Gas Density and Rail Pressure Effects on Diesel ... - ACS Publications

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Energy & Fuels 2009, 23, 1832–1842

Gas Density and Rail Pressure Effects on Diesel Spray Growth from a Heavy-Duty Common Rail Injector† R. J. H. Klein-Douwel,*,‡,§ P. J. M. Frijters,‡,| X. L. J. Seykens,‡ L. M. T. Somers,‡ and R. S. G. Baert‡,⊥ Faculty of Mechanical Engineering, EindhoVen UniVersity of Technology, P.O. Box 513, 5600 MB, EindhoVen, The Netherlands ReceiVed May 15, 2008. ReVised Manuscript ReceiVed August 29, 2008

Formation of nonevaporating sprays from diesel fuel injection through a realistic heavy duty multihole common rail injector is studied in a newly developed high-pressure, high-temperature cell, using digital highspeed shadowgraphy at 4500 frames/s. Gas pressure was varied from 13 to 37 bar (corresponding to densities of 15-42 kg/m3, using N2 at room temperature) and rail pressure from 750 to 1500 bar. The nozzle is carefully characterized and all injection data are analyzed by the method as described in previous work (Klein-Douwel, R. J. H.; et al. Fuel, 2007, 86, 1994-2007). Time evolution of the spray angle and penetration and possible dependences of these two variables on gas density and rail pressure are studied. It is found that after an exponential decay the spray angle reaches equilibrium values between 25° and 31°, which slightly depend on gas density. For spray penetration the dependences on gas density (power of -0.38 ( 0.01) and rail pressure (power of 0.4-0.6) are more pronounced. By using a reference length and time with which penetration data is scaled, it is shown that all data, independent of injection conditions, collapses very well onto a single line which increases as time to the power 0.56 ( 0.01.

Introduction

literature.3-5 Heavy duty injection systems have been studied by (among others) Naber and Siebers6 and Arre`gle et al.7

For the diesel engine development engineer, knowledge of spray shape evolution is very important. A few illustrations: a well-known rule of thumb in conventional diesel combustion is that ignition should occur before the fuel spray hits the piston bowl wall. Similarly, in designing HCCI combustion engines, spray growth estimates are used for selecting an optimum match between nozzle protrusion, spray injection angle, and injection timing to avoid wall wetting. Furthermore, spray volume growth is linked to turbulent air entrainment, which in turn determines combustion rate. Spray growth information is therefore input to many phenomenological models for diesel combustion and emissions formation. Finally, this same information is used to validate computational fluid dynamics (CFD) models. And in assessing the quality of new fuelling equipment, fuel spray growth analysis is used increasingly.1,2

For describing a (mature) spray, typically macroscopic characteristics such as spray length (penetration) and spray cone angle are used. Several studies have tried to correlate these parameters with time and with other variables such as injection pressure and ambient gas pressure and temperature. Some of these models are semiempirical or are based on a dimensionless number analysis.8 The majority, however, postulate a similarity between the structure and behavior of a (mature) spray and that of a (quasi-steady) turbulent gas jet. Already in 1960, Wakuri et al.9 derived a spray penetration correlation that expresses conservation of momentum in the growing turbulent spray. In this expression, spray angle was an independent variable. In 1971, Dent suggested a similar expression, but now assuming a fixed value for spray angle.3 With this (simpler) expression he obtained good results. After that, most studies disregarded the interaction between spray angle and penetration and aimed at improving the correlation of spray penetration with time, with nozzle geometry and with ambient gas properties (most worthy mentioning being the work by Hiroyasu and co-workers5,10-12). Only more recently the interaction between spray penetration

Fuel spray propagation has been the subject of research for decades, and several review articles have been published in the

† From the Conference on Fuels and Combustion in Engines. * To whom correspondence should be addressed. E-mail: [email protected]. ‡ Eindhoven University of Technology. § Current address: Applied Molecular Physics, Institute for Molecules and Materials, Radboud University Nijmegen, The Netherlands. | Current address: DAF Trucks N.V., Eindhoven, The Netherlands. ⊥ Also at TNO Automotive, Helmond, The Netherlands. (1) Reckers, W.; Lucchini, J. F.; Petit, C.; Kneer, R.; Spadafora, P. THIESEL 2002 Conference on Thermo- and Fluid-Dynamic Processes in Diesel Engines. 2002, pp 95-106. (2) Winter, J.; Dittus, B.; Kerst, A.; Muck, O.; Schulz, R.; Vogel, A. THIESEL 2004 Conference on Thermo- and Fluid-Dynamic Processes in Diesel Engines. 2004, pp 19-34.

(3) Dent, J. C. SAE Paper 710571, 1971. (4) Hay, N.; Jones, P. L. SAE Paper 720776, 1972. (5) Hiroyasu, H.; Arai, M. SAE Paper 900475, 1990. (6) Naber, J. D.; Siebers, D. L. SAE Paper 960034, 1996. (7) Arre`gle, J.; Pastor, J. V.; Ruiz, S. SAE Paper 1999 01-0200, 1999. (8) Varde, K. S.; Popa, D. M. SAE Paper 830448, 1983. (9) Wakuri, Y.; Fujji, M.; Amitani, T.; Tsuneya, R. Bull. J.S.M.E. 1960, 3, 123–130. (10) Arai, M.; Tabata, M.; Hiroyasu, H.; Shimizu, M. SAE Paper 840275, 1984. (11) Suzuki, M.; Nishida, K.; Hiroyasu, H. SAE Paper 930863, 1993. (12) Hiroyasu, H.; Arai, M. Trans. JSAE 1980, 21, 5–11.

10.1021/ef8003569 CCC: $40.75  2009 American Chemical Society Published on Web 11/04/2008

Density and Pressure Effects on Diesel Spray Growth

Figure 1. Schematic of fuel injection equipment: the dotted circle indicates the entrance/exit windows for the collimated light beam, which travels perpendicularly to the figure plane (camera and optics not shown); DA ) data acquisition, CR ) common rail.

and angle with turbulent sprays has been receiving more attention again.6,13 In the model of Naber and Siebers,6 the spray penetration is made dimensionless by taking the ratio to some reference distance, which depends (among others) on the gas density, nozzle diameter, and spray angle, and to a reference time, which in addition depends on the fuel injection velocity. With this approach they (and others after them) obtained very good results. However, partly due to the lack of good spray angle correlations and because spray angle information is difficult to determine, Araneo et al.14 (although following the approach of Naber and Siebers6) abandoned the dependence on spray angle in the reference length and time; instead they use extra fitting parameters to make the nondimensionalized injection data collapse onto a single curve. This paper reports on work that aims to confirm and extend our understanding of (the interaction of) spray angle and spray penetration for nonevaporating sprays at room temperature (although aerodynamic drag may cause slight evaporation, only temperature related evaporation is meant here). In this work, both Pgas and Prail were varied and their effects on spray angle and penetration were studied. A comparison is made to work presented by Baert and Vermeulen13 and Naber and Siebers,6 regarding dependence of spray length and angle on Pgas and Prail. Fuel Injection Experiments Experimental Setup. The experimental setup, image acquisition, processing steps, and subsequent analysis have been described in detail in previous work,15 but a short summary will be given here. Fuel injection experiments are performed in N2 at room temperature in the Eindhoven high-pressure, high-temperature cell, which is designed to create realistic heavy duty engine-like conditions. It has a cubic inner volume of 1083 mm3 and three 100 mm φ quartz windows. The latter limit the maximum pressure to 100 bar. Since this work has been performed, sapphire windows have been mounted, allowing pressures up to 300 bar. Figure 1 shows a schematic of the fuel injection equipment. The fuel used is regular, commercially available EN590 diesel fuel, in order for the experiments to be as realistic as possible. Fuel specifications are given in ref 15. The fuel pump is an air-driven pump connected to a common rail system, capable of delivering a rail pressure of up to 2000 bar. The injector is an 8-hole Bosch (13) Baert, R. S. G.; Vermeulen, E. J. Proceedings of the IMechE Seminar Measurement and Observation Analysis of Combustion in Engines, 1994; pp 27-37 (ISBN 0 85298930). (14) Araneo, L.; Coghe, A.; Brunello, G.; Cossali, G. E. SAE Paper 1999 01-0525, 1999. (15) Klein-Douwel, R. J. H.; Frijters, P. J. M.; Somers, L. M. T.; de Boer, W. A.; Baert, R. S. G. Fuel 2007, 86, 1994–2007.

Energy & Fuels, Vol. 23, 2009 1833 heavy duty common rail sack-hole nozzle (DLLZ160PV3771013 864), with 0.184 mm φ orifices and a length/diameter ratio of ≈5. In order to study a single fuel spray from this 8-hole injector, a kind of thimble is constructed, which covers all but one orifice. The fuel delivered by the seven covered orifices is led to the bottom of the cell by a drainpipe. Needle lift and common rail pressure transients are recorded at 1 MHz sampling rate in order to accurately determine the actual start of fuel mass injection and the initial common rail pressure before injection. The gas pressure is recorded as well. In all experiments the injection actuation duration was 5000 ( 1 µs. Data Acquisition and Processing. Shadowgraph images are acquired by a digital high-speed camera (Kodak EktaPro HS Motion Analyzer, model 4540) at a rate of 4500 images/s. Fuel injection is carefully synchronized to the internal camera clock. The minor window fouling and background illumination inhomogeneities are corrected for. Spray penetration is determined by lateral integration of the spray shadow and a macroscopic spray cone angle ϑcone is assigned, based on the near-constancy of the local angle ϑcone(x).15 An example of an analyzed spray image is presented in Figure 2a; in this figure also the spray contour and the lines marking ϑcone are indicated. Test Program. Whereas in previous work15 only one specific set of conditions was used, Pgas and Prail have been varied in the current work as indicated in Table 1. For every set of conditions, several injection experiments have been performed. The injection parameters have been chosen to be representative for diesel engine conditions. A wider range, comprising different and more combinations of conditions, is outside the scope of the research project presented here. Due to the characteristics of the fuel supply system, the initial common rail pressure varies slightly from one injection to another. Table 1 also gives the actual rail pressure and standard error (2.5% or better), averaged over all injections at the same nominal conditions. The nominal gas pressure in Table 1 is relative to atmospheric pressure. The actual absolute gas pressure (not shown in Table 1), which is averaged similarly to the initial rail pressure, is used to calculate the pressure difference ∆P over the nozzle opening and the density Fgas. For the combination of Prail,nom ) 1500 bar and Pgas,nom ) 29 bar, two sets were taken (on different days). These two sets are treated separately in the further analysis; this will give an indication of experimental accuracy/reproducibility. The results of these two sets have already been presented previously,15 but they are included here as well, since they are a good complement to the other injection conditions discussed in this work. Prail,nom and Pgas,nom are used here mainly for presentation purposes and for grouping relevant data together in calculations (as discussed below). Spray Angle Definition. In the literature, different spray angle definitions are in use. Sometimes it refers to the spray angle close to the injector nozzle hole. This angle is strongly influenced by (i.e., characteristic of) the nozzle design. It is also a parameter that is used to define the boundary conditions for a computational fluid dynamics model of the spray formation process. For describing the spray mixing process, the spray angle is usually determined at a larger distance from the nozzle, and therefore for a (more) mature spray. The latter angle is often referred to as the spray cone angle ϑcone. A more elaborate discussion of various definitions of spray angles can be found in ref 15. As discussed in ref 15, the definition of ϑcone used in this work makes it relatively sensitive to the actual spray shape. The more or less straight lateral edges of the spray may exhibit short-lived, smallscale distortions (caused by turbulence) during an injection that cause the upstream part of the spray to deviate from a smooth triangular shape.13,15,16 This sensitivity of ϑcone for spray shape therefore makes ϑcone reflect actual changes that do occur during an injection, but it might somewhat hamper a further analysis, when looking for more general trends of the dependence of the spray cone angle on parameters like gas density and common rail pressure (16) Yule, A. J.; Aval, S. M. Fuel 1989, 68, 1558–1564.

1834 Energy & Fuels, Vol. 23, 2009

Klein-Douwel et al.

Figure 2. (a) Example of spray image analysis, as outlined in ref 15. The red line represents the spray contour, the blue lines the calculated cone angle ϑcone. (b) Spray contour, equivalent isosceles triangle with an area equal to the upstream half of the spray (A1/2,obs, red) and indication of ϑcone and ϑ∆ (eq 1). Table 1. Injection Conditions: Pressure in bar, Density in kg/m3a Prail,nomb

Pgas,nomb

1500 1500c 1500c 1000 1000 1000 1000 750 750 750

37 29c 29c 37 29 19 13 37 28 19

Prail 1532 ( 11 1514 ( 12 1501 ( 5 1048 ( 21 998 ( 15 979 ( 6 1009 ( 10 771 ( 27 782 ( 19 773 ( 16

∆P

Fgas

1494 1485 1472 1009 969 958 995 733 753 753

44.0 33.1 33.4 44.0 33.3 23.2 16.5 44.0 33.2 23.1

a Errors are derived from averaging over several injections at nominally identical conditions. The error in ∆P is equal to that of Prail, since the error in Pgas (not shown) is negligible. The error in Fgas ranges from 0.1 to 0.5%. b Nominal values: used in figure legends and for grouping data together, but not for calculations. c Two sets performed on different days, treated separately in further analysis (taken from ref 15).

(as will be discussed later). Therefore a so-called triangular spray angle ϑ∆ is introduced, similar to the definition of Naber and Siebers:6 ϑ∆ equals the acute angle of an isosceles triangle which has an area and height equal to those of the upstream half of the spray. Because of the thimble around the injector, the very first part of the spray is not observed. This leads to the following definition of ϑ∆:

tan

( )

ϑ∆ A1/2,obs h02 ) 1 2 h2 h2

-1

(1)

in which A1/2,obs is the observed spray area between x ) 0 and x ) h, h ) S/2 is half the spray length, and h0 is the length of the first unobserved part of the spray. Figure 2b reveals the difference between ϑcone and ϑ∆. Shortly after injection, the fraction h0/h will be relatively large, but it will rapidly decrease as the spray matures. If the upstream half of the spray resembles a triangle, ϑcone and ϑ∆ will be approximately equal (as is the case in Figure 2). But any information about the shape is lost in ϑ∆, ironing out all possible spray anomalies. By considering only the upstream half of the spray for ϑ∆, the unsteady head and the turbulent processes influencing it are ignored. This is different from the “ice cream cone” approach used by Araneo et al.,14 who approximate the entire spray by an isosceles triangle with a semicircle on top of it.

cavitation set up inside the nozzle during the injection process. This degree of cavitation in turn is determined by the ratio of the flow cavitation number CaN and the nozzle critical cavitation number CaNcrit (discussed in more detail below). The cavitation number CaN is defined as CaN )

Pup - Pdown Pdown - Pvap

(2)

where Pup and Pdown are the pressure upstream and downstream of the nozzle, respectively, and Pvap is the fuel vapor pressure. The fuel flow area reduction in the orifice exit, due to cavitation, is represented by the area contraction coefficient Ca, and the velocity coefficient Cv accounts for orifice velocity losses due to cavitation. Combining Ca and Cv yields the discharge coefficient Cd of the nozzle: Cd ) CaCv

(3)

In order to obtain the fuel mass flow rate m ˙ f of a cavitating flow, the relation Cd )

m ˙f A0√2Ff∆P

(4)

is used, in which A0 is the geometrical nozzle cross section, Ff the fuel density, and ∆P ) Pup - Pdown the pressure difference over the nozzle opening. Combining these equations leads to the mass flow rate m ˙ f being given by 1 1 + CaN

m ˙ f ) A0√2Ff∆P · Ccd

(5)

in which Ccd is the discharge coefficient for a fully cavitating flow. The last two terms in eq 5 represent the discharge coefficient Cd for the case CaN > CaNcrit: 1 1 + CaN

Cd ) Ccd

∀ CaN > CaNcrit

(6)

Nozzle Characterization. Several studies (e.g., ref 17) have shown that for a given injection pressure, different (internal) nozzle geometries will result in different internal flows and, as a result, also in a different angle of the spray upon exiting. This difference has furthermore been linked to the degree of

From this equation it is clear that lower cavitation levels will result in higher (effective) discharge coefficients. For the nozzle studied here, both discharge coefficients and momentum coefficient have been determined. The motivation for this was 2-fold: first, in doing so, this would enable comparison of the nozzle design to that of other nozzles examined in the literature, and second, as will be shown later, these characteristics are also needed when checking the correlation of Naber and Siebers.6 The discharge coefficient of the nozzle had been estimated before by fitting the results of fuel injection experiments (performed using a Zeuch-type chamber) to the predictions made using a simulation model.18 In the

(17) Payri, F.; Bermu´dez, V.; Payri, R.; Salvador, F. J. Fuel 2004, 83, 419–431.

(18) Seykens, X. L. J.; Somers, L. M. T.; Baert, R. S. G. Mecca, Journal of Middle European Construction and Design of Cars 2005, III, 30-40.

Results and Discussion


AMESim injector model,19 the value of the discharge coefficient of the nozzle holes at maximum cavitation (CaN f ∞) was tuned to a value of 0.765 ( 0.018 to fit the injection measurement data. This is a realistic value. For the length/ diameter ratio of the nozzle hole used in this work, the correlation of Lichtarowicz et al.,20 which is valid for noncavitating flow through a sharp-edged nozzle hole, gives a discharge coefficient of 0.78. Discharge coefficients in the range of 0.69-0.73 are found for a fully cavitating flow by several authors such as Arcoumanis et al.,21 Favennec et al.,22 and Von Kuensberg Sarre et al.23 There are also authors who use significantly higher values. Ganippa et al.,24 for instance, found discharge coefficients in the order of 0.78-0.8 for cavitation numbers in the range of 10-20. Even higher values are used by Goney and Corradini.25 For a cavitating flow in a sharpedged nozzle hole they found values in the range of 0.8-0.925.25 For noncavitating flow through a nozzle hole with high inlet rounding, values in the range of 0.85-0.975 are mentioned.25 It is worthwhile mentioning here that, in contrast to many other authors, Goney and Corradini25 used actual sac-pressure measurements for determining Cd values. In the injection experiments CaN values ranged between ≈19 (for 800 bar rail pressure) and ≈34 (for 1400 bar rail pressure). With critical cavitation numbers CaNcrit of nozzle holes typically in the range of 1.5-5,17,21,22,24,25 eq 5 gives discharge coefficients in the range of 0.838-0.988 at the onset of cavitation in case Ccd is taken equal to the tuned value of 0.765. These values seem relatively high. That is why it was decided to check the validity of the tuned value for the nozzle hole discharge coefficient by additional measurements. In these experiments, the following setup was used: continuous fuel injection into the Zeuch chamber; increased injector needle lift such that the needle is no restriction to the flow; seven out of eight nozzle holes blocked; variation of cavitation number through both injection pressure and Zeuch chamber pressure change; Zeuch chamber pressure variation through throttling of the fuel outflow; and direct measurement of the injected mass flow rate downstream of the Zeuch chamber by a Coriolis type mass flow meter. Figure 3 shows the measured mass flow rate versus the square root of the pressure difference across the nozzle hole. Tests were done at four different injection pressure levels. For every injection pressure level the Zeuch chamber pressure was varied. Except for the injection pressure of 200 bar, the mass flow rate was independent from the pressure drop. This is because the flow is fully cavitating in these conditions, and the flow through the injection nozzle hole is choked. Analogous to a compressible flow at sonic conditions, the flow is no longer dependent on the downstream conditions. For an injection pressure of 200 bar, the transition from cavitating flow to noncavitating flow can be seen when the downstream pressure is increased, i.e., a smaller pressure drop over the nozzle hole. The critical cavitation number CaNcrit is defined as the value of CaN at this transition from noncavitating to cavitating flow. For noncavitating conditions, the mass flow rate is proportional to the square root of the pressure drop across the nozzle hole. From Figure 3 it can (19) www.amesim.com. (20) Lichtarowicz, A.; Duggings, R. K.; Markland, E. J. Mech. Eng. Sci. 1965, 7, 210–219. (21) Arcoumanis, C.; Flora, H.; Gavaises, M.; Badami, M. SAE Paper 2000 01-1249, 2000. (22) Favennec, A.; Lebrun, M. The Sixth Scandinavian Conference on fluid Power SICF’991999. (23) Von Kuensberg Sarre, C., Kong, S. C.; Reitz, R. D. SAE Paper 1999 01-0912, 1999. (24) Ganippa, L. C., Andersson, S.; Chomiak, J. SAE Paper 2000 012788, 2000. (25) Goney, K. H.; Corradini, M. L. SAE Paper 2000 01-2043, 2000.

Energy & Fuels, Vol. 23, 2009 1835

Figure 3. Injected mass flow rate versus square root of the pressure drop over the nozzle hole (legend gives injection pressure).

Figure 4. Measured nozzle hole discharge coefficient Cd as function of cavitation number CaN.

be concluded that once cavitation occurs, the mass flow rate collapses and is no longer a function of the pressure drop over the nozzle. This can also be seen when the calculated discharge coefficient is depicted as a function of the cavitation number, as is shown in Figure 4. For low cavitation numbers (CaN < 1.8), the discharge coefficient increases until the maximum value is reached at the critical cavitation number. Further increase in the cavitation number leads to a rapid decrease of the discharge coefficient to an asymptotic value Ccd at infinite cavitation number (CaN f ∞). From Figure 4, several conclusions can be drawn. First, the critical cavitation number of the nozzle hole is CaNcrit ≈ 1.8, which lies in the range of values found in literature. The corresponding maximum value of the discharge coefficient is c 0.887+0.028 -0.006. Second, for the asymptotic discharge coefficient Cd, +0.014 a value of 0.75-0.007 is determined. This value is in good agreement with the tuned discharge coefficient for maximum cavitation used in the injector model. And last, it can be concluded that for the range of cavitation numbers used during the injection measurements (19-34) the flow was almost fully cavitating and the discharge coefficient was nearly constant. Equation 5 is used in AMESim to calculate the mass flow rate through a restriction (for instance, a nozzle hole) for operating conditions between the onset of cavitation and fully cavitating flow. Now that the tuned value of the discharge coefficient for fully cavitating flow has been validated, the correctness of the equation used in AMESim can be checked. In order to check the validity of eq 5, the measured discharge coefficients have been fitted with eq 6, where Ccd is taken as 0.75. With a correlation coefficient R2 ) 0.9972, the validity of eq 5 to simulate the mass flow rate for cavitating flow is strongly supported.


Klein-Douwel et al.

Figure 5. (a) ϑcone versus time for all individual injections (several injections for each condition in Table 1); legend given in (b). Values outside the most common range 25°-30 ° are discussed in the text. (b) Similar to (a), but now for ϑ∆. Data points for which ϑ∆ > 42° are considered outliers and are not considered in further analysis. The first number in the legend is Prail,nom, and the second is Pgas,nom.

Spray Angle. Time EVolution. The values of ϑcone versus time are plotted in Figure 5a for each individual injection (several injections for each condition listed in Table 1). These data show that the main range of ϑcone is limited to 25°-30°. This is in line with data in the literature: for strongly cavitating (cylindrical) nozzles, Payri et al.17 observed spray cone angles between 25° and 30°, and Schneider26 and Boulouchos and co-workers27 have also found angles between 25° and 30° at low temperatures, like in the work presented here. New experiments at 600-1200 K reveal smaller angles of about 15°-20° for evaporating sprays. This distinction between evaporating and nonevaporating sprays is also clear from ref 6. As is evident from Figure 5a and indicated before and in ref 15, ϑcone may well vary within this 25°-30° range within one single injection event as a result of spray shape changes taking place. In the early phase of the injection, spray shapes often do not exhibit a roughly triangular shape, whence the calculated ϑcone may be much larger than ≈30°. For some sprays the image noise toward the end of injection becomes noticeable, also leading to an apparent ϑcone (much) larger than ≈30°. The scatter in ϑcone is such that any possible dependence of ϑcone on Fgas or Prail is completely disguised by it. A somewhat clearer picture is obtained by using ϑ∆ instead of ϑcone, as is shown in Figure 5b. Although some information is ignored when using ϑ∆ instead of ϑcone (as discussed above), the latter is hardly suited for further analysis of any time and/or pressure dependences, whereas for ϑ∆ the situation is much better, as may already be glimpsed from Figure 5b. Therefore, in the remainder of the work presented here, ϑ∆ will be used in further analysis. When considering the time evolution of ϑ∆, shown in Figure 5b, it becomes apparent that after around 3 ms after start of injection, ϑ∆ more or less reaches an equilibrium value. But before this time, ϑ∆ steadily decreases with time. In order to check for a simple functional time dependence in the early phase, first the equilibrium value ϑ∆,eq for each ϑ∆(t) is determined. Figure 6 shows these equilibrium values, which are the average (and corresponding standard deviation) of ϑ∆(t) for 3.5 e t e 4.5 ms. This is the period where the time derivative |dϑ∆(t)/dt| is smallest. After 4.5 ms the fluctuations in ϑ∆(t) appear to increase slightly again, but this may be due to rail pressure fluctuations near the end of fuel injection, which takes place at 5 ms. Possible relations between ϑ∆,eq and Fgas or ∆P are discussed in the next section. (26) Schneider, B. M. Ph.D. Thesis, ETH Zu¨rich, 2003 (Dissertation 15004). (27) Boulouchos, K.; Margari, O.; Escher, A.; Barroso, G.; Schneider, B. M.; Kunte, S. Proc. 6th Int. Symp. Internal Combust. Diagnostics 2004, 235-249.

Figure 6. Equilibrium values ϑ∆,eq and corresponding standard deviation for all individual injections, determined from ϑ∆(t) for 3.5 e t e 4.5 ms (Figure 5b).

Figure 7. ϑ∆(t) - ϑ∆,eq versus time on a semilogarithmic scale, in order to establish a possible exponential decay (eq 7). The two dashed lines indicate exemplary decay times τ.

The equilibrium values ϑ∆,eq are subtracted from ϑ∆(t) before attempting to determine a time dependence for the early phase. Plotting the data in a semilogarithmic plot corresponds to testing a time behavior of the form ϑ∆(t) ) ce-t ⁄τ + ϑ∆,eq

(7)

The result is shown in Figure 7 from which it is clear that an exponential decay of ϑ∆(t) in the early phase appears to be reasonable until t ≈ 3 ms. The spray angle decay time τ and the proportionality constant c of eq 7 are calculated by fitting straight lines to the data in Figure 7 [equivalent to taking the logarithm of eq 7] for 0 e t e 3 ms. The results are presented in Figure 8. Since the scatter in the data in Figure 7 is significant, it is taken into account by calculating the uncertainty estimates ∆τ and ∆c as well, using the least-squares method as outlined



Figure 8. (a) Decay time τ and (b) proportionality constant c (including uncertainties) of eq 7 for all individual injections. Data of Figure 7 between 0 and 3 ms is used.

in ref 28. Most values of τ lie between 0.4 and 1.4 ms, while for c the majority lies between 5° and 50°. The value of ϑ∆(t) will be very close to ϑ∆,eq in just a few decay times τ. No clear trend is observed between either τ and c on the one hand and rail pressure or gas density on the other. The time dependence of ϑ∆(t) as given by eq 7 therefore seems a reasonable description, although such a dependence appears not to have been observed or analyzed before. The only other time analysis of ϑ(t) encountered in literature is that by Gupta and co-workers,29 who find tan(ϑ(t)/2) ∝ t-0.4. But in that work, only the much shorter time interval of 0.3-2.1 ms after start of injection is considered. At 2.1 ms, equilibrium has not yet been reached, as can be seen in Figure 3 in ref 29 and in Figure 5b (this work). In fact, the interval used in ref 29 is so short that eq 7 would describe those results very well also. Furthermore, for a mature spray it would be expected that some sort of equilibrium is reached. This is inherent in eq 7 and visible in Figure 5b, but in a power law ϑ(t) ∝ tn there is no equilibrium. Gas Density and Rail Pressure. Based on dimensional analysis, a general dependence of the form ϑ mϑ ∆PnϑdRh ϑtβϑ tan ∝ Fgas 2

(8)

can be put forward, where dh is the hydraulic diameter of the injector nozzle. Table 2 gives an overview of the data for the parameters in eq 8 as found in the literature. While for the spray angle decay time τ (eq 7) no clear relation with Fgas or ∆P has been found, the equilibrium angle ϑ∆,eq may be correlated to these two parameters. This information is already present in Figure 6, but in order to allow a more detailed investigation, data of Figure 6 is replotted as log tan ϑ∆,eq/2 versus log Fgas in Figure 9a-c, now for each value of Prail,nom separately (plotting the logarithms allows verification of eq 8 later on). In eq 8 tan ϑ/2 is used and ϑ in eq 7, but since both ϑ/2 and ϑ∆(t) - ϑ∆,eq do not exceed approximately 15°, the difference of at most 2.3% between the angle and its tangens is negligible. An analysis-of-variance (ANOVA) has been performed on the data in Figure 9a-c, in order to check whether or not the data are independent and hence a trend can be confidently (28) Squires, G. L. Practical Physics; McGraw-Hill: London, 1968 (Dutch translation J. Kuperus, 1979). (29) Gupta, S. E.; Poola, R.; Sekar, R. SAE Paper 2000 01-2787, 2000. (30) Kang, J.; Bae, C.; Lee, K. O. Int. J. Engine Res. 2003, 4, 283–298. (31) Delacourt, E.; Desmet, B.; Besson, B. Fuel 2005, 84, 859–867. (32) Chang, C. T.; Farrell, P. V. SAE Paper 970353, 1997. (33) Verhoeven, D.; Vanhemelryck, J. L.; Baritaud, T. SAE Paper 981069, 1998. (34) Taylor, D. H.; Walsham, B. E. Diesel Engine Combustion Symposium, Proceedings ImechE 1970, 184, part 3J, 53-62. (35) Varde, K. S.; Popa, D. M.; Varde, L. K. SAE Paper 841055, 1984.

Table 2. Powers mT, nT, rT, and βT of Eq 8 for the Dependence of tan(T/2) on Various Observables, As Found in the Literaturea mϑ (Fgas) 0.10 0.10 ( 0.04 0.15 0.18 0.184 0.19 0.19 0.25 0.26 0.33 0.335 0.34 0.40 0.50 0.50 c

nϑ (∆P)

Rϑ (dh)

b

-0.115

-0.40

0.25 0.15 0.00943

0.508 0.5

mS + mϑ/2

βϑ (t)

0.35 0

-0.33 ( 0.02 -0.25 -0.23 -0.26 -0.27 -0.16/-0.26 -0.12 -0.34 -0.239 -0.08/-0.28 -0.05 0

0.32

author Sitkei38 this work Taylor34 Fujimoto39 Gupta29 Baert13 Naber6 Hiroyasu12 Hiroyasu5 Varde8,35 Arrègle7 Wakuri9 Payri40 Reitz41 Araneo14 Yokota42

a In the calculation of m + m /2, used for checking eq 13, m is S ϑ S taken from Table 3. b Exponential decay observed. c Exponential dependence found.

established. If ANOVA indicates independence, the variation within a data set at a specific value of Fgas is smaller than the variation between data sets at different values of Fgas. This can also be directly seen in Figure 9a-c. For example, for Prail,nom ) 750 bar (Figure 9c) the variation within the data set for Pgas,nom ) 37 bar (log Fgas ) 1.64) is smaller than the variation between this data set and the other two sets at Pgas,nom ) 19 and 28 bar (log Fgas ) 1.36 and 1.52, respectively), so in this case a Fgas dependence of ϑ∆,eq can be confidently established (the data sets at Pgas,nom ) 19 and 28 bar, however, are not independent between themselves). For Prail,nom ) 1000 bar (Figure 9b) most data sets are independent as well, also allowing a trend with gas density to be established (only the combinations Pgas,nom ) {13, 19} and {29, 37} bar are dependent between themselves). At Prail,nom ) 1500 bar (Figure 9a), however, the scatter in all data is such that independence is not present. Therefore, although due care is needed in view of the ANOVA results, eq 8 is tested by fitting straight lines to the data in Figure 9a-c. In this calculation, all data for a single value of Prail,nom are combined, which is allowed, since the actual values of Prail differ only slightly. And by considering ϑ∆,eq, (36) Siebers, D. L.; Higgins, B. S.; Pickett, L. M. SAE Paper 2002 010890, 2002. (37) Seykens, X. L. J.; Somers, L. M. T.; Baert, R. S. G. Proceedings of the International Conference on Vehicles Alternative Fuel Systems & Environmental Protection 2004, 72-77. (38) Sitkei, G. Kraftstoffaufbereitung und Verbrennung bei Dieselmotoren; Springer Verlag: Berlin, 1964. (39) Fujimoto, H.; Tanabe, H.; Kuniyoshi, H.; Sato, G. T. Bull. J.S.M.E. 1982, 25, 249–256.


Klein-Douwel et al.

Figure 9. log(tan ϑ∆,eq/2) versus log F for (a) Prail,nom ) 1500, (b) 1000, and (c) 750 bar, revealing possible trends in ϑ∆,eq and allowing verification of eq 8. (d) Resulting values mϑ (including uncertainty) from the fits in (a-c) (data at 1500 bar only shown for completeness).

the factor tβϑ is effectively removed from eq 8. Figure 9d summarizes the obtained values of mϑ versus Prail, where the value at Prail,nom ) 1500 bar is only shown for the sake of completeness, since in this case a confident fit cannot be made (as discussed above and reflected by the large error bar in Figure 9d). Data scatter is taken into account by calculating the uncertainties in the slopes28 mϑ (Figure 9d). A dependence of mϑ on Prail is not detected and the average value (for Prail,nom ) 750-1000 bar) of m j ϑ ) 0.10 ( 0.04 is in line with the lowest values presented in Table 2. In order to check the relation between ∆P and ϑ∆,eq in eq 8, plots similar to Figure 9 have been made, only now with ∆P on the abscissa. These are not shown, since it is observed that a value of nϑ ) -0.05 ( 0.1 in eq 8 is obtained. Therefore nϑ ) 0 is listed in Table 2 and no clear dependence of ϑ∆,eq on ∆P is detected, contrary to a few other studies (see Table 2 for references). Spray Length. Time Dependence. As has already been observed in the previous study15 and by Baert and Vermeulen13 and discussed in for instance ref 16, individual sprays often reveal small, short-lived deviations from an “ideal” triangular shape. These deviations may vary from injection to injection, but they are still relatively small compared to the average of all injections under identical conditions. Therefore, in the current work mostly only such an average is considered. The average spray penetration S versus time is shown in Figure 10 for all conditions listed in Table 1. The experimental uncertainty in S is ∆S ) (0.2 mm. It is easily seen here that the lower Prail and the higher Pgas are, the slower the spray penetrates the ambient gas. For all (averaged) injections, a fit has been made of the spray penetration S of the mature spray to the equation (9) S ) atb as used in ref 15. The resulting values of the power of time b are shown in Figure 11. The time interval used for fitting to eq

Figure 10. Spray penetration S (averaged over several injections) for all conditions listed in Table 1 (experimental uncertainty ∆S ) (0.2 mm not shown). Around 90 mm, the opposite edge of the observation window is reached.

9 (see ref 15) is determined for each injection condition separately. First, a short time interval is chosen in which the spray penetration matches eq 9 very well, then the interval is expanded by the next data point, until a minimum in the error ∆b of the power b is obtained (which also corresponds to the maximum covariance between S and t of the data points concerned). Although the fitting procedure yields uncertainty estimates ∆b,28 the experimental reproducibility may be derived from inspection of the results for the two nominally identical injection conditions (Prail,nom ) 1500 bar, Pgas,nom ) 29 bar), which are treated separately in the analysis. The difference in b of ≈0.01 for these two sets of injections is about equal to their values of ∆b as derived from the fit. Therefore, an experimental error in b of (0.01 is assumed. (40) Payri, F.; Desantes, J. M.; Arre`gle, J. SAE Paper 960774, 1996. (41) Reitz, R. D.; Bracco, F. V. Phys. Fluids 1982, 25, 1730–1742. (42) Yokota, K.; Matsuoka, S. Trans. J.S.M.E. 1977, 43, 3455.


Energy & Fuels, Vol. 23, 2009 1839 Table 3. Powers mS, nS, rS, and βS of Eq 11, for the Dependence of Spray Penetration S on Various Observables, As Found in the Literature a mS (Fgas)

Figure 11. Power of time b in eq 9 with which the mature spray grows, for all conditions listed in Table 1 (Prail,nom given in the legend). Error bars indicate statistical uncertainty resulting from the fit, and experimental uncertainty is estimated at (0.01.

It is observed in Figure 11 that the values for b range from 0.50 to 0.67. So most of the values for b observed here are above the often observed or postulated value of 0.5 (see, for instance, refs 3, 5-7, 9, 10, 13, 17, and 30-32), but values above 0.5 have been observed as well: values of 0.45-0.53 are given in ref 33, 0.55 in ref 8, 0.55-0.59 in ref 26, 0.57 in ref 7, and 0.64 in ref 34. No clear trend is observable, however, in Figure 11, but the use of dimensionless correlations (discussed below) provides more insight. Gas Density and Rail Pressure Dependence. Wakuri et al.9 established the following relationship for the spray penetration S, based on the assumption of conservation of mass and momentum, but allowing for a dependence of spray angle on gas density:

-0.23 -0.25 -0.25 -0.25 -0.25 -0.25 -/-0.25a -0.25/-0.35 -0.25/-0.45 -0.32 -0.32 -0.35 -0.36 -0.38 ( 0.01 -0.406 -0.50 -0.50 -0.544 a

nS (∆P)

Rs (dh)

0.27 0.25 0.25 0.5 0.5

0.46 0.50 0.50

0.50/0.25a 0.25 0.25 0.32

-/0.50a 0.50 0.50 0.18 0.54 0.5 0.50

0.25 0.25 0.43-0.64 0.262 0.30 0.5 0.354

0.50

0.37 0.59 0.50

βs (t)

author

0.54 0.50 0.50 0.50 0.50 0.5 1/0.50a 0.50 0.50 0.64 0.38 0.5 0.50 0.56 ( 0.01 0.57 ( 0.02 0.568 0.55 0.50 0.303

Lustgarten43 Dent3 Arai10 Payri40 Chang32 Araneo14 Hiroyasu5 Naber6 Wakuri9 Taylor34 Fujimoto39 Gupta29 Baert13 this work Klein-Douwel15 Arrègle7 Varde8,35 Farrell44 Takeuchi45

First value for early spray, second value for mature spray.

The dependence of S on Fgas is checked by using the injections at Pgas,nom ) 37 bar as reference. Figures 12a-c plot log S/S0 versus log Fgas/Fgas,0 for each value of Prail,nom. The underlying implicit assumption that ∆P/∆P0 ) 1 for each of the plots is justified, since for a specific Prail,nom the change in ∆P is at most 2.4% due to Fgas variation and the slight variation in actual Prail

values (Table 1) is almost negligible, as in the application of eq 8. Furthermore, the values of ti at which either S or S0 g 88 mm (see Figure 10) are excluded from the analysis of eq 12. If eq 12 holds, then the data points should lie on a straight line which has to go through the origin. Experimental uncertainties ∆S and ∆S0 propagate into an uncertainty of at most (0.005 for log S/S0. Because little or no interaction can be observed between density and time effects, the vertical scatter within data sets at specific Fgas/Fgas,0 ratios is attributed to variation in spray shape. Only data for which log Fgas/Fgas,0 * 0 is included in the fit. The resulting slopes mS and their uncertainty estimates are given in Figure 12d versus Prail,nom. Within their error margins, the obtained values of mS show overlap and a weighted average (over all Prail,nom) of m j S ) -0.38 ( 0.01 can be established. Baert and Vermeulen,13 using the same method under different conditions and with a different injector, obtain a value of -0.36. The error in their value (not given) is expected to be somewhat larger than (0.01 (due to data scatter), whence there is good agreement between the current work and ref 13. Reasonable agreement with some other literature is observed as well (see Table 3). In a similar manner the dependence of S on ∆P is checked, using eq 12, for each set of constant Pgas,nom (in which the variation of Fgas is very small and Fgas/Fgas,0 ) 1 is therefore assumed), using the injections at Prail,nom ) 1000 bar as reference. The results are shown in Figures 13a-c, Figure 13d summarizing the obtained values (and uncertainties) for nS in eq 12 as a function of Fgas (Pgas). It is observed that nS ≈ 0.4-0.5 for Pgas,nom g 28 bar, which is in the range of some studies listed in Table 3, but nS ) 0.64 for Pgas,nom ) 19 bar, which is higher than found in other studies (Table 3). The cause for this higher value of nS at this lower density is not yet clear. The apparent decrease of nS with increasing Fgas could suggest that the effect of ∆P on S (eqs 11 and 12) might not be completely independent from that of Fgas. mϑ (eq 8) has In the above analysis, the relation tan ϑ/2 ∝ Fgas not been used. However, it can be used to check the validity of eq 10 by inserting the density dependence of tan ϑ/2 in eq 10, m* with m* ) -1/4 - m /2. If eq 10 holds, which yields S ∝ Fgas ϑ then m* should be equal to mS (eq 11), or

(43) Lustgarten, G. Ph.D. Thesis, ETH Zu¨rich, 1973. (44) Farrell, P. V.; Chang, C. T.; Su, T. F. SAE Paper 960860, 1996. (45) Takeuchi, K.; Senda, J.; Shikuya, M. SAE Paper 830449, 1983.

(13) mS + mϑ ⁄ 2 ) -1 ⁄ 4 (if eq 10 holds) Using the values m j S and m j ϑ of the current study yields m jS + m j ϑ/2 ) -0.33 ( 0.02. This clearly violates eq 13 and therefore

S∝

(√

t

Fgas tan ϑ ⁄ 2

)

1⁄2

(10)

which is also implicit in the derivation by Naber and Siebers.6 For a constant spray angle, this implies a dependence on gas density of F-1/4 gas . The applicability of eq 10 will be tested below. The weak dependence of spray angle on density shown above (and found in the literature) suggests, however, an effectively different power. Taking this into account, eq 10 is given in a more general form by ϑ (11) 2 with Table 3 giving a literature overview of the data for the parameters in eq 11. In order to check the spray penetration data for a dependence on Fgas or ∆P, the time t has to be divided out. This is done, following the reasoning of Baert and Vermeulen,13 by considering the spray penetration S at density Fgas and pressure difference ∆P relative to a reference penetration S0 at Fgas,0 and ∆P0 for all times ti at which data is collected: mS S ∝ Fgas ∆PnSdRh StβS tan-1⁄2

( )( )

S(ti, Fgas, ∆P) Fgas ) S0(ti, Fgas,0, ∆P0) Fgas,0

mS

∆P ∆P0

nS

∀ ti

(12)


Klein-Douwel et al.

Figure 12. Ratio S/S0 versus F/F0 (eq 12) for (a) Prail,nom ) 1500, (b) 1000, and (c) 750 bar [reference data at (0,0) only shown for completeness; uncertainty of at most (0.005 in log S/S0 not shown]. (d) Resulting values mS (including uncertainty) from the fits in (a-c).

Figure 13. Similar to Figure 12, now plotting S/S0 versus ∆P/∆P0 (eq 12), for (a) Pgas,nom ) 37, (b) 28-29, and (c) 19 bar. (d) Resulting values nS (including uncertainty) from the fits in (a-c).

the relationship of Wakuri (eq 10) cannot be used to described the current results. From work by Varde et al.8,35 mS + mϑ/2 ) -0.34 may be derived, in good agreement with the present results. In contrast to this, however, results of some (but not

all) studies listed in Table 2 (penultimate column) do confirm eq 13 and hence the applicability of Wakuri’s relationship (eq 10). Resolving this apparent dilemma needs further theoretical and/or experimental work.



Figure 14. (a) x+ and (b) t+ as calculated from eqs 14 and 15.

Dimensionless Correlations. In the preceding sections, the macroscopic spray characteristics length and angle have been treated separately. Here their properties will be combined in a nondimensional analysis, in which a reference length and time are used to scale individual spray propagation data. If these reference values describe the experimental conditions completely and correctly, all spray penetration data points will collapse onto a single line. The approach presented here closely follows that of Naber and Siebers.6 In that study, a reference length x+ and reference time t+ are defined by x+ )

df√Ff ⁄ Fgas a tan ϑ ⁄ 2

(14)

and t+ ) x+ ⁄ Uf

(15)

df ) √Cad0

(16)

where

Uf ) Cv

2

∆P Ff

(17)

in which Ff is the fuel density, df is the effective diameter of fuel stream exiting the orifice of (geometric) diameter d0 and Uf is the fuel velocity at the orifice exit. The value for the scaling constant a in eq 14 is taken from Naber and Siebers:6 a ) 0.66 (although later on also a value of 0.75 was suggested36). The relation between Ca, Cv, and Cd is given by eq 3. A value of Cd ) 0.765 was established before. Further, the momentum experiments resulted in a value of Cv ≈ 0.925. The values for Uf, however, are not calculated by using eq 17, but are derived from separate injector characterization measurements.18,37 Since these experiments have been performed at slightly different common rail pressures, Uf has been interpolated with eq 17 for the pressure differences observed in the current work. In applying eq 14, the equilibrium value ϑ∆,eq for the appropriate set of injections is used. The resulting x+ and t+ are shown in Figure 14. It can be seen that x+ lies between 4 and 8 mm, depending on Fgas. Due to the relatively large values of Uf (between 335 and 491 m/s) compared to other literature, the values of t+ are rather small. The results of nondimensionalizing the data in Figure 10 are shown in Figure 15. The reference line of slope 1/2 corresponds to the model of Naber and Siebers.6 From this graph it is clear that the nondimensionalized penetration collapses rather well onto a single line. Its slope is obtained by a fit to all data points for which t/t+ g 125. This results in a slope of 0.56 ( 0.01, which corresponds well to the results for the power b in eq 9,

Figure 15. Nondimensionalized spray penetration (log-log scale) for all conditions listed in Table 1, with x+ and t+ defined by eqs 14 and 15, respectively. For each injection condition, the corresponding average of ϑ∆,eq is used. The value of 0.56 for the slope of the solid reference line is derived from fitting all data for which t/t+ g 125, and the dotted reference line has slope 1/2.

shown in Figure 11, and also to the value of 0.57 ( 0.02 found in previous work.15 The slope observed in Figure 15 is effectively a combination of the various powers of time b. Only for S/x+ < 8 are the data points somewhat more scattered, with the deviation from the line of slope 0.56 being largest for the smallest Prail. Another observation is that x+ in eq 14 varies -1/2 and does not depend on ∆P, whereas in the more with Fgas general eq 11 the dependence of S on Fgas and ∆P differs from that of x+ and is also not constant, as shown in Figures 12 and 13. For the highest Prail of 1500 bar, however, the entire range of data points fits very well to a straight line. In the derivation by Naber and Siebers,6 spray penetration varies linearly with time until t ) t+ and S ) x+, at which point it bends over to a behavior as the square root of time. In the data presented here, both S/x+ and t/t+ are already larger than 1 at early measurement times, indicating that the early phase of fuel injection cannot be observed in the current setup. This has been discussed before here and in previous work15 and is mainly due to the covering of the injector by a thimble. A bending point is observed in the current data (Figure 15) as well, only not at t ) t+, but around t ≈ 100t+. In addition to this, it must be noted that 100t+ ≈ τ (the spray angle decay time for ϑ∆(t) in eq 7). This may indicate that the spray is only mature (i.e., penetrating with a power law and with a constant angle) after a time τ. Comparing the results of these analyses of the current data according to the methods described by Naber and Siebers6 shows that the current spray penetration data collapse well onto a single straight line for larger times and lengths. Deviation for smaller lengths and times is somewhat larger. This effect may be ascribed to the variation in spray shape, including the effects


of short-lived, small-scale anomalies (discussed above and in previous work15), which may be relatively large for short sprays. Short sprays also tend to be younger and less similar to the quasi-steady reference jet. Conclusions In the current study, diesel fuel injections and growth analyses of nonevaporating sprays have been presented for a range of injection conditions (density 15-42 kg/m3, rail pressure 750-1500 bar) that complement and expand the result presented in a previous study.15 These experiments extend the database on fuel spray penetration and help in improving semiempirical models. At the same time these data will be helpful in validating better theoretical (phenomenological and CFD) models. As a prerequisite for further analysis, first the flow through the nozzle is characterized in detail with regard to cavitation and mass flow rate. In order for the spray angle to be less sensitive to short-lived, small-scale spray shape variations, a triangular spray angle ϑ∆ is defined, similar to ref 6. Using this definition, it is also easier to establish any possible trend with density or rail pressure for the spray angle. It is observed that the equilibrium value ϑ∆,eq mϑ, with an average lies between 25° and 31° and varies as Fgas value of m j ϑ ) 0.10 ( 0.04. A clear dependence on rail pressure is not observed. The equilibrium value ϑ∆,eq is reached after an initial period of decreasing ϑ∆(t), which is relatively well described by an exponential decay with a time constant τ of 0.4-1.4 ms. The value of τ may be indicative of the spray becoming mature after this time. The dependence of spray penetration S on the gas density mS, where the Fgas is investigated and it turns out that S ∝ Fgas average value m j S ) -0.38 ( 0.01, in good agreement with ref 13. This value is different from the theoretically expected and also sometimes observed value of -0.25. The power nS with which S depends on the pressure difference ∆P decreases from nS ) 0.64 for Fgas ) 23 kg/m3 to 0.43 for 44 kg/m3. Combining the gas density effects on both spray angle and penetration (mS and mϑ, eq 13) reveals that the often used

Klein-Douwel et al.

relationship for spray penetration given by Wakuri et al.9 (eq 10) is not applicable to the current results. From Table 2 it may be deduced that for some studies this is also the case, but that in some other studies eq 10 does apply. This dilemma needs more research in order to be resolved. Analyzing the growth of the relatively mature spray with eq 9 shows a power of time b which lies between 0.5 and 0.67 for the conditions presented here, where some scatter in b is observed. A better description, however, is obtained by nondimensionalizing the spray penetration data by reference lengths and times, according to the method presented by Naber and Siebers.6 This reveals that the observed spray growth data collapse very well onto a single line for all injection conditions used here. The slope of this line, corresponding to a general power of time with which the sprays grow, is 0.56 ( 0.01, whereas ref 6 gives a slope of 0.5. The value of 0.56 ( 0.01 is in line with the values of the power b discussed before, but using the reference length and time clearly describes the results much better. Only for early times (young sprays) a minor deviation from this linear fit is observed. Good agreement is observed between previous work15 and the current value of 0.56 ( 0.01. Therefore, in general it can be said that the use of predictive spray models is limited, since so many different values are found in the literature for the various parameters, and that more theoretical and experimental research (also on nonevaporating sprays, as they behave significantly different from evaporating sprays) is needed to get a more complete description of spray processes and to further improve insights which are beneficial in developing computational fluid dynamics tools for engine development. Acknowledgment. Discussions with DAF Trucks N.V. are gratefully acknowledged, as well as financial support from Technology Foundation STW, and we also acknowledge W. A. de Boer, D. Bindraban, and M. F. W. Willekens for technical support, and K.-N. Lee for help in compiling Tables 2 and 3. EF8003569

Gas Density and Rail Pressure Effects on Diesel ... - ACS Publications

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