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Comparison between different hole to hole measurement techniques in Diesel injection nozzle

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2005-01-2094 Comparison between different hole to hole measurement techniques in a Diesel injection nozzle F. Payri, R. Payri, F.J. Salvador, J. Gimeno CMT Motores Termicos, Universidad Politécnica de Valencia, Spain Copyright © 2005 SAE International ABSTRACT In order to study differences between Diesel nozzle holes, four methodologies have been tested. The techniques compared in this paper are: the internal geometry determination, hole to hole mass flow measurement, spray momentum flux and macroscopic spray visualization. The first one is capable of obtaining the internal geometry of each of the orifice of the nozzle; the second one is capable of measuring the mass flow of each nozzle hole in both, continuous and real injections. The third one gives the momentum flux of each orifice, and finally, with the macroscopic spray visualization, the spray penetration and spray cone angle of each hole, are obtained. Generally, all these techniques can be used in order to determine the hole to hole dispersion due to different angle inclination of the holes, different internal geometry of orifices, deposits, nozzle needle off-center, needle deflection, etc. Moreover, the results obtained from theses techniques are a very useful tool in order to study the injection process. Special attention deserves the new capability developed to carry out the hole to hole mass flow measurement. In fact, although Diesel nozzle mass flow measurement, either injection rate or continuous mass flow, is a technique widely used, it has the disadvantage that the complete nozzle mass flow is characterized without a distinction between the mass flow from each of the orifices. Here, a new test rig is presented in order to achieve this kind of measurements. INTRODUCTION In modern Diesel engines, especially in high-speed direct injection engines, the performance, efficiency, noise and pollutant emissions have a strong dependency on the characteristics of fuel injection. Nowadays, the amount of fuel injected is not only the most relevant characteristic of the injection process. The instantaneous fuel mass flow rate introduced into the combustion chamber, the evolution of the spray and its interaction with the air are also important [1-4]. One important phenomenon in this process is the flow behavior across the nozzle holes in the injectors, which is influenced by nozzle geometry and which affects spray characteristics and therefore atomization process (droplet formation) and fuel-air mixing [3-7]. Atomization and the fuel-air mixing are decisive for engine performance and pollutant formation. The most influential parameters on droplet formation and fuel-air interaction are fuel injection rate, spray momentum and orifice effective flow area. These parameters can be affected by other phenomena as cavitation [3, 4, 6, 8- 13]. Nowadays Direct Injection Diesel engines are equipped with multi-hole nozzles. The intention of using multi-hole nozzles is to improve the fuel-air mixing process inside the combustion chamber. Nevertheless, this kind of nozzles, can be affected, as stated before, by hole to hole dispersion which can affect the uniformity and so the combustion performance. In the present paper four measurement techniques are going to be compared to evaluate the uniformity of fuel mass distribution of injectors with multi-hole nozzles. These techniques are: internal geometry determination with the silicone technique [3, 14], mass flow measurement over each orifice of the nozzle, spray momentum [4, 12] and spray macroscopic visualization [3, 6, 8, 15-17]. As an example, the four methodologies will be used in order to study the hole to hole variations in a micro-sac nozzle with three symmetric holes which have different internal geometry. In this case, therefore, only differences related to the nozzle manufacture process are expected. The paper is divided into three main sections. The first section gives a brief description of the experimental capabilities that will be used with a description of the four methodologies. Next, the results obtained in the different test rig are described and compared with each other, and finally a conclusion summary is presented.
Transcript

2005-01-2094

Comparison between different hole to hole measurement techniques in a Diesel injection nozzle

F. Payri, R. Payri, F.J. Salvador, J. Gimeno CMT Motores Termicos, Universidad Politécnica de Valencia, Spain

Copyright © 2005 SAE International

ABSTRACT

In order to study differences between Diesel nozzle holes, four methodologies have been tested. The techniques compared in this paper are: the internal geometry determination, hole to hole mass flow measurement, spray momentum flux and macroscopic spray visualization. The first one is capable of obtaining the internal geometry of each of the orifice of the nozzle; the second one is capable of measuring the mass flow of each nozzle hole in both, continuous and real injections. The third one gives the momentum flux of each orifice, and finally, with the macroscopic spray visualization, the spray penetration and spray cone angle of each hole, are obtained. Generally, all these techniques can be used in order to determine the hole to hole dispersion due to different angle inclination of the holes, different internal geometry of orifices, deposits, nozzle needle off-center, needle deflection, etc. Moreover, the results obtained from theses techniques are a very useful tool in order to study the injection process.

Special attention deserves the new capability developed to carry out the hole to hole mass flow measurement. In fact, although Diesel nozzle mass flow measurement, either injection rate or continuous mass flow, is a technique widely used, it has the disadvantage that the complete nozzle mass flow is characterized without a distinction between the mass flow from each of the orifices. Here, a new test rig is presented in order to achieve this kind of measurements.

INTRODUCTION

In modern Diesel engines, especially in high-speed direct injection engines, the performance, efficiency, noise and pollutant emissions have a strong dependency on the characteristics of fuel injection. Nowadays, the amount of fuel injected is not only the most relevant characteristic of the injection process. The instantaneous fuel mass flow rate introduced into the combustion chamber, the evolution of the spray and its interaction with the air are also important [1-4]. One

important phenomenon in this process is the flow behavior across the nozzle holes in the injectors, which is influenced by nozzle geometry and which affects spray characteristics and therefore atomization process (droplet formation) and fuel-air mixing [3-7]. Atomization and the fuel-air mixing are decisive for engine performance and pollutant formation. The most influential parameters on droplet formation and fuel-air interaction are fuel injection rate, spray momentum and orifice effective flow area. These parameters can be affected by other phenomena as cavitation [3, 4, 6, 8-13].

Nowadays Direct Injection Diesel engines are equipped with multi-hole nozzles. The intention of using multi-hole nozzles is to improve the fuel-air mixing process inside the combustion chamber. Nevertheless, this kind of nozzles, can be affected, as stated before, by hole to hole dispersion which can affect the uniformity and so the combustion performance.

In the present paper four measurement techniques are going to be compared to evaluate the uniformity of fuel mass distribution of injectors with multi-hole nozzles. These techniques are: internal geometry determination with the silicone technique [3, 14], mass flow measurement over each orifice of the nozzle, spray momentum [4, 12] and spray macroscopic visualization [3, 6, 8, 15-17]. As an example, the four methodologies will be used in order to study the hole to hole variations in a micro-sac nozzle with three symmetric holes which have different internal geometry. In this case, therefore, only differences related to the nozzle manufacture process are expected.

The paper is divided into three main sections. The first section gives a brief description of the experimental capabilities that will be used with a description of the four methodologies. Next, the results obtained in the different test rig are described and compared with each other, and finally a conclusion summary is presented.

EXPERIMENTAL CAPABILITIES

INTERNAL ORIFICE GEOMETRY DETERMINATION

In order to analyze the internal geometrical characteristics of the nozzles, the methodology described in [14] was followed. This methodology is based on the use of a special type of silicone to obtain the internal moulds of the nozzle. Once the moulds have been obtained, it is necessary to take pictures of them with an electronic microscope. This microscope allows high quality pictures with a large magnification range to be obtained. The pictures obtained with the electronic microscope come with a reference dimension as shown in Figure 1. With this information it is possible to load the pictures in the CAD (computer-aided design) software with the appropriate scale factor. Since the exact magnification factor is used, it is not difficult to obtain the actual dimensions of the nozzle.

This non-destructive methodology allows all the dimensions of non-optical accessible parts of the nozzle to be characterized. This experimental tool is useful for the study of Diesel sprays because it enables researchers to establish relationships between internal geometry, internal flow and spray characteristics [3, 4, 6, 10, 11, 14].

Figure 1. Pictures of silicon mould: general view of micro-sac nozzle and bottom measurement of the outlet diameter.

Figure 1 shows photographs taken for one orifice of the nozzle studied in this work. The most important parameter obtained is the orifice outlet diameter but information about the shape of the orifice can also be obtained, which could be an interesting help in a posterior investigation of the orifice internal flow and spray characteristics.

HOLE TO HOLE MASS FLOW TEST RIG

A new test rig has been developed; the test rig is capable to measure the mass flow of each single hole of a nozzle.

The test rig operates separating each spray by means of a special piece where a conical hole for each spray is machined. The fuel mass of each spray mixed with air is carried to a siphon where liquid fuel and air are separated. From the siphon it is obtained the injected fuel mass. The air pushed by each spray is recirculated so that it is possible to separate the fuel and the air. Figure 2 shows a sketch of the test rig.

Figure 2. Hole to hole mass flow test rig.

The hole to hole mass flow test rig is able to operate in steady conditions [13], or with real pulsating injections. A different separation flow device has to be constructed depending on the number of orifices of the nozzle.

SPRAY MOMENTUM TEST RIG

With this experimental equipment it is possible to determine the impact force of a spray on a surface. This force is equivalent to the spray momentum flux. Figure 3 shows a sketch of the momentum test rig. Sprays are injected into a chamber that can be pressurized with

nitrogen up to 8 MPa, in order to simulate pressure discharge conditions that are representative of real pressure conditions inside the engine combustion chamber during the injection process.

Acquisition System

Injector

Rail

High pressure pump

Force Sensor

Back pressure sensor

Nitrogen up to 100 bar

Injection pressure sensor

Spray momentum

rig

Injection control system

Figure 3. Spray momentum test rig

Figure 4 shows a sketch of the spray momentum measuring principle. The impact force is measured with a calibrated piezo-electric pressure sensor in order to measure force, which is placed at 5 mm from the hole exit. The sensor frontal area and position are selected so that spray impingement area is much smaller than that of the sensor. Under this assumption, and due to the conservation of momentum, the force measured by the sensor will be the same as the momentum flux at the hole outlet or at any other axial location, since the pressure inside the chamber is constant and surrounds the entire spray and fuel deflected is perpendicular to the axis direction.

Figure 4. Spray momentum measurement system diagram

MACROSCOPIC SPRAY VISUALIZATION

In order to visualize the sprays from the different nozzle holes, the nitrogen test rig is used. It basically consists of a steel cube with a chamber and various connecting flanges machined into it. The design is modular, and ancillaries can be added depending on the required experiment [17]. The rig and ancillaries are designed for a maximum pressure of 70 bar. It is necessary to circulate the nitrogen through the rig because otherwise the injected Diesel would obscure the windows and severely degrade the quality of the images. Furthermore, it is important to keep rig pressure (Pb) and nitrogen temperature constant during each experiment. Two filters collect the fuel injected to keep the gas stream clean. The temperature of the nitrogen can be set to values between 15 and 50 ºC in order to obtain the desired density inside the chamber. The test rig operates in cold conditions thus avoiding fuel evaporation. In figure 5 a photograph of the N2 test rig is shown.

Figure 5. Photograph of the N2 test rig injection chamber.

Image acquisition system and image processing software.

The images are taken with a 12-bit colour CCD camera (Pixel Fly by PCO) with a spatial resolution of 1280 x 1024 pixels, a minimum exposure time of 10 microseconds with a jitter of ± 5 microseconds. Illumination is ensured by a high power xenon flash lamp.

All the experimental equipment (camera-flash-injection) has been synchronized with a purpose-built electronic system, using the injector trigger signal as a reference to take the image sequences. Very low injection frequency (0.25 Hz) is used. This high time interval between injections is required for the N2 flow within the rig to be able to remove the fuel droplets from the previous injection, and thus maintain good optical access to the spray.

The injector is mounted so that all the spray axis are visualized simultaneously through the frontal window as could be seen in figure 6. The images are digitally

processed using purpose-developed software. The segmentation algorithm used, based on the log-likelihood ratio test (LRT), has the advantage of using the three channels of RGB images for a proper determination of boundaries that are not well defined, as in the case of sprays. This method proved to be almost completely insensitive to intensity fluctuations between pictures for the tested cases, and provided better results than some other algorithms checked. Prior to the systematic use of the algorithm for parametric studies, the influence of the illumination quality on the results was evaluated in specific tests. Results demonstrated that the algorithm properly detects the estimated spray boundaries even in case of comparatively poor illumination. Details of the image processing software are available in [15].

Figure 6. Three holes nozzle spray visualization sample. Pinj=130MPa, t=0.9ms.

EXPERIMENTAL SETUP

The injection system used was a conventional Common Rail Fuel Injection system [18, 19], which allows fuel injection under high (up to 180 MPa) and relatively constant pressure. The same system has been used for all experimental installations so that the measurements could be compared.

In order to perform this study a micro-sac nozzle with three symmetric holes which have different internal geometry has been used.

RESULTS

The results obtained following the different facilities are shown here.

INTERNAL GEOMETRY

In the following table the dimensions of the three holes are shown. As it can be seen all holes are a little divergent (negative k-factor). The hole 1 has the biggest outlet and inlet diameters. The other two (hole 2 and hole 3) have the same outlet diameter, although the inlet diameter of hole 2 is bigger than that of hole 3 one. All holes have a similar rounding radius.

Hole 1 Hole 2 Hole 3

Di inlet (µm) 138 137 135

Do outlet (µm) 142 141 141

k-factor -0.4 -0.4 -0.6

R round (µm) 13 14 12

Table 1. Internal dimensions of the nozzle used.

Figure 7 shows the relative inlet and outlet area of each hole. They have been calculated dividing the inlet and outlet area of each orifice by the mean value of the three orifices. As can be seen from the figure, hole 1 has the highest values while hole 3 shows the lowest.

Hole 1 Hole 2 Hole 30.97

0.98

0.99

1.00

1.01

1.02

Rea

live

area

Inlet areaOutlet area

Figure 7. Relative area of each hole.

HOLE TO HOLE MASS FLOW MEASUREMENTS

The following three operating points have been measured in the hole to hole mass flow test rig:

Injection pressure Energizing time

I 130 MPa 3 ms

II 130 MPa 1.5 ms

III 60 MPa 3 ms Table 2. Hole to hole mass flow operating points.

Two different injection pressures and two different energizing times have been used in order to study the influence of the operating conditions on the results.

Figure 8 displays the relative mass flow per stroke of each hole for the three operating points. As well as in the relative area defined in the previous section, iIt has been worked out dividing the mass flow per stroke from each single hole by the mean value obtained of the three holes.

Hole 1 Hole 2 Hole 30.96

0.98

1.00

1.02

1.04

Rea

live

hole

mas

s flo

w

130MPa - 3ms130MPa - 1.5ms60 MPa - 3ms

Figure 8. Relative hole mass flow of each hole.

As shown in the figure, the hole 1 has the highest mass flow and the hole 3 the lowest. This behavior is the same for the three operating conditions tested. When comparing these results with the results related to the internal geometry examined previously, it is possible to point out that the relative hole mass flow behaves a similar way as the relative area: the bigger outlet diameter, the higher mass flow. Therefore, hole 1 has the biggest outlet diameter and the highest mass flow. And, although holes 2 and 3 have the same outlet diameter, hole 2 has a bigger inlet diameter than hole 3, so the geometrical dimensions could explain the differences in mass flow through each orifice.

SPRAY MOMENTUM

Table 3 represents the measured points for spray momentum. The same operating conditions that in the previous case have been characterized with an additional measuring point (IV).

Injection pressure Energizing time

I 130 MPa 3 ms

II 130 MPa 1.5 ms

III 60 MPa 3 ms

IV 60 MPa 1.5 ms Table 3. Spray momentum operating points.

Figure 9 shows an example of the spray momentum flow for the point IV. The spray momentum signals have been integrated in order to compare with single hole mass results. The signal of spray momentum rate is similar to injection rate [4, 12].

0 1 2 3 4 5 6Time (ms)

-0.40

0.00

0.40

0.80

1.20

1.60

Spra

y m

omen

tum

flow

(N

) Hole 1Hole 2Hole 3

Figure 9. Spray momentum for each orifice. Lower graph: electrical signal to control the injector (without units).

With the spray momentum integrated values of each hole, the relative spray momentum has been calculated dividing each one by the average value of the three orifices. These results are depicted in Figure 10.

Hole 1 Hole 2 Hole 30.94

0.96

0.98

1.00

1.02

1.04

Rea

live

spra

y m

omen

tum

130MPa - 3ms130MPa - 1.5ms60MPa - 3ms60MPa - 1.5ms

Figure 10. Relative spray momentum of each hole.

The agreement of these results with the hole to hole mass flow results (Fig. 8) is very high in behavior and in magnitudes.

MACROSCOPIC SPRAY VISUALIZATION

Table 4 shows the operating points characterized in the nitrogen test rig. The same injection pressures and two different back pressures have been used, since it is well know that chamber density affects significantly the spray behavior [3, 6, 16, 17, 20]. The energizing time was set to 1.5 ms in all cases.

Injection pressure Back Pressure

I 130 MPa 2 MPa

II 130 MPa 4 MPa

III 60 MPa 2 MPa

IV 60 MPa 4 MPa Table 3. Spray visualization operating points.

In Figure 11 and Figure 12 the results of spray penetration and spray angle for the 60-2 MPa point are depicted for the three holes.

0 0.2 0.4 0.6 0.8 1Time (ms)

0

10

20

30

40

50

Spra

y pe

netra

tion

(mm

)

Hole 1Hole 2Hole 3

Pinj = 60 MPaPback = 20 MPa

Figure 11. Spray penetration versus time

Higher penetration corresponding to a lower spreading angle is consistent with conservation of spray momentum [3, 6, 16, 20]. It can be seen, that, for example, hole 3 shows the highest spray cone angle and the lowest penetration. Because of this, and, in order to compare the results obtained with results of momentum and mass, penetrations values should be corrected to eliminate the effect of the spray angle variations. To account for such variations on the spray cone angle the spray tip correlation shown by equation (1) is used. It is widely demonstrated that this equation govern the spray tip penetration behavior with a high degree of accuracy [3, 16, 17, 20]

21414121

2////

p tMtankS ⋅ρ⋅⋅θ

⋅= −− & (1)

where S is the penetration in function of time, θ is the spray cone angle, ρ is the air density, t is the time, M& is the momentum flux and finally kp is a constant value.

0 0.2 0.4 0.6 0.8 1Time (ms)

14

16

18

20

22

24

Spra

y an

gle

(º)

Hole 1Hole 2Hole 3

Pinj = 60 MPaPback = 20 MPa

Figure 12. Spray cone angle versus time

The terms in equation (1) can be regrouped to obtain the corrected spray penetration as shown by equation (2).

2/14/14/1

2tan tMkS p ⋅⋅⋅=⋅ −ρθ & (2)

Hole 1 Hole 2 Hole 30.97

0.98

0.99

1.00

1.01

1.02

Rel

ativ

e co

rrec

ted

spra

y pe

netra

tion

130MPa-4MPa130MPa-2MPa60MPa - 4MPa60MPa - 2MPa

Figure 13. Relative corrected spray penetration of each hole

Corrected penetration of each hole was obtained from the spray penetration and angle results. A relative corrected spray penetration can be calculated dividing the corrected spray penetration of each hole by the average of all three. Taking account equation (2), the relative corrected spray penetration should be the same as the relative spray momentum powered by ¼, as shown in Figure 13. The results obtained agree qualitatively and quantitatively with results of momentum flux and mass flow examined previously.

COMPARISON AND ANALYSIS OF THE RESULTS

Figure 14 summarizes the results examined previously. In this figure, the inlet and outlet relative area (in discontinuous line) and the results of single hole mass flow, spray momentum flux and corrected spray penetration (in continuous line) are compared.

As can be observed, all the relative results show the same tendency: the relatives values decrease from hole 1 to hole 3. This indicates the ability of the four methodologies to study the hole to hole dispersion of real multi-hole nozzles.

Hole 1 Hole 2 Hole 30.96

0.98

1.00

1.02

1.04

Rel

ativ

e re

sults

Inlet areaOutlet areaHole mass flowSpray momentumCorrec. penetration

Figure 14. Comparison of the different measurements techniques.

The higher agreement is given between mass flow and spray momentum. This result was expected because they are proportional. In fact, spray momentum flow is conceptually the mass flow multiplied by velocity [4, 12]. However, the relative corrected spray penetration has lower values than the relative mass and spray momentum. This is because, as stated by equation (2), penetration depends on momentum flow to the power of 1/4.

CONCLUSIONS

In order to study differences between holes, four capabilities have been tested. The techniques compared in this paper have been: internal geometry determination, hole to hole mass flow measurement, spray momentum flux and macroscopic spray visualization.

As an example, the four methodologies have been used in order to study the hole to hole variations in a micro-sac nozzle with three symmetric holes which have different internal geometry. In this case, therefore, only differences related to the nozzle manufacture process were expected.

The results obtained using the different methodologies have shown similar tendencies so it is possible to conclude that they are efficient tools to study hole to hole variations.

ACKNOWLEDGMENTS

The authors would like to thank José Enrique del Rey (*) for his collaboration in the experimental measurements.

(*) From CMT-Motores Térmicos. Universidad Politécnica de Valencia.

REFERENCES

1. Timoney, D. J., Smith W. J., 1995, “Correlation of Injection Rate Shapes with D.I. Diesel Exhaust Emissions,” SAE Paper No. 950214.

2. Ganippa, L.C., Andersson, S., Chomiak, J., Matsson A., 2003, “Combustion characteristics of diesel sprays from equivalent nozzles with sharp and rounded inlet geometries”, Combustion science and technology 175 (6), pp 1015-1032.

3. Payri F., Bermúdez V., Payri R., Salvador F.J. “The influence of cavitation on the internal flow and the Spray characteristics in diesel injection nozzles”. Fuel 2004, Vol 83, pp. 419-431.

4. Payri, R., García, J.M., Salvador, F.J., Gimeno J., “Using spray momentum flux measurements to understand the influence of Diesel nozzle geometry on spray characteristics”. Fuel, vol. 84, nº 5, pp. 553-563, 2005.

5. Koo, J. Y., Hong, S. T., Shakal, J. S., Goto, S., 1997, “Influence of Fuel Injector Nozzle Geometry on Internal and External Flow Characteristics,” SAE Paper No. 970354.

6. Payri, R., Molina, S., Salvador, F.J., Gimeno, J.”A study of the relation between nozzle geometry, internal flow and sprays characteristics in Diesel Fuel injection systems”. KSME International Journal, vol. 18, Nº 7, pp. 1222-1235, 2004.

7. Payri, R., Climent, H., Salvador, F.J., Favennec, A.G. “Diesel injection system modelling. Methodology and application for a first-generation common rail system”. Proc. Instn. Mech. Engrs. vol. 218, Part D: Automobile Engineering, pp. 81-91, 2004.

8. Benajes, J., Pastor, J., V., Payri, R., Plazas, A. H., 2004, “Analysis of the influence of diesel nozzle geometry in the injection rate characteristic,” Journal of Fluids Engineering, Vol 126, number 1, pp. 63-71.

9. Arcoumanis, C., Gavaises, M., French B., 1997, “Effect of Fuel Injection Processes on the Structure of Diesel Sprays,” SAE Paper No. 970799.

10. Payri R, Margot X, Salvador FJ. “A Numerical Study of the Influence of Diesel Nozzle Geometry on the

Inner Cavitating Flow”. SAE Paper 2002-01-215; 2002.

11. Macián V., Payri R., Margot X., Salvador F.J. “A CFD Analysis of the Influence of Diesel Nozzle Geometry on the inception of Cavitation”. Atomization and Sprays 2003, Vol. 13, pp. 579-604.

12. Desantes JM, Payri R, Salvador FJ, Gimeno J. “Measurements of spray momentum for the study of cavitation in diesel injection nozzles”. SAE Paper 2003-01-0703; 2003.

13. Payri, R., Guardiola, C., Salvador, F.J., Gimeno, J., “Critical cavitation number determination in Diesel injection nozzles”. Exp. Tech 2004; 28(3), pp. 49-52.

14. Macián, V., Bermúdez, V., Payri, R., Gimeno, J., “New technique for the determination of the internal geometry of Diesel nozzle with the use of the silicone methodology”. Exp. Tech 2003; 27(2), pp. 39-43.

15. Pastor, J.V., Arrègle, J., Palomares, A., “Diesel spray image segmentation with a likelihood ratio test”. Applied Optics, vol. 40, No. 17, pp. 2876-2885, 2001.

16. Arrègle, J., Pastor, J.V., Ruiz, S., “The influence of injection parameters on Diesel Spray characteristics”. SAE Paper 1999-01-0200, 1999.

17. Desantes, J.M., Payri, R., Salvador, F.J., Soare, V. “Study of the influence of geometrical and injection parameters on Diesel spray characteristics in isothermal conditions”. SAE Paper 2005-01-0913, 2005.

18. Stumpp, G., Ricco, M., “Common Rail – An attractive fuel injection system for passenger car DI diesel engines”, SAE paper 960870, 1996.

19. Flaig, U., Polach, W., Ziegler, G., “Common Rail System (CR-System) for passenger car DI diesel

engines; Experiences with applications for series production projects”, SAE paper 1999-01-0191, 1999.

20. Naber, J., Siebers, D.L., “Effects of gas density and vaporisation on penetration and dispersion of Diesel sprays”. SAE Paper 960034, 1996.

CONTACT

Dr. Raul Payri, [email protected]

DEFINITIONS, ACRONYMS, ABBREVIATIONS

Di Inlet diameter of the nozzles holes.

Do Outlet diameter of the nozzle holes.

R Inlet rounding radius of the nozzle holes.

k-factor Convergence or divergence factor.

Kp Constant in penetration equation.

M& Momentum Flux.

ρ Air density.

θ Spray cone angle.

t time.


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