Measurement of particle size distributions in Diesel emission ...Measurement of particle size distributions in Diesel emission gasses 4 Chapter 1 Introduction Diesel engines are widely

Eindhoven, University of technologyFaculty of Mechanical EngineeringSection Procestechnical constructions

Measurement of particlesize distributions in Diesel

emission gasses

K.M.J Verschuur 414614

CompanionDr. ir. H.P. Van Kemenade

Eindhoven, 27th of March 2000

Measurement of particle size distributions in Diesel emission gasses

2

Contents

1. Introduction 4

2. Particle size distributions in Diesel engines 5

2.1 Diesel engines 52.2 options for separation techniques 6

3. the measurement technique 8

3.1 Operating principles 83.2 Particle size distributions 103.3 Experimental parameters 11

4. Spheriglass and smoke experiments 12

4.1 The Diesel emission test rig 124.2 Pressure calculations 134.3 The Spheriglass experiments 14

4.3.1 the test rig 154.3.2 results 15

4.4 Smoke experiment 164.5 Explanation of possible problems 16

5. Diesel emission experiment 18

6. Conclusion and recommendations 19

Literature 20

Appendix 1. Geometric loss factors 21Appendix 2. Numerical results of the measurements 23Appendix 3. Fraunhofer theory 27


3

List of symbols

a acceleration [m s-2]

D crack height [m]

dp particle diameter [m]

F drag force [N]

f friction factor [-]

g gravitational acceleration [m s-2]

k geometric loss factor [-]

L length [m]

m mass [kg]

p pressure [Pa]

Re Reynolds number [-]

up particle velocity [m s-1]

z height [m]

ε roughness [m]

λ wavelength [nm]

ρ density [kg m-3]

µ dynamic viscosity [m2 s-1]

ν kinematic viscosity [kg m-1 s-1]

σ standard deviation [-]


4

Chapter 1

Introduction

Diesel engines are widely used of their low fuel consumption and durability in manycommercial machines, i.e. passenger vehicles. Compared to petrol enginesthe exhaust gasses contain less carbon monoxde (CO) and hydrocarbons (HC), far morenitro oxide (NOx) and particulate matter (PM). Particulate matter is sometimes visible asblack smoke.For successful application of the Diesel engine in the future, research of filtering techniquesfor the automotive sector is called far to satisfy (future) legislation. Calsonic UK Newcastleand the University of technology Eindhoven started a project evaluating the applicability of alaser diffracto meter for measuring the particle size distribution of a Diesel engine.This is the topic of this project. In this report first the various methods of filtering arediscussed. After this the measurement technique for the determination of the particle sizedistribution is explained in Chapter 3. In Chaper 4 follow the experiments of firstly solidparticles with a familiar size and secondly measurements with smoke. Than in Chapter 5 isspoken about the actual experiment with the Diesel emission gasses. This rapport will endwith some conclusions and recommendations for further research.


5

Chapter 2

Particle size distributions in Diesel Engines

This Chapter describes the importance of particle sizes in Diesel engines and the reasons forresearching this subject. Then the possible options of measurement techniques which areinvestigated (in the past) are discussed. Also the Rotating Particle Separator (RPS) comesup for discussion. This is the direct cause of this project, because a robust measuringtechnique has to be developed for the aerosol sampling in this RPS. The goal of thisresearch is to decide in which direction future development needs to be taken.

2.1 Diesel engines

Lately environmental and health risks of particulate emission with respect to their particlesize and distribution has become more important. The European regulations for the emissionof Hydrocarbons and NitroOxides in 2005 are three times as strict as they were in 1992 andfor CarbonDioxide even more than five times [3] (Table 1).

Tier Year HC + NOX NOX CO PM

Euro I 1992 0.97 - 2.72 0.14

Euro II – IDI 1996 0.70 - 1.0 0.08

Euro II – DI 1999 0.90 - 1.0 0.10

Euro III 2000 0.56 0.50 0.64 0.05

Euro IV 2005 0.30 0.25 0.50 0.025

Table 1. EU emission standards for Diesel cars, g/kg


6

Faced with this new legislation manufacturers have to re-examine their available technologyto meet this challenge. Up till now regulation has focussed on the emission in terms ofweight, but it’s expected that attention will shift to the size distribution.Former measurements indicate that in case of Diesel engine emission, the size of theparticles is characterised by a bi-nominal distribution. This distribution has one large peakaround 10 µm as a consequence of mechanical processes (f.e. agglomeration) and a smallerpeak due to physical influences (phase change, nucleation) below 1 µm. the last peak evencan’t be rejected because of the sensitivity of the human lungs to particles in this range.Due to this new legislations and the danger for the lungs, also these small sizes have tofiltered out of the emissions. One of the main issues of this project is to precise the size ofthis small peak for further investigation of the filtering techniques

2.2 options for separation techniques

During the last years the following separation techniques have been developed to reduce theparticulate emission. In principle these methods are used for different purposes, but withsome further research and re-design of the familiar plans they probably can be used inautomotive systems [3]:

-1. impact traps-2. cyclones-3. rotating particle separator-4. electrostatic filters-5. cracking

Impact traps in combination with regeneration is the only technique which has matured to thepoint that commercial introduction is imminent. These filters can catch large particles due tointerception and very small particles can migrate to the filter surface by diffusion. Theproblem is that between these areas the filter is less efficient and probably this is just aroundthe small peak in the particle size distribution of Diesel emission. A second thing is theregeneration which is also problem.For a continuous removal of particles with no moving parts a cyclone is very effective. Butthe range of particles which the cyclone can filter has a lower limit of 5 µm, so the interestingsecond peak is not measurable.The Rotating Particle Separator addresses this problem by including a rotating cone withvery small channels of 1mm (figure 1). By reducing the distance between particle and wallthe cut of size can be reduced to 0.2 µm, which might be sufficient for Diesel engines.


7

Figure 1. Rotating Particle Separator

Electrostatic filters perform well for large scale combustion, but due to therelatively high investments in a high voltage generator the filter does not scaleeconomically.Thermal Cracking uses an additional oxidation process to convert the particles intoH2O and CO2. The efficiency is high, because the conversion takes place on a molecularlevel. The drawback is the required burner, what complicates the designand integration of these systems in a vehicle considerably.When the advantages and the disadvantages of the different techniques will take intoconsideration a RPS based system, with the possibility to measure the small peak around1um, is a possible solution for filtering in small applications. It is conceivable that also thismethod does not satisfy future regulations, so the growth of ultra fine particles byagglomeration to a size which can be filtered is also an important research subject. If thisproves to be impossible thermal cracking is the only solution for these very small particles.


8

Chapter 3

The measurement technique

In this Chapter a possible technique for measuring the particle size is discussed. Themachine which is used during the measurements was a Malvern Mastersizer X. Besides thesize of the particles this machine can also measure the particle concentration and thedistribution. The Mastersizer X is an optical measurement unit, which is based on lightscattering. With the method the size structure of a material phase in another can bemeasured. The only qualification of the technique is that each phase must distinct opticallyfrom the other and the medium must be transperant to the laser wavelength. This means, inpractice, that the refractive index of the material has to be different from the medium in whichit is supported. Some advantages are that the method is precise, it is fast and there is nocalibration required, because the instrument is based on fundamental physical principles.In the first section of this chapter the operating principles of the Mastersizer X will beexplained, after which something is said about the particle size distributions. At last theexperimental parameters come to order.

3.1 operating principles

The Mastersizer X is based on the principle of laser ensemble light scattering [4,5]. It falls inthe category of non imagine optical systems due to the fact that sizing is accomplishedwithout forming an image of the particle onto a detector.The optical configuration which is used is the conventional Fourier optics. There is also asecond, more accurate configuration, the reverse optics configuration, but this method canonly be used for particles dispersed in liquid suspension. So this is not useful formeasurements on diesel emissions.The conventional Fourier Optics configuration is shown diagrammatically in figure 2. With thismethod particles can be measured in a range from 0.5 µ to 600 µm. The light from a lowpower Helium-Neon laser, with a wavelength of 624 nm, is used to form a collimated andmonochromatic beam of light. The beam of light (analyser beam) will scatter when it meetsthe particles in the sample area. The particles are introduced to the analyser beam by directspraying through the measurement area or with the help of a cell or pipe of glass, which goesalong the laser beam. This is why a laser is chosen with a wavelength of 624 nm: in this casethe refraction despite of most sorts of glass is, especially with large particles, negligible.


9

Figure 2. Conventional Fourier Optics

The light scattered by the particles and the unscattered remainder are incident on a receiverlens. This lens is the Fourier Transform Lens and forms the far field diffraction pattern of thescattered light at it’s focal plane. Here a custom designed detector, in the form of series ofangular sectors, gathers the scattered light over a range of solid angles of scatter.On the detector the unscattered light is brought to focus and passes through a small aperturein the detector out of the optical system. With the total laser power passing out of the systemin this way the volume concentration can be determined.The Fourier Transform Lens has the useful property that wherever the particle is in theanalyser beam its defraction pattern is stationary and centred on the detector. This is shownis figure 3. Thanks to this property it does not matter that a particle is moving through thesample area. The diffraction area stays stationary. It also does not matter where in theanalyser beam the particle passes. The pattern stays constant at any lens distance. Onlyhigh particle velocities (in comparison with the measuring velocity) can influence this pattern,but because the lens transformation is optical an thus fast, there are no sample velocitieshigh enough to cause a deviation from this property.

Figure 3. Properties of the Fourier Transform Lens

The scattered light what falls on the detector is the sum of all individual patterns. So thesystem measures an integral scattering pattern form all the particles in the beam. In a typicalmeasurement the number of particles needed for an adequate measurement is 100-1000depending on their size. Further can 1 single measurement cause statistical significanceproblems, because the cross section of the material is to small. To avoid this problems the


10

method works with a time averaged observation, which gives a more representative samplingof the bulk material.An unique light intensity characteristic is produced by the particle when it scatters the light.So the detector measures a peak at a favoured scattering area which is related to thediameter of the particle. In figure 4 is shown that small particles have peak energies in largeangles of scatter and vice versa.

Figure 4. large against small particle angles

3.2 particle size distributions

In this section facts about the particle size distribution, which are important for theinterpretation of the experiment are discussed. The most important point to remember ininterpreting results is that the fundamental size distribution derived with the Mastersizer X isvolume based. This means that if there is a percentage of particles with a certain diameter,the volume of these particles are that percentage of the total volume. So this method will notgive the number of particles with that diameter. This means that the larger particles willpreponderate. In figure 5 is shown what the difference can be between the two distributions.The results in this figure are from the same experiment.

Figure 5. volume against number distribution

Another point is that the distribution is expressed in volume equivalent spheres. In this caseall non-spherical particles will be transformed during the analysis. This has to be done toavoid that the height of a cylindrical particle will be seen as the diameter of the particle andthat the particle according to the analysis is a lot bigger than it actually is.


11

At last the scattering of large particles is almost independent of the optical properties of thematerial and is caused by the diffraction of light around the particles. Light that couples intothe particle is absorbed in all common cases and can be ignored. When the particles aresmaller the refractive index dependence becomes more significant due to the fact that atsuch small sizes the light coupled into a particle in not completely attenuated and canemerge as a refracted ray. For this additional component a scattering model is required. TheMastersizer X uses the Fraunhofer theory [Appendix 3].

3.3 experimental parameters

For a correct measurement with the demanded accuracy three parameters have to becorrect. The first is the instrumental range. When the distribution is roughly known, the lenswith to correct significance can be used, otherwise two measurements are necessary.Another point is the set-up presentation. This means that data about material andsuspension, like the refractive index have to be known. At last the analysis model isimportant. There are two models available in the Mastersizer X software: the polydisperseand the monodispers model. There are two differences between the two models. First is theaccuracy [2]:

iMonodispers: the particles have homogeneous physical properties and a log-normaldiffraction, with a standard deviation of σ ≤ 1.2.iPolydispers: the particles have homogeneous physical properties and a bi-normaldiffraction, with a standard deviation of σ ≥ 1.2.

Another difference is that in the monodispers model analysis only the most significant peak isdetected. This model is only useful if the result falls in a familiar one narrow mode. Thepolydispers model can measure more peaks in a larger area, but this is at the cost of thestandard deviation. In the emission gasses of Diesel are two peaks expected: one largerpeak at 10 µm and a more interesting smaller peak around 1 µm. Because of the large peakthe more accurate monodispers model is unusable, so the polydispers model will be used.


12

Chapter 4

Spheriglass and smoke experiments

An important issue is the reliability of the results of the measurements with the Dieselemission gasses. The Mastersizer X has to measure accurate and the obtained data has tobe analysed correct. Therefore the machine tested with a familiar distribution of solidSpheriglass particles. This will be discussed is section 4.3. Also it is necessary to verify themachine can measure a gas like a Diesel emission. For this reason first an experiment isdone with a smoke sample. The experiment and the results are in section 4.4. Thesemeasurements acquire a compatible fan, which can circulate the air. Therefore somecalculations has to be made to find the required power of the fan (4.2). These calculationsare based on the test rig, which shall be used in the final Diesel emission experiment, so thischapter will start with an explanation about this rig.

4.1 The Diesel emission test rig

In this section the test rig for the Diesel experiment. This is shown in figure 6. The emissiongasses from the car are flown through the tube to the T-part. The stream here will be dividedin two streams. One goes to the Mastersizer, the other one is blown away. The function ofthis second stream is to aviod an over pressure in the system de to the power of the engine.After the Mastersizer a fan is placed, which will drive the gasses through the laser beam inthe measuring machine. After the fan also these gasses can be removed.

Figure 6. Diesel engine test rig

A B

C D

A CarB T-partC MastersizerD Fan


13

4.2 Pressure calculations

The fan that shall be used has to create a pressure difference what can circulate theparticles. To calculate this pressure a flow velocity is needed, which is 1 m/s in themeasurements. To create a flow which carries on the particles, the flow velocity has to besignificantly higher than the particle velocity, otherwise the gravitational forces on theparticles influence the flow. So first a rough calculation will be done, to find the order of theparticle velocity. To calculate the particle velocity Newtons law (eq. 4.1 ) can be applied toone particle.

In this formula m is the mass of a particle, a the acceleration of a particle, what is equal tothe gravitational acceleration g. F is the drag force. For one particle this is:

With νf the kinematic viscosity, dp the diameter and up the velocity both of one particle.Formula 4.1 can be written as:

Here m is written as the volume of a particle multiplied with the density, which is settled withthe kinematic viscosity ν. Now this becomes the dynamic viscosity µ.The viscosity of air is 2.16*10-5 and g is 9.81 so out of 4.3 follows up=151dp. The meandiameter is in order of micrometers, so as a conclusion can be said that 1 m/s for the flowvelocity is much higher than the particle velocity and can be used in the pressure calculationsand the experiments.For the calculation of the pressure the Bernouilli equation will be used [1]. When frictionlosses and losses due to the geometry of the canals are added, the equation becomes:

In equation 4.4 p is the pressure, ρ the density, z the height, v the velocity, f the frictionfactor, L the pipe length, D the diameter of the pipe and k the geometric loss factor. thesubscript 1 is for the place at the beginning of the pipe just after the car and subscript 2 atthe end after the fan. In this system v1 = v2, z1 = z2 so 4.4 reduces to:

amF ⋅=

ppf udF ⋅⋅⋅=23 νπ

ppfp udgd ⋅⋅⋅=⋅23 3

6µπ

π

g

vk

g

v

D

fLz

g

v

g

pz

g

v

g

p

2222

22

2

222

1

211 ⋅∑+⋅∑+++=++

ρρ

22

22 vk

v

D

fLp

ρρ⋅∑+⋅∑=∆

4.1

4.2

4.3

4.4

4.5


14

In appendix 1 a table is given with geometric loss factors k. For the different parts of the testrig the following k values can be found:

-T part 1.9-Inlet 1.0-inlet fan 1.0-----------------------total 3.9

For the calculation of the friction factor f the Reynolds number is needed:

The viscosity has a value of 2.16*10-5 and v is 1 m/s (see above). In the test rig rubber tubeswith a diameter of 25mm are used and for the density of emission gasses an approximationis made by comparing it with air. (ρ = 1.06 kg/m3). The Reynolds number then becomes1.47*103. Now the friction factor can be found in figure 7. For ε / D a value of 5*10-7 is used,so a friction factor of 0,054 will follow.

Figure 7. Moody diagram

When the total length of the pipes is 5 meters the total pressure fall can be calculated withequation 5 This will be 6.5 Pa. To cause this pressure fall, a fan of the company ABC.A typeCK 125C exp. is used.

4.3 The Spheriglass experiment

For the inspection of the Mastersizer X an experiment has been done with Spheriglassparticles. This is a material what is used in road building for the sparkling of the white marks.From former experiments with a different measuring technique, the particle size distribution isknown. This method can be used for solid particles with sizes which are not smaller than 5µm, but for emission gasses it is not suitable.

µρvD

=Re 4.6


15

4.3.1 the test rigIn the experiment a flow of solid particles has to cross the laser beam. To prevent that as aconsequence of scattering the flow is not measureble, a pipe of glass is used to lead theparticles through the laser beam. In the Diesel emission experiment this technique isn’tpossible because the refraction of the glass is large in comparison with the small diameter ofthe particles in the second peak (Chapter 3.3). Thanks to the larger diameters of theShperiglass particles, it is not a problem in this experiment.In figure 8 the test rig is shown. Due to the suction force of the fan an air circuit arises, whatleads the particles around. In this experiment a problem was that the fan which wascalculated for emission gasses was not capable moving the particles, so the fan wasreplaced by a vacuum cleaner.

Figure 8. test rig of the Spheriglass experiment

4.3.2 the resultsDuring the experiment the following results have been measured (figure 9, app. 2). If thesevalues are compared with the results of former measurements of Van Beek, the top of bothgraphs are comparable and lie around 60 µm.

Figure 9. The Mastersizer experiment Van Beeks experiment

A difference is that the particle size distribution in this experiment is wider. A possibleexplanation is that the Mastersizer has less measuring points so the distance between these

B A

C

D

A FanB MastersizerC pipe of glassD hose of rubber

Particle Diameter (µm.)

Volume %

0

10

20

30

0

10

20

30

40

50

60

70

80

90

100

1.0 10.0 100.0 1000.0


Volume %

0

10

20

30

0

10

20

30

40

50

60

70

80

90

100

1.0 10.0 100.0 1000.0


16

points is more than at Van Beeks experiment. Due to this also the volumetric percentage isnot the same. Despite of these differences the conclusion can be made that the MastersizerX is compatible and the experimental parameters (Section 3.3) are correct.

4.4 smoke experiment

In this experiment smoke of tobacco is used to control if the Mastersizer is capable tomeasure the small particles in this gas. During the test the smoke was blown directly throughthe laser beam, without using any fan or circuit. This is done to avoid the pipe of glass, whichinfluences the results (4.3.1). The problem that was risen in the Spheriglass experiment (thescattering of the gas before the laser beam was crossed) is not a problem here, becausesmoke can be blown directly through the Mastersizer. This is not possible with solid particles,because of gravity influences on these particlesIn figure 10 (and app. 2) the results are shown. A large peak around 15 µm can be noticed,but also the second, for the RPS more interesting small peak in measured. This peak liesabout 0.75 µm. As a conclusion can be said that the Mastersizer is capable to measuresmoke and has to be able to measure emission gasses as well

Figure 10. Results smoke experiment

4.5 explanation of possible problems

During the measurements some problems can arise, which can cause a difference betweenthe real diffraction pattern and the measured one. This paragraph gives an explanation forthe difference.First the pipe of glass causes a deviation. The refractive index of glass can influence thescattering of the light and for some wavelengths of light, the glass will not let the lightthrough. So the glass cannot be thick (up to 2 mm) and has to let through a wavelength of633 nm (the wavelength of the laser light). Also the pollution of the pipe can cause a differentrefractive index and through that deviation.Another point is the transformation of non-spherical particles to particles with equivalentspheres. For small particles this is not a problem, but the deviation becomes larger if theparticles are larger. In emission gasses appear besides small particles also very large


Volume %

0

10

20

0

10

20

30

40

50

60

70

80

90

100

0.1 1.0 10.0 100.0 1000.0


17

particles (soot or ash). The number of these very large particles is not high but they can havea big influence in a volume based distribution.Further the light has to cross the gasses. For the surrounding material a refractive index isgiven to the model. This is the index for air, the emission gases, which flow through the pipecan cause a deviation, because the refractive index for this gas is not exactly the same.At last some small particles can stay behind in the rubber tube before the laser, as aconsequence of the roughness of the wall.


18

Chapter 5

Diesel emission experiment

In this chapter the measurements with Diesel emission gasses are discussed. The gassesproduced by a car are led along the laser lens and measured by the Mastersizer. Twoexperiments were done. In the first experiment the car was only started, without adding morefuel. In the second one this was actually done. The results are graphed in figures 11 andAppendix 2

Figure 11. results without extra gas results with extra gas

When gas is added larger particles are measured. A logical explanation is that moreemission gasses with lager particles are produced , because not all the fuel, which is addedcan be burned. An important result is that the interesting small peak in can be measured.This peak lies around 0.8 µm (figure 11). In the right figure this peak falls away for the peakwith lager particles. So the Mastersizer meets the demands, if the larger particle peaks canbe suppressed.


Volume %

0

10

20

0

10

20

30

40

50

60

70

80

90

100

0.1 1.0 10.0 100.0


Volume %

0

10

20

0

10

20

30

40

50

60

70

80

90

100

0.1 1.0 10.0 100.0 1000.0


19

Chapter 6

Conclusion and recommendation

One of the most important power sources this time is the Diesel engine. This is because oftheir low fuel consumption and their durability. A problem is the emission gasses, which haveto become cleaner in the future to satisfy the environmental legislations. For this reason thefiltering techniques become more important and a lot of research is done on this subject.For further research on filtering techniques first a measurement technique for the particlesize distribution has to be developed. This was done in this project, to examine whether itwas possible to measure this size distribution with a laser diffracto meter, a MelvernMastersizer X.After positive results in testing the Mastersizer with a familiar size distribution of Spheriglassparticles and smoke, measurements were done with emission gasses. As a conclusion canbe said that the laser diffracto meter can be used for the regulation of particle sizedistributions as can be seen in the results of Chapter 4 and 5.

On this subject no recommendations have to be made. With this measurement technique theparticle size distribution can be measured. A better alternative for further research are thefiltering techniques itself, for example utilising the Rotating Particle Separator automotive.


20

Literature

1. William S. Janna, Design of fluid thermal systems, 1993, ISBN 0-534-93373-4

2. B.A.R. van Peer, seeding for LDA in het bijzonder voor toepassing inverbrandingsmotoren, rapportnummer 97017,1997

3. H.P.van Kemenade, W.Sampers, Proposal for an investigation on Diesel particulateemissions and after treatment technology, 1999

4. Malvern Instruments, Applying advanced particle science in instrumental & research,Instrumental manual, Manual number 0054

5. Malvern Instruments, Applying advanced particle science in instrumental & research,Windows sizer reference manual, manual number 0073

6. Douglas C. Giancoli, Natuurkunde voor wetenschap en techniek deel II, 1993, ISBN 9062339077


21

Appendix 1

Geometric loss factors


22


23

Appendix 2

The numerical results of the measurements

Spheriglass experiment (figure 9)

Particle Volumesize percentage

0.2 0.080.48 0.270.59 0.420.71 0.480.86 0.461.04 0.37 1.26 0.241.52 0.131.84 02.23 02.7 03.27 03.96 04.79 05.79 0 7.01 08.48 010.27 012.43 015.05 018.21 0 22.04 0.0826.68 0.8632.29 3.7939.08 11.2847.3 20.0957.25 22.7969.3 19.1583.87 12.57101.52 5.8122.87 1.15148.72 0


24

Smoke experiment (figure 10)


0.20 0.490.48 1.890.59 2.720.71 2.810.86 2.291.04 1.491.26 0.751.52 0.251.84 02.23 02.70 03.27 03.96 04.79 0.205.79 1.367.01 3.908.48 8.0210.27 12.6312.43 15.7115.05 15.9818.21 13.5522.04 9.2026.68 4.8132.29 1.7539.08 0.1847.30 057.25 069.30 083.87 0101.52 0122.87 0148.72 0


25

Diesel emission experiment without adding extra fuel (figure 11)

Particle VolumeSize percentage

0.20 0.770.48 3.710.59 5.960.71 7.210.86 7.431.04 6.881.26 5.951.52 5.051.84 4.432.23 4.062.70 3.773.27 3.443.96 2.914.79 2.285.79 1.797.01 1.558.48 1.6010.27 1.8812.43 2.3515.05 2.8718.21 3.3322.04 3.6126.68 3.6232.29 3.3439.08 2.9447.30 2.5657.25 2.1369.30 1.6683.87 0.92101.52 0122.87 0148.72 0


26

Diesel emission experiment with adding extra fuel (figure 11)


0.20 0.190.48 0.180.59 0.100.71 00.86 01.04 0.041.26 0.401.52 0.901.84 1.492.23 2.292.70 3.573.27 5.533.96 7.354.79 8.205.79 8.047.01 7.478.48 6.8910.27 6.1812.43 5.4315.05 4.8318.21 4.2722.04 3.7126.68 3.1632.29 2.6139.08 2.1247.30 1.7157.25 1.4169.30 1.2183.87 1.35101.52 1.78122.87 2.69148.73 4.88


27

Appendix 3

Fraunhofer theory

Suppose a monochramatic source of light which falls through a crack [figure A1]. The widthof the crack is D and the light consists of parallel beam. Is the screen placed on a infinitedistance the diffraction is called Fraunhofer, instead of when the screen is placed nearby thecrack, then it’s Fresnel diffraction [6].

Figure A1 monogramatic parallel beam through crack

Because the screen is at an infinite distance the beam stays parallel until an arbitrary pointon the screen. In figure A1.a a beam goes straight through the crack. All the streaks of lighthave the same phase so a clear spot arises. When the beam falls through the crack under anangle the streaks above has a longer optical path to travel than the lowest streak. In figureA1.b the difference between the middle and the lowest streak is λ/2, so the phase differenceis 180°. Therefor they interfere destructive. this also counts for the difference between themiddle and the highest streak. The consequence of this interference in pairs is that no lightreaches the screen under this angle. This angle is:

D/sin λθ = A.1.


28

When the difference in distance is larger, for example 1,5 λ, the destructive interference inpairs arises between the lowest streak and the streak at one third, because this difference isλ/2 [A1.c]. The light from the highest streak do arise at the screen, only the spot is muchweaker than the spot in the middle. The following light pattern arises [figure A2]

Figure A2 Fraunhofer light pattern

Documents

Measurement of particle size distributions in Diesel emission ...Measurement of particle size distributions in Diesel emission gasses 4 Chapter 1 Introduction Diesel engines are widely