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Effect of Bioethanol-Biodiesel Blending Ratio on Fuel Spray Behavior and Atomization Characteristics Su Han Park, Hyun Kyu Suh, and Chang Sik Lee* Department of Mechanical Engineering, Hanyang UniVersity, 17 Haengdang-dong, Sungdong-gu, Seoul, 133-791, Korea ReceiVed January 23, 2009. ReVised Manuscript ReceiVed May 18, 2009
The aim of this work is to investigate the effect of the bioethanol addition on the spray behavior and atomization characteristics of biodiesel fuel. Spray behavior characteristics were studied by analyzing the spray tip penetration, spray centroid, and spray cone angle. In addition, the spray tip penetrations estimated by theoretical and empirical equations were compared with the experimental results. Droplet size and axial velocity were investigated for analyzing the fuel atomization characteristics. Bioethanol fuel was blended with biodiesel fuel derived from soybean oil in a volumetric ratio from 10 to 30% in 10% intervals. It was revealed that the blending ratio of bioethanol fuel had little effect on the spray tip penetration. The spray cone angle of blended fuels was increased by adding the bioethanol fuel. When the ambient gas temperature increased, the spray tip penetration of an undiluted biodiesel fuel increased due to the decrease in ambient gas density. However, the spray tip penetration of bioethanol-biodiesel blended fuels decreased due to fuel evaporation caused by high ambient gas temperature. This is due to the fact that bioethanol has high volatility and a low boiling point (about 78.3 °C). In the case of the atomization characteristics, when bioethanol was added to biodiesel, the droplet size of bioethanol blended fuels decreased and the ratio of smaller size droplets increased. Based on these results, it is possible to maintain the overall spray characteristics of biodiesel and simultaneously improve atomization performance when bioethanol is added to biodiesel.
1. Introduction Among alternative fuels, biodiesel is a promising alternative to diesel fuel since it is biodegradable, environmentally friendly, and can reduce air pollution from automotive emissions. Biodiesel fuel can be used in diesel engines with high thermal efficiency without engine modification. It improves combustion performance and fuel consumption since the fuel itself includes oxygen. For these reasons, many studies on biodiesel fuel have been performed.1-4 Lee et al.5 studied the effect of biodiesel blending ratio in a compression ignition engine and reported that HC and CO emissions are decreased and the ignition delay is shortened when the blending ratio of the biodiesel increased. Bhale et al.6 studied the improvement of the low temperature properties of biodiesel fuel. They observed the improvement of flow characteristics of biodiesel fuel using ethanol and kerosene as an additive. However, biodiesel fuel also has some disadvantages, such as difficulty in storage and the decline of flow characteristics at low fuel temperatures. To solve these problems, research on blended biodiesel fuels is underway. * Corresponding author: phone: +82-2-2220-0427; fax: +82-2-22815286; e-mail:
[email protected]. (1) Kegl, B.; Hribernik, A. Energy Fuels 2006, 20, 2239–2248. (2) Suh, H. K.; Roh, H. G.; Lee, C. S. J. Eng. Gas Turbines Power 2008, 130, 032807. (3) Ahmed, M. A.; Ejim, C. E.; Fleck, B. A.; Amirfazli, A., SAE Technical Paper SAE 2006-01-0893, 2006. (4) Yoon, S. H.; Park, S. W.; Kim, D. S.; Kwon, S. I.; Lee, C. S. Proceedings of ICEF2005 on ASME Internal Combustion Engine Division, 2005, ICEF2005-1258. (5) Lee, C. S.; Park, S. W.; Kwon, S. I. Energy Fuels 2005, 19, 2201– 2208. (6) Bhale, P. V.; Deshpande, N. V.; Thombre, S. B. Renewable Energy 2009, 34, 794–800.
Unlike biodiesel, bioethanol has a low cetane number and low viscosity. Moreover, its crystallization temperature is very low compared to biodiesel fuel; therefore, it can be expected that flow characteristics of biodiesel and bioethanol blended fuels would be superior to biodiesel fuel under cold flow conditions. Shudo et al.7 conducted an experimental study on the flow and emission characteristics of ethanol-blended biodiesel fuels to improve cold flow characteristics of biodiesel fuel. They reported that cold flow characteristics were improved by 30% with 10% ethanol fuel. The addition of ethanol and the retardation of fuel injection timing also resulted in simultaneous reduction of NOx and smoke, without loss of thermal efficiency. Chen et al.8 added a biodiesel fuel to prevent the phase separation of ethanol-diesel blended fuels, because phase separation disturbs the blending stability of ethanol and diesel fuels. They also reported that smoke and particulate matter can be reduced simultaneously, along with lengthening the injection delay, increasing maximum combustion pressure and shortening the combustion duration when the blending ratio of ethanol in fuels is increased. Besides the studies mentioned above, Yoon et al.9 and Park et al.10 investigated the effect of spray characteristics on the reduction of exhaust emissions and fuel properties as a function of fuel temperature using biodiesel and ethanol blended fuels, respectively. Although there are many advantages of blended fuels, such as the improvement in viscosity coefficient and cold-start ability, (7) Shudo, T.; Fujibe, A.; Kazahaya, M.; Aoyagi, Y.; Ishii, H.; Goto, Y.; Noda, A. SAE Technical Paper SAE 2005-01-3707, 2005. (8) Chen, H.; Shuai, S. J.; Wang, J. X. Proc. Combust. Inst. 2007, 31. (9) Yoon, S. H.; Park, S. H.; Suh, H. K.; Lee, C. S. Proceedings of Energy Sustainability 2008, 2008, ES2008-54227. (10) Park, S. H.; Yoon, S. H.; Suh, H. K.; Lee, C. S. Oil Gas Sci. Technol. 2008, 63-6, 737–745.
10.1021/ef900068a CCC: $40.75 2009 American Chemical Society Published on Web 07/10/2009
Biodiesel Blending Ratio and Fuel Spray BehaVior
Figure 1. Schematic of the injection rate measuring system.
there is insufficient literature addressing spray and atomization characteristics in biodiesel and bioethanol blended fuel, compared with studies on combustion and exhaust emissions. Therefore, studies on the spray behavior and atomization characteristics are still needed to understand the effect of combustion and emission characteristics in a diesel engine. The purpose of this work is to investigate spray behavior and atomization characteristics of biodiesel and bioethanol blended fuels under various injection and ambient conditions. For the analysis of the macroscopic spray characteristics, spray tip penetration and spray angle were examined. For the analysis of the atomization characteristics of biodiesel and bioethanol blended fuels, the droplet size and axial mean velocity were investigated at various measuring points. In addition, the applicability of theoretical and empirical equations for spray tip penetration of biodiesel-bioethanol blended fuels was also evaluated. 2. Experimental Setup and Procedure 2.1. Test Fuels and Fuel Injection Rate Measuring System. For studying the effects of bioethanol addition on the overall spray characteristics, four test fuels were used: B100 (an undiluted biodiesel fuel derived from soybean oil), BE10 (biodiesel 90% + bioethanol 10%), BE20 (biodiesel 80% + bioethanol 20%), and BE30 (biodiesel 70% + bioethanol 30%). To investigate the effect of the mixing ratio of bioethanol and biodiesel fuel on the spray behavior and atomization characteristics, a single hole injector with 0.3 mm diameter and 0.8 mm orifice depth was used. The test injector was controlled by a peak current of 21.0 A and a hold current of 11.0 A. An injector driver and a digital delay/pulse generator were used to control the injection timing and energizing duration of the spray. In this study, the injection rate of test fuels was measured to evaluate the applicability of a theoretical equation by Desantes et al.11 for spray tip penetration in biodiesel-bioethanol blended fuels. A schematic diagram of the injection rate measuring system is shown in Figure 1. It consists of two parts, fuel injection and data acquisition. An injection rate measuring system was used to determine the time-resolved injection profile.12 This apparatus is based on the pressure variation of a tube filled with fuel when the fuel is injected into the tube. During the experiment, the pressure in the tube was set equal to 4.0 MPa and was measured using a piezo-type pressure sensor. The injection quantity was measured by averaging 2000 continuous injections for each test case. 2.2. Visualization and Droplet Measuring Systems. The experimental system was composed of a spray visualization system and a droplet measuring system, as illustrated in Figure 2. Fuel (11) Desantes, J. M.; Payri, R.; Salvador, F. J.; Gil, A. Fuel 2006, 85, 910–917. (12) Bosch, W. SAE Technical Paper SAE660749, 1966.
Energy & Fuels, Vol. 23, 2009 4093 supply and injector operation were controlled by a high-pressure pump and injector driver (TEMS, TDA-3200H), respectively. The macroscopic spray structure, that is, spray tip penetration and overall spray behaviors, can be analyzed from the spray images obtained from the spray visualization system, which is composed of a Nd: YAG laser (Continuum, SL2-10), cylindrical lenses and mirrors, a digital delay/pulse generator (Berkeley Nucleonics Corp, Model 555), an ICCD camera (intensified charge couple device, the Cooke Corporation, Dicam-PRO), and image acquisition software. As a light source, a Nd:YAG laser with a 532 nm wavelength was used, and cylindrical lenses, which form a laser sheet beam less than 1 mm of thickness, were used to illuminate the spray evolution. A high-pressure chamber, which can be pressurized up to 4.0 MPa, was used to generate the high ambient pressure and ambient temperature conditions using nitrogen gas and a heating coil, respectively. The specifications of the spray visualization system are listed in Table 1. The phase Doppler particle analyzer (PDPA) system, illustrated in Figure 1, was used to obtain the mean droplet size and axial velocity. It consists of an Ar-ion laser, a transmitter, a receiver, and a signal analyzer. On the basis of the data rate and the signal intensity of the signal analyzer, the laser output of the Ar-ion laser and the PMT voltage were determined to be 700mW and 500 V, respectively. The subrange of the diameter, that is, the effective range of the PDPA signal analyzer, was set from 2 to 75 µm, considering that the nozzle diameter was 300 µm, and approximately 20 000 droplets were collected and averaged at each measurement point. To obtain time-resolved data, the signal analyzer was synchronized with the injection driver and the delay/pulse generator. The specifications of the droplet measuring system are also listed in Table 1. The fuel droplet size and velocity were measured every 5 mm, from 5 to 100 mm along the axial direction, and every 2 mm along the radial direction at 40, 50, and 60 mm from the nozzle tip. To determine the effect of ambient temperature on the spray characteristics, the ambient temperature in a high-pressure chamber was adjusted from 300 to 400K. The droplet measuring experiment was conducted under an injection pressure of 60 MPa, an ambient pressure of 0.1 MPa, an ambient temperature of 300 K, and an energizing duration of 0.8 ms. Detailed experimental conditions of this work are listed in Table 2. Variations in fuel properties, including surface tension, kinematic viscosity, and fuel density are shown in Figure 3 for different blending ratios. Surface tension of the test fuels was measured using a surface tension measuring meter (ITOH Seisakusho Ltd., No. 514-B2), and fuel density and kinematic viscosity were taken from the experimental results of Park et al.10 As shown in Figure 3, the addition of bioethanol to biodiesel caused a reduction of each property because bioethanol has very low density, kinematic viscosity, and surface tension.
3. Theoretical and Empirical Equations for Spray Tip Penetration Using the concept of momentum flux in the nozzle flow, a theoretical equation for the spray tip penetration was suggested by Desantes et al.11 From the momentum flux and axial velocity, the theoretical spray tip penetration was derived as follows:
()
-1/4 1/2 ˙ 1/4 S ) 1.26M tasoi tan-1/2 o Fa
θu 2
(1)
˙ o is the momentum flux at the orifice outlet, and θu is where M the spray cone angle. In this work, the injection rate and axial velocity were measured such that the momentum flux could be calculated. The empirical equation suggested by Hiroyasu and Arai13 was used for estimation of the spray tip penetration. It describes the spray tip penetration as two regions, that is, before and after the droplet breakup time (tb). At first, when the time after the
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Figure 2. Schematic of visualization and droplet measuring system. Table 1. Specifications of the Spray Visualization System and Droplet Measuring System spray visualization system light source wavelength laser power
droplet measuring system
Nd:YAG laser light source 532 nm wavelength 270 mJ focal length
beam thickness ∼0.1 mm
Ar-ion laser 514.4 nm, 488 nm transmitter 250 mm receiver 250 mm collection angle 30°
Table 2. Experimental Conditions spray visualization injection pressure ambient pressure ambient temperature energizing duration
60, 80, 120 MPa 0.1, 2.0 MPa 300, 350, 400K 1.2 ms
droplet measuring 60 MPa 0.1 MPa 300K 0.8 ms
start of injection is shorter than the breakup time (tb), spray tip penetration can be expressed as follow: S ) 0.39tasoi√(2∆P)/Ff (tasoi e tb)
(2)
where S is the spray tip penetration, tasoi is the time after start of injection, ∆P is the difference between the injection and ambient pressures, and Ff is the fuel density. When the time after start of injection is longer than the breakup time (tb), spray tip penetration can be expressed as S ) 2.59√Dtasoi(2∆P/Fg)0.25 (tasoi g tb)
(3)
where D is the diameter of nozzle orifice, and Fg is the ambient gas density. The breakup time is given by tb ) 28.65FfD/(Fg∆P)0.5
(4)
The theoretical and empirical equations above were developed for diesel fuel spray applications. In this study these equations are applied to alternative fuels such as an undiluted biodiesel and biodiesel-bioethanol blended fuels to estimate the spray tip penetration, and these calculated results were compared with experimental results. 4. Results and Discussion 4.1. Spray Tip Penetration and Spray Cone Angle of Bioethanol Blended Biodiesel Fuel. In this section, the effect of bioethanol blending ratio on a spray tip penetration and spray
cone angle of blended fuel was investigated and analyzed. Spray tip penetration was defined as the maximum distance of injected spray from a nozzle tip at a specific time, and the spray cone angle was defined as the angle formed between the nozzle tip and two lines that delineate the maximum outer region of the injected spray. Figure 4 illustrates the spray development process of B100, BE10, BE20, and BE30 for an injection pressure of 120 MPa, an ambient pressure of 2 MPa, an ambient temperature of 300 K and an energizing duration of 1.2 ms. As shown in Figure 4, the spray tip penetration for the biodiesel fuel shows longer penetration compared to blended fuels at the same elapsed time. The three diluted biodiesel-bioethanol blended fuels (BE10, BE20, and BE30) have similar growth in velocity and penetration, whereas the spray cone angle increased with increasing ethanol concentration. This is the reason why the density reduction of the blended fuels induced the decrease of the injection velocity. Then, the reduction of the axial spray momentum is larger than that of the radial spray momentum. Therefore, the relative spray cone angle of blended fuels increased when the mixing rate of bioethanol in the blended fuels increased. At the same injection and ambient conditions, the spray cone angle was affected by the fuel density and ambient gas density.13 Therefore, it can be concluded that the decrease in fuel density due to the addition of bioethanol fuel caused the increase in injected fuel. From spray evolution images, a quantitative analysis of the spray tip penetration was performed; Figure 5 shows the spray tip penetration of the fuels at two injection pressures, 60 and 120 MPa. As shown in Figure 5, four test fuels have very similar patterns of spray tip penetration, although a slight difference between B100 and BE30 is apparent. This result indicates that the blending ratio of test fuels has little effect on the spray tip penetration. In addition, the slope of spray tip penetration in Figure 5, panels a and b, changed suddenly near the time after the start of injection at 0.3 and 0.2 ms, respectively. It was guessed that this point is indicative of the droplet breakup time for the fuel spray. Using an empirical eq 3, the droplet breakup times for B100 at injection pressures of 60 and 120 MPa are
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Figure 3. Fuel property characteristics for the addition of bioethanol fuel.
Figure 4. Spray development process of B100, BE10, BE20, and BE30 fuels (Pinj ) 120 MPa, Pamb ) 2 MPa, teng ) 1.2 ms).
0.2 and 0.14 ms, respectively. After breakup of droplets, the growth of spray tip penetration decelerated due to loss in spray momentum. Basically, the spray region was divided into two regions, that is, the main region and the front edge of the spray as suggested by Roisman et al.14 The main region of the spray was affected by the inertia of the injected liquid spray and the momentum of the entrapped ambient air. The front edge of the spray was affected by the inertia of the droplets entering it from the main region and the aerodynamic drag force. In addition, the spray tip penetration was determined by the inertia of the liquid and air mixture in the conical region of the spray, and the particular conditions near the leading edge of the spray, which were affected by high gradients of spray concentration and the formation of the vortex-like structures. Figure 6 shows the development process of the spray centroid of B100 and BE30. In this case, the spray centroid means the center of axial and radial distance in the spray area. Unlike the result for spray tip penetration, the spray centroid of BE30 showed a lower value than that of B100. In addition, the difference between B100 and BE30 became larger with increasing time after the start of injection. In this work, the development (13) Hiroyasu, H.; Arai, M. SAE Technical Paper SAE900475, 1990. (14) Roisman, I. V.; Araneo, L.; Tropea, C. Int. J. Multiphase Flow 2007, 33, 904–920.
Figure 5. Spray tip penetration characteristics according to the addition of bioethanol to biodiesel fuel (teng ) 1.2 ms).
Figure 6. Comparison of the spray centroid of B100 and BE30.
of spray centroid has the same meaning as the development of the main region suggested by Roisman et al.14 Therefore, it can be said that the centroid penetration of BE30 was slow compared to B100 because BE30 fuel has a low momentum of entrained ambient air and lower inertia of injected spray.
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Figure 7. Comparison of the spray tip penetration among the theoretical, empirical equations, and experimental results (teng ) 1.2 ms).
Figure 7 shows the comparison between the theoretical equation, empirical equation, and the experimental results on the spray tip penetration. As shown in Figure 7, the spray tip penetrations estimated by theoretical and empirical equations are in good agreement with the experimental spray tip penetration. The theoretical equation is more accurate than empirical equation because the theoretical equation results are based on the injection rate, which was measured from the injection rate meter in this investigation. Figure 8 shows the effect of ambient gas temperature on the spray tip penetration. Test conditions were an injection pressure of 80 MPa, an ambient pressure of 0.1 MPa, and an energizing duration of 1.2 ms. Ambient gas temperatures were 300, 350, and 400 K. As shown in Figure 8a, the spray tip penetration of B100 increased slightly from 0.8 ms from the start of injection because the ambient gas density decreased due to the increase in ambient gas temperature. However, the spray tip penetration of BE30, as shown in Figure 8b, decreased with increasing ambient gas temperature because bioethanol fuel has a low boiling temperature (about 78.3 °C) and high volatility, which promoted the fuel evaporation of BE30. 4.2. Fuel Atomization Characteristics of Biodiesel-Bioethanol Blended Fuels. Fuel atomization performance, including the droplet size and velocity, is an important factor that affects the combustion and emission characteristics in a direct injection
Park et al.
Figure 8. Spray tip penetration characteristics on the variation of an ambient gas temperature (Pinj ) 80 MPa, Pamb ) 0.1 MPa, teng ) 1.2 ms).
Figure 9. Fuel atomization characteristics on the addition of bioethanol to biodiesel fuel (I) (Pinj ) 60 MPa, Pamb ) 0.1 MPa, teng ) 0.8 ms).
diesel engine. Figure 9 shows the local Sauter mean diameter (SMD) distribution of B100, BE10, BE20, and BE30 along the
Biodiesel Blending Ratio and Fuel Spray BehaVior
Figure 10. Fuel atomization characteristics on the addition of bioethanol to biodiesel fuel (II) (Pinj ) 60 MPa, Pamb ) 0.1 MPa, teng ) 0.8 ms).
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Figure 12. Correlation between the overall velocity and overall SMD.
Figure 13. Probability density function of spray droplets. Figure 11. Comparison of the spray arrival time and overall spray velocity among B100, BE10, and BE20 (Pinj ) 60 MPa, Pamb ) 0.1 MPa, teng ) 0.8 ms).
spray axis. The definition of the local SMD is the average SMD calculated at the specific measuring point in the whole measuring time. Experiments for investigating the atomization performance were conducted under an injection pressure of 60 MPa, an
ambient pressure of 0.1 MPa, and an energizing duration of 0.8 ms for convenience. Test fuels had the highest SMD at the initial stage of spray, and afterward SMD gradually decreased. When bioethanol fuel is added, the blended fuel has a smaller droplet size than undiluted biodiesel fuel, and as the blending ratio increases, the SMD distribution becomes smaller. This is due to the fact that bioethanol fuel has a low kinematic viscosity
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and low surface tension, resulting in a more active breakup process. Figure 10 depicts the overall SMD distribution, which shows the mean value of whole spray droplets at the same time after the start of injection. In Figure 10, bioethanol blended biodiesel fuels also have a smaller droplet size than that of an undiluted biodiesel fuel. Figure 11a shows the spray arrival time at which the spray edge reached the measuring position of B100, BE10, BE20, and BE30. The comparison of spray arrival time shows that B100 fuel reached each measuring point more quickly because the large droplet momentum in B100 coupled with high viscosity and surface tension promotes rapid spray velocity, as shown in Figure 11a. Bioethanol blended biodiesel fuels traveled more slowly due to the evaporation and atomization. In addition, in Figure 11b, B100 fuel has the highest overall velocity near the injector nozzle. The overall velocity means the average velocity of all captured droplets at the specific time in the whole measuring points. The overall velocity could be determined with the following equation. Overall velocity )
1 n
(∑ ∑ ) t+∆t/2
n
t-∆t/2
i)1
Vi
(5)
The correlation between the overall velocity and overall SMD is shown in Figure 12. Generally, in case of the same fuel, Figure 12 shows that the high velocity induced the decrease of the droplet size. It means that the high droplet velocity induced the high relative velocity between the injected spray and ambient gas, and then the injected droplets actively atomized. On the other hand, B100 has a larger overall SMD at the same overall velocity, because the fuel kinematic viscosity of B100 is larger than other test fuels. In addition, B100 has a larger overall velocity at the same overall SMD because the density of B100 is larger than other test fuels. Figure 13 illustrates the probability density function, which is defined as the ratio of droplet number according to the diameter and total droplet number, of test fuels at LZ ) 30 mm and LZ ) 50 mm (LZ: axial distance from the nozzle tip). The rectangular and circular symbols indicate the ratio of droplet sizes from 0.1 to 5.0 µm and from 5.1 to 10.0 µm, respectively. When the bioethanol blending ratio was increased, the ratio of small droplet size also increased, and the ratio of large droplet size decreased. In addition, at LZ ) 50 mm, the ratio of small droplet size decreased. These droplet distributions can be expected based on the results of Figure 9 and Figure 10. 5. Conclusions In this work, the spray behavior and atomization performance of biodiesel and bioethanol-biodiesel blends were investigated and analyzed under various blending ratio and injection conditions. To compare the influence of blending ratios, spray tip penetrations estimated by the theoretical and empirical equation
were compared with experimental results. Results from experiment and theoretical analysis are summarized as follows. (1) Undiluted biodiesel fuel and biodiesel-bioethanol blended fuels have very similar spray development processes and spray tip penetrations, although the spray cone angle of biodieselbioethanol blended fuels is larger than that of undiluted biodiesel fuel. Therefore, it can be concluded that the addition of bioethanol fuel to biodiesel fuel has little effect on the development of the spray tip penetration, whereas it promotes the increase in the spray cone angle. (2) The spray tip penetration estimated by both the theoretical equation based on the momentum flux and the empirical equation agreed well with experimental spray tip penetration results for biodiesel and biodiesel-bioethanol blended fuels. Therefore, it can be said that the theoretical and empirical equations applied in this study for the prediction of the spray tip penetration of diesel fuel are applicable to alternative fuels, such as biodiesel and biodiesel-bioethanol blended fuels. (3) When the ambient gas temperature increased, the spray tip penetration of B100 increased due to a decrease in ambient gas density. However, the spray tip penetration of BE30 decreased because the bioethanol fuel has high volatility and low boiling point, which promotes fuel evaporation. (4) The addition of bioethanol fuel improved the fuel atomization performance of biodiesel-bioethanol blended fuels due to a more active breakup process influenced by the low kinematic viscosity and increased fuel evaporation of bioethanol fuel. Acknowledgment. This work was supported in part by the CEFV (Center for Environmentally Friendly Vehicle) of the Eco-STAR project of the MOE (Ministry of the Environment in Seoul, Republic of Korea). Also, this study was also supported by the Second Brain Korea 21 Project in 2007. Nomenclature
BEx ) biodiesel-bioethanol blended fuels B100 ) undiluted biodiesel fuel D ) nozzle hole diameter (mm) LZ ) axial distance from the nozzle tip (mm) ˙ ) momentum flux at the orifice outlet (N) M ∆P ) difference between injection and ambient pressure (MPa) Pinj ) injection pressure (MPa) Pamb ) ambient pressure (MPa) S ) spray tip penetration (mm) tasoi ) time after the start of injection (ms) tb ) droplet breakup time (ms) teng ) energizing duration (ms) Tamb ) ambient gas temperature (K) Ff ) fuel density (kg/m3) Fg ) ambient gas density (kg/m3) θu ) spray cone angle (deg) EF900068A
