory. The trajectories resolved from the windward edge of the jet were then compared between cases, at each downstream location in the viewing window. Variance at particular x locations, given by
(3)
is considered as a metric for flow independence of jet trajectory, with lower variances indicating more independent injectors. Figure 5 provides an example of how the variance is calculated; Fig. 5(c) shows the baseline trajectories, and Fig. 5(d) shows the resulting variance.
Fig. 5
(a) Time-averaged images of the LJIC for the baseline cases with no pintile in the flow path, (b) the binarized images, (c) the windward jet trajectories obtained from the binarized images, and (d) the variance amongst the five flow conditions
Fig. 5
(a) Time-averaged images of the LJIC for the baseline cases with no pintile in the flow path, (b) the binarized images, (c) the windward jet trajectories obtained from the binarized images, and (d) the variance amongst the five flow conditions
Close modal

The results obtained from image processing have their own associated uncertainties, which are related to the size of the spatial size of the pixel and the instrumentation used to calculate it. The size of the pixel is calibrated as 0.143 mm, with a potential error in calibration of 1.25%. This results in an overall uncertainty in the position of 0.145 mm, which, in the units of the plots shown, equates to an error in the position of 0.18 jet diameters. When the uncertainty is propagated to the error in variance, the overall uncertainty in the variance of the position of 0.81 jet diameters.

Additionally, variance in the spread of the jet in the x–y plane, defined as the vertical distance between the windward and leeward edges of the jet, is used as another indication of the flow independence of the fuel injector. The particle size at the test section outlet was also considered to observe the performance of the new injectors relative to the standard bare jets.

3 Results

The following sections describe the effects of adding the various pintiles into the LJIC system with the goal of assessing flow independence. The primary variable of interest is the trajectory of the liquid jet. The influence of each individual design variable is discussed independently and includes physical explanations to describe the witnessed phenomena. The final section characterizes other relevant parameters that influence combustion characteristics, such as the spread of the jet and liquid droplet sizes to ensure uniform trajectories can be obtained without jeopardizing other performance metrics.

In general, interaction with the pintile resulted in a lateral spread of the liquid jet and a loss of momentum in the vertical direction. The collected data indicate that the effects of the pintile on both the lateral spread and momentum loss are more significant at higher momentum flux ratios. The uneven effects of the pintile across momentum flux ratios result in a collapse of the trajectories between the flow cases, resulting in increased flow independence. This was true for all the tested pintiles, indicating that the presence of any pintile is an improvement over a bare jet, in terms of flow independence. The increase in the lateral spread is due to the Coanda effect [37], where the injected liquid wraps around the solid surface until the momentum of the fluid forces the liquid to separate from the pintile surface. This proves to be an important factor in the behavior of the jets when the pintile coverage and angle are varied. In addition, the presence of the pintile creates a low-velocity wake region downstream of the pintile, which temporarily reduces the effect of the crossflow on the liquid jet, which produces especially dramatic effects when taller pintiles are used.

3.1 Effects of Orifice Coverage.

The parameter found to have the most dramatic effect on the flow independence of the injector was the orifice coverage, defined here as the fraction of the jet orifice that is covered by the pintile (Fig. 3). Figure 6(a) demonstrates the effect of increasing orifice coverage by plotting the variance of the trajectory across each of the cases. It was found that increasing the orifice coverage decreased the trajectory variance. This effect was present regardless of the height of the pintiles. The decreased variability in the jet trajectory is indicative of enhanced flow independence, where the jet trajectories tend to coalesce across the five flow conditions. A visual example is provided in Fig. 6(b), which plots the trajectories of the baseline cases and the 100% orifice coverage pintiles at a height of 4.8djet. For the baseline cases, there is a notable difference in the windward edge trajectory between the five flow conditions. The variability in the windward trajectory is suppressed with the addition of the 100% orifice coverage pintile, and the trajectories merge together.

Fig. 6
(a) The influence of pintile orifice coverage on the variation in jet trajectories between the five flow conditions (test cases A–E) and (b) jet trajectories for two selected pintiles
Fig. 6
(a) The influence of pintile orifice coverage on the variation in jet trajectories between the five flow conditions (test cases A–E) and (b) jet trajectories for two selected pintiles
Close modal
Due to the three-dimensionality of the LJIC, spanwise information is useful to better understand the mechanisms that control the jet behavior. The x–z images show that as the injected liquid contacts the obstruction, the liquid is dispersed in the z-direction. As the injected liquid spreads out, the effective area of the jet increases, while the total momentum of the jet is mostly conserved, though a small portion is lost due to friction. With the momentum flux of the jet being given by
(4)
increasing the jet area as indicated in Fig. 7 by the increasing spread in the x–z direction (δxz) causes a decrease in the effective momentum flux for each case. Since the trajectory of the jet is controlled primarily by the momentum flux ratio, this decreasing momentum flux of the jet causes the trajectories to be reduced when δxz is increased. Because the high momentum flux cases are more heavily impacted by the presence of the obstruction than the low momentum flux cases are, the overall impact of variation in flow conditions is neutralized, resulting in a more flow-independent fuel injector. As the orifice coverage increases, the increase of δxz becomes more dramatic, resulting in an enhanced flow independence case, and this can be observed in Fig. 6.
Fig. 7
Time-averaged images of the LJIC from the x–z plane. The span of the jet is outlined by the dashed white lines.
Fig. 7
Time-averaged images of the LJIC from the x–z plane. The span of the jet is outlined by the dashed white lines.
Close modal

3.2 Effects of Pintile Height.

Pintile height, defined as the height of the pintile edge above the surface (see Fig. 3), was also shown to affect the flow independence of the injectors. Figure 8 shows the trajectory variance of each of the pintiles, varying height, at both 50% and 100% orifice coverage. As the pintiles increase in height, the variance in the windward jet trajectory is decreased. This is especially prominent when the orifice coverage is 100%. At low orifice coverage, the benefit gained from increased pintile height decreases substantially, and at 50%, the effect is eliminated. The effect that increasing height has on flow independence is substantially smaller than the effect that orifice coverage has. However, this effect can still prove relevant when designing improved injectors.

Fig. 8
Trajectory variance changing the pintile height, at 100% orifice coverage (top) and 50% orifice coverage (bottom)
Fig. 8
Trajectory variance changing the pintile height, at 100% orifice coverage (top) and 50% orifice coverage (bottom)
Close modal

To discern the mechanism that provides greater flow independence, Fig. 9 provides instantaneous snapshots of the LJIC for the baseline case and the three different pintile heights. For the baseline case with no pintile in the flow path, the liquid column is immediately deflected in the direction of the crossflow, and the multimode breakup is evident at the inlet [27]. However, the same phenomenon is not witnessed when the pintile is added to the flow path. Specifically, the pintile induces a low-velocity wake region near the liquid injector, and three primary observations are noticed: (1) the liquid column maintains its vertical trajectory within the wake of the pintile and is minimally deflected by the crossflow, (2) the liquid column maintains a coherent structure in the wake region of the pintile, and (3) the breakup process does not initiate until the liquid jet leaves the pintile wake region. This suggests that the wake region behind the pintile provides a shielding effect, minimizing the interaction between the jet and crossflow. This shielding effect is amplified as the height of the pintile increases due to an increased size of the wake region. Specifically, increasing the size of the wake region prohibits column deflection and shearing of the liquid column. This is witnessed in the bottom two images of Fig. 9 (corresponding to pintile heights at 3.2djet and 4.8djet, respectively), which remain completely intact before contacting the pintile or reaching beyond the top edge of the pintile. This is consistent with studies of the wake regions of finite cylinders with free ends, wherein low-velocity regions end abruptly at the free and of the cylinder [38]. Previous research has suggested that the wake and low-velocity regions behind angled cylinders, such as the present pintile, are substantial throughout the entire range of yaw angles studied in the following section [3942], indicating that this result should be applicable without respect to the angle being studied. The results of the present study also show that there may be a substantial benefit to leveraging previous research on the topic to further advance this technology, for example by varying the end condition of the pintile [43].

Fig. 9
Demonstration of increasing pintile height on the LJIC system
Fig. 9
Demonstration of increasing pintile height on the LJIC system
Close modal

3.3 Effects of Angle Variation.

The final variable of interest is the angle of the pintile (θ). To isolate the effects of the angle, the height and orifice coverage were maintained at 1.6djet and 75%, respectively. The influence of the pintile angle on the variability of the windward jet trajectories is shown in Fig. 10. It is first noticed that the 60-deg angle pintile provides greater flow independence than the baseline tests. The best results, however, were observed with the 30-deg and 45-deg pintiles, which provided consistent results.

Fig. 10
Variance in the windward edge trajectories as a function of the pintile angle
Fig. 10
Variance in the windward edge trajectories as a function of the pintile angle
Close modal

To understand how the angle influences the windward trajectory variance, time-averaged images of the near field jet inlet are shown in Fig. 11(a). Within the time-averaged images, it is apparent that the liquid flow is deflected in a direction perpendicular to the pintile cylinder, pointing vertically (the positive y-direction and upstream (the negative x-direction), as highlighted by the left portion of the dotted red line.

Fig. 11
(a) Demonstration of pintile-induced backflow velocity and trajectory deflections (from test case D) and (b) Sketch of flow deflection due to jet–pintile interactions. The most notable term, the pintile-induced backflow velocity, is labeled and expected to be of the order of vj cos θ sin θ.
Fig. 11
(a) Demonstration of pintile-induced backflow velocity and trajectory deflections (from test case D) and (b) Sketch of flow deflection due to jet–pintile interactions. The most notable term, the pintile-induced backflow velocity, is labeled and expected to be of the order of vj cos θ sin θ.
Close modal

The angle of the pintile influences the direction at which the injected liquid is deflected from its initial trajectory. This is a manifestation of the Coanda effect (as mentioned at the beginning of the results section) [37], where when viewed in two dimensions, the liquid is deflected in two apparent directions: perpendicular and parallel to the pintile cylinder, as shown in Fig. 11(b) and seen in Fig. 11(a). To conceptualize the influence of the Coanda effect on the jet trajectory, and on pintile-induced backflow, a two-dimensional inviscid fluid analysis is considered in Fig. 11(b). Within the two-dimensional (2D) analysis, the pintile is expected to deflect the liquid jet in two primary directions: normal and tangent to the length of the pintle. Assuming all liquid momentum is conserved, the component of the flow which leaves backward (upstream into the crossflow) from the surface leaves with a velocity on the order of vjet cos θ sin θ (see vector decomposition in Fig. 11(b)). This induced velocity produces the small flow protrusions witnessed in Fig. 11(a). Based on conservation laws, any induced backflow momentum must also be accompanied by an equivalent component of streamwise momentum (that follows the direction of the crossflow). Thus, whichever pintile produces the greatest backflow momentum, which is shown in Fig. 11(b) to be 45 deg, must also induce the greatest streamwise momentum. Increasing this streamwise momentum allows the liquid jet to be more easily aligned with the crossflow. Because this effect is stronger for high momentum flux cases than low momentum flux cases, this forces the trajectories of each of the conditions to be more similar. From this analysis, it is expected that the 45-deg pintile would provide the greatest flow independence. Although this is not entirely witnessed in Fig. 11(a) because of the low pintile height at which these angles were tested, it is anticipated that at higher orifice coverages, the 45-deg pintile will further outperform the 30-deg pintile than is shown here.

3.4 Comparison of Pintile Performance.

In order to assess the improvement provided by the pintiles, they are compared to the baseline quantitatively. This comparison is made by establishing a ratio of variance of the trajectories with the pintile to the trajectories using only a bare jet. The equation used to determine the reduction in variance is given by
(5)

The reduction in variance parameter given in Eq. 5 establishes a quantitative comparison to the baseline (bare jet) case, in which higher numbers indicate more flow-independent injectors. The reduction in variance is also averaged along the domain to obtain a single value representative of the overall performance of the pintiles. The analysis shows that as seen in the previous sections, pintiles with higher orifice coverage and larger heights are more effective for establishing flow independence. These results are listed in table 3.

Table 3

Jet trajectory variance reduction across pintiles, as shown by Eq. (5)

Pintile numberReduction in variance (%)
x/dj = 10x/dj = 15x/dj = 20Average
167564653
284797577
37672N/A74
468574553
583817779
661544651
779676467
887878686
960545053
1088858284
1188908989
Pintile numberReduction in variance (%)
x/dj = 10x/dj = 15x/dj = 20Average
167564653
284797577
37672N/A74
468574553
583817779
661544651
779676467
887878686
960545053
1088858284
1188908989

3.5 Relevant Performance Characteristics.

The analysis of the previous sections has shown how the three tested parameters of a pintile obstruction affect the LJIC trajectory and breakup. Specifically, flow independence was improved by increasing the jet orifice coverage and the pintile height. Combining these effects, the pintile with full jet coverage at height of 4.8djet and at an angle of 45 deg resulted in the most flow-independent trajectory. However, it is important to ensure that other relevant combustion parameters, such as jet spread and droplet size, are not negatively impacted by the pintiles.

The jet spread in the x–y plane is displayed in Fig. 12 for the baseline LJIC and the same test with the most flow-independent pintile. The presence of the pintile promotes jet spread at the orifice location and in the near region downstream. However, the spread at farther downstream positions equalizes for both cases. The improved spread performance in the nearfield jet with the pintile is advantageous in applications involving close-coupled combustion, where the location of flame stabilization is close to the jet inlet.

Fig. 12
Transverse jet spread in the x–y plane comparing the best case pintile to baseline
Fig. 12
Transverse jet spread in the x–y plane comparing the best case pintile to baseline
Close modal

The droplet size distributions of selected cases are shown in Fig. 13. The droplet distributions are nominally the same across all cases, although higher fractions of droplets less than 10 µm are evident with the pintile for these cases. This indicates augmented breakup performance with the pintile. Smaller liquid droplets are favorable for combustion by improving fuel–air mixing and evaporation rates [31]. Additionally, the variance of the mean droplet size across flow conditions was also found to decrease slightly from 5.4 µm2 to 3.7 µm2. Thus, the droplet size was also found to be more flow independent with the pintile injector.

Fig. 13
Normalized histogram of droplet sizes, comparing the best case pintile to baseline, for test conditions C and D
Fig. 13
Normalized histogram of droplet sizes, comparing the best case pintile to baseline, for test conditions C and D
Close modal

4 Conclusions

Throughout this study, it was found that three mechanisms were primarily responsible for the improved flow independence of LJIC systems. The first of these mechanisms is observed by increasing the orifice coverage, which was found to minimize the variability of the jet trajectories between the five flow conditions. This effect was attributed to a more pronounced interaction between the fluid column and the pintile, which results in a larger spanwise spreading of the jet. The increased spreading of the jet effectively decreases the momentum flux ratio between the jet and crossflow, which will limit the jet penetration into the crossflow. The effective decrease in the momentum flux with higher orifice coverage allows the jet to be more easily swept into the crossflow and ultimately improves flow independence amongst the range of conditions explored.

The initial deflection and breakup of the jet were also observed when altering the height of the pintiles. Increasing the pintile height was also determined to reduce the variability in the jet trajectories amongst the flow conditions. Larger pintile heights allowed a larger wake region to form near the jet injector. The low-velocity wake provided a shielding effect from the crossflow, which allowed the jet to sustain a coherent liquid column without being immediately deflected into the crossflow. It also delayed the breakup of the jet column until it interacted with the pintile surface. In this manner, the pintile dampens the interactions between the jet and crossflow, which would typically be the only mechanism controlling the LJIC characteristics.

The splash/spray characteristics induced by the solid–liquid–gas interaction were altered by varying the angle of the pintile with respect to the crossflow. Amongst the pintile angles tested, the 45-deg pintile was deemed to provide the greatest flow independence. A simplified inviscid momentum analysis was conducted to describe the Coanda effect that the pintile induces on the liquid stream, and it was determined that the largest components of axial momentum are induced at 45 deg. This conclusion was also supported by the time-averaged images, indicated by the deflection of the fluid stream by the pintile. Since the 45-deg pintile provided the greatest axial flow momentum, it provided the greatest flow independence.

The three trends mentioned earlier have complimentary effects when combined into a single design; the best flow independence was observed for the pintile with 100% orifice coverage, the largest height, and the 45-deg angle. This combination induces the most significant splashing effects and liquid breakup at the injection zone, while simultaneously mitigating the initial deflection of the liquid jet and maximizing its axial momentum. Furthermore, when comparing other important combustion characteristics, it was determined that the best pintile design maintained a larger transverse jet spread over the baseline case in the region near injection. While the trend of droplet size was similar between the two cases, the best case pintile resulted in a greater percentage of smaller droplets. This ensures that the jet trajectory can be held nominally constant over a range of flow conditions without inhibiting combustion characteristics.

From a broader perspective, the results demonstrate that liquid injectors can be optimized and refined to provide consistent performance over a wide range of conditions. Based on current results, flow-independent fuel injection is in general achieved when the liquid–gas interactions that typically govern the behavior of LJICs are suppressed in favor of a solid–liquid–gas interaction. These results show that passive design solutions can improve liquid fuel injection for combustion and propulsion applications. However, the inclusion of this technology into engines should consider additional design features to minimize losses within the crossflow and minimize fuel pooling on the injection surface.

Future work will expand on this research and explore how the mechanisms discussed in this paper influence reacting flame and flow dynamics, as well as explore design solutions to mitigate the potential drawbacks of the technology.

Footnote

1

kareem.ahmed@ucf.edu

Acknowledgment

This work was sponsored by the Office of Naval Research (ONR), under Grant No. N00014-20-1-2555, Program Officer: Dr. Steven Martens. The authors would like to thank Dr. Jeffery Lovett at Pratt and Whitney for providing us with the relevant engine conditions for the liquid spray testing.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The data sets generated and supporting the findings of this article are obtainable upon reasonable request.1 The data and information that support the findings of this article are freely available online. The authors attest that all data for this study are included in the paper. Data provided by a third party are listed in Acknowledgments. No data, models, or code were generated or used for this paper.

Nomenclature

=

diameter

q =

momentum flux

v =

velocity

x =

axial direction

y =

transverse direction

z =

direction established by right-hand rule between x and y

A =

area

D =

length scale

H =

height of the obstruction

Q =

momentum flux ratio

m,h =

empirical constants in the Ingebo correlation

Re =

Reynolds number

We =

Weber number

ξ =

trajectory variance between flow conditions

ρ =

density

σ =

fluid surface tension

Subscripts

∞ =

crossflow condition

jet, j =

condition of liquid jet

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