Effects of nozzle geometry on the characteristics of an evaporating diesel spray.
It is known that spray development influences combustion-related variables in diesel engines such as the combustion efficiency and engine-out emissions, and spray development is strongly affected by atomization and rates of air entrainment into the spray. Air entrainment into the spray can be increased and engine-out soot emissions reduced by using high injection pressures while suppressing cavitation inside the nozzle, according to experiments performed with injection pressures of up to 3200 bar and injector nozzles with a k-factor of 2 and 25% hydro-grinding . Several studies have also shown that using injectors whose orifices are more convergent (i.e. which have higher k-factor) or have more hydrogrinded nozzle orifices can reduce diesel engines' soot emissions by increasing air entrainment [2, 3, 4]. However, other investigations have suggested that these combustion variables are independent of the nozzles' internal flow properties and depend only on spray momentum and air entrainment resulting from the fuel jet's momentum. This conclusion was drawn on the basis of experiments conducted using two nozzles with the same momentum (one with 0% hydro-grinding and another with 20% hydro-grinding) . It was also stated by Siebers  that vaporization in a diesel spray is controlled by air entrainment into the spray (i.e. by turbulent mixing) based on extensive experimental spray data.
However, there are uncertainties about the effects of nozzle geometries on spray properties, partly because cavitation inside the nozzle can enhance the primary break-up and subsequent atomization of the liquid jet [7, 8]. It was also reported that under cavitation conditions a cylindrical nozzle produces a better air-fuel mixture than a convergent nozzle because it generates a greater spreading angle and outlet velocity . Furthermore, a non-hydro-grinding nozzle reportedly generated stronger cavitation and thus smaller ligaments in a liquid jet than a hydro-grinding nozzle . Finally, a CFD study of various nozzle configurations indicated that a cylindrical nozzle enhanced primary break up and therefore produced smaller droplets (and thus a less fuel-rich reaction zone and lower soot emissions) than a convergent nozzle .
As summarized above, there is no clear consensus concerning the effects of nozzle conicity and the associated cavitation on spray properties. This work aims to clarify these issues by presenting new data on the relationship between nozzle conicity and the characteristics of the evaporating spray.
Many different nozzle types can be used in spray experiments. Nozzle conicity can be varied by varying the inlet diameter while maintaining a constant outlet diameter, or vice versa [11, 12, 13]. In the experiments reported here, since the injection rate and spray properties are affected by the nozzle outlet diameter and k-factor, three different nozzles were used: one with a k-factor of 0 and 140 pm outlet diameter, and two with a k-factor of 2 but different outlet diameters (140 pm and 136 pm). The latter of which has the same nominal flow rate as the cylindrical nozzle. High speed cameras were used to capture images showing the development of liquid and vapor sprays formed by these three nozzles.
The experiments presented herein were conducted under evaporating conditions because in the operating range of a real heavy-duty diesel engine, the injected liquid fuel is vaporized within a few hundred microseconds. Payri et al.  recently investigated the liquid length resulting from different nozzle geometries under evaporating conditions, while the effect of nozzle geometry on the liquid/vapor length and vapor spreading angle have been studied by Zhang et al. . However, it is not possible to determine the effects of nozzle geometry on the distribution of fuel between the liquid and vapor phases by considering only the liquid/vapor length and the spray's spreading angle. Therefore, we conducted qualitative measurements of the vapor volume fraction by using a light absorption and scattering (LAS) approach that resembles the laser absorption and scattering technique used by Nishida and co-workers [14, 15, 16]. In addition, we measured the liquid and vapor phase local cone angle and length.
PRINCIPLES OF THE OPTICAL MEASUREMENTS
The LAS technique is a line-of-sight extinction technique that generally has several advantages such as a high signal-to-noise ratio, low ambient temperature dependence and no fluorescence quenching. It commonly uses two wavelengths, one wavelength (typically in the visible, i.e. 400-700 nm) that is scattered by liquid droplets but not absorbed and another (usually in the ultraviolet, or UV, range) that is used to detect the absorbance of the vaporized fuel. To quantitatively measure vaporized spray concentrations, LAS experiments [14, 15] have been performed using model fuels such as 1,3-dimethylnaphthalene [141 or a mixture of 97.5% n-tridecane and 2.5% 1-methylnaphthalene ([alpha]-MN) . Mixtures of n-dodecane with 2% and 10% [alpha]-MN were recently tested as LAS tracer fuels under evaporating conditions in our lab . These preliminary experiments yielded promising results, demonstrating that the technique could be used to measure the distribution of fuel between liquid and vapor phases in diesel sprays. All of these tested fuels include an aromatic component that functions as a UV light absorber and is diluted with a non-absorbing alkane to control the degree of absorption because the aromatic component is a strong absorber of UV light.
Commercial diesel fuel is a complex mixture of many hydrocarbon components, most of which are paraffinic, naphthenic or aromatic. Paraffinic and naphthenic hydrocarbons in diesel fuel are almost transparent to UV light with a wavelength above ~240 nm. However, the aromatic components in diesel fuel are strong ultraviolet absorbers at wavelengths shorter than 300-360 nm. Commercial Swedish market sold MK1 diesel fuel without added rapeseed methyl ester (RME) contains at most 5% aromatics by volume. This makes it possible to measure the UV light absorption of vaporized diesel sprays. A spray's UV light absorbance is proportional to the concentration of fuel in the vapor phase, and relative fuel concentrations can be measured qualitatively on the basis of absorption in the vapor parts of the spray. Moreover, visible light scattering can be used to qualitatively measure the distribution of liquid phase fuel in a spray.
Main Idea of Light Absorption Scattering
As shown in Figure 1, when a UV light beam passes through a mixture of vaporized diesel fuel (containing aromatics) and liquid droplets, the vaporized fuel absorbs UV light while the liquid droplets scatter and absorb it. Therefore, the transmissivity of UV light in a vaporized fuel can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where the subscripts V, UV, l, v, sc and ab signify visible light, UV light, liquid droplets, vapor phase, scattering, and absorption of light, respectively. It has been shown by Zhang et al.  that under certain conditions, the transmissivity of UV light due to liquid droplet scattering and absorption can be assumed to be almost identical to the transmissivity of visible light wavelength ([[lambda].sub.V]) due to liquid droplet scattering. Consequently, the final two terms on the right hand side of Equation (1) can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
Combining Equations (1) and (2) yields the following expression for the transmissivity of UV light in a vaporized fuel:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
To obtain the transmissivity resulting from the scattering and absorption of UV light by liquid droplets, the transmission of visible light is measured at the same time as that of UV light. The fuel droplets do not absorb visible light, so visible light attenuation is due to droplet scattering alone. Equation (3) makes it possible to separate the light attenuation signals due to liquid and vapor in light absorption scattering (LAS) experiments.
Detailed derivations of the equations used to describe these processes are presented elsewhere [14, 15, 17], here only the main equations are shown. The vapor concentration can be described as:
[bar.[C.sub.v]] = 1/[epsilon]([[lambda].sub.UV])[L.sub.v][log[[I.sub.0]([[lambda].sub.UV])/I([[lambda].sub.UV]) - G x log[[I.sub.0]([[lambda].sub.V])/I([[lambda].sub.V])]] (4)
where [bar.[C.sub.v]] is the vapor concentration (mol/[m.sup.3]); [epsilon]([[lambda].sub.UV]) is the absorption coefficient of vaporized fuel at wavelength [[lambda].sub.UV] ([m.sup.2]/niol); [L.sub.v] is the optical path length of light beam in the vapor phase (m); log[[I.sub.0]([[lambda].sub.UV])/I([[lambda].sub.UV])] is the transmissivity of UV light; G is the ratio of the optical thickness of the droplet cloud for UV and visible light, and log[[I.sub.0]([[lambda].sub.V])/I([[lambda].sub.V])] is the transmissivity of visible light. The ratio G approaches one as the droplet diameter becomes large relative to the incident wavelength , and it was also shown by Zhang et al. 1141 that the droplet optical thickness ratio G approaches one when using a UV wavelength of 266 nm and a visible wavelength of 532 nm except in regions where the spray is very dense. In the vaporized fuel spray region, the total extinction is dominated by vapor absorption, which implies that the differences in the droplets' optical thickness at the two wavelengths have little effect on the measured vapor concentrations.
To calculate the vapor phase concentration using Equation (4), it is necessary to determine the transmissivity of UV and visible light, log[[I.sub.0]([[lambda].sub.V])/I([[lambda].sub.UV])] and log[[I.sub.0]([[lambda].sub.V])/I([[lambda].sub.V])], which can be measured with CCD cameras or high-speed video cameras. It is also necessary to determine the absorption coefficient [epsilon]([[lambda].sub.UV]), which can be measured using an optical spectrometer and a high-pressure and high-temperature cell. The optical path length [L.sub.v] can be measured by assuming the fuel distribution in the spray is axisymmetric. Once these quantities are obtained, the local vapor phase concentration can be calculated.
Qualitative Vapor Concentration Measurement
The approach used for quantitative measurement of the vapor concentration was discussed above to facilitate understanding of the qualitative measurements of vapor concentration used in this work. Because diesel fuel is a mixture of different hydrocarbon components with different boiling points, the lighter components vaporize more rapidly and have higher vapor concentrations during the early stages of vaporization. In addition, the absorption coefficient [epsilon]([[lambda].sub.UV]) depends on the fuel components' molecular structure, the ambient temperature, and the gas density. All these factors make it difficult to quantitatively measure absolute vapor concentrations in a diesel fuel spray. However, qualitative estimates of the vapor concentration can be obtained by making some assumptions:
1. Regions of the spray with negligible visible light extinction can be considered to be fully vaporized.
2. The fuel composition in a fully vaporized spray region is homogenous, i.e. the same distribution of fuel components is present everywhere in a vaporized spray region.
3. Given assumption 2, the absorption coefficient [epsilon]([[lambda].sub.UV]) is the same at all points under fixed experimental conditions.
To approach assumption 1, the evaporating ambient temperature was set to 673 K and the gas density was set to 15 or 30 kg/[m.sup.3]; under those conditions, the diesel fuel will evaporate rapidly. Furthermore, a low threshold was imposed when defining the liquid phase boundary in a vaporized spray, ensuring that the region defined as containing the vapor spray was free from droplets, and that the measured UV light absorption for this region was due to the vapor alone.
One important factor is that the fuel components do not undergo any changes beyond changes of state as they transition from the liquid to the vapor phase; no ignition or other chemical reactions take place. A constant flow of air with an oxygen concentration of 21% was maintained through the high-pressure and high-temperature chamber (see the Experimental Apparatus section for details). As such, there was a risk that ignition might occur given the high experimental ambient temperature (673 K). However, no ignition was observed during the injection period. If ignition had occurred, we would have expected to see a strong increase in UV light absorption in the vapor phase region due to the carbonyl structure in the aldehydes such as formaldehyde (C[H.sub.2]O), which are present in cool flames, absorbs UV light between 195 and 275 nm . Sudden increases in UV light absorption in the vapor part of the spray have previously been observed with our apparatus under other experimental conditions, but no trace at any point during this work. An estimate of the ignition delay under the studied conditions supports the hypothesis that ignition does not occur during the injection period.
Ignition delay (i.e. the timing of onset of high-temperature combustion chemistry) has been predicted by Pickett et al.  based on extensive experiments in a pre-combustion vessel. Although formaldehyde is produced in cool flames, which develop a few hundred [micro]s before the start of high-temperature combustion, we considered the ignition delay for the start of high-temperature combustion because values for this parameter are available in the literature. As shown in Equation (5), the ignition delay for a diesel spray can be fitted to the Arrhenius expression :
[[tau].sub.ig] = Aexp(E/[RT.sub.a]) (5)
[[tau].sub.ig] = the ignition delay;
A = the pre-exponential constant [ms];
E = the global activation energy;
R = the universal gas constant;
[T.sub.a] = the ambient temperature [K];
The coefficients of the Arrhenius expression A, E/R and [T.sub.a] are as referred to the work of Pickett et al. . Figure 2 shows the ignition delay predicted for gas densitis 14.8 kg/[m.sup.3] and 30 kg/[m.sup.3] and nozzle outlet diameters of 0.1 and 0.18 mm from the datasheet . By interpolation, the ignition delays estimated for our experimental conditions, i.e. gas densities of 15 and 30 kg/[m.sup.3] with an ambient temperature of 673 K, and an outlet nozzle diameter 0.14 mm were 5.25 and 2.94 ms, respectively. Our experiments were performed using commercial Swedish market sold MK1 diesel without RME whose cetane number and distillation temperature (initial and 90%) are close to those of the #2 diesel fuel used by Pickett et al. It is therefore reasonable to suppose that the predicted ignition delays for the two fuels should be similar at a given fuel temperature. However, it is expected that ignition delay under our experimental conditions is slightly longer than predicted ignition delay. Since it was shown by Payri et al.  that there is a relationship between ignition delay and fuel temperature ([T.sub.f]) as [[tau].sub.ig] [varies] [T.sup.-0.38.sub.f] The body of injector nozzle was cooled continuously with cold tap water (temperature ~288K) in our case and it is much lower than the fuel temperature of 436 K which was used by Pickett et al. In addition, the ignition delay increases with decreasing injection pressure. The injection pressure of 1380 bar was used in prediction model, so it should underpredict the ignition delay for two of the injection pressures (800 and 1200 bar) and slightly overpredict it for the injection pressure (1600 bar) in our experiments.
Results for vapor phase images recorded up to 2 ms after start of injection (ASOI) (of the total recording time 2.6 ms ASOI) are presented. During this period, as shown in Figure 2, only at gas density 30 kg/[m.sup.3], there is a risk of ignition. If it is assumed that formaldehyde is formed at this condition, strong additional UV absorption would occur and later disappear, because the formaldehyde is consumed by subsequent high-temperature combustion. This experimental observation was shown by Kosaka et al. . However, this type of phenomena was not observed
during the injection period in our cases. In addition, as shown in Figure A1, it further justifies that the formation of C[H.sub.2]O is not expected during 0-2.0 ms ASOI, see details in Appendix. Overall, during injection event in our case, it can be assumed that the fuel composition remains constant in all of the studied cases.
Because the absorption coefficient [epsilon]([[lambda].sub.UV]) is expected to depend on the ambient temperature and gas density, comparisons of estimated vapor phase volume fractions generated by the different injectors under different ambient conditions would be of questionable value. Therefore, we only compare results obtained under identical ambient conditions.
Qualitative Description for the Liquid Phase' Optical Depth
When visible light crosses the liquid droplets, the Lambert--Beer law can be used to express the liquid concentration Q as
[bar.[C.sub.l]] = [1/[[sigma].sub.ext]([[lambda].sub.V])[L.sub.t]]log[[I.sub.0]([[lambda].sub.V])/I([[lambda].sub.V])] (6)
where [bar.[C.sub.l]] is the liquid concentration; [L.sub.I] is the optical path length of the liquid phase spray and [[sigma].sub.ext]([[lambda].sub.V]) is the extinction coefficient of droplets at wavelength [[lambda].sub.V]. Since the absorption of liquid droplets in the spray can be neglected, the extinction cross section is reduced to the scattering cross section, [[sigma].sub.ext] = [[sigma].sub.sca]. The scattering cross section of the droplets depends on their diameter, and the diameter distribution should be determined for fuel concentration measurements. We did not attempt quantitative measurement of liquid phase concentration; instead, we used the optical depth (OD) to describe different region of the liquid phase spray. Three different regions were defined: the high density, the mildly diluted, and very thin liquid phase zones. For details, see the image processing section.
A Scania XPI injector with a single-hole nozzle was mounted in the bottom part of a previously described continuous-gas-flow type high-pressure/high-temperature (HP/HT) chamber , and the injected fuel spray was directed upwards against the direction of air flow. The air flow rate was limited to ~0.1 m/s, so the gas conditions inside the chamber were considered quiescent compared to the initial fuel spray velocity of over 100 m/s. The fuel temperature was controlled by cold tap water flowing around the injector head. The injection frequency was 0.2 Hz, and the fuel was a standard diesel fuel sold in Sweden (with no RME), designated MK1. A common rail fuel supply system was used together with three solenoid type single-hole injectors with nozzle geometries specified in Table 1. The conicity of the nozzle is described by the k-factor, which is calculated as ([D.sub.i] - [D.sub.o])/10 [micro]m, where [D.sub.i] and [D.sub.o] are the inlet and outlet diameter in pm, respectively. The nozzle configurations were selected to test the effect of conicity while maintaining a constant outlet diameter (nozzles N1 and N2), and the effect of conicity while maintaining a constant mass flow rate at the applied fuel pressure of 137.9 bar, or 2000 psi (nozzles N1 and N3). As shown in Table 2, the ambient temperature was kept constant in all cases. In each case, the energized injection pulse was set for 2.0 ms, but the actual injection duration (determined by high-speed video recordings) was about 2.6 ms.
Figure 3 shows the optical setup for capturing liquid and vapor phase images simultaneously. Diffuse background illumination was achieved by illuminating a ground quartz plate, with the light from two halogen lamps for broadband visible light extinction, and one mercury arc lamp with strong emission at 254 nm for UV light extinction. Diffuse illumination can reduce the influence of beam steering effects. A dichroic mirror reflecting 248 [+ or -] 25 nm directed the UV light towards one camera system, and it was further filtered using a UV filter centered at 254 nm with 40 nm FWHM. The camera system consisted of one Phantom V7 high-speed video COMS camera and a Hamamatsu C9548-04 image intensifier with a Nikon UV 105 mm lens with f/5.6. The intensifier gate time and camera exposure time were set to 25 [micro]s, the camera's pixel resolution was 336x136 and its spatial resolution was 3.65 pixel/mm. One Phantom V1210 high-speed video CMOS camera was used to capture visible light images with pixel and spatial resolutions of 256x640 and 6.5 pixel/mm, respectively; its exposure time was set as 10 [micro]s. A Nikon 50 mm lens with f/5.6 was used with the V1210 camera. Both Phantom cameras were synchronized by a Stanford Research DG645, and the frame rate was set to 36,000 Hz. One Stanford Research DG535 was set as the master, triggering both the injector driver and the DG645 at 0.2 Hz. The focus of both cameras was set on the plane normal to the nozzle tip.
Stability of Visible and UV Light Intensity
Given the instability in the light intensity of both the mercury arc lamp (UV light) and the halogen lamps (visible light), the light intensity varied over the course of each injection event period, especially for the UV light. The light intensity varied by less than 2.5% over an injection period in the visible images but variation of up to 30-40% occurred in the UV images. Consequently, it was necessary to introduce a correction term when calculating the light transmissivity (I/[I.sub.o]) of the spray. It was found that although the light intensity differed in different areas of the visible or UV images, the magnitude of the change in intensity with time was identical at all points in the image, see details in Figure A2 in the appendix. In other words, the light intensity varies simultaneously and proportionally across the whole image area. To account for this variation in the light intensity, a pixel block that was not affected by the spray was selected as shown in Figure 4. The correction coefficient for each time step is calculated by normalizing the mean light intensity of selected block in the spray image against the mean light intensity of selected block in the background image. This correction was applied to all of the processed images presented below.
Processing of Liquid Phase Images
The signal-to-noise ratio for the liquid phase images (taken with visible light) was higher than that for the UV images, and their processing was relatively straightforward. Only one threshold value was generally used to extract the liquid phase boundary. For example, the threshold could be defined as the midpoint of a relative light intensity slope with a logarithmic scale . The spray image in Figure 5 (a) has been normalized against a background image in which no liquid spray is present, and shows the light extinction level in the liquid spray (darker colors correspond to greater optical depths). The three different liquid phase zones are indicated with red lines--the high density liquid phase zone A, the mildly diluted zone B, and the very thin density liquid phase zone C.
These three zones are defined by three different levels in the light transmission intensity curve as shown in Figure 5 (b). In our case, to extract the whole area with the liquid droplets present, a threshold corresponding to 0.905 (i.e. 231 out of 255 or OD = 0.1) was used. Pixels with values above the threshold 0.905 (corresponding to an OD below 0.1) are considered as part of ambient gas, because the light attenuation in the corresponding regions is very low and the liquid droplet density is only a small fraction of that in the vapor phase regions of the spray. When selecting the lowest threshold value, it is important to recall that the results are not influenced by noise and other effects not related to droplet scattering, such as the schlieren effect of the vapor phase in front of the spray head (see at the right edge around 75 mm from the nozzle tip in Figure 5 (a)). Liquid lengths shown in figures below measured for optical depths of 0.1 and 0.5.
After the lowest threshold is determined from a plot such as that shown in Figure 5(b), the normalized image is displayed as a color map image as shown in Figure 5 (c). Figure 5 (c) clearly shows that the high density liquid phase zone is in the center of the spray (corresponding to the light and dark blue regions), while the low density liquid zone is shown in red.
Processing of UV images
The UV images were processed using a five-step process involving: 1) normalization against a background image recorded immediately before the injection event--a representative normalized image is shown in Figure 6 (a); 2) masking the normalized image to extract only the interesting spray region; 3) filtering the masked image using a median filter with matrix 8x8, which proved suitable for our purposes --the normalized light intensity along the spray axis with different median filter matrix sizes is shown in Figure 6 (b); 4) converting the filtered image into a binary image with a threshold value of 0.8 (OD=0.22) to detect the fuel-containing spray region; 5) determining the binary image area in the originally normalized images by filtering with a median 5x5 matrix filter to yield a final image as shown in Figure 6 (c). Note that the term 'UV image' refers to an image acquired using UV light that might contain both liquid and vapor phases, whereas 'vapor images' depict only the vapor phase that obtained through excluding liquid phase from the UV images.
Because of the fluctuation and the weakness of the light intensity at the UV wavelength of 254 nm in the mercury arc lamp, UV spray image exhibited salt-and-pepper noise as shown in Figure 6 (a). The normalized light transmission intensity along the nozzle tip central line is drawn as shown in Figure 6 (b).
Except for the area close to nozzle tip, there are two distinct light intensity slopes A and B as shown in Figure 6 (b). These two slopes correspond to the edges of the dense liquid core and the vaporized fuel, respectively. Based on slope B, a threshold value can be chosen to extract the area of the image in which both the liquid and vapor spray are causing light attenuation. As can be seen in Figure 6 (b), the original normalized light transmission intensity fluctuates strongly, and the relatively noisy character of the UV image is due to the comparatively weak light source and the use of the image intensifier. To reduce the influence of such fluctuations, median filters with different matrixes were tested. With matrix 3 (3x3), there are still strong fluctuations, and a risk of identifying noise outside of the fuel cloud. However, matrixes 5 (5x5) and 8 (8x8) make the normalized light intensity much smoother while preserving the image's dynamic information; the larger matrix 10 (10x10) removes some dynamic information and introduces a risk of measuring out the border between the spray and the surrounding air. The 8x8 matrix is considered most suitable for edge identification in the current set of images because it can remove noise effectively without significantly distorting the spray edge.
The selected threshold level is based on analyses of the normalized light transmission intensity with different median filter matrixes. As shown in Figure 6 (b), slope B is steep and a threshold value anywhere between 0.6 and 0.9 could reasonably be selected. With a low threshold of 0.6, regions of the UV image with low light attenuation (including some parts of the vapor phase regions) might be removed, whereas a high threshold of 0.9 may not be very effective at eliminating noise. Based on these considerations, an intermediate threshold of 0.8 was used to determine the spray edge.
The normalized image is masked to eliminate regions that are obviously not part of the spray and include areas where fuel is present. As can be seen in Figure 6 (b), the light transmission intensity near the nozzle tip is low, but not as low as in the visible image, which it should be in reality. Furthermore, applying a median filter in the area where the spray has a small width may result in overly high transmission in the filtered images. Therefore, the regions of the UV images corresponding to the distances of less than 16.4 mm from the nozzle tip were not further analyzed. The removal of this area does not affect the vapor phase dominated area further downstream.
After the relevant part of spray has been defined, the original normalized image is filtered with a 5x5 matrix using a median filter in order to preserve the dynamic information in the image as much as possible, while still smoothing it and reducing noise.
Combining Visible and UV Images
The visible and UV images shown in Figures 5 (c) and 6 (c) were acquired simultaneously, and Figures 5 (c) and 6 (c) were combined as shown in Figure 7 (a). This image clearly shows that the vapor phase region in the UV image is not detected by the visible light shadow imaging technique used to generate the liquid phase image, implying that the vapor phase region of the vaporized spray can be captured successfully by using UV light and an image intensifier. Moreover, the vapor phase boundary is larger than liquid phase boundary in Figure 7 (a), indicating that the detection of the vapor phase boundary is not affected by the liquid phase.
Based on Equation (3), the light attenuation intensity of the vapor phase can be calculated as:
[[I([[lambda].sub.UV])/[I.sub.0]([[lambda].sub.UV])].sub.v,ab] = I([[lambda].sub.UV])/[I.sub.0]([[lambda].sub.UV])/[[I([[lambda].sub.V])/[I.sub.0]([[lambda].sub.V])].sub.l,sc] (7)
Light attenuation in the UV image is partially due to the liquid phase scattering. Therefore, to extract the light attenuation due to the vapor phase alone, the processed UV image is normalized against the processed liquid phase image. Figure 7 (b) shows the light attenuation due to the vapor phase. Comparing Figures 7 (b) and 6 (c), it can be seen that the dark region towards the nozzle tip in Figure 6 (c) is removed and appears white in Figure 7 (b). In the area where the liquid phase dominates light attenuation, the signal-to-noise ratio of the original images makes it difficult to accurately determine the vapor fraction. This section outlines the method used to extract vapor phase spray data in the combined region, but it should be noted that all the results presented below are derived from the UV images.
Definition of Penetration and Local Cone Angle
Penetration is defined as the longest distance from the nozzle tip to the leading edge of the spray. Commonly, only one spray cone angle parameter is used to describe the spreading angle of liquid or vapor phase sprays. Since it was found that spreading angle varies along the spray contour , the local spray cone angle is here described by a spray contour profile. The detailed definition that is adopted from a previous report , is shown in Figure A3 in the appendix.
RESULTS AND DISCUSSIONS
There are different expressions that relate cavitation to a cavitation number. For example, the cavitation number can be expressed as:
K = [P.sub.inj] - [P.sub.vapor]/[P.sub.inj] - [P.sub.amb] (8)
where [P.sub.inj] is the injection pressure, [P.sub.vapor] is the fuel vapor pressure and [P.sub.amb] is the ambient pressure. Equation (8) was defined by Nurick  and used by Payri et al.  to obtain critical cavitation numbers for different injection pressures when using a diesel injector with a cylindrical nozzle. They found that the critical cavitation number [K.sub.cri] is 1.2 for an injection pressure of 800 bar, and cavitation occurred when K was below 1.2. Figure 8 shows the cavitation number K calculated for the cylindrical injector N1. The occurrence of cavitation would be expected with this nozzle under all injection pressures, because the cavitation number K is always below the critical cavitation number [K.sub.cri] 1.2.
A more complex cavitation number equation was recently proposed by Sou et al. [28, 29], and it is expressed as
[[sigma].sub.c] = [C.sup.2.sub.s][[P.sub.amb] - [P.sub.vapor]/[1/2][[rho].sub.f][u.sup.2.sub.o] + [phi][L.sub.N]/[D.sub.H] + 1] (9)
[C.sub.s] = 0.61 for a cylindrical nozzle when [C.sub.u] = [([D.sub.sac]/[D.sub.o]).sup.2] [greater than or equal to] 10, in which [D.sub.sac] is the diameter of the sac hole for the diesel solenoid injector.
[u.sup.o] = velocity at the nozzle exit.
[phi] = [??][0.3164/[R.sup.0.25.sub.e]], where [??] = 1 for a cylindrical nozzle, [R.sub.e] is the Reynolds number.
[L.sub.N] = the length of the nozzle hole.
[D.sub.H] = the hydraulic diameter. For the cylindrical nozzle, [D.sub.H] = [D.sub.o].
Using Equation (9), super cavitation and the cavitation length in the nozzle hole were well predicted for both cylindrical and rectangular nozzles by Sou et al. [28, 29]. The cavitation number [[sigma].sub.c] predicted using this equation for nozzle N1 at injection pressures of 800, 1200 and 1600 bar and ambient pressure 1, 29 and 58 bar are in the range of 0.45-0.49. The velocities, [u.sub.o], at ambient pressures of 29 bar and 58 bar were adjusted based on the value determined at an ambient pressure of 1 bar in an earlier study . The predicted cavitation numbers [[sigma].sub.c] of 0.45-0.49 are not consistent with the occurrence of cavitation (which would be expected at [[sigma].sub.c] is around 0.8) or supercavitation, which occurs when [[sigma].sub.c] is around 1. This discrepancy may occur because the predicted cavitation number [[sigma].sub.c] is based on a relatively large nozzle, and the nozzle hole length used by Sou [28, 29] was 30 mm, which is much longer than our nozzles. This makes it harder to predict cavitation for our case. However, besides the prediction of cavitation number, the visualization of flow in transparent real size diesel injectors has shown that there was cavitation inside cylindrical nozzles even when the inlet edge of the nozzle orifice was rounded. Both authors [30, 31] showed free cavitation inside the convergent nozzles (i.e. one with a positive k-factor). Therefore, a higher tendency of cavitation is expected in the nozzle N1, but a much lower tendency of cavitation or no cavitation is expected for nozzles N2 and N3.
The Vapor Phase Local Cone Angle
Before analyzing the vapor phase local cone angle, the results concerning the liquid local cone angle presented in our previous report  will be summarized. Under non-evaporating conditions, the cylindrical nozzle N1 yielded sprays with larger local liquid cone angles than the convergent nozzles N2 and N3 (which have a k-factor of 2) at 15 kg/[m.sup.3] gas density, and the differences became more pronounced as the injection pressure increased. At the higher gas density (30 kg/[m.sup.3]) the differences between the nozzles became even clearer, especially when the injection pressure was increased from 800 bar to 1200 bar or 1600 bar. Similar observations were obtained for the vapor phase local cone angle under evaporating conditions as shown Figure 9 and 10.
Under evaporating conditions, at distances shorter than 30 mm from the nozzle tip, the local vapor spray cone angle generated with cylindrical nozzle N1 is larger than with convergent nozzles N2 or N3, and the difference becomes more pronounced as the injection pressure increases from 800 to 1600 bar as shown in Figures 9 and 10. A similar trend (i.e. cylindrical nozzles yielding larger cone angle under non-evaporating conditions) was observed in our previous study  and also by other research groups. Kong and Bae  observed that the spray column of a convergent nozzle (k-factor of 2) was half that of a cylindrical nozzle close to the nozzle tip. Payri et al.  and Blessing et al.  also observed that cylindrical nozzles generated larger spray cone angles than convergent nozzles within their studied range of cavitation flows. One reason for the larger cone angle with cylindrical nozzle is that the flow rate fluctuations and reduction are more pronounced than in the convergent nozzle, as was predicted by CFD modelling . Moreover, it was shown in a simulation by Liu et al.  that a non-hydro-grinding nozzle that generated cavitation inside the nozzle had much higher radial velocity (i.e. perpendicular to the nozzle axis) than a hydro-grinding nozzle that generated much less cavitation. This implies that cavitation inside the nozzle tends to spread out the fuel flow in the radial direction, making the spray more dispersed near the nozzle. When the injection pressure is increased, the difference between cylindrical and convergent nozzles becomes bigger. The main reason for this may be that the local cone angle is reduced as the injection pressure increases for nozzles N2 and N3, but no such change occurs for nozzle N1. The results for the cylindrical nozzle N1 also exhibit a higher standard deviation than those for the convergent nozzles N2 and N3, meaning that there are more pronounced fluctuations in the radial direction inside the cylindrical nozzle. This finding is consistent with the observations of Payri et al. . To show more details, the root mean square (RMS) of deviation from the mean image is shown in Figure A4 and A5 that correspond to the data displayed in Figure 10. It can clearly be seen that there is wider span in the upstream spray region (i.e. the region within 30 mm from the nozzle tip) and wider fluctuating regions for the nozzle N1 than nozzles N2 and N3. This confirms again that there is higher radial direction disturbance in cylindrical nozzle N1 than in convergent nozzles N2 and N3.
Figure 9 and 10 clearly show that the local cone angles for the three nozzles are very similar at distances longer than 30 mm from the nozzle tip. This implies that under evaporating conditions, the difference in the nozzle's conicity mainly affects the local cone angle in the upstream spray region, where the droplet density is high; its effect on the further downstream is negligible. In the far downstream spray, spray vaporization is primarily controlled by turbulent mixing. As noted above, the cylindrical nozzle N1 generates a larger local cone angle under non-evaporating conditions, so it is naturally expected that the vapor local cone angle is larger for the cylindrical nozzle N1 under evaporating conditions. However, the exactly same local cone angle for the same nozzle under the non-evaporating and evaporating conditions is not expected.
To better understand the effects of the three nozzles on the vapor spreading angle, we compared our experimental data to results obtained using the empirical equation developed by Siebers . Based on extensive experimental data, Siebers proposed that the spreading angle could be calculated as:
tan([theta]/2) = B x [[([[rho].sub.a]/[[rho].sub.f]).sup.0.19] - 0.0043 x [square root of [[rho].sub.f]/[[rho].sub.a]]] (10)
where the coefficient B only depends on the orifice outlet diameter, and the spreading angle is mainly dominated by the ambient gas/fuel ratio, which is represented by the first term in the Equation (10). The second term in Equation (10) accounts for the effect of vaporizing on the spreading angle. Siebers also concluded that injection pressure (or orifice pressure drop) has little effect on the spreading angle. Since the coefficient B is only available for orifice diameters of 100 and 180 pm, its value for an orifice diameter of 140 pm was estimated by interpolation, giving a value of 0.263. Figure 11 compares the averaged measured cone angle and the spreading angle predicted using Equation (10). The averaged cone angle is determined in the region between 16.4 mm and 30 mm from the nozzle tip, and during time period 1.44-1.7 ms ASOI. By doing this, the considered region represents the upstream part of the spray, and 30 mm from the nozzle tip is approximately half of the vapor phase length or less during the considered time period. It should be also noted that the selected region is smaller than that studied by Siebers. Figure 11 (b) shows that the predicted spreading angle overlaps with that for nozzle N2 within two standard deviations 2a for gas densities of 15 and 30 kg/ [m.sup.3] and an injection pressure of 1600 bar. The predicted spreading angle also overlaps with that for nozzle N3 for a gas density of 30 kg/ [m.sup.3] and an injection pressure of 1600 bar. In all other cases, the equation underpredicts the spreading angle. The underestimation is particularly noticeable in the case of the cylindrical nozzle N1, for which the difference between the averaged local cone angle and the predicted angle can be up to 40% at a gas density of 15 kg/[m.sup.3]. Figure 11 (a) and (b) show that as the injection pressure is increased to 1600 bar, Equation (10) provides better predictions for nozzles N2 and N3. A possible reason for this is that the local cone angle decreases more sharply over time when the injection pressure is 1600 bar than when it is 800 bar. Zhang et al.  also observed that the spreading angle decreased as the injection pressure increased when using a convergent nozzle (with a k-factor of 1.5) but was insensitive to the injection pressure when using a cylindrical nozzle. This is completely consistent with our results. The decrease in the local cone angle at higher injection pressures may occur because the higher pressure promotes fuel vaporization, leading to stronger contraction effects on the spray. However, for the cylindrical nozzle, one would expect a non-zero radial velocity in the upstream spray, which would reduce the magnitude of the contraction effect relative to that seen with convergent nozzles. It is important to recognize that the empirical Equation (10) is based on data gathered from time-integrated images (i.e. images acquired with long exposure times) so as to account for the effect of the spreading angle over the complete injection period. Overall, Equation (10) underestimates the angle for the cylindrical nozzle N1, suggesting that it should be modified to include a term relating to nozzle geometry.
Another interesting observation is that nozzle N1 always generated a greater averaged cone angle than nozzles N2 and N3, again suggesting that the likely occurrence of cavitation in the nozzle N1 increases the dispersion of the cone angle to a greater extent than occurs with nozzles N2 and N3. Under evaporating conditions, the cone angle (or spreading angle) observed for a cylindrical nozzle by Zhang et al. was greater than that for a conical nozzle . This was explained by suggesting that the cylindrical nozzle generated a higher exit velocity, which would increase air entrainment and thus the spreading angle. However, it is not clear that the cylindrical nozzle does actually generate a higher exit velocity. Several studies have shown that convergent nozzles produce higher exit velocities, and that cavitating nozzles generate sprays with appreciable radial velocity .
Liquid and Vapor Phase Penetration
Figure 12 shows averaged liquid and vapor spray penetration values (from observations of about 50 injections for each case) at the selected injection pressures and ambient gas densities under evaporating conditions. The error bars correspond to four standard deviations (cover 95% of the observations in a normal distributed sample) for nozzle N2, and error bars are shown at every other time point ASOI. Steady liquid penetration was established after 1.0 ms ASOI in each case, so mean penetration values and mean standard deviations from 1.0 to 2.0 ms ASOI were considered in the comparisons. The effects of nozzle geometry on the liquid spray penetration have already been discussed in detail in the previous report  and are therefore only briefly summarized here: Nozzle N3 (with a k-factor of 2) produced sprays with shorter liquid phase penetration than nozzle N1 due to higher air entrainment and a lower mass flow rate. In addition, at the higher gas density (30 kg/[m.sup.3]), nozzle N2 (with a k-factor of 2) yielded longer liquid phase penetration than the cylindrical nozzle N1, partly because nozzle N2 provides higher mass flow rate and partly because of stronger cavitation in nozzle N1.
For the vapor phase penetration, there is no big difference between nozzles N3 and N1, but nozzle N2 shows a slightly longer vapor phase penetration than either under all conditions. This difference becomes clearer as the injection pressure increases. When comparing nozzles with the same outlet diameter but different k-factor, the orifice with the higher k-factor produced a greater vapor penetration than that with a k-factor of 0 [12, 36]. In our case, nozzle N2 (which has a higher k-factor of 2) shows longer vapor penetration than the nozzle N1 (k-factor 0), which is fully consistent with the results of Zhang et al.  and Bergstrand et al. . It was shown by Bergstrand et al. that the mass flow rate for nozzles with higher k-factors was greater than that for nozzles with a k-factor of zero at a given outlet diameter. In addition, Zhang et al. showed that nozzles with higher k-factors produced greater mass flows at injection pressures of 700 and 1200 bar than did nozzles with a k-factor of zero. It is believed that the vapor penetration rate is mainly determined by the transformation of momentum , which is fully consistent with our results. Momentum flux measurements  indicated that the momentum flux of nozzle N1 is slightly greater than that of nozzle N3 but substantially lower than that of nozzle N2, which may explain the greater vapor phase penetration of the latter and the similar vapor penetration for nozzles N1 and N3. Moreover, it was also shown  that nozzle N2 had a higher mass flow rate than nozzle N1 and N3, while N1 and N3 had similar mass flows. This is again identical with the results of Zhang et al. and Bergstrand et al. One final interesting observation is that the liquid lengths measured with different optical thicknesses (OD = 0.5 and 0.1) exhibited near-identical trends even though the absolute values differed.
Vapor Phase Optical Thickness and Volume Fraction
Figure 13 depicts the calculation of the optical thickness for one set of UV images acquired at 2.0 ms ASOI during the steady injection period when the vapor spray structure is fully developed. It should be noted that liquid droplets contributed to the optical thicknesses determined in UV images. The cyan line represents the averaged steady liquid length with the addition of two standard deviations. This corresponds to the furthest distance a few liquid droplets travel; beyond this distance, the contribution of liquid droplets to the vapor optical thickness is insignificant. The vapor optical thickness for each nozzle was therefore estimated using measurements acquired at a distance 60 mm from the nozzle tips (indicated by the red dashed line). However, for the lower gas density of 15 kg/[m.sup.3], a distance of 70 mm was chosen.
Figure 15 shows the averaged optical thickness along the radial direction at a fixed distance from the nozzle tip. The optical thickness is averaged from about 50 UV images acquired at 2.0 ms ASOI. For the sake of clarity, error bars with lengths of four standard deviations length are only at every third point, and only for the nozzle N2. At a gas density of 15 kg/[m.sup.3], the optical thickness is identical for all three nozzles at an injection pressure of 800 bar. However, as the injection pressure is increased to 1600 bar, the optical thickness is highest in the center of the spray for nozzle N2 and lowest for nozzle N3. Moreover, nozzle N1 produces a slightly greater width in the radial direction than N2 or N3 at an injection pressure of 1600 bar, but there is no clear systematic trend. At a gas density of 30 kg/[m.sup.3], the difference between the three nozzles is readily apparent. Nozzle N2 always shows the highest optical thickness and nozzle N3 shows the lowest. In addition, nozzle N2 also generates the greatest width and nozzle N3 shows the smallest. The high optical thickness achieved with nozzle N2 can be explained by the fact that it has the highest mass flow rate and the longest optical path length (i.e. the greatest width), and vice versa for nozzle N3.
From Equation (4), one can show that the mean vapor volume fraction [f.sub.v](the vapor phase fuel volume in a unit of space) is proportional to:
[d.sub.v] [varies] OD/[L.sub.v] (11)
where OD is the optical thickness of the vapor phase and [L.sub.v] is its optical path length. Since in our case, the absorption coefficient [epsilon]([[lambda].sub.UV]) is unknown, the quantitative vapor concentration [bar.[C.sub.v] cannot be measured. However, the relative vapor volume fraction can be obtained as shown in Equation (11). Figure 16 shows the mean vapor volume fraction along a line passing through the center of averaged UV images. If one assumes that the spray structure is axisymmetric, the optical path length [L.sub.v] can be calculated from averaged UV images. All of the images were acquired at 2.0 ms ASOI, and the start distance was set as the averaged steady liquid phase penetration length for each condition. As can be seen in Figure 16, at the injection pressure of 800 bar for gas densities of both 15 and 30 kg/[m.sup.3], the vapor volume fraction is slightly higher for nozzle N2 in most regions than for nozzle N1 or N3. The vapor volume fractions for N1 and N3 are almost identical at a gas density of 15 kg/[m.sup.3], which is consistent with the vapor phase penetration trend shown in Figure 12 (a). At a gas density of 30 kg/[m.sup.3], the vapor volume fraction of N3 is somewhat higher than that of N1 at 50-57 mm from the nozzle tip, and N1 yields a higher volume fraction than N3 at shorter and longer distances. As the injection pressure is increased to 1600 bar under both gas densities, nozzle N2 shows a significantly higher volume fraction than nozzles N1 and N3, but N3 shows a slightly lower volume fraction than nozzle N1 at a gas density of 30 kg/[m.sup.3]. These results can be compared to predictions made using the one-dimensional transient diesel jet model.
Discussion Based on the One-Dimensional Transient Diesel Jet Model
The one-dimensional transient diesel jet model developed by Musculus and Kattke  is an extension of the existing uniform-profile spray/jet model of Naber and Siebers . Although the uniform-profile spray/jet model was derived for non-vaporizing sprays, its predictions of jet penetration for a vaporizing spray agree well with experimental penetration data . Based on the conservation of mass and momentum for a steady fuel injection into a developing control volume, Naber and Siebers developed the uniform-profile spray/jet model and assumed that the velocity and mass distributions within a conical envelope for the jet were radially uniform at any axial distance from the nozzle tip. To add a realistic radial distribution of fuel mass and velocity, the one-dimensional transient diesel jet model was developed by Musculus and Kattke . This model accurately predicted quantitative experimental data for evaporating diesel sprays and was validated by Pickett et al. . Figure 14 depicts the model and its key variables.
The mass radial profiles are given as:
[[bar.X].sub.f]/[[bar.X].sub.f,c] = [(1 - [[xi].sup.[alpha]]).sup.2] (12)
where [[bar.X].sup.f] is the turbulent mean volume fraction, the subscript c denotes the values on the jet centerline, and [xi] = y/Y is the ratio of the radial coordinatey to the jet width Y = tan([theta]/2) x', and [theta] is the full spreading angle. For a fully developed shape at some distance downstream of the jet, the exponent [alpha] = 1.5. The mass distribution profile has the same radial velocity profile as shown in Figure 14, and resembles to a Gaussian function. The model makes some assumptions, such as no velocity slip between injected fuel and entrained gases, and that the jet is non-vaporizing. Accordingly, the composition of the local fuel-ambient mixture is independent of the presence of liquid droplets or vaporized fuel. In other words, droplet size has no effect on this model and all sprays with the same momentum and mass flow rate behave identically. We only present some of the relevant equations, and more details can be found elsewhere [38, 39]. The cross-sectionally averaged fuel volume fraction [[??].sub.f] is related to the velocity u and mass flow rate:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
where the double overbars signify cross sectionally averaged values and the subscript o indicates conditions at the nozzle exit, and [[??].sub.f], [[rho].sub.f] and S are mass flow rate, fuel density and cross section area, respectively. The term [beta] is related to the shape of the fuel volume fraction and velocity profiles, and it is given as
[beta] = 6([alpha] + 1)([alpha] + 2)/(3[alpha] + 2)(2[alpha] + 1) (14)
For a fully developed jet, [beta] is approximately equal to 2 with [alpha] = 1.5. In a downstream jet, the cross-sectionally averaged fuel volume fraction at a given axial distance can be expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
where [[rho].sub.a], [C.sub.a] and [d.sub.0] are the ambient gas density, area contraction coefficient and the outlet diameter of nozzle orifice. The centerline averaged volume fraction is related as
[[bar.X].sub.f,c] = [([alpha] + 1)([alpha] + 2)/[[alpha].sup.2]][[??].sub.f] (16)
From Equation 1161. it can be seen that [[bar.X].sub.f,c] is proportional to [[??].sub.f] since the term [alpha] is constant and equal to 1.5 for a fully developed jet. From Equation (15), it can be seen that at a fixed axial distance x' under the same ambient conditions and fuel density (i.e. constant [[rho].sub.a]/[[rho].sup.f]), the value [[??].sub.f] depends on [C.sub.a], [d.sub.o] and the spreading angle tan([theta]/2). Nozzles N1 and N2 have the same outlet diameter [d.sub.o], and both nozzles N1 and N2 have 30% of hydro-grinding. Although nozzle N1 is cylindrical, the difference in the area contraction between nozzles N1 and N2 is small. However, nozzle N1 has a larger spreading angle than nozzle N2 as shown in Figure 11 (a) and (b). The spreading angle is measured in the upstream region of the vapor spray, as shown in Figure 10. Because the model of Musculus and Kattke assumes that the spreading angle is constant, the same approach is used here. As shown in Figure 11, at an injection pressure of 800 bar, the spreading angle tan([theta]/2 of nozzle N2 is about 7-12% lower than that of nozzle N1, and 18-28% lower than that of nozzle N1 when the injection pressure is increased to 1600 bar. Accordingly, [[??].sub.f] is expected to be higher for nozzle N2 than nozzle N1. Essentially, the [[??].sub.f,c] of nozzle N2 is higher than that of nozzle N1, because [[bar.X].sub.f,c] is proportional to [[??].sub.f], This is consistent with the results shown in Figure 16. Nozzles N2 and N3 have the same conicity (k-factor of 2) and level of hydro-grinding, but nozzle N3 has a slightly smaller outlet diameter. They can be assumed to have the same area contraction coefficient [C.sub.a] even though their outlet diameters differ slightly. The spreading angle for nozzle N2 and N3 differ by ~1% or less difference, as shown in Figure 11. However, the outlet diameter for N3 is about 3% smaller than that for N2. Elence it can be expected that [[??].sub.f] is lower for N3 than N2 as expressed by Equation 1151. Above all, the [[??].sup.f,c] of nozzle N3 is lower than that for nozzle N2, as shown in Figure 16. In our momentum flux measurement , nozzle N3 showed an 8.5% lower mass flow rate and a 3.2% lower exit injection velocity than nozzle N2. From Equation 1131 also justifies the lower value of [[??].sub.f] (and thus a lower value of [[bar.X].sub.f,c]) for nozzle N3. Nozzles N1 has a lower area contraction coefficient, a larger spreading angle, and a larger outlet diameter than N3. The former two factors could reduce the value of [[??].sub.f], but the latter factor would tend to increase the value of [[??].sup.f]. Figure 16 shows that the fuel volume fraction ([[bar.X].sub.f,c]) for nozzle N1 is slightly greater than that of N3 only at a gas density of 30 kg/[m.sup.3]. Meanwhile, the momentum flux measurement indicated that the mass flow rate of N1 was 4% greater than that of N3, while file velocity was 2% lower. Overall, this gives N1 a slightly higher value of [[??].sup.f] for nozzle N1 as can be seen in Equation (151. and thus a slightly higher [[bar.X].sub.f,c] for N1 than that for N3.
Our experimental measurements of the vapor phase volume fraction in diesel sprays generated by the three studied nozzles were well explained by the one-dimensional transient diesel jet model. This implies that under evaporating conditions, the effects of varying the nozzle geometry are primarily due to the resulting effects on the mixing of the fuel jet with the ambient air, which is primarily governed by turbulent mixing. This is also consistent with the conclusion that the vaporization of diesel spray is controlled by fuel/ air mixing [6, 13]. Notably, Siebers  concluded that the local interphase driving forces controlling liquid jet breakup and droplet evaporation, such as the transport rates of mass, momentum and energy, do not limit the overall rate of vaporization.
The measured vapor phase penetration and liquid phase length values for the three nozzles were also explained well by the turbulent mixing. This again supports the conclusion that diesel spray formation under evaporating conditions is controlled by turbulent fuel-air mixing.
The effect of nozzle conicity on diesel spray characteristics under evaporating conditions has been studied using the LAS technique. Several conclusions can be drawn:
* Using the LAS technique with high-speed video recording, it is possible to measure diesel vapor phase distribution qualitatively in a commercial diesel fuel. The signal-to-noise is sufficiently high to determine the liquid and vapor phase boundaries as well.
* Sprays from the cylindrical nozzle N1 had greater local cone angles than those from the convergent nozzles N2 and N3 in the upstream region of the vapor spray. This is consistent with observations done by other researchers.
* Siebers' empirical equation for calculating the spread angle  should be modified to account for the effects of nozzle geometry. This equation significantly underestimated the spreading angle for the cylindrical nozzle N1 in our studies.
* Vapor phase penetration correlates well with measured momentum fluxes, confirming that vapor phase penetration is driven by the transformation of momentum.
* The difference in the fuel volume fraction along the center line of spray between the three nozzles can be explained by the one-dimensional transient diesel spray model. This justifies describing the vaporization of the diesel spray as being controlled by turbulent air mixing. The effects of nozzle conicity on the spray properties is mainly due to differences in the mass flow rate, spray momentum and spreading angle.
Chengjun Du, Mats Andersson, and Sven Andersson
Chalmers University of Technology
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[35.] Siebers, D., "Scaling Liquid-Phase Fuel Penetration in Diesel Sprays Based on Mixing-Limited Vaporization," SAE Technical Paper 1999-010528, 1999, doi: 10.4271/1999-01-0528.
[36.] Bergstrand, P., Persson, F., Forsth, M., and Denbratt, I., "A Study of the Influence of Nozzle Orifice Geometries on Fuel Evaporation using Laser-Induced Exciplex Fluorescence," SAE Technical Paper 2003-011836, 2003, doi: 10.4271/2003-01-1836.
[37.] Naber, J. and Siebers, D., "Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays," SAE Technical Paper 960034, 1996, doi:10.4271/960034.
[38.] Musculus, M. and Kattke, K., "Entrainment Waves in Diesel Jets," SAE Int. J. Engines 2(1):1170-1193, 2009, doi:10.4271/2009-01-1355.
[39.] Pickett, L., Manin, J., Genzale, C., Siebers, D. et al., "Relationship Between Diesel Fuel Spray Vapor Penetration/ Dispersion and Local Fuel Mixture Fraction," SAE Int. J. Engines 4(1):764-799, 2011, doi:10.4271/2011-01-0686.
[40.] Gustavsson, J. and Golovitchev, V., "Spray Combustion Simulation Based on Detailed Chemistry Approach for Diesel Fuel Surrogate Model," SAE Technical Paper 2003-01-1848, 2003, doi:10.4271/200301-1848.
[41.] Fieweger, K., Blumenthal, R. and Adomeit G. "Shock-Tube Investigations on the Self-Ignition of Hydrocarbon-Air Mixtures at High Pressures," Twenty-Fifth Symposium (International) on Combustion, 25(1): 1579-1585, 1994, doi:10.1016/S0082-0784(06)80803-9.
Sven B Andersson
Financial support from CERC (Combustion Engine Research Centre at Chalmers) and its participant companies is gratefully acknowledged, especially Scania CV AB who provided injectors. The assistance from research engineer, Mr. Patrik Wahlin, is also gratefully acknowledged.
ASOI--After start of injection
LAS--Light absorption and scattering
RME--Rapeseed methyl ester
RMS image--Root mean square of standard deviation from the mean image
ab--Subscript denoting light absorption
[alpha]--Velocity or fuel volume fraction profile factor
B--Coefficient in Siebers's spreading angle equation
[beta]--Velocity or fuel volume fraction profile factor
c--Subscript denoting along the jet centerline
[C.sub.a]--Area contraction coefficient
[C.sub.s]--Coefficient in Sou's cavitation number equation
[D.sub.i]--Inlet diameter of orifice
[D.sub.o]--Outlet diameter of orifice
E--Global activation energy
[f.sub.v]--Vapor volume fraction
G--Droplets optical thickness ratio
[theta]--Spreading angle of spray
I--Transmitted light intensity
[I.sub.0]--Incident light intensity
K--Nurick's cavitation number
l--Subscript denoting liquid phase fuel or droplets
L--Optical path length
[L.sub.N]--Length of nozzle hole
[[??].sub.f]--Mass flow rate
[xi]--Non-dimensional radial coordinate
OD--Optical depth or optical thickness
[P.sub.vapor]--Fuel vapor pressure
[p.sub.a]--Ambient gas density
[[sigma].sub.c]--Sou's cavitation number
R--Universal gas constant
sc--Subscript denoting light scattering
S--Cross section area
[u.sub.o]--Velocity at the nozzle exit
UV--Subscript denoting UV light
v--Subscript denoting vapor phase fuel
V--Subscript denoting visible light
[[bar.X].sub.f]--Turbulent mean volume fraction
[[??].sub.f]--Cross-sectionally averaged fuel volume fraction
[phi]--Coefficient in Sou's cavitation number
PREDICTED DEVELOPMENT OF FORMALDEHYDE
Initiation of chemical reactions could change the optical properties of the fuel and affect the light extinction measurements. As shown in Figure 2, there might be a risk of ignition during 0-2.0 ms ASOI at gas density 30 kg/[m.sup.3]. Therefore, at gas density 30 kg/[m.sup.3] and ambient temperature 673 K, the development of formaldehyde (C[H.sub.2]O) that is a representative of cool flame appearance has been predicted using Chemkin software based on a well-stirred reactor model and a mechanism for a diesel surrogate fuel developed by Gustavsson and Golovitchev at Chalmers . This model has predicted successfully experimental data . As shown in Figure A1, the mole fraction of C[H.sub.2]O starts to increasing at around 2.0 ms under fuel rich mixture (equivalence ratio =2.5). For leaner equivalence ratios, the formation of C[H.sub.2]O occurs after 2.0 ms. It should be noted that in the model the zero time in Figure A1 means that the fuel-air is already well mixed at the chamber air temperature, i.e. it does not include the time for vaporization and heating of the fuel and mixing fuel and air. In a real spray the temperature will be lower the higher the equivalence ratio, due to the heat of vaporization of the fuel. Therefore, the time for the formation of C[H.sub.2]O must be longer in our experiments than that shown in Figure A1.
LIGHT INTENSITY SHIFTING
The accuracy of extinction methods is dependent on the stability of the light source, and the effect of lamp stability was addressed in our recent report on the application of the LAS technique  from which Figure A2 is adopted. As shown in Figure A2, the mean light intensity in the three different blocks varies significantly during the injection event, but the trends are the same for all three blocks both for visible and UV images. There is less than [+ or -] 2.5% difference in the relative light intensity between three blocks, which means the light intensity in the whole image area varies simultaneously. The origin of the fluctuations are the lamps which are affected by the 50 Hz AC mains supply. Exactly the same visible lamp, UV lamp and image intensifier, which were used for the report , were used in this study. Thus, the same light intensity shifting is expected in this report. In the report , to take light intensity shifting into account, mean light intensity in block 1 was selected because it is located in the spray penetration line and not affected by the spray penetration during 0-3.5 ms period. The correction coefficient was calculated through normalizing mean light intensity of block 1 in spray images by the mean light intensity of block 1 in the background image. In this report, a pixel block shown in Figure 4 is chosen because it is not disturbed by the spray.
MEASUREMENT OF THE LOCAL SPRAY CONE ANGLE AND THE PENETRATION LENGTH
Figure A3 is adopted from a previous report , and Figure A3 tat shows the definition of the local liquid spray cone angle [[theta].sub.s]. It is measured between two vectors [??] and [??], drawn from the nozzle tip to the intersection points (a and b) at the outer contour of spray at a distance S along the spray axis x. Using the law of cosines [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], local spray cone angle [[theta].sub.s] is calculated and shown in Figure A3 (bl. The penetration length D is defined as the longest distance from the nozzle tip to the spray head.
In order to analyze statistical variations, deviations between normalized vapor phase instantaneous images and the mean vapor phase images are calculated, then the root mean square of deviations (RMS) are obtained. The results are shown Figure A4 and A5. Darker blue color indicates less fluctuating regions, which correlates with in the center of the spray. Light blue and yellow indicate higher fluctuating regions, which correlates the spray boundary region. Span length is calculated in RMS images as the width at the distance 20 mm away from the nozzle tip.
Table 1. Nozzle specifications Nozzle Outlet k-factor Hydro- Flow rate diameter grinding at 137.9 bar N1 140 [micro]m 0 30% 1.90 mg/ms N2 140 [micro]m 2 30% 2.09 mg/ms N3 136 [micro]m 2 30% 1.90 mg/ms Table 2. Experimental conditions Ambient Gas density Ambient Injection Injection temperature (kg/[m.sup.3]) pressure pressure duration (K) (bar) (bar) (ms) 673 15 29 800, ~2.6 30 58 1200, 1600
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|Author:||Du, Chengjun; Andersson, Mats; Andersson, Sven|
|Publication:||SAE International Journal of Fuels and Lubricants|
|Date:||Nov 1, 2016|
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