ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015

Fluctuation Mechanisms in Single Hole Diesel Injectors

A.B. Swantek*, D. Duke, C. F. Powell Energy Systems Division

Argonne National Laboratory Lemont, IL, USA 60439

A.L. Kastengren

X-Ray Science Division Argonne National Laboratory

Lemont, IL, USA 60439

Abstract

Recently, single shot measurements at Argonne National Laboratory’s Advanced Photon Source have provided in-sight into the nature of fluctuations resulting from shot-to-shot variations in single-hole diesel injectors. These shot-to-shot variations represent incoherent fluctuations in the mass of the fuel in the path of the beam, and are indicative of stochastic spray atomization and mixing. Fluctuations have spatial and magnitude dependencies on injection pres-sure, ambient pressure, and, to a lesser degree, nozzle hole size. In the current work, we perform a proper orthogo-nal decomposition (POD) analysis during the steady spray of these same single shot data to complement the previ-ous analysis. POD analysis decomposes a set of potentially correlated mass data into components which are uncorre-lated to all other modes. This serves to indicate regions of the spray with coherent, repeatable fluctuations (though not necessarily in phase from shot to shot). Shot-to-shot variation analysis indicates that incoherent/stochastic fluc-tuations are strongest several millimeters (> 2-5 mm) downstream of the nozzle. In contrast, the POD analysis re-veals that the coherent, although much smaller in magnitude, fluctuations occur in the region very near to the nozzle (< 2 mm). Several conditions are investigated and a simplistic physical description is explored. We lastly examine the shot-to-shot variation in mean mass during the steady spray at a single spatial location near to the nozzle exit. These values are observed to have significant trends with diameter, rail pressure, and ambient pressure.

* Corresponding author: aswantek@anl.gov

Introduction Fuel injection dynamics have been well estab-

lished in influencing performance, efficiency and emissions [1]. With manufacturer’s trends toward increasing injection pressure, decreasing hole size, and implementing novel injection strategies, deter-mining and understanding operating envelopes be-comes increasingly important. Moreover, stringent emissions requirements demand deeper understand-ing of the coupling of the fuel injection and in-cylinder combustion.

Historically, x-ray mass absorption measure-ments have focused on capturing the ensemble aver-aged behavior of the liquid flow during injection. Capturing both the fluctuations and the mean, via measurements of individual spray events, is a signifi-cant enhancement of these measurements, and allows for better comparison of these data to state-of-the-art simulations and models. Large Eddy Simulations (LES) can leverage these unique, single-shot data as they are able to realize shot-to-shot differences in spray events with randomized boundary conditions [2]. Additionally, these simulations exhibit better agreement with individual event auto-ignition and flame lift-off experiments. Understanding shot-to-shot variation is critical in the understanding of spray dynamics and determining engine coefficient of vari-ances. These comparisons necessitate detailed, quan-titative measurements in the near nozzle region, which x-ray measurements excel at providing.

A suite of x-ray diagnostics have been developed and refined at Argonne National Laboratory to exam-ine the structure, droplet size, and quantitative fuel distribution from single- and multi-hole diesel, gaso-line, and natural gas sprays. Techniques include: phase contrast imaging for external spray morpholo-gy and internal flow/valve motion, ultra-small angle scattering for droplet sizing, and x-ray radiography for quantitative mass measurements of the fuel distri-bution [3].

X-ray radiography measurements have been ap-plied to both diesel and gasoline sprays [4], as well as gas jet injection [5]. In addition to mass, various other flow features can be extracted, including pene-tration speed [6], mass-based measurements of cone angle, spray density [7], liquid axial velocity [8], entrainment wave behavior [9], and end-of-injection fuel dribble behavior [10].

Nearly all the above works have examined en-semble averaged measurements. While they have resolved the mean, they fail to provide information about the shot-to-shot variation. Kastengren et al. were the first to study single shot behavior with x-ray radiography in an axial single-hole nozzle [11]. A 208 µm, axial, single hole nozzle was studied at two rail pressures (Prail=500 and 1000 bar), and one ambi-

ent pressure (Pamb=5 bar, N2 at 25°C) with a time resolution of 1.84 µs. Several ensemble averaged traces at two spatial locations were presented along with overlaid single shot traces. Multiple features resulting from the single shot data were observed, including: variability in the leading and tailing edges, noise in the single shot measurements, and autocorre-lation analysis.

A previous work by our group [12] focused on using the ensemble standard deviation as a metric for investigating shot-to-shot fluctuations. A transition to steady state after the start of injection was observed very distinctly in the fluctuating field compared to the mean field. Various trends with rail and ambient pressure were evident in the steady state fluctuation field. Regions of elevated shot-to-shot variation were expected to be a result of instabilities and the onset of atomization and mixing.

In this work we utilize x-ray radiography to in-vestigate a data set spanning multiple nozzle hole sizes, rail pressures, and ambient pressures. At each spatial location, multiple events are acquired to ena-ble an investigation of spray statistics. This data is used to compute ensemble statistics (indicative of incoherent fluctuations), to decompose the fluctua-tions into orthogonal modes (indicative of coherent fluctuations), and to investigate single event statistics and their variance from event to event. Experimental Method

The experiments in this work were performed at the 7-BM beamline at the Advanced Photon Source at Argonne National Laboratory [13]. X-ray radiog-raphy was used to acquire single-event, mass-absorption data in three different nozzles, under vari-ous injection and ambient pressures.

A focused, monochromatic x-ray beam with a photon energy of 8 keV was passed through a pres-surized chamber which contains the injector nozzle. The spray was housed in a pressurized gas vessel with 75 mm gas pathlength between x-ray transparent polyimide windows. After interacting with the spray, the x-ray beam is passed to a Hamamatsu PIN diode (10x10mm, assembled by an in-house detector group); the signal was recorded by an oscilloscope and saved to a PC. The setup schematic is shown in Figure 1.

Figure 1. 1. A schematic of the x-ray radiography setup. X-rays travel from right to left.

Three separate hydroground injector nozzles

(D=110 µm, 130 µm, and 180 µm) with a nominal Ks=1.5 were used. Each was affixed to an off-the-shelf solenoid-actuated diesel injector. An automo-tive common rail diesel fuel system was used in con-junction with a stand-alone injector driver hardware and software system to control the injector. This fuel system supplied a commercial diesel calibration fluid (Viscor 1487), doped with a cerium contrast agent (Rhodia DPX9 at 0.2% Ce by mass) to increase the absorption of x-rays. The nitrogen gas used to pres-surize the chamber flowed at a rate of 4 L/min to re-duce the buildup of spray droplets in the chamber.

Three rail pressures (Prail=500, 1000, 1500 bar) were used in combination with 3 ambient pressures (Pamb=1, 10, 20 bar). Commanded injection time was 1 ms for all cases, which allows for the spray to reach quasi-steady state conditions. Only select combina-tions of these parameters were tested due to time lim-itations.

For each spray event, 5 ms of data were recorded at an initial resolution of 4 ns. The time resolution of the measurement is fundamentally limited by the repetition rate of x-ray pulses from the synchrotron. Each pulse is integrated, resulting in a final time resolution of 153 ns. The flow field is raster scanned from zero to 9mm downstream of the nozzle exit (x coordinate), and at each x location, 40-60 transverse locations are acquired (y coordinate). A total of ap-proximately 750 spatial coordinates are interrogated, and 32 individual events are recorded at each of these spatial locations. Figure 2 shows a typical measure-ment grid.

Figure 2. A typical raster scan measurement grid for the current experiments. The nozzle exit centerline is at x=0, y=0 and flow moves from left to right.

Results

Intensity data are collected by the PIN diode both before (I0(x,y)) and during the spray (I(x,y,t)). The Lambert-Beer law (Eq. 1) gives the relationship between intensity at the PIN diode and the projected mass M(x,y,t) (µg/mm2). Projected mass is a function of both spatial coordinates, x and y, and time, t.

, ,

,, , (1)

The mass absorption coefficient, µ (mm2/µg), is

determined from calibration of the fuel’s absorption in a cuvette of known size.

The ensemble average projected density of the individual traces is calculated via Eq. 2, and the en-semble standard deviation in projected density is cal-culated via Eq. 3.

, ,∑ , ,

(2)

′ , ,∑ , , , ,

(3)

At each point in time, and spatial location (x,y),

the ensemble standard deviation is calculated from the 32 individual events and their ensemble average. The spatial extent and temporal dependence of the shot-to-shot fluctuations can then be visualized by plotting M’. More details of this can be found in a previous work [12]. The current work focuses exclu-sively on the quasi-steady-state portion of the spray, excluding start-of-injection and end-of-injection tran-sients

These images are comprised of a blue layer rep-resenting the ensemble average, and a red layer indi-cating the ensemble standard deviation. They have been projected to 8-bit (0-255) red/blue images via Equations (4) and (5).

, ,

∙ 255 (4)

, , , ,

∙ 255 (5)

B is the 0-255 level representing the average

flow with Mmax = 150 µg/mm2. R is the 0-255 level representing fluctuations with Mmax=15 µg/mm2. Calculated levels for both B and R above 255 and below 0 are set to 255 and 0 respectively. In Equation 5, M(x,y,tpre) is the pre-spray standard deviation which is subtracted ensemble standard deviation to remove baseline fluctuations. Blue indicates regions where the mean flow is dominant, while red indicates regions where the shot-to-shot fluctuations are domi-nant. Purple regions are an overlap of the two.

Figure 3 shows three different images the three different nozzle hole sizes, at Prail = 500 bar, and Pamb

= 1 bar. Elevated levels of fluctuations are seen downstream of 2 mm for all cases. The start of this region does not appear to have a strong dependence on orifice size. As would be expected, the width of the fluctuating region increases with increasing di-ameter, due to the increased size of the spray plume as seen in the mean profile upstream.

Figure 4 presents a series of composite images for three different rail pressures in the 110 µm nozzle at Pamb=1 bar. With increasing rail pressure, the re-gion of elevated shot-to-shot fluctuations is observed to move upstream. In a previous work, this behavior was attributed to the onset of mixing and atomization occurring closer to the orifice [12].

In Figure 5, the effects of ambient pressure are observed in three composite images for the 180 µm nozzle, and Prail= 500 bar condition. Similar to the trends of Fig. 4, with increasing ambient pressure, the region of elevated fluctuations moves upstream. Ad-ditionally, the width of the fluctuating profile (and consequently, the width of the mean profile) both increase with increasing ambient pressure, which is in agreement with previous work [13].

(a)

(b)

(c)

Figure 3. Composite images for the (a) 110 µm, (b) 130 µm, and (c) 180 µm nozzle in the Prail=500 bar, Pamb=20 bar condition.

(a)

(b)

(c)

Figure 4. Composite images for the (a) 500 bar, (b) 1000 bar, and (c) 1500 bar rail pressures in the D= 110 µm, Pamb=1 bar condition.

All of these data sets indicate that shot-to-shot fluctu-ations do not become significant until the fuel has traveled some distance downstream of the nozzle exits. Upstream, toward the nozzle exit, these fluctua-tions are minimal.

Standard deviation is a metric of shot-to-shot variation that includes both coherent (occurring in a similar temporal fashion between injection events, though perhaps different in phase) and incoherent (truly random) fluctuations. In order to understand the contribution of coherent fluctuations to the shot-to-shot variation, a proper orthogonal decomposition (POD) was performed.

The POD calculation starts with removing the ensemble averaged mean (Eq. 2) from each of the individual realizations, leaving only the fluctuating component of each realization. This series is then truncated to contain only the quasi-steady state por-tion of the spray, designated as m'(x,y,t,n). The re-moval of this mean implies that the sum of all the POD modes will not add up to the original mean field, but rather the sum of the fluctuations. Since fluctuations have both positive and negative sign, the sum of the fluctuations across all the realizations is substantially smaller than the standard deviation.

POD attempts to decompose any data set into the minimum number of orthogonal modes or “principal components,” such that Equation (6) is satisfied.

, , , ∑ , , (6)

Each successive mode k represents a decreasing

fraction of the variance of m as the POD mode num-ber k increases from 1 to K total modes. (k) is the temporal scalar coefficient of mode k at any instant in time, and Φ(k)(x,y,n) is the spatial mode shape, de-scribing the distribution of the mode in space and across each of the 32 realizations denoted by n. To compute the POD modes using the snapshot method [14], we solve an eigenvalue problem given in Equa-tion (7).

0 (7) C is the auto covariance matrix given by

C=VTV, with V being the snapshot matrix, contain-ing a time-snapshot of m' in each row. The eigenval-ues (k) represent the fractional contribution of each mode to the total fluctuations, and the eigenvectors (k) represent a discrete vector form of the temporal scalar coefficients. Once (k) is computed, the spatial mode Φ(k)(x,y,n) can now be solved for via Equation 8;

(a)

(b)

(c)

Figure 5. Composite images for the (a) 1 bar, (b) 10 bar, and (c) 20 bar ambient pressures in the D= 180 µm, Prail=500 bar condition.

, , ∑ ∙ , , , (8)

The spatial mode is more useful to be looked at

via ensemble averaging over each event, thus leaving only Φ(k)(x,y), which is the quantity discussed below. Averaging this quantity will remove any non-repeatable fluctuation modes in each shot, and aug-ment fluctuating modes with similar time profiles at a given spatial location.

In the following section, various data sets are presented which qualitatively visualize the ensemble average, the ensemble standard deviation, and the magnitude of the POD calculations. The ensemble average and ensemble standard deviation have been time-binned through the steady test time. The POD calculations have been performed during the steady test time to allow a comparison with the time-binned ensemble statistics.

The sum of the first five POD modes is comput-ed. These first 5 modes describe approximately 85% of the sum of the fluctuations. At each x-location, this sum is integrated in the transverse (y) direction to reduce the data. This is shown in Equation (9) and (10), with P being the normalized quadrature sum of the first 5 modes, and TIP (Transverse Integrated POD modes) being the integral.

, ∑ , (9)

, (10)

The TIP serves to visualize the axial extent of the

coherent fluctuations present in every shot. In the next several figures, TIP will be compared to the transverse integrated fluctuations (TIF), which is the standard deviation, time-binned and integrated over y, calculated via Equation (11). The TIF serves to visualize the axial extent of the total shot-to-shot var-iations, both coherent and incoherent.

, ,

(11) The next series of figures visualizes the TIP and

the TIF in tandem. TIP data are shown as closed symbols, while TIF data are shown as white filled symbols. The effects of each of the three parameters are investigated, and correspond with data sets from Figures 3-5 respectively.

Figure 6 compares the effect of nozzle hole size on these three parameters. When x <1.8 mm, POD modes are at their highest levels. They monotonically

increase from x=0 mm, dropping off sharply at x=1.8 mm to zero and remaining there throughout the rest of the domain. TIF levels remain near 0 between the nozzle and x=1 mm, and begin to slowly rise between x=1 and 2 mm. Beyond x=2 mm the TIF levels begin to rise significantly. Interestingly, the normalized TIP levels increase with decreasing orifice diameter, while the downstream TIF behavior is opposite of this, increasing with diameter.

Figure 6. The TIP and TIF are shown for the Prail=500 bar, Pamb=20 bar test condition for the 110 µm, 130 µm, and 180 µm nozzles.

In Figure 7, the effect of Prail is shown on the TIP

and TIF profiles. Similarly to Figure 3, TIP levels at x locations less than 2 mm are elevated, and drop off sharply downstream. TIF levels, however, remain low and do not increase drastically until x> 5 mm. Elevated rail pressures corresponds with higher levels of TIP at x<2.0 mm. This behavior is not as distinct as the behavior with nozzle size. Interestingly, far downstream, increasing rail pressure corresponds with decreasing TIF levels.

Figure 7. The TIP and TIF are shown for the D=110 µm nozzle, Pamb=1 bar at 500 bar, 1000 bar, and 1500 bar ambient pressures.

Figure 8 illustrates the effect of Pamb on TIP and TIF. In the TIP profiles, the two lowest ambient pres-sures (1 and 10 bar), lie very close to each other, and are much lower than the 20 bar case. As before, they drop off to zero before x=2 mm. The TIF profiles show a much more distinct trend with Pamb, where increasing Pamb leads to increased TIF levels. The TIF in the 20 bar case begins to rise quickly after 3mm, while this is moved downstream to approximately 5 and 7 mm for the 10 and 1 bar cases. Contrary to the other two parameters investigated in Figures 6 and 7, the trends for TIP and TIF, with Pamb, are not inverse.

Figure 8. The TIP and TIF are shown for the D=180 µm nozzle, Prail=500 bar at 1 bar, 10 bar, and 20 bar ambient pressures.

Figures 6-8 serve as a qualitative assessment of

the regions where coherent, repeatable fluctuations (POD) are a significant contribution to the shot-to-shot variation, compared with regions where the standard deviation (representing the total of the co-herent and incoherent fluctuations) are dominant. While the POD as calculated here is not a quantita-tive metric of the coherent fluctuations, in the down-stream regions where the POD is near zero it can be assumed that the standard deviation is predominantly composed of incoherent fluctuations. The coherent fluctuations are seen to be concentrated very near to the nozzle and fall off sharply at x>2 mm, while the incoherent are more dominant downstream of this location.

POD modes (and consequently TIP) are believed to be the result of coherent oscillations, and they are most significant in the region very near to the nozzle. This is characteristic of the early onset of instability in the mostly intact liquid core, before larger scale atomization and mixing begin. These fluctuations may be due to either hydrodynamic fluctuations of the liquid core, or pressure fluctuations in the en-trainment field. In contrast, the shot-shot fluctuations

indicated by the standard deviation (and consequently the TIF) seem to be indicative of incoherent fluctua-tions. These are a result of large scale mixing and atomization, and the magnitude of the fluctuations can be on the order of 20-30% of the mean flow downstream (x=7 to 9 mm).

Lastly, we cast shot-to-shot statistics in a differ-ent way to investigate the variation in the near nozzle flow for individual events. We first time average (and compute the standard deviation) for each individual spray event during the steady flow. This is done for each case shown in Figures 3-5. The time binned, single-shot means and normalized standard devia-tions are shown in Equations 12 and 13 as , and (x,y). The standard deviations are representa-tive of the fluctuations within each single shot, during the steady spray time, and the pre-flow (baseline) standard deviation has been subtracted in quadrature as it is not zero.

,∑ , ,2

1 (12)

,

∑ , , ,

221

,100 (13)

These are computed at the nozzle centerline, at

the closest axial point to the nozzle; x=0.1 mm and y=0.0 mm for this study. At this location, we expect that the flow is almost entirely a liquid core. As 32 realizations are acquired for this work, 32 of these values are obtained for each parameter. The means of each set of 32 parameters is computed and listed in Tables 9 and 10. For the results of Equation 12, the square root of the variance of the 32 parameters is listed as a percentage. This is an indication of how much the mean mass during the quasi-steady spray varies from event-to-event. Table 9 presents the effect of the ambient pressure on the single shot means and standard deviations for the 180 µm nozzle and Prail=500 bar at 1 bar, 10 bar, and 20 bar ambient pressure. There is a strong trend in the mean decreasing with increasing ambient pres-sure. Additionally, there is an increase in the variance of the mean with increasing ambient pressure. Over-all, there is an increase in normalized standard devia-tion with increasing ambient pressure.

Table 10 illustrates the effect of the rail pressure on the single-shot means and standard deviations for the 110 µm nozzle and Pamb=1 bar at 500 bar, 1000 bar, and 1500 bar rail pressure. Interestingly, there is a distinct decrease in the projected mass with increas-ing rail pressure. Correspondingly there is an increase in the variation of these mean values. There are not

strong trends in the standard deviations of the single shot traces.

Mean of: 1 bar 10 bar 20 bar

, , % variance

181.8, 0.38%

180.3, 0.78%

155.3, 0.88%

, 1.49% 1.46% 2.04%

Table 9. The single shot means and standard devia-tions are shown for the D=180 µm nozzle, Prail=500 bar at 1 bar, 10 bar, and 20 bar ambient pressures.

, is in units of µg/mm2.

Mean of: 500 bar 1000 bar 1500 bar

, , % variance

110.5, 0.49%

109.03, 1.02%

104.9, 3.35%

, 1.88% 1.94% 2.00%

Table 10. The single shot means and standard devia-tions are shown for the D=180 µm nozzle, Pamb=1 bar at 500 bar, 1000 bar, and 1500 bar rail pressures. , is in units of µg/mm2.

The data in Tables 9-10, show strong trends for the single-shot mean and its variance as a function of D, Prail, and Pamb. Trends with the single-shot, stand-ard deviation, and its variance are also apparent. Alt-hough we measured projected mass at a single point, these data may have implications for relating to the variance of the total mass injected from shot to shot. Overall, the mean projected mass varies from 0.4 to 3.4 % across all the conditions.

Conclusions and Future Work

This work has examined multiple sources of fluctuations including full field, time binned shot-to-shot standard deviation, time binned transverse inte-grated fluctuations, time binned transverse integrated POD modes, and mean steady-spray mass variation.

Stochastic shot-to-shot variation is represented by the ensemble standard deviation. In this work it has been condensed to TIF, which increases with increasing downstream location from the nozzle. In fact at x<2-3mm, their magnitudes are very low. These types of fluctuations may be indicative of mix-ing and atomization, which is corroborated by the dependence of TIF profiles on nozzle diameter, rail pressure, and ambient pressure.

Coherent, repeatable fluctuation modes are in-vestigated using proper orthogonal decomposition. These are found to be highest near the nozzle, and although they are small in magnitude, the authors

believe these to be indicative of coherent instabilities in the liquid core and surrounding entrainment field, where little atomization is occurring. It should be noted here that the magnitude of the POD modes is qualitative in nature. At locations of x>2mm, POD contribution asymptotes to zero. This suggests con-tributions from coherent fluctuations to the standard deviation are minimal in this region.

Lastly we have investigated the variation in the time averaged, projected mass at a location very near to the nozzle exit (x< nozzle diameter). Distinct changes in the mean and its variance are observed with the different parameters. At this location, very close to the nozzle, these may be indicative of the variation of injected mass from each location, alt-hough more data is needed to make this correlation.

In future studies we aim to investigate these same parameters with a larger data set (200-400 real-izations, rather than 32) to increase statistical resolu-tion. We also aim to extend the parameter space to higher rail pressures (up to 3000 bar), and higher ambient pressures (up to 30 bar).

Another future goal is to investigate the mean, steady-spray behavior as close to the nozzle as our experimental techniques will allow (approximately 10 µm). This will give the most accurate measure of the shot-to-shot variation of the fuel mass being in-jected. Also desirable is a quantification of the shot-to-shot variation in injected mass for the current se-ries of injectors from a bench top test. This will aid in exploring if a link exists between the x-ray point measurements and the more global mass measure-ment. Nomenclature D nozzle diameter P pressure µ fuel absorptionM projected mass X axial coordinate Y transverse coordinate T time N number of realizations K total number of POD modes Φ spatial mode shape temporal scalar coefficient Subscripts rail rail condition amb ambient condition 1 start of steady time 2 end of steady time Superscripts k kth POD mode

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