Measurements in diesel sprays are ideally nonintru-sive and typically rely on laser interactions with thedroplet field. To monitor spray properties close to thediesel injector tip, the experimental technique mustbe able to monitor droplet sizes in spite of high num-ber densities and high levels of attenuation.1 There-fore we have developed an infrared scattering dropletmeasurement technique, which was applied to acombusting, a room-temperature, and a high-temperature evaporating diesel spray. This tech-nique is spatially resolved and has been applied to allregions of the spray at a distance greater than 15 mmfrom the injector orifice.2
Attenuation and multiple-scattering errors in-crease with the optical depth of a system, which is theproduct of number density, optical cross section, andpath length.3 Off-the-shelf measurement systemstypically rely on visible wavelengths and are plaguedby high attenuation levels and large multiple-scattering errors. Infrared scattering, as we previ-ously demonstrated, is more effective at probing thediesel spray than visible wavelength techniques.2However, just as visible-based techniques becomelimited by multiple scattering, the infrared measure-ments can also be affected by multiple scattering.Therefore it is necessary to quantify the multiple-scattering effects; the results of these experimentsare presented in this paper.
2. Motivation and Background
Existing laser-based droplet measurements canbroadly be categorized as single-droplet techniques,ensemble-averaging techniques, and imaging tech-niques. Single-droplet techniques such as phaseDoppler measurements4,5 or imaging measurementsthat rely on separate images of droplets6 are not ap-
The authors are with the Division of Engineering, ColoradoSchool of Mines, Golden, Colorado 80401-1887. The e-mail addressfor T. E. Parker is [email protected].
Received 3 January 2005; revised manuscript received 18 April2005; accepted 21 April 2005.
plicable to regions of high droplet number densitiestypical of the near-injector centerline region of dieselsprays. However, ensemble-averaging techniquesand imaging techniques can be applied to areaswhere numerous droplets populate the probe volume.Unfortunately, these techniques are susceptible tomultiple-scattering errors because implicit in each ofthese techniques is the approximation that each pho-ton that reaches the detector is scattered only once.
Multiple scattering occurs when the spacing is suf-ficiently small that a single photon readily interactswith more than one droplet before reaching the de-tector. A common ensemble measurement techniquerelies on diffraction and collects the forward-scattered light from the probe volume.7 Because ofthe error due to multiple scattering, many research-ers have developed both theoretical and empiricalcorrections for large obscuration levels.8–12 These cor-rections are typically specific to the system of interestand rely on characteristics that may be difficult toquantify, such as the spatial distribution of differentsized droplets within the spray. Another ensembletechnique utilizes the polarization ratio of side-scattered visible light13; however, rigorous applica-tion of this technique produces a limited dynamicrange and, again, is susceptible to multiple-scattering effects.
Additionally, imaging techniques can be applied tosprays, but again, with multiple-scattering effectscausing significant error for optically thick regions ofthe spray. Jermy and Allen have developed a compu-tational tool for quantifying the multiple-scatteringeffects on imaging techniques and have concludedthat multiple scattering becomes more serious as theparticles near the Rayleigh limit and as the systemthickness increases.14
Laser-based measurements for droplets in spraysare relatively mature with high-quality, high-reliability commercial instruments available for usewith low number density systems. Unfortunately, thedense, near-centerline diesel spray is optically thickfor visible wavelengths; thus off-the-shelf dilutespray measurement systems provide little informa-tion about this region of the spray. This provides themotivation for the development of the infrared scat-tering droplet measurement technique. Previouspublications have discussed the development of thismethod; however, a brief overview will be givenhere.15,16
3. Experimental Techniques
Optical measurements were based on dual-wave-length coaxial beam scattering, and extinction andoptical access was provided normal to the injectoraxis in two orthogonal directions through barium flu-oride windows (chosen for their visible and infraredtransmittance properties). Figure 1 depicts a sche-matic of the measurement layout. This system used atunable CO2 laser operated at 9.27 �m and a Nd:YAGlaser operated at the fundamental frequency�1.06 �m�, both cw, to produce the probe volumes.The beams were focused and combined to produce
coaxial beams with experimentally verified identicalwaists (Gaussian, 150 �m diameter) and positions atthe center of the spray (within the combustion ves-sel). Probe volume length along the beams was300 �m for the 1.06 �m beam and 430 �m for the9.27 �m beam. Polarization for both probe beamswas vertical and scattering was monitored at 90° and10.9° for the 1.06 and 9.27 �m wavelengths, respec-tively. By use of sufficiently fast detectors (of theorder of 100 kHz, data-acquisition rate of 500 kHz,InGaAs for the 1.06 �m measurements and cryogenicHgCdTe for the 9.27 �m measurements), light thattraversed the spray zone (extinction measurement)and scattered light from within the probe volume atboth wavelengths were measured. Acceptance half-angle for the extinction measurement was 1.6° and1.9° for the 1.06 and 9.27 �m measurements, respec-tively. This implies an extinction error of less than 1%for a field of 5 �m droplets.17
Since a scattering signal is proportional to numberdensity and optical cross section, a ratio of signals atdifferent wavelengths and angles can be used to pro-duce size information for the droplets in the probevolume. Note that the traditional scattering equa-tions have been modified to include an optical thick-ness correction as shown in Eq. (1); details areprovided in Labs and Parker.2 The ratio of two sig-nals eliminates number density from the system, andthe signal ratio is a function of droplet diameter andsize distribution. A log-normal distribution was usedto represent the spray, and the Sauter mean diame-ter (SMD) indicated by the measurement is relativelyinsensitive to the width of the distribution.16 Thusthe scattering signal ratio provides a measure of the
Fig. 1. Optical layout for droplet sizing measurement. Unshadedrectangles represent beam splitters and the shaded rectanglesrepresent the first surface mirrors.
Scattering signals are assumed to be from photonsthat are scattered only once. See Labs and Parker2 fora complete discussion of the scattering technique em-ployed, the spray and background conditions used,and two-dimensional experimental results. Sampleresults for a combusting spray are shown in Figs. 2and 3. These results are 100 �s averages for the timeafter start of injection noted in the figures. Resultsshow SMD and liquid volume fraction in a high-pressure diesel spray.
For this infrared scattering technique, valid inter-pretation requires an exact overlap of the probe vol-umes and implicitly assumes homogeneity within theprobe volume. The significance of factors such as sizedistribution width, droplet sphericity, and beamsteering on the data set has been addressed in detailin Parker et al.15 and has been found to be negligiblefor the present system. This paper addresses, for thefirst time to our knowledge, experimentally deter-mined multiple-scattering effects for the infrareddroplet sizing technique. As with a majority of opticaldiagnostics, the infrared droplet sizing technique as-sumes that the light collected is scattered only once.The effort reported in this paper estimates the erroron reported droplet size and volume fraction (fromthe infrared scattering droplet sizing measurement)due to multiple scattering.
The measurement of multiple scattering is basedon the unique scattering properties of a sphere; spe-cifically, no cross-polarization term is produced. As-pheric drops, which do produce cross polarization in
scattering signals, can therefore complicate quanti-tative measurement of the multiple scattering. Pre-vious work for diesel sprays has concluded that, afterthe initial breakup, the Weber number for the drop-lets is approximately 1.5 decades below the valuerequired for breakup. Thus the disturbing force thatwould tend to produce aspheric droplets is small.16 Inregions of the spray near the tip where liquid breakupoccurs, one should include the possibility of depolar-ization from nonspherical particles; for example, pro-late spheroids with a 1.5 to 1 axis ratio in the sizerange observed in the spray can produce depolariza-tion up to 20% for 90° scattering.18,19
Figure 4 depicts the layout used to determine themultiple-scattering effects for the above-discussed in-
Fig. 2. SMD as a function of axial and radial position during eachof the characteristic time periods (spray development, 0.55 ms;steady state, 2.05 ms; and spray dissipation, 3.45 ms) for the com-busting spray. Initial conditions were 873 K and 12.5 atm.
Fig. 3. Liquid volume fraction as a function of axial and radialposition during each of the characteristic time periods (spray de-velopment, 0.55 ms; steady state, 2.05 ms; and spray dissipation,3.45 ms) for the combusting spray. Initial conditions were 873 Kand 12.5 atm.
Fig. 4. Optical layout for multiple-scattering measurements.
frared scattering droplet measurement technique. Acube polarizer was inserted into the optical train thatmonitored the Nd:YAG laser light scattering. Theextinction ratio for the polarizing cube was 20:1 forvertical polarization and 1000:1 for horizontal polar-ization and the probe beam was vertically polarized.Thus the perpendicular and parallel polarizationscattered light signals from the perpendicular probebeam were monitored simultaneously.
Figure 5 illustrates the scattering cross sections, atthe measurement conditions and angles, as a func-tion of diameter assuming a log-normal distributionwith a geometric standard deviation of 1.2. Multiple-scattering effects will be greater for systems withlarger scattering cross sections3 so that scatteringfrom the 1.06 �m probe laser will be most adverselyaffected by multiple scattering for regions wheredroplets are smaller than 3 �m. The infrared particlesizing method developed by the authors is based on aratio of the 1.06 �m scattering signal to the 9.27 �msignal. To correct for multiple scattering, one wouldneed to monitor both scattering polarizations fromboth probe beams. The goal, however, was to estimatethe error due to multiple scattering. The 1.06 �mscattering signal was chosen for the multiple-scattering measurement because the region near thecenterline is most adversely affected by multiple scat-tering and contains the smallest droplets of any re-gion of the spray (�3 �m for the combusting case).
The goal for this work was to estimate the sizingerrors due to multiple scattering, and this estimate isbased on a correction to the 1.06 �m scattering signaland the ensuing change in the scattering signal ratio.Total scattering cross sections (see Fig. 5) illustratethat, for droplets smaller than 3 �m, the scattering
cross section for 1.06 �m is dominant and thereforemultiple scattering at 1.06 �m will be greater thanthat for the 9.27 �m signal. Droplet sizing is based ona ratio of the two signals, and multiple-scatteringcorrections always decrease the observed signal level.Therefore multiple-scattering corrections act some-what in opposition to each other so that includingonly one correction can produce an extreme result.Thus, where the 1.06 �m multiple scattering is largerthan the multiple scattering for the 9.27 �m signal(i.e., for a field of 3 �m and smaller diameter drop-lets), the calculated error in size is an upper boundvalue. For sprays where the droplet sizes are domi-nantly greater than 3 �m, the error estimates pro-duced are not upper bounds but are estimates.
As shown in Fig. 4, the cube polarizer splits thescattered light into parallel and perpendicularly po-larized components (S� and S�), both of which weremonitored using InGaAs detectors. Single-scatteredlight from a spherical droplet retains the polarizationstate of the incident light (laser) if the probe polar-ization is either perpendicular or parallel to thedetection plane (for this system, perpendicularly po-larized light was used). However, multiple-scatteredlight does not retain the original perpendicular po-larization state.21 Instead, the polarization state isrotated and therefore has a perpendicular and paral-lel component. In the limit of many multiple-scattering events, the probe polarization is lost andthe scattering signal is randomly polarized.
Signals proportional to the amount of light withperpendicular polarization �S�� and parallel polariza-tion �S�� were generated using InGaAs detectors tocollect the signal from each polarization state of the90° angle 1.06 �m scattered light. Using these sig-nals (S� and S�) the single-scattering signal �Ss� forthe 1.06 �m signal could be estimated. Over the en-semble of scattering directions and collection pathsthat lead to the detectors, multiple scattering willproduce a near-random polarization signal with halfof the signal in the parallel state and half in theperpendicular state at the limit of complete multiplescattering.22 Because single-scattered light retainsthe polarization of the laser (perpendicular), the de-tector monitoring the parallel-polarized light re-sponds only to multiple-scattered light, and theresulting signal is equal to half of the total signal dueto multiple scattering �0.5 Sm�. The perpendicularlypolarized light consists of the total signal due to sin-gle scattering �Ss� and half of the total signal due tomultiple scattering �0.5 Sm�. Therefore a ratio (R) ofthe parallel-polarized light signal �S�� to the perpen-dicularly polarized light signal �S�� can be producedexperimentally and is represented by Eq. (2), which isbased on the signal definitions (in the limit of com-plete multiple scattering):
S�
S�
�0.5 Sm
Ss 0.5 Sm� R. (2)
A relationship between the signal due to single-
Fig. 5. Volume-normalized total scattering cross section as afunction of droplet diameter for both infrared wavelengths. Curvesare calculated for spherical droplets, a real index of 1.42 for bothwavelengths, and an imaginary index of 4.4 � 10�7 and 0.0012 for1.06 and 9.27 �m wavelengths, respectively.16 The geometric de-viation of 1.2 for the log-normal distribution has been used previ-ously for diesel sprays.16,20
scattered light �Ss� and the measured quantity S� isnecessary to determine the effects of multiple scat-tering and is given in Eq. (3), which can be found byalgebraically manipulating Eq. (2):
Ss � S�(1 � R). (3)
As R becomes large, multiple-scattering effects be-come significant. However, as R nears zero, Ss ap-proaches S�, and multiple-scattering effects can beneglected. Note that the analysis assumes that mul-tiple scattering is isotropic in polarization, and theresults ultimately provide an estimate of the sizingerror incurred when multiple scattering is ignored.True correction of the scattering signals for multiplescattering would require additional modeling or mea-surement that is beyond the scope of the currentwork.
For this system, R was measured on a point-by-point basis at time intervals of 2 �s for a given posi-tion. Data were collected over a number of sprayevents at varying positions within the spray; thesepositions were identical to those that were examinedusing the infrared scattering droplet sizing tech-nique. Because of the high number of data pointscollected by the system, R must be averaged to effi-ciently examine the consequences of multiple scatter-ing at any given position. Previously, the relevanttime periods for this type of spray were identified.2Figure 6 shows R as an error weighted mean fordifferent time periods: the spray development period�0–0.75 ms�, the steady-state spray period�0.75–3.5 ms�, and the total spray duration�0–3.5 ms�. Results are similar with the exception ofthe 1.8 mm radial position; however, the ratio at thislocation is small, which indicates no significantmultiple-scattering effect. Because of this consis-tency, for the results presented in the rest of this
paper, R is averaged over the entire duration of thespray pulse and is reported as an error weightedmean (see Eq. 4.17 from Bevington and Robinson23).
4. Results
Calculation of the estimated single-scattering signalfor the 1.06 �m probe beam allows a correction to oneof the two terms used to size droplets (recall that thesizing calculation is based on a ratio of scattered lightat two wavelengths as discussed in Labs andParker2). In fact, as noted previously, full correctionfor multiple scattering would require correction toboth scattering signals. Comparison of results fromuncorrected signals with those from a ratio that usesa corrected signal (1.06 �m scattering) and an uncor-rected signal (9.27 �m scattering) produces an esti-mate of the error due to multiple scattering. For casesin which the dominant correction is in the 1.06 �mscattering signal, this error estimate will be an upperbound on the error since any correction to the9.27 �m scattering signal would move the signalcloser to its uncorrected value. For systems that aredominated by droplets less than 3 �m in diameter,the 1.06 �m scattering correction will be dominant.Although this somewhat describes the combustingdroplet field, spatial variation of diameters does notallow one to state unequivocally that the droplet sizesfor the combusting case are always less than 3 �m indiameter. Thus, for the combusting case where thedroplets are small, one can consider the calculatederror to be large and approaching an upper bound onthe possible error. For the room ambient case wheredroplet sizes are slightly bigger (of the order of 5 �m),the calculated error is simply an estimate of the error.Therefore the error in the reported droplet size as afunction of the measured ratio R was calculated andis reported as a function of the ratio R for a range indroplet sizes. Figure 7 shows these results presented
Fig. 6. Error weighted mean of the ratio averaged over differenttime intervals: spray development, steady-state spray, and totalspray duration.
Fig. 7. Relative change in droplet diameter as a function of theratio R and initial reported droplet size.
as the relative change in droplet size for ratio valuesup to 0.5 (i.e., the parallel signal is one half the sizeof the perpendicular signal). As shown in Fig. 7, theerror increases as R increases for all droplet sizes,and smaller droplets produce a smaller error thanlarge droplets at the same value of R. For example, ifa 3 �m droplet was initially reported for a region ofthe spray where the polarization ratio was experi-mentally determined to be approximately 0.4, thecorrected size (from multiple-scattering errors in the1.06 �m beam only) is 3.3 �m; the initially reporteddroplet size was small by 10% (or 0.3 �m).
Additionally, the relative error in the volume frac-tion due to multiple scattering of the 1.06 �m signalwas calculated and is given as a function of the po-larization ratio for a range of droplet sizes. In con-trast to the droplet size error where multiplescattering always produced a positive error, volumefraction errors can be of either sign. The smallestdroplet diameter investigated �1 �m� produces a 44%underestimate of volume fraction at a ratio of 0.5whereas a 60% overestimate of volume fraction isproduced by a 16 �m SMD and a ratio of 0.5. It is ofinterest to note that the relative change in the vol-ume fraction can be negative or positive. Volume frac-tion is the product of number density and particlevolume and is calculated from the optical scatteringsignals, which are products of number density anddifferential scattering cross section. The volume frac-tion is calculated by finding the droplet SMD andthen uses this SMD to determine the differentialscattering cross section for the 9.27 �m probe wave-length. Using the 9.27 �m scattering signal and thedifferential scattering cross section (which does notvary monotonically with diameter), the number den-sity is calculated. Thus volume fraction, as currentlycalculated, is a function of droplet diameter and thedifferential scattering cross section. This leads to thebehavior in Fig. 8 that is a volume fraction error
dependence that ranges from an underestimate forsmall droplets to an overestimate for large droplets.An example of how to interpret Fig. 8 is given here: Inthe thickest regions of the combusting spray wherevolume fraction levels near 0.0075 and droplets are ofthe order of 3 �m, the maximum ratio measured was�0.2. Therefore the relative error in the reportedvolume fraction is approximately �12%, changingthe reported volume fraction to 0.0066.
The polarization ratio was experimentally deter-mined using three different background conditionsfor dodecane at constant injection conditions: peakfuel injection pressure of 80 MPa, nozzle orifice of160 �m, orifice length-to-diameter ratio of 4, dura-tion of approximately 3 ms.24 A combusting case wasexamined where the fuel was injected into an airbackground of 873 K and 12.5 atm absolute (again,see Labs and Parker for complete details24). Resultsfrom a high-pressure case in which the fuel was in-jected into a nitrogen background at room tempera-ture and 12.5 atm are also presented. Finally, resultsfrom injection into nitrogen at room ambient temper-ature and pressure are presented. For the remainderof this paper, these cases are termed combusting,high-pressure, and room ambient, respectively.
Figure 9 shows droplet sizing results from the in-frared scattering technique with errors due to onlymultiple scattering illustrated by the error bars.These results are from the region 25 mm below theinjector orifice beginning at centerline and movingoutward to the edge of the spray. It is clear that thespray into a high-pressure background spreads sig-nificantly more than the other two cases at this axialposition, and that the errors are larger. The combus-ting spray is expected to be the most optically thin ofthe three cases due to the evaporation of droplets andis therefore the least susceptible to errors from mul-
Fig. 8. Relative change in the volume fraction as a function ofdroplet size and ratio R. Fig. 9. Reported droplet size with error due to multiple scattering
depicted for three spray cases as a function of radial positionduring steady state.
tiple scattering. Results support this hypothesis andshow that, of the three cases examined, the combus-ting case is the least affected by multiple scattering.
The polarization ratio as a function of radial posi-tion was experimentally determined at two axial lo-cations for the high-pressure and room ambient spraycases and the results are presented in Fig. 10. Ratiovalues fall with distance from the centerline becausethe spray becomes thinner and the path that thescattered light must travel to reach the detector be-comes less attenuated.
It is clear that significant errors due to multiplescattering exist for the high-pressure case, most no-tably in the region nearest to the centerline. At10 mm from the orifice, the ratio rapidly drops off tolevels at or below 0.2 at a distance of 0.6 mm from thecenterline. However, at 25 mm from the injector ori-fice, the ratio values remain greater than 0.2 to adistance of 3 mm from the centerline.
Notable errors exist for the room ambient case atregions very near the centerline � 1.0 mm�. Both ax-ial positions show a drop of ratio value below 0.2 at aradial distance of approximately 1.0 mm. Thereforemultiple-scattering effects are negligible for roomambient conditions in regions greater than 1.0 mmfrom the centerline. This conclusion is also supportedby the data shown in Fig. 9.
Figure 11 shows a two-dimensional plot of ratio Ras a function of axial and radial position for the com-busting case. The greatest ratio value exhibited bythe combusting spray was near 0.2, indicating thatfor all regions investigated (greater than 10 mm fromthe injector orifice) multiple-scattering effects arenegligible (this was also apparent in Fig. 9). It is,however, interesting to note that the region with thelargest ratio value was not closest to the injectororifice as originally hypothesized by the authors. Ex-amination of Fig. 11 illustrates that the region of the
greatest ratio value was at an axial position of 15 mmalong the centerline.
5. Discussion
An interesting feature of the data is that the highestvalue of the polarization ratio does not directly cor-respond to the area of the spray with the highestoptical depth; optical depth is defined as the naturallog of the ratio I0�I for the Nd:YAG �1.06 �m� laser.Optical depth and the polarization ratio R as a func-tion of axial and radial position for the combustingcase are presented in Fig. 11. These results show thatthere is a lack of correlation between the opticaldepth and the errors due to multiple scattering. Thisresult strongly suggests that spray geometry plays animportant role in multiple-scattering effects.
The most glaring example of the effects of spraygeometry on the reported R value for the system isvery near the injector orifice. In this region, the sprayis relatively narrow with a high number density. Theoptical depth falls rapidly with distance from thespray centerline; however, the ratio values remainrelatively high for all regions near the injector orifice.Although the optical depth is low at the spray periph-ery near the orifice, a photon that is scattered awayfrom the detector into the thicker region of the sprayhas a good chance of being scattered again by anotherdroplet in the central region of the spray. With thissecond scattering event, the photon could enter thecollection volume and create error in the infraredscattering droplet sizing measurement.
Additionally, for a wide, more diffuse spray, themultiple-scattering errors will also demonstrate a de-pendence on geometry. For the region 25 mm fromthe injector tip, the optical depth is relatively large.However, the value for the ratio is not large presum-ably because it is relatively easy for photons to escapethe central, high number density regions. Therefore
Fig. 10. Measured ratio as a function of radial position for thehigh-pressure and room ambient cases during steady state.
Fig. 11. Measured ratio and optical depth reported as a functionof axial and radial position for the combusting case during steadystate.
errors due to multiple scattering not only depend onthe optical thickness of a system, but the systemgeometry as well.
The primary purpose of this investigation was todetermine regions within three types of spray condi-tion that were adversely affected by multiple scatter-ing. The multiple-scattering effects are considered tobe negligible when the values of R fall below 0.2; thiscriterion was determined by examining Fig. 7. At R� 0.2, the largest error possible is approximately 14%of a 16 �m droplet, which is 2.2 �m. However, forsmaller droplets (which are characteristic of combus-ting sprays24) this number drops significantly; at R� 0.2 the error for a 5 �m droplet nears 5%, which is0.25 �m. Notable errors occur in regions of the spraywith 0.2 R 0.4 and in regions where R � 0.4 isconsidered to be significantly affected by multiplescattering.
Throughout experimentation, the highest values ofR were exhibited by the high-pressure spray case;this case exhibits maximum values of R greater than0.5. When droplets are injected into an atmosphere ofhigh pressure, the enhanced fuel–air mixing at thespray periphery results in a wider, slower movingspray (compared with injection into a lower back-ground pressure). With increased temperature, thisimproved mixing enhances evaporation; liquid drop-lets are then moved to the gas phase, and overall thespray contains less liquid fuel mass, resulting in anoptically thinner spray. However, if the temperatureis not elevated, evaporation is insignificant and thisspreading and loss of velocity causes more droplets toremain near the injector orifice for longer time peri-ods (see Labs and Parker24 for a full discussion onspray characteristics). Effectively, the high-pressurecase will be most adversely affected by multiple scat-tering due to the wide geometry of the spray and thelarge liquid fuel mass near the injector orifice.
The room ambient case was also affected by mul-tiple scattering in some regions, although not as sig-nificantly as the effects on the high-pressure case.Within 1 mm of the spray centerline at both axialpositions investigated by this study (10 and 25 mm),the multiple-scattering effects on the spray into roomambient conditions are notable. However, outside thecentral 1 mm region, R values drop below 0.2 andmultiple-scattering effects near the spray peripherycan be considered negligible. The central region of theroom ambient spray is a very high-velocity region ofhigh liquid mass; however, the periphery is where themixing occurs and liquid volume fraction falls. There-fore the highest multiple-scattering errors are ex-pected near the centerline with these errors droppingwith increased radius.
The combusting spray exhibited the least suscep-tibility to multiple-scattering effects. With the high-est reported R value near 0.2, the entire spray regionexamined is negligibly affected by multiple scattering(see Fig. 11). Again, this result is due to the evapo-ration of the liquid droplets into the gas phase. Withless fuel in the liquid form, the spray becomes moreoptically thin and it is easier for photons to make it
out of the spray region without being scattered mul-tiple times.
6. Conclusions
Y A technique to quantify errors from multiple-scattering effects for the infrared scattering dropletsizing measurements has been developed and imple-mented. This technique was successfully applied tothree different background cases: a room ambientcase, a high-pressure case, and a combusting case.
Y Results from experimentation indicate thatmultiple-scattering effects are not only a function ofoptical depth, but system geometry as well.
Y Overall, the high-pressure, room ambient casedemonstrated the largest errors due to multiple-scattering effects. The room ambient case showedsome susceptibility near the centerline. However, thecombusting case was negligibly affected by multiplescattering throughout the region of interest. Thus thehigh-pressure and room ambient experiments wouldbenefit from cross-polarization measurements anderror correction in both scattering signals for someregions of the spray. However, for the regions 10 mmfrom the spray tip and beyond, for the combustingspray, no multiple-scattering error correction isnecessary.
Appendix A: Nomenclature
S�, signal in parallel polarization state,S�, signal in perpendicular polarization state,Sm, signal due to multiply scattered light,Ss, signal due to single-scattered light,R, ratio of parallel to perpendicular signal,S, scattering signal (V),G, gain for detector (unitless),R�, detector responsivity �V�W�,�sys, transmissivity of system (unitless),P�, beam power (W),N, droplet number density �m�3�,�, detector image width at the probe volume (m),�, scattering angle (rad),�, solid angle (st),I, beam irradiance �W�m2�,nDd
This research has been supported by a NationalScience Foundation (NSF) Career Award CTS-9502481 and NSF CTS-0072967; Farley Fisher, Con-tract Manager and NREL; Shaine Tyson, ContractManager; and partial research student support froma GANN grant, Department of Education. RayconCorporation conducted the custom drilling of the in-jector nozzle.
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