Abstract

We present a method for the trajectory and the velocity measurement of a particle in spray by digital holography. Based on multiple exposure digital in-line holography, a sequence of digital holograms of a dynamic spray particle field at different times are recorded with a CW laser and a high-speed CCD. The time evolution of the serial positions of particles, i.e., the motion trajectories of the particles, is obtained by numerically reconstructing the synthetic hologram of a sequence of digital holograms. The center coordinate (x,y) of each particle image can be extracted using a Hough transform and subpixel precision computing, and the velocity of an individual particle can also be obtained, which is then applied to measuring the velocity of diesel spray and alcohol spray. The research shows that the method presented in this paper for measuring spray field is feasible.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Denis, C. Fournier, and T. Fournel. “Direct extraction of the mean particle size from a digital hologram,” Appl. Opt. 45, 944-952 (2006).
    [CrossRef] [PubMed]
  2. L. J. Cao, G. Pen, J. de Jong, S. Woodward, and H. Meng, “Hybrid digital holographic imaging system for three-dimensional dense particle field measurement,” Appl. Opt. 47, 4501-4507(2008).
    [CrossRef] [PubMed]
  3. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893-3901 (2006).
    [CrossRef] [PubMed]
  4. S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
    [CrossRef]
  5. M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
    [CrossRef] [PubMed]
  6. K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61-R72 (2002).
    [CrossRef]
  7. Y. Yang and B. Kang, “Measurements of the characteristics of spray droplets using in-line digital particle holography,” J. Mech. Sci. Technol. 23, 1670-1679 (2009).
    [CrossRef]
  8. Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697-7708 (2005).
    [CrossRef] [PubMed]
  9. M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
    [CrossRef]
  10. G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43, 1039-1055 (2005).
    [CrossRef]
  11. S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
    [CrossRef]
  12. Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
    [CrossRef]
  13. S. Kim and S. J. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623-631 (2008).
    [CrossRef]
  14. N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
    [CrossRef]
  15. W. Xu, M. H. Jericho, and H. J. Kreuzer. “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28, 164-166 (2003).
    [CrossRef] [PubMed]
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  17. Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
    [CrossRef]
  18. Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.
  19. United Kingdom Accreditation Service, “The expression of uncertainty and confidence in measurement, Edition 2, M 3003 (United Kingdom Accreditation Service, 2007), pp. 16-36.
  20. H. Royer, “ An application of high-speed microholgraphy: the metrology of fogs,” Nouv. Rev. Opt. 5, 87-93 (1974).
    [CrossRef]

2009 (2)

Y. Yang and B. Kang, “Measurements of the characteristics of spray droplets using in-line digital particle holography,” J. Mech. Sci. Technol. 23, 1670-1679 (2009).
[CrossRef]

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

2008 (3)

S. Kim and S. J. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623-631 (2008).
[CrossRef]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

L. J. Cao, G. Pen, J. de Jong, S. Woodward, and H. Meng, “Hybrid digital holographic imaging system for three-dimensional dense particle field measurement,” Appl. Opt. 47, 4501-4507(2008).
[CrossRef] [PubMed]

2006 (4)

L. Denis, C. Fournier, and T. Fournel. “Direct extraction of the mean particle size from a digital hologram,” Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893-3901 (2006).
[CrossRef] [PubMed]

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

2005 (3)

S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Y. Pu and H. Meng, “Four-dimensional dynamic flow measurement by holographic particle image velocimetry,” Appl. Opt. 44, 7697-7708 (2005).
[CrossRef] [PubMed]

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43, 1039-1055 (2005).
[CrossRef]

2004 (2)

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
[CrossRef] [PubMed]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

2003 (2)

Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.

W. Xu, M. H. Jericho, and H. J. Kreuzer. “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett. 28, 164-166 (2003).
[CrossRef] [PubMed]

2002 (1)

K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

1974 (1)

H. Royer, “ An application of high-speed microholgraphy: the metrology of fogs,” Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

Allano, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
[CrossRef] [PubMed]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

Andreas, S.

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Cao, L. J.

Coëtmellec, S.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
[CrossRef] [PubMed]

de Jong, J.

Denis, L.

Fournel, T.

Fournier, C.

Gao, Y.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Ge, B.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Godard, G.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hinsch, K. D.

K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

Ito, T.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Jericho, M. H.

Jurgen, K.

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Kanamori, H.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Kang, B.

Y. Yang and B. Kang, “Measurements of the characteristics of spray droplets using in-line digital particle holography,” J. Mech. Sci. Technol. 23, 1670-1679 (2009).
[CrossRef]

Katz, J.

Kim, S.

S. Kim and S. J. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623-631 (2008).
[CrossRef]

Kreuzer, H. J.

Kunugi, T.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Lebrum, D.

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

Lebrun, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
[CrossRef] [PubMed]

Lee, S. J.

S. Kim and S. J. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623-631 (2008).
[CrossRef]

Liu, C.

Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.

Lü, Q.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Ma, Z.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Malek, M.

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270-2279 (2004).
[CrossRef] [PubMed]

Malkiel, E.

Meng, H.

Özkul, C.

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

Paranthoën, P.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

Pen, G.

Pu, S. L.

S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Pu, Y.

Rouland, B. P.

S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Royer, H.

H. Royer, “ An application of high-speed microholgraphy: the metrology of fogs,” Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

Salah, N.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

Satake, S.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Sato, K.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Service, United Kingdom Accreditation

United Kingdom Accreditation Service, “The expression of uncertainty and confidence in measurement, Edition 2, M 3003 (United Kingdom Accreditation Service, 2007), pp. 16-36.

Shen, G.

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43, 1039-1055 (2005).
[CrossRef]

Sheng, J.

Taniguchi, J.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

Wei, R.

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43, 1039-1055 (2005).
[CrossRef]

Woodward, S.

Xi, D.

Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.

Xu, W.

Yang, Y.

Y. Yang and B. Kang, “Measurements of the characteristics of spray droplets using in-line digital particle holography,” J. Mech. Sci. Technol. 23, 1670-1679 (2009).
[CrossRef]

Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.

Zhang, Y.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Zhao, C.

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Appl. Opt. (4)

Chin. J. Laser (1)

Q. Lü, Y. Gao, B. Ge, Z. Ma, C. Zhao, and Y. Zhang, “Digital holographic particle sizing with Hough transform,” Chin. J. Laser 36, 940-944 (2009), in Chinese.
[CrossRef]

Exp. Fluids (2)

S. Kim and S. J. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623-631 (2008).
[CrossRef]

S. L. Pu, D. Allano, and B. P. Rouland, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1-9 (2005).
[CrossRef]

J. Mech. Sci. Technol. (1)

Y. Yang and B. Kang, “Measurements of the characteristics of spray droplets using in-line digital particle holography,” J. Mech. Sci. Technol. 23, 1670-1679 (2009).
[CrossRef]

Meas. Sci. Technol. (4)

K. D. Hinsch, “Holographic particle image velocimetry,” Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

M. Malek, D. Allano, S. Coëtmellec, C. Özkul, and D. Lebrum, “Digital in-line holography for three-dimensional-two-components particle tracking velocimetry,” Meas. Sci. Technol. 15, 699-705 (2004).
[CrossRef]

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurement of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647-1651 (2006).
[CrossRef]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, and S. Coëtmellec, “Application of multiple exposure digital in-line holography to particle tracking in a Bénard-von Kármán vortex flow,” Meas. Sci. Technol. 19, 074001(2008).
[CrossRef]

Motorcycle Technology (1)

Y. Yang, C. Liu, and D. Xi, “FAI technique applied to 4-stroke motorcycles,” Motorcycle Technology 10, 25-28(2003), in Chinese.

Nouv. Rev. Opt. (1)

H. Royer, “ An application of high-speed microholgraphy: the metrology of fogs,” Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

Opt. Eng. (1)

Y. Zhang, G. Shen, S. Andreas, and K. Jurgen, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Lasers Eng. 43, 1039-1055 (2005).
[CrossRef]

Opt. Lett. (1)

Other (2)

United Kingdom Accreditation Service, “The expression of uncertainty and confidence in measurement, Edition 2, M 3003 (United Kingdom Accreditation Service, 2007), pp. 16-36.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Coordinate system.

Fig. 2
Fig. 2

Schematic experimental setup.

Fig. 3
Fig. 3

Photograph of a FAI system.

Fig. 4
Fig. 4

Diagram of the recording point of spray.

Fig. 5
Fig. 5

Holograms and reconstructions of diesel spray: (a) single hologram; (b) sum of 10 difference holograms from 20 sequence holograms; (c) and (d) reconstructed images at z = 320 mm and 350 mm , respectively.

Fig. 6
Fig. 6

Results of diesel spray: (a) sum of three difference holograms from six sequence holograms, (b) reconstructed trajectories at z = 320 mm , (c) trajectory of the particles, (d) correlation between droplet diameter and droplet velocity.

Fig. 7
Fig. 7

Results of alcohol spray: (a) sum of three difference holograms from six sequence holograms, (b) reconstructed trajectories at z = 320 mm , (c) and (d) trajectories of particles.

Fig. 8
Fig. 8

Variation of the extracted particle numbers ( E p ) versus particle number density ( n s ).

Fig. 9
Fig. 9

Velocity measured for different particle number densities.

Fig. 10
Fig. 10

Number of particle trajectories at different positions with the pulse width of the injector for diesel spray and alcohol spray.

Tables (2)

Tables Icon

Table 1 Average Velocities of Different Trajectories of Diesel Spray

Tables Icon

Table 2 Average Velocities of Different Trajectories of Alcohol Spray in Fig. 7c

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

u ( x , y ) = [ 1 o ( x , y ) ] * h z ( x , y ) ,
o ( x , y ) = circ ( x 2 + y 2 d / 2 ) = { 1 x 2 + y 2 d / 2 0 x 2 + y 2 > d / 2 ,
I ( x , y ) = | [ 1 o ( x , y ) ] * h z ( x , y ) | 2 = 1 o ( x , y ) * h z ( x , y ) o ( x , y ) * h z * ( x , y ) + | o ( x , y ) * h z ( x , y ) | 2 ,
I ( x , y ) = 1 o ( x , y ) * h z ( x , y ) o ( x , y ) * h z * ( x , y ) .
u ( x , y ) = t ( x , y ) * h z ( x , y ) = 1 o ( x , y ) o ( x , y ) * h 2 z ( x , y ) ,
I ( x , y ) = 1 o ( x , y ) o ( x , y ) * [ h 2 z ( x , y ) + h 2 z * ( x , y ) ] .
I i ( x , y ; t i ) = 1 o i ( x , y ) * h z ( x , y ) o i ( x , y ) * h z * ( x , y ) ,
Δ I ( x , y ) = [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * h z ( x , y ) + [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * h z * ( x , y ) .
I C ( x , y ) = i = 1 n / 2 { [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * h z ( x , y ) + [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * h z * ( x , y ) } ,
u C ( x , y ) = 1 i = 1 n / 2 [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] i = 1 n / 2 [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * h 2 z ( x , y ) ,
I C ( x , y ) = 1 i = 1 n / 2 [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] i = 1 n / 2 [ o 2 i ( x , y ) o 2 i 1 ( x , y ) ] * [ h 2 z ( x , y ) + h 2 z * ( x , y ) ] .
v = Δ s Δ t ,

Metrics