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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 7 — Apr. 8, 2002
  • pp: 309–323
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Planar Laser-Induced Fluorescence fuel concentration measurements in isothermal Diesel sprays

José V. Pastor, José J. López, J. Enrique Juliá, and Jesús V. Benajes  »View Author Affiliations


Optics Express, Vol. 10, Issue 7, pp. 309-323 (2002)
http://dx.doi.org/10.1364/OE.10.000309


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Abstract

This paper presents a complete methodology to perform fuel concentration measurements of Diesel sprays in isothermal conditions using the Planar Laser-Induced Fluorescence (PLIF) technique. The natural fluorescence of a commercial Diesel fuel is used with an excitation wavelength of 355 nm. The correction and calibration procedures to perform accurate measurements are studied. These procedures include the study of the fluorescence characteristics of the fuel as well as the correction of the laser sheet non–homogeneities and the losses due to Mie scattering, absorption and autoabsorption. The results obtained are compared with theoretical models and other experimental techniques.

© 2002 Optical Society of America

1. Introduction

Several researchers have performed a large number of experiments to improve the understanding of the processes and to isolate the parameters controlling the spray behavior [1–6

1. P. Schihl, W. Bryzik, and A. Atreya, “Analysis of current spray penetration models and proposal of a phenomenological cone penetration model,” SAE Paper 960773 (Society of Automotive Engineers, Warrendale, Pa., 1996).

]. These experiments have tried to provide either empirical correlations [1–5

1. P. Schihl, W. Bryzik, and A. Atreya, “Analysis of current spray penetration models and proposal of a phenomenological cone penetration model,” SAE Paper 960773 (Society of Automotive Engineers, Warrendale, Pa., 1996).

] or simple models [1

1. P. Schihl, W. Bryzik, and A. Atreya, “Analysis of current spray penetration models and proposal of a phenomenological cone penetration model,” SAE Paper 960773 (Society of Automotive Engineers, Warrendale, Pa., 1996).

,6

6. J. V. Pastor, E. Encabo, and S. Ruiz, “New modelling approach for fast on-line calculations in sprays,” SAE Paper 2000-01-0287 (Society of Automotive Engineers, Warrendale, Pa., 2000).

] to predict the spray behavior under different situations on the basis of the experimental evidence.

All these studies consider spray characterization from two different approaches: microscopic measurements to determine internal spray features such as droplet velocity and size distributions, and macroscopic measurements are used for the determination of geometric features of the spray such as spray tip penetration, cone angle, air entrained by the spray, etc.

PLIF is an imaging technique that allows measurements from both approaches. On the one hand it is possible to measure fuel concentrations and relative Sauter diameter distributions (in that case combining PLIF images with Mie scattering ones) [7

7. M.C. Jermy and D.A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000). [CrossRef]

]. On the other, it is possible to determine the geometric characteristics of the spray, as in other imaging optical techniques such as shadowgraphy, but with a higher signal to noise ratio.

Further advantages of this technique are the high intensity of the fluorescence radiation, its proportionality to the concentration of the substance under study and its red shift. All these facts make PLIF a widespread technique in engine research work.

Fluorescence techniques have been applied to different topics within the engine research field. One application has been the measurement of the presence and concentration of some reactants during combustion [8–10

8. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, Amsterdam, 1996).

]. A second application, with similar objectives as in the present work but under different experimental conditions, is the measurement of fuel concentrations in sprays [11–14

11. C. Nan Yeh, T. Kamimoto, H. Kosaka, and S. Kobori, “Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,” SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).

].

The purpose of this study is the development of an automated system to measure fuel concentrations in isothermal Diesel sprays using multicomponent commercial Diesel fuel, considering all calibration and correction procedures necessary to get accurate measurements.

The forthcoming sections provide a short overview of PLIF basics; a description of the experimental setup used in the experiments; a detailed study of the calibration and correction procedures performed to quantify fuel concentration in isothermal conditions; and some sample results including comparison with predictions given either by theoretical models or other experimental techniques.

2. PLIF basics

The fluorescence phenomenon can be briefly explained as the reemission of part of the incident radiation in a longer wavelength when some substances are illuminated. From Einstein equations for the two level model and the Beer – Lambert law it is possible to relate the measured fluorescence intensity with the density of the fluorescent substance. This connection, assuming non–saturated fluorescence conditions, is summarized in the following expression [8

8. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, Amsterdam, 1996).

,11

11. C. Nan Yeh, T. Kamimoto, H. Kosaka, and S. Kobori, “Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,” SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).

,13

13. H. Zhao and N. Ladommatos, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998). [CrossRef]

]:

IF=KI0(1eαρL)
(1)

where IF is the fluorescence intensity radiation (ph s-1 m-2), I0 the laser irradiance (ph s-1 m-2), ρ the fluorescent substance density (kg m-3), α the absorption coefficient of the fluorescent substance (m2 kg-1), L the optical path (m), and K a proportionality constant.

Due to its high energy, short duration and the possibility of working with light sheets, pulsed lasers are commonly used as a light source together with intensified CCD cameras (ICCD) to record images of the fluorescence intensity field in the so called Planar Laser Induced Fluorescence (PLIF) technique. This implies that both IF and I0 will be functions of the space coordinates (x,y).

SF(x,y)=Koptical system(x,y)ϕ(x,y)Kautoabs(x,y)I0(x,y)(1eαρL)
(2)

where SF is the digital signal of the fluorescence radiation as registered by the ICCD (once substracted the ICCD dark noise and background reflections) or, equivalently, the product of IF (x,y) and Koptical system (x,y). The physical meaning of the different parameters of this equation and their dependences are discussed below:

Koptical system(x,y) and ϕ(x,y):

The measured fluorescence depends on the efficiency of the optical system used. This includes the ICCD, objective and the illumination and visualization windows. This efficiency depends on (x,y) because of the response of each ICCD pixel is not constant and window contamination can occur during the experiments.

The ϕ(x,y) parameter is the quantum yield of the fluorescent substance given by

ϕ(x,y)=B12(x,y)A21(x,y)A21(x,y)+Q21(x,y)
(3)

where the A21 and B12 are the spontaneous emission and stimulated absorption coefficients from the Einstein equations. Working with a fluorescent liquid in a calibration cell these parameters are constant. However, in the case of a two-phase spray, some droplets could act as high-quality factor optical cavities, changing the A21 parameter and modifying the fluorescent spectra with the appearance of morphology-dependent resonances (MDRs) [17

17. M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Enhanced fluorescence yields through cavity quantum-electrodinamics effects in micro droplets,” J. Opt. Soc. Am. B 11, 1297–1924 (1994). [CrossRef]

,18

18. G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplets characterization: application of morphology dependent resonances,” Prog. Energy Combust. Sci. 22, 163–188 (1996). [CrossRef]

]. This effect is known to depend on droplet diameter and dopant concentration and some past papers [11

11. C. Nan Yeh, T. Kamimoto, H. Kosaka, and S. Kobori, “Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,” SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).

,14

14. A.A. Rotunno, M. Winter, G. M. Dobbs, and L. A. Melton “Direct Calibration Procedures for Exciplex-Based Vapor/Liquid Visualization of Fuel Sprays,” Combust. Sci. and Tech. 71, 247–261 (1990). [CrossRef]

] have shown that MDRs do not appear in the working conditions of this experiment, at least at the working fluorescence wavelength (400 nm).

The Q21 parameter is the quenching coefficient. The quenching effect is defined as the loss of fluorescence intensity due to the part of the excited molecules of the dopant that are de-excited by collision with other molecules. It is absolutely negligible in liquid phase and isothermal conditions [12

12. J. Senda, T. Kanda, M. Kobayashi, and H. Fujimoto, “Quantitative analysis of Fuel Vapor Concentration in Diesel spray by Exciplex Fluorescence Method,” SAE Paper 970796 (Society of Automotive Engineers, Warrendale, Pa., 1997).

].

Kautoabs (x,y):

The effect of the autoabsorption is caused by the fraction of the spray placed between the laser sheet and the ICCD, which absorbs part of the fluorescence radiation due to the cross talk between the absorption and emission spectra of the dopant.

I0(x,y):

Finally, for the particular case of αρL being sensitively lower than unity (it is our case, as will be seen later), then Eq. (2) can be approximated as:

SF(x,y)=Koptical system(x,y)ϕ(x,y)Kautoabs(x,y)I0(x,y)(αρL)=KF(x,y)ρ(x,y)
(4)

3. Experimental setup

3.1. High-Density Injection Rig

The experiments have been performed in a constant volume vessel filled in with SF6. It is a closed-loop facility which simulates the in-cylinder air density existing in the real engine at injection start. Due to its high molecular weight, SF6 allows to perform experiments at a density of 30 kg/m3 with a relatively low pressure of less than 0.5 MPa at room temperature. In addition, SF6 is an inert gas, avoiding corrosive effects on the rig and its viscosity and optical properties are very similar to those of the air.

A Roots compressor ensures a controlled gas velocity inside the test rig of about 4 m/s, which was found to be low enough to assume that the fuel is injected in stagnant conditions but high enough to scavenge the test chamber during the time between two consecutive injections. Upstream of the injection chamber, a flow straightener of the honeycomb type has been used to force a coaxial velocity of gas and fuel and to avoid recirculation zones in the chamber. The gas temperature is kept constant by means of a heat exchanger placed at the exit of the compressor and controlled by a temperature sensor and a PID (Proportional Integral Derivative) system.

A common-rail injection system was used to generate the Diesel sprays. The nozzle used was of the DLLA mini-sac type by Bosch with a wall thickness of 1 mm but only 1 hole in the same position as one of the orifices in the standard 5-hole nozzle. Hole diameter is 0.11 mm, and injection pressure ranged between 30 and 110 MPa. Commercial Diesel (ELF-CEC RF73A 93) has been used as fuel, using the natural fluorescence of some of its components for the measurements.

The injection chamber has three perpendicular optical accesses for visualization: two quartz windows for illumination (laser sheet entry and exit respectively) and one Polymethyl methacrylate (PMMA) window for visualization. Details about the high density injection rig are given in [2

2. J. Arrègle, J. V. Pastor, and S. Ruiz, “The influence of injection parameters on Diesel spray characteristics,” SAE Paper 1999-01-0200 (Society of Automotive Engineers, Warrendale, Pa., 1999).

,3

3. F. Payri, J. M. Desantes, and J. Arrègle, “Characterization of D.I. Diesel sprays in high density conditions,” SAE Paper 960774 (Society of Automotive Engineers, Warrendale, Pa., 1996).

].

3.2. Image Acquisition System

The light source used is a Nd:YAG pulsed laser (Continuum SureLite II) with maximum pulse energy of 102 mJ at the 355nm (working wavelength), and a pulse duration of 7 ns. The beam is steered to the rig with a 7 mirror articulated arm. The laser sheet is formed with a three fused silica lenses head: two spherical lenses for focusing (f1=-25 mm, f2=50 mm) and a cylindrical one for making the sheet (f3=-25mm). In this work a laser sheet of 0.5 mm thickness focused at 1 m from the light sheet head was used. The thickness was measured using the knife method [19

19. A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986).

].

The images have been taken with a 16-bit ICCD camera (Dynamight LaVision) 512×512 pixels with a 60 mm focal length objective (Nikkor). A stereoscope (LaVision) with two interference filters (400 nm, 10 nm FWHM for LIF; 532 nm, 2 nm FWHM for Mie scattering) is used to take simultaneously the Mie and PLIF images. All the experimental equipment has been synchronized with a purpose made electronic system, using the injector trigger signal as reference signal to take the image sequences. Fig. 1 shows a sketch of the experimental setup.

Fig. 1. Experimental setup sketch. 1-Laser source, 2-lenses head, 3-laser sheet, 4-injector, 5-ICCD, 6-camera lens, 7-stereoscope

4. System calibration

To perform fuel concentrations measurements using equation (4) it is necessary to calibrate the measuring system and to determine some relevant parameters of the fluorescent substance. These parameters will influence the selection of the proper experimental settings.

4.1. Fluorescence emission spectra and decay time

The fluorescence emission spectra of the blend, in this case commercial Diesel (ELF-CEC RF73A 93), needs to be known in order to choose the appropriate optical filters for the camera. Fig. 2a depicts the emission fluorescence spectrum of the fuel used in this work. Since maximum fluorescence intensity has been obtained at 396 nm, an interference filter centered at 400 nm and with a FWHM of 10 nm. Moreover, the Mie scattering information at 532 nm is avoided.

The characteristic decay time is defined as the time necessary for the 86.5 % of the fluorescence intensity to be emitted. To estimate this decay time, several laser sheet trace images in a calibration cell have been taken with the ICCD camera at minimum gate (5 ns). Delaying the ICCD trigger from the laser trigger has allowed calibration of the time response of the fluorescence of the fuel as shown in Fig. 2b. From this plot, the decay time of the fuel used in the experiments has been estimated in 80 ns at λ=400 nm. Thus, for all the experiments, the camera gate was fixed at 200 ns.

Fig. 2. Fluorescence a) emission spectra at excitation wavelength of 355 nm, and b) time response of the fuel ELF-CEC RF73A 93

4.2. Absorption and autoabsorption coefficients of the fuel

I(x)=I0exp[0xρoptical(x)dx]
(5)

where I(x) is the transmitted irradiance at a distance x and I0 is the incident irradiance.

If the optical density is due to absorption, then it is possible to rewrite Eq. (5) as:

I(x)=I0exp(αρL)
(6)

where α is the absorption coefficient, ρ is the density of the dopant and L is the optical path length. In such way, the absorption coefficient at 355 nm wavelength for this fuel was found to be 2.0 10-2 cm2/mg. According to e.g. [21

21. R. Bazile and D. Stepowski, “Measurements of vaporized and liquid fuel concentration fields in a burning spray jet of acetone using planar laser induced fluorescence,” Exp. in Fluids 20, 1–9 (1995). [CrossRef]

], it can be admitted that for α ρ d / 3 ≪ 1, being d the droplet diameter, then the fluorescence signal scales to droplet volume. In our case, for typical droplets diameter of around 20 microns, α ρ d / 3 ~ 0.011 is obtained. More detailed calculations for single droplets taking into account light paths inside droplets [7

7. M.C. Jermy and D.A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000). [CrossRef]

, 22

22. R. Domann and Y. Hardalupas, “Evaluation of planar Doppler Sizing (PDS) technique,” Eight International Conference on Liquid Atomization and Spray Systems, Pasadena, CA, (2000).

] indicate that the fluorescence intensity is proportional to droplet diameter to the power n where n is in our case above 2.85 (estimated from the data provided in [22

22. R. Domann and Y. Hardalupas, “Evaluation of planar Doppler Sizing (PDS) technique,” Eight International Conference on Liquid Atomization and Spray Systems, Pasadena, CA, (2000).

]) for the vast majority of droplets in the Diesel spray, although n will be lower for the largest droplets which will be present mainly near the nozzle orifice. This is obviously a source of error in the method proposed here, but it cannot be avoided working with real fuels.

Another important fluorescence parameter is the autoabsorption coefficient Kautoabs. To determine this value, different fluorescence pictures with different quantities of dopant between the laser sheet and the ICCD have been taken in a calibration cell. Applying the Lambert – Beer law, this coefficient was found to be 5.3 10-4 cm2/mg for the fuel used.

4.3. Fluorescence intensity calibration

ρE=ρfuelVFVT
(7)

Thus, the fluorescence intensity is proportional to the equivalent density, which depends on the fuel volume fraction. As previously commented, with L=0.1mm, α=2.0 10-2 cm2/mg, and the expected values of ρE, the linear approximation made in Eq. (4) is perfectly valid and KF(x,y) is the proportionality constant between the measured digital level SF(x,y) and the equivalent density ρE(x,y).

There are two possibilities to measure KF. The first method is an a priori calibration using a calibration cell, which has been used in this work. In this way, it is necessary to use the same laser sheet as in the spray (i.e. the same I0(x,y)), to illuminate a liquid with a known dopant density and to take the fluorescence images with the same optical system. In the case of commercial Diesel, due to its high absorption coefficient as well as the natural fluorescence of the quartz glass walls of the cell, it is not possible to get a good image with pure Diesel. A possible solution is to take images of solutions with different densities of pure Diesel in a solvent with similar polarity (hexadecane, 98% purity), in order not to change the A21 coefficient [23

23. I.B. Berlman, Handbook of fluorescence spectra of aromatic molecules (Academic Press, London, 1971).

]. Then, using Eq. (2) it is possible to get the correct value of the fluorescence intensity signal for the pure Diesel.

Fig. 3 shows the calibration function measured for the Diesel (ELF-CEC RF73A 93). The blue points are the measured fluorescence intensity (before background subtraction) while the solid lines correspond to two different fits of the experimental data: the theoretical exponential curve to get the pure Diesel fluorescence value and its linear regression.

The second possible method is the in-situ measurement of the droplets fluorescence [14

14. A.A. Rotunno, M. Winter, G. M. Dobbs, and L. A. Melton “Direct Calibration Procedures for Exciplex-Based Vapor/Liquid Visualization of Fuel Sprays,” Combust. Sci. and Tech. 71, 247–261 (1990). [CrossRef]

], visualizing the fluorescence of individual droplets from the spray. For this purpose, it is necessary to use a high optical magnification with a long distance microscope objective [24

24. H. Sjöberg, G. Manneberg, and A. Cronhjort, “Long-working-distance microscope used for diesel injection spray imaging,” Opt. Eng. 35, 3591–3596 (1996). [CrossRef]

] or a telephoto objective using close-up lenses. Therefore, it is possible to do the fluorescence – density calibration knowing the optical magnification.

Fig. 3. Fluorescence intensity calibration

5. PLIF correction procedures

The KF value is not constant along the fluorescence image since both I0 and Koptical system depend on (x,y). When their space dependence is due only to the optical setup, a correction matrix CM(x,y), identical for all the images of a given experiment, can be first estimated and then applied to all the images. However, if the space dependence is due to the spray nature, then a different matrix, here labeled “correction factor CF(x,y)” to facilitate understanding, must be calculated for every image separately. The estimation of these two kinds of correction are treated in the following paragraphs.

5.1. Optical system correction procedures

A. Laser sheet characterization

As a consequence of the pseudo-gaussian profile of the laser beam and the geometrical characteristics (aperture angle and thickness) of the laser sheet, the irradiance I0 arriving to each portion of the spray (pixel) depends on its position on the sheet. To correct these non-homogeneities, an image of the laser sheet trace in a calibration cell with low dopant concentration was obtained (see Fig. 4a). In this image three sources of losses of I0 appear: absorption of the fuel, laser profile and sheet aperture.

SF(x,y)=SF(x,y)exp(αρL)
(8)

where SF(x,y) is the original image trace, ρ is the dopant constant, and L is the path length of the ray inside the calibration cell before arriving to pixel (x,y).

Once the absorption losses are corrected, the image is the trace of the laser sheet, so it is possible to correct both laser profile and aperture. To correct the laser sheet aperture it is necessary to find the waist parameter [19

19. A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986).

], w(y), of the profile in every pixel row. Then, assuming energy conservation, it is possible to demonstrate that the correction factor of row y is given by w(y)/w(y-1). To correct the laser profile it is sufficient to find the maximum intensity in every row of the matrix image, SF(y)max , and then adapt all the pixels of the row to this maximum value.

SF(x,y)=(SF(y))maxw(y)w(y1)
(9)

In this way, it will be possible to get a compensation matrix for the losses of I0 due to laser sheet non-homogeneities by digital image processing. This matrixes be given by,

CMlaser sheet(x,y)=((SF(y)exp(αρL)maxSF(x,y)w(y)w(y1))
(10)

Hence, using a calibration cell with a liquid dopant of known density it is possible to get the matrix correction of the laser sheet non–homogeneities. To get the laser sheet trace images it is very important to reproduce the same experimental conditions that will be used in the spray experiments in order to use the same laser sheet characteristics.

Note that, with this procedure, the non-uniform response of the ICCD pixels is also corrected since it is taken as a part of the laser sheet non-homogeneity. This is possible because that response is a characteristic of the ICCD, i.e. constant in all the experiments.

The images in Fig. 4 are an example of laser sheet correction. The dopant used was commercial Diesel (ELF-CEC RF73A 93) 4 mg/cm3 and the solvent Hexadecane (98% purity). The images shown are originally 16 bit gray-level but are displayed in false color. The laser sheet enters into the calibration cell by the upper part of Fig. 4.a).

Fig. 4. a) Original and b) corrected laser sheet trace. The sheet enters in the y-axis direction

b) Laser pulse energy fluctuations

The Nd:YAG laser systems have shot to shot energy fluctuations due to the intensity fluctuations of the lamps used as excitation sources. These energy fluctuations affect directly the I0 value. To make shot-to-shot absolute fuel concentrations measurements it is necessary to use an on–line energy control system [11

11. C. Nan Yeh, T. Kamimoto, H. Kosaka, and S. Kobori, “Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,” SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).

].

An alternative method is working with average images, knowing the minimum number of laser shots to avoid the fluctuation problems. To calculate this minimum number of shots, laser sheet trace images have been taken. The average intensity of these single images has been measured, as well as the average intensity of averaged images using a increasing number of individual images. The results plotted at Fig. 5 show that maximum fluctuations are around 10% of the average intensity, and that the minimum number of shots to avoid fluctuations problems is around 80. Note that concentration measurements taken from single shot images will have a maximum error of 10% due to this problem.

Fig. 5. Laser pulse energy fluctuations

Additional errors could occur using this method if the nozzle exit diameter (e) is smaller than the sheet thickness (t). In that case, it is necessary to correct the fluorescence intensity measured from the spray when the spray width Sw(y) is smaller than the laser sheet thickness. This correction factor, CFsheetthickness(x,y) depends on y and is given by the ratio,

CFsheetthickness(x,y)=tSw(y)whileSw(y)<t
(11)

5.2. Spray correction procedures

The actual irradiation arriving to a given portion of the spray I0(x,y) differs from the corresponding value estimated in the calibration cell, as a consequence of the peculiar spray structure. Main phenomena originating this difference are irradiance absorption by droplets in the sheet path and Mie scattering. Besides, the fluorescence emitted by the portion of spray (pixel) under evaluation is partly absorbed by the fuel located between the sheet and the camera (fluorescence autoabsorption), but its effect is negligible in the present case (Kautoabs=5.3 10-4 cm2/mg).

An alternative technique is to correct them separately, using an additional simultaneous Mie scattering picture free of absorption losses. Thus, Mie scattering losses can be estimated, and then applied directly to the fluorescence image. In this work, a stereoscope was used to take simultaneously images of the fluorescence of the 355 nm excitation radiation and of the Mie scattering of the residual 532 nm radiation (due to the imperfection of the dicroic mirrors, and estimated as 5% of the total incident radiation). Using this spurious 532nm laser radiation allows isolation of the Mie scattering information, since the absorption coefficient of the fuel at wavelength 532 nm is negligible. Additional advantages of this procedure are: i) a UV camera lens is not necessary, ii) it is possible to obtain Sauter Mean Diameter images making the ratio PLIF/MIE image [7

7. M.C. Jermy and D.A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000). [CrossRef]

], more accurately since the Mie picture is nearly free of absorption losses, and iii) a reflection of the 532 radiation on the nozzle tip could be used to monitorize and eventually correct the shot-to-shot laser energy fluctuations. As a drawback, the thickness and divergence of the sheets at two different wavelengths may be different [19

19. A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986).

], but using long focusing distance and big size sheets minimizes its effect. Also the Mie scattering has a wavelength dependency, but its effect in the procedure used here is negligible [26

26. H. C. van de Hulst, Light scattering by small particles (Dover Publications Inc., New York, 1981).

].

A. Mie scattering correction

To compensate Mie scattering losses it is possible to use the Eq. (5), but it is necessary to relate the scattered light captured by the ICCD, SMie(x,y), to the optical density due to Mie scattering in the spray, ρMie(x,y). To do that it is possible to use the method developed by Abu-Gharbieh et al. [27

27. R. Abu-Gharbieh, J. L. Persson, M. Försth, A. Rosén, A. Karlström, and T. Gustavsson, “Compensation method for attenuated planar laser images of optically dense sprays,” Appl. Opt. 39, 1260–1267 (2000). [CrossRef]

] due to its relative simplicity and good results in Diesel sprays.

ρMie(x,y)=SMie(x,y)s0(y)ρ0(y)0xSMie(x)dx
(12)

All the parameters in this equation are know, except the parameter s00 which is a different constant for each row y. To calculate this parameter it is necessary to use the following equation and assume, as the second and last hypothesis, axial symmetry.

SMienew(x,y)=SMie(x,y)exp[ρ0(y)s0(y)0xSMienew(x)dx]
(13)

This makes possible to calculate the optical density due to Mie scattering using solely Mie scattering images (corrected with the CMlaser sheet), and then applying eq, (5) to correct them. So it is possible to get the correction factors as:

CFMie scattering(x,y)=(exp[0xρMie(x,y)dx])
(14)

B. Absorption correction

Once the correction factor from the Mie scattering losses is obtained, it is possible to correct the absorption looses in the PLIF image. To do so, the image is scanned row by row (y axis), every pixel value is multiplied by the correspondent Mie correction factor already calculated and then Eq. (6) is used again with the absorption coefficient measured for the commercial Diesel fuel. In this case the density of the fuel will be the equivalent one, measured in the pixel (y-1), and it is necessary to presume that the first pixel has not absorption. Note that it is also necessary to apply the CMlaser sheet and CMsheet thickness. This way,

SFCorrected(x,y)=CMlaser sheetCMsheer thicknessCMMie scatteringexp(αρE(x,y1)L)SF(x.y)
(15)

where L is the pixel size.

Now it is possible to apply the fluorescence – concentration function and calculate the ρE in each pixel of the PLIF image.

In Fig. 6.a) an example of an Mie scattering-PLIF image is given. The image in Fig. 6.b) is the Sauter Mean Diameter image from Fig. 6.a). The laser sheet enters into the spray rig by the upper part of the figure.

Fig. 6. PLIF/Mie scattering image. Injection pressure = 30 MPa, gas density=30 Kg/m3, injection duration = 1400 μs.

6. Results

The method presented has been applied to three different test cases with injection pressure of 30, 70 and 110 MPa. For each case, 100 pictures per instant at intervals of 200 μs have been taken. All of these pictures have been processed with a purpose-made software, including the boundaries detection method developed in [28

28. J.V. Pastor, J. Arrègle, and A. Palomares, “Diesel spray image segmentation with a likelihood ratio test,” Appl. Opt. 40, 1–10 (2001). [CrossRef]

], and all the correction procedures described before.

Fig. 7 (movie) shows a sequence of PLIF images of Diesel sprays at different times after start of injection (ASOI), after the application of all the corrections discussed. The images are average images of 100 shots, and the laser sheet enters into the spray rig through the upper part of the figure.

Fig. 7. (1.4 MB) PLIF movie of Diesel spray. Injection pressure = 30 MPa, gas density=30 Kg/m3 . The frame shown corresponds to 1400 μs ASOI.

First, it must be mentioned that a Diesel spray injected in stagnant conditions is expected to be axisymmetric, at least in average images. However, any laser sheet based image of Diesel sprays presents higher intensity in the side of the beam entry. So, any accurate correction procedure should, at least, improve the image symmetry.

As a first approach to analyze the spray symmetry, a parameter here labeled as “symmetry ratio” is defined as the ratio of the total fluorescence detected in all pixels at the upper part of the spray (laser sheet entry) and the value obtained at the lower part (sheet exit). This magnitude is plotted in Fig. 8 versus the time after start of injection for average pictures, after applying the different correction procedures. As expected, the laser sheet correction does not affect at all the spray symmetry, maintaining the original value of around 35% at all time instants (except at the injection beginning which will be discussed later). The Mie scattering and absorption corrections have almost the same effect in the spray. With any of them a decrease of the symmetry ratio up to approximately 15% is achieved. Applying all corrections sequentially, the final value goes down to 5%.

Fig. 8. Symmetry Ratio vs. time ASOI

A similar analysis is shown in Fig. 9 for two different radial profiles in average spray images. The sheet correction does not change the symmetry of the profile, as expected, but Mie scattering and absorption corrections increase it. Both are expected from the design of the algorithms.

Fig. 9. Radial profiles with the different corrections. Injection pressure = 30 MPa, gas density=30 Kg/m3, injection duration = 1600 μs. a) 10 mm b) 30 mm from the nozzle exit

It order to check the accuracy (or, at least, the consistency) of the measurements, PLIF results have been compared both with predictions given by theoretical models (FLUENT code and an own-developed phenomenological spray code DIES [6

6. J. V. Pastor, E. Encabo, and S. Ruiz, “New modelling approach for fast on-line calculations in sprays,” SAE Paper 2000-01-0287 (Society of Automotive Engineers, Warrendale, Pa., 2000).

]) and with results obtained with the light extinction method [29–31

29. T. Kamimoto, Ahn S. K., Y. J. Chang, H. Kobayashi, and S. Matsuoka, “Measurement of droplet-diameter and fuel concentration in a non-evaporating Diesel spray by means of an image analisis of shadow photographs,” SAE Paper 840276 (Society of Automotive Engineers, Warrendale, Pa., 1984).

].

The FLUENT code is based on CFD (Computational Fluid Dynamics) and considers the fuel spray as a gaseous jet with the same density as the liquid fuel, being injected into SF6. The inputs of the code are the injection rate curve and the environmental gas conditions. DIES is a simple model that solves 1-D mass and momentum conservation equations with the radial velocity and concentration profiles of a gaseous turbulent jet and uses as inputs the cone angle of the Diesel spray, measured with PLIF, as well as the experimental injection rate curve and environmental gas conditions.

The light extinction method allows the measurement of fuel concentration combining spray pictures with back illumination and the droplets diameter field measured with Phase Doppler Anemometry.

As a sample of the results comparisons, in Fig. 10.a) the PLIF radial profiles of mass concentration (defined as mass of fuel over total mass of mixture) at different sections from the nozzle are compared with predictions by DIES and with the results obtained with the light extinction method. It can be seen that the results from PLIF and DIES have a reasonable agreement up to 20 mm from the nozzle exit (which corresponds to the steady part of the spray). It must be mentioned that the transient part of the spray in the DIES code is fitted to an arbitrary function [6

6. J. V. Pastor, E. Encabo, and S. Ruiz, “New modelling approach for fast on-line calculations in sprays,” SAE Paper 2000-01-0287 (Society of Automotive Engineers, Warrendale, Pa., 2000).

] without very strong experimental evidence or validated theoretical arguments. The agreement with the results of the light extinction method is only acceptable for the 30 mm section and only near the spray axis.

The radial profiles of mass concentration measured with PLIF and its comparison with the predictions of the FLUENT code are plotted in Fig. 10.b). Note that in this case the mass concentration is represented in a normalized way to allow comparison: local concentration over concentration at the centerline is plotted vs. radial position over axial distance.

Fig. 10. Radial profiles comparison. a) DIES, PLIF and light extinction method. b) FLUENT and PLIF. .Injection pressure = 30 MPa, gas density=30 Kg/m3, injection duration = 1400 μs.

Absolute PLIF values of mass concentration in the spray centerline for different instants are compared in Fig. 11 with predictions by FLUENT and DIES models. It can be seen that the experimental results show a fair agreement with model predictions at distances from the nozzle higher than 10 mm (except for times below 600 μs ASOI, where the spray has not reached steady conditions yet), although they fail near the nozzle orifice where fuel concentration was expected to be higher. Discrepancies near the nozzle may be due to four reasons, three of them already mentioned: the problems associated to apply the Lambert-Beer law in high optical density media, inappropriate Mie scattering correction method for regions of incomplete atomization, and poor image spatial resolution in these regions. A fourth reason which must be considered concerns cavitation effects: for the nozzle used with a cylindrical hole, and taking into account the low back pressure in the vessel, high cavitation inside the nozzle is expected and, consequently, part of the fuel is injected in vapor phase. Taking into account that vapor fluorescence is too low to be properly detected in the present configuration, the maximum value of fuel concentration measurable will be in any case lower than 0.9. This effect is not considered in the simulation. Regarding discrepancies near the spray tip, it must be mentioned that: i) in this work, FLUENT simulations consider a gaseous spray (so concentration decay in the spray tip may not be comparable), and ii) the transient part of the spray in the DIES code has not been plotted here, for the reason mentioned previously.

Finally, the amount of fuel present in the PLIF images, obtained by integration of the fuel concentration pictures is compared in figure 12 with the measured amount of fuel injected up to every instant, as obtained from the injection rate measurements with the standard Bosch anechoic tube method.

Fig. 11. Spray centerline concentration results. Injection pressure= a) 30 MPa, b) 70 MPa.
Fig. 12. Comparison between amount of fuel injected as obtained from the integration of PLIF images (average of 100 images per instant; error bars correspond to ± the standard deviation) and the values from injection rate measurements.

7. Conclusions

Acknowledgments

This work has been partly performed in the frame of the DIME project (ENK6-CT2000-00101), funded by the European Community under the Energy Programme, and partly in project GV00-119-11 funded by Generalitat Valenciana.

Fluent is a registered trade mark of Fluent INC.

References and links

1.

P. Schihl, W. Bryzik, and A. Atreya, “Analysis of current spray penetration models and proposal of a phenomenological cone penetration model,” SAE Paper 960773 (Society of Automotive Engineers, Warrendale, Pa., 1996).

2.

J. Arrègle, J. V. Pastor, and S. Ruiz, “The influence of injection parameters on Diesel spray characteristics,” SAE Paper 1999-01-0200 (Society of Automotive Engineers, Warrendale, Pa., 1999).

3.

F. Payri, J. M. Desantes, and J. Arrègle, “Characterization of D.I. Diesel sprays in high density conditions,” SAE Paper 960774 (Society of Automotive Engineers, Warrendale, Pa., 1996).

4.

J. D. Naber and D. L. Siebers, “Effects of gas density and vaporization on penetration and dispersion of Diesel sprays,” SAE Paper 960034 (Society of Automotive Engineers, Warrendale, Pa., 1996).

5.

D. L. Siebers, “Liquid-phase fuel penetration in Diesel sprays,” SAE Paper 980809 (Society of Automotive Engineers, Warrendale, Pa., 1998).

6.

J. V. Pastor, E. Encabo, and S. Ruiz, “New modelling approach for fast on-line calculations in sprays,” SAE Paper 2000-01-0287 (Society of Automotive Engineers, Warrendale, Pa., 2000).

7.

M.C. Jermy and D.A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000). [CrossRef]

8.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, Amsterdam, 1996).

9.

A. Arnold, H. Becker, R. Hemberger, W. Hentschel, W. Ketterle, M. Kollner, W. Meinrburg, P. Monkhouse, H. Neckel, M. Shafer, K. P. Schindler, V. Sick, R. Suntz, and J. Wolfrum, “Laser in situ monitoring of combustion processes,” Appl. Opt. 29, 4860–4872 (1990). [CrossRef] [PubMed]

10.

K. Kohse-Höinghaus, “Laser techniques for the quantitative detection of reactives intermediates in combustion systems,” Prog. Energy Combust. Sci. 20, 203–279 (1994). [CrossRef]

11.

C. Nan Yeh, T. Kamimoto, H. Kosaka, and S. Kobori, “Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,” SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).

12.

J. Senda, T. Kanda, M. Kobayashi, and H. Fujimoto, “Quantitative analysis of Fuel Vapor Concentration in Diesel spray by Exciplex Fluorescence Method,” SAE Paper 970796 (Society of Automotive Engineers, Warrendale, Pa., 1997).

13.

H. Zhao and N. Ladommatos, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998). [CrossRef]

14.

A.A. Rotunno, M. Winter, G. M. Dobbs, and L. A. Melton “Direct Calibration Procedures for Exciplex-Based Vapor/Liquid Visualization of Fuel Sprays,” Combust. Sci. and Tech. 71, 247–261 (1990). [CrossRef]

15.

J. M. Desantes, J. Arrègle, J. V. Pastor, and A. Delage, “Influence of the fuel characteristics on the injection process in a D.I. diesel engine,” SAE Transactions. Journal of Engines. 107, pp. 1185–1195. (Society of Automotive Engineers, Warrendale, Pa., 1998).

16.

H. P. Fuchs and E. Winklhofer, “Diesel fuel spray visualization by laser induced fluorescence,” SAE Paper 914166 (Society of Automotive Engineers, Warrendale, Pa., 1991).

17.

M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Enhanced fluorescence yields through cavity quantum-electrodinamics effects in micro droplets,” J. Opt. Soc. Am. B 11, 1297–1924 (1994). [CrossRef]

18.

G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, and W. P. Acker, “Laser diagnostics for droplets characterization: application of morphology dependent resonances,” Prog. Energy Combust. Sci. 22, 163–188 (1996). [CrossRef]

19.

A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986).

20.

N. L. Swanson, B. D. Billard, and T. L. Gennaro, “Limits of optical transmission measurements with application to particle sizing techniques,” Appl. Opt. 38, 5887–5893 (1999). [CrossRef]

21.

R. Bazile and D. Stepowski, “Measurements of vaporized and liquid fuel concentration fields in a burning spray jet of acetone using planar laser induced fluorescence,” Exp. in Fluids 20, 1–9 (1995). [CrossRef]

22.

R. Domann and Y. Hardalupas, “Evaluation of planar Doppler Sizing (PDS) technique,” Eight International Conference on Liquid Atomization and Spray Systems, Pasadena, CA, (2000).

23.

I.B. Berlman, Handbook of fluorescence spectra of aromatic molecules (Academic Press, London, 1971).

24.

H. Sjöberg, G. Manneberg, and A. Cronhjort, “Long-working-distance microscope used for diesel injection spray imaging,” Opt. Eng. 35, 3591–3596 (1996). [CrossRef]

25.

G. G. M. Stoffels, S. Stoks, N. Dam, and J. J. ter Meulen, “Methods to correct planar laser-induced fluorescence distributions for local nonuniform laser attenuation,” Appl. Opt. 39, 5547–5559 (2000). [CrossRef]

26.

H. C. van de Hulst, Light scattering by small particles (Dover Publications Inc., New York, 1981).

27.

R. Abu-Gharbieh, J. L. Persson, M. Försth, A. Rosén, A. Karlström, and T. Gustavsson, “Compensation method for attenuated planar laser images of optically dense sprays,” Appl. Opt. 39, 1260–1267 (2000). [CrossRef]

28.

J.V. Pastor, J. Arrègle, and A. Palomares, “Diesel spray image segmentation with a likelihood ratio test,” Appl. Opt. 40, 1–10 (2001). [CrossRef]

29.

T. Kamimoto, Ahn S. K., Y. J. Chang, H. Kobayashi, and S. Matsuoka, “Measurement of droplet-diameter and fuel concentration in a non-evaporating Diesel spray by means of an image analisis of shadow photographs,” SAE Paper 840276 (Society of Automotive Engineers, Warrendale, Pa., 1984).

30.

F. V. Tinaut, A. Melgar, F. Castro, M. L. Sánchez, and B. Jiménez, “A method to determine liquid spray concentration in non-stationary axisymmetric sprays,” Exp. in Fluids 23, 299–305 (1997). [CrossRef]

31.

A. Palomares, Image Analysis of Diesel Sprays (In spanish)., Ph.D. Thesis Universidad Politécnica de Valencia (2001).

OCIS Codes
(100.0100) Image processing : Image processing
(100.2960) Image processing : Image analysis
(300.2530) Spectroscopy : Fluorescence, laser-induced

ToC Category:
Research Papers

History
Original Manuscript: February 19, 2002
Revised Manuscript: March 25, 2002
Published: April 8, 2002

Citation
Jos� Pastor, Jos� L�pez, J. Juli�, and Jes�s Benajes, "Planar Laser-Induced Fluorescence fuel concentration measurements in isothermal Diesel sprays," Opt. Express 10, 309-323 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-7-309


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References

  1. P. Schihl, W. Bryzik and A. Atreya, �Analysis of current spray penetration models and proposal of a phenomenological cone penetration model,� SAE Paper 960773 (Society of Automotive Engineers, Warrendale, Pa., 1996).
  2. J. Arr�gle, J. V. Pastor and S. Ruiz, �The influence of injection parameters on Diesel spray characteristics,� SAE Paper 1999-01-0200 (Society of Automotive Engineers, Warrendale, Pa., 1999).
  3. F. Payri, J. M. Desantes and J. Arr�gle, �Characterization of D.I. Diesel sprays in high density conditions,� SAE Paper 960774 (Society of Automotive Engineers, Warrendale, Pa., 1996).
  4. J. D. Naber and D. L. Siebers, �Effects of gas density and vaporization on penetration and dispersion of Diesel sprays,� SAE Paper 960034 (Society of Automotive Engineers, Warrendale, Pa., 1996).
  5. D. L. Siebers, �Liquid-phase fuel penetration in Diesel sprays,� SAE Paper 980809 (Society of Automotive Engineers, Warrendale, Pa., 1998).
  6. J. V. Pastor, E. Encabo, and S. Ruiz, �New modelling approach for fast on-line calculations in sprays,� SAE Paper 2000-01-0287 (Society of Automotive Engineers, Warrendale, Pa., 2000).
  7. M. C. Jermy and D. A. Greenhalgh, �Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,� Appl. Phys. B 71, 703-710 (2000). [CrossRef]
  8. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach Publishers, Amsterdam, 1996).
  9. A. Arnold, H. Becker, R. Hemberger, W. Hentschel, W. Ketterle, M. Kollner, W. Meinrburg, P. Monkhouse, H. Neckel, M. Shafer, K. P. Schindler, V. Sick, R. Suntz and J. Wolfrum, �Laser in situ monitoring of combustion processes,� Appl. Opt. 29, 4860-4872 (1990). [CrossRef] [PubMed]
  10. K. Kohse-H�inghaus, �Laser techniques for the quantitative detection of reactives intermediates in combustion systems,� Prog. Energy Combust. Sci. 20, 203-279 (1994). [CrossRef]
  11. C. Nan Yeh, T. Kamimoto, H. Kosaka and S. Kobori, �Quantitative measurements of 2D Fuel vapor concentration in a Transient Spray via Laser Induced Fluorescence Technique,� SAE Paper 941953 (Society of Automotive Engineers, Warrendale, Pa., 1994).
  12. J. Senda, T. Kanda, M. Kobayashi and H. Fujimoto, �Quantitative analysis of Fuel Vapor Concentration in Diesel spray by Exciplex Fluorescence Method,� SAE Paper 970796 (Society of Automotive Engineers, Warrendale, Pa., 1997).
  13. H. Zhao and N. Ladommatos, �Optical diagnostics for in-cylinder mixture formation measurements in IC engines,� Prog. Energy Combust. Sci. 24, 297-336 (1998). [CrossRef]
  14. A. A. Rotunno, M. Winter, G. M. Dobbs and L. A. Melton �Direct Calibration Procedures for Exciplex-Based Vapor/Liquid Visualization of Fuel Sprays,� Combust. Sci. and Tech. 71, 247-261 (1990). [CrossRef]
  15. J. M. Desantes, J. Arr�gle, J. V. Pastor, A. Delage, �Influence of the fuel characteristics on the injection process in a D.I. diesel engine,� SAE Transactions. Journal of Engines. 107, 1185-1195. (Society of Automotive Engineers, Warrendale, Pa., 1998).
  16. H. P. Fuchs and E. Winklhofer, �Diesel fuel spray visualization by laser induced fluorescence,� SAE Paper 914166 (Society of Automotive Engineers, Warrendale, Pa., 1991).
  17. M. D. Barnes, W. B. Whitten and J. M. Ramsey, �Enhanced fluorescence yields through cavity quantumelectrodinamics effects in micro droplets,� J. Opt. Soc. Am. B 11, 1297-1924 (1994). [CrossRef]
  18. G. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal and W. P. Acker, �Laser diagnostics for droplets characterization: application of morphology dependent resonances,� Prog. Energy Combust. Sci. 22, 163-188 (1996). [CrossRef]
  19. A. E. Siegman, Lasers (University Science Books, Mill Valley CA, 1986).
  20. N. L. Swanson, B. D. Billard and T. L. Gennaro, �Limits of optical transmission measurements with application to particle sizing techniques,� Appl. Opt. 38, 5887-5893 (1999). [CrossRef]
  21. R. Bazile and D. Stepowski, �Measurements of vaporized and liquid fuel concentration fields in a burning spray jet of acetone using planar laser induced fluorescence,� Exp. in Fluids 20, 1-9 (1995). [CrossRef]
  22. R. Domann and Y. Hardalupas, �Evaluation of planar Doppler Sizing (PDS) technique,� Eight International Conference on Liquid Atomization and Spray Systems, Pasadena, CA, (2000).
  23. I. B. Berlman, Handbook of fluorescence spectra of aromatic molecules (Academic Press, London, 1971).
  24. H. Sj�berg, G. Manneberg, and A. Cronhjort, �Long-working-distance microscope used for diesel injection spray imaging,� Opt. Eng. 35, 3591-3596 (1996). [CrossRef]
  25. H. C. van de Hulst, Light scattering by small particles (Dover Publications Inc., New York, 1981). [CrossRef]
  26. R. Abu-Gharbieh, J. L. Persson, M. F�rsth, A. Ros�n, A. Karlstr�m and T. Gustavsson, �Compensation method for attenuated planar laser images of optically dense sprays,� Appl. Opt. 39, 1260-1267 (2000). [CrossRef]
  27. J. V. Pastor, J. Arr�gle, A. Palomares, "Diesel spray image segmentation with a likelihood ratio test,� Appl. Opt. 40, 1-10 (2001). [CrossRef]
  28. T. Kamimoto, S. K. Ahn, Y. J. Chang, H. Kobayashi, S. Matsuoka, �Measurement of droplet-diameter and fuel concentration in a non-evaporating Diesel spray by means of an image analysis of shadow photographs,� SAE Paper 840276 (Society of Automotive Engineers, Warrendale, Pa., 1984).
  29. F. V. Tinaut, A. Melgar, F. Castro, M. L. S�nchez, B. Jim�nez, �A method to determine liquid spray concentration in non-stationary axisymmetric sprays,� Exp. in Fluids 23, 299-305 (1997). [CrossRef]
  30. A. Palomares, Image Analysis of Diesel Sprays (In spanish)., Ph.D. Thesis Universidad Polit�cnica de Valencia (2001).
  31. G. G. M. Stoffels, S. Stoks, N. Dam and J. J. ter Meulen, �Methods to correct planar laser-induced fluorescence distributions for local nonuniform laser attenuation,� Appl. Opt. 39, 5547-5559 (2000).

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