ILASS – Europe 2010, 23rd Annual Conference on Liquid Atomization and Spray Systems, Brno, Czech Republic, September 2010Pre-filming primary atomization: Experiments and modelingS. Gepperth*, D. Guildenbecher, R. Koch, and H.-J. BauerInstitute of Thermal Turbomachinery (ITS),Karlsruhe Institute of Technology (KIT)Campus Süd, 76131 Karlsruhe, GermanyAbstractPrimary atomization in a planar pre-filming atomizer has been studied using high magnification shadowgraphycoupled with particle and ligament tracking. From this, mean drop sizes are reported for upstream locationswhich are inaccessible using PDA techniques. In addition, film thickness measurements and high speed visualizations have been performed. Based on these results, a new physics based model is derived to predict D32. Preliminary results indicate accuracy is within 30% of the measured values. This model has a number of advantages compared to previous alternatives, including prediction of upstream drop sizes and no reliance on unknownflow properties.IntroductionPre-filming air blast atomizers such as those shown in Figure 1(a) are widely used for fuel injection in gasturbine engines and have a number of advantages including fine atomization, relatively little change in performance over a wide range of fuel flow rates, and low pressure losses [1]. Currently, such atomizers are beinginvestigated for use in lean burn combustors which promise the additional advantages of fuel efficiency and lowpollution, particularly NOx [2]. However, because these designs operate below the stoichiometric fuel to air ratio, they are susceptible to flame instability and extinction. To overcome this, advanced designs are required toprecisely control fuel atomization and dispersion.Much of the previous investigations into atomizers of this type consist of spray measurements at elevatedpressures and temperatures using either actual nozzles [3] or simplified planar injectors [4]. Flows are typicallynon-reacting, and due to limited optical techniques fragment sizes are measured downstream where atomizationis complete and drops are approximately spherical.However, in reacting flows, drop evaporation and combustion is likely to be significant upstream of the coldflow measurement location. Consequently, simulations using inlet conditions from such measurement have limited accuracy. To remedy this, the first half of this work reports measurements of fragment sizes in the upstream dense spray region using a unique image processing routine. Additionally, film thickness measurementsare reported along with high speed videos of the primary atomization process.Currently few models exist to predict initial fragment sizes in pre-film atomizers, and those that are availablerequire knowledge of film properties which are difficult to estimate [5]. As a result, nozzle design must oftenrely on costly experimental trial and error. To address this, in the second half of this work a new atomizationmodel is derived to predict D32 based on known physics and experimental observations. Particular attention ispaid to ensuring that the model is well suited to future implementation in numerical simulation.Experimental setupIn order to enhance optical accessibility, a two-dimensional abstraction of an axis-symmetric airblast atomizer was used for all experiments. Figure 1(b) shows a cross section of the pre-filming surface and the surrounding duct. To ensure a two-dimensional air flow and avoid interfering corner vorticities, the duct has a wideaspect ratio [6]. The out of plane dimension is b 50 mm and all measurements were taken at the centerline.Furthermore, the air flowing around the pre-filming surface has no swirl. All measurements were performed atambient test conditions (ρg 1.2 kg/m-3, νg 1.5x10-5 m²/s), and the mean air velocity could be adjusted betweenūg 20 to 60 m/s.Liquid was supplied through 50 small vertical drill holes. Upon exiting the holes air shear caused the liquidto form a thin film travelling in the x-direction. The film load could be adjusted between V/b 25 to 75 mm²/s.For all film loads it was ensured, that the wetting of the surface was uniform and there was no film separationfrom the surface.To investigate the effect of different liquid properties on the primary breakup, four different liquids weretested in the experiment. Their relevant physical properties are shown in Table 1.*Corresponding author: [email protected]

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modeling grectangular duct prefilming surfaceyair flowxinlet 25mmz8mmx edge 69.5mmxatomizing edgeliquid injectionholes(a)(b)Figure 1. (a) typical gas turbine pre-film atomizer, (b) experimental atomizerTable 1. Liquid physical propertiesliquid50% propanediol-50% water (v/v)Shellsol D100Shellsol D70Shellsol D40dynamicviscosity, l[kg/m·s]0.006270.002550.001560.00089density, l[kg/m³]1004.3797.0792.0780.0kinematicviscosity, etension, [kg/s²]0.04540.03800.02600.0250ShadowgraphyThe disintegration of the liquid was analyzed by means of background illumination technique, using the optical setup shown in Figure 2. A dual cavity Nd:YAG pulse laser provided short time, high power back light illumination. The beam profile was broadened by an expansion lens and homogenized in intensity by means of adiffuser disc. Due to interference effects, laser speckles were generated at the diffuser which had the potential toreduce image quality. To overcome this phenomenon, a cuvette containing laser dye was inserted into the optical path. It absorbed the coherent laser light and emitted incoherent light of a different wavelength [7]. Singleframe shadowgraph images where recorded with a PIV camera in the xz-plane of the pre-filming surface. Theimage size was 15.2 mm in the z-direction and 7 mm in the y-direction. Examples are shown in Figure 3.The shadowgraphic images were analyzed using the MATLAB image processing code discussed in [6]. Acontouring algorithm performed a thresholding of the pixel array intensities with sub pixel accuracy, and all visible particle outlines were represented by a closed polygon. Open polygons represented particles at the borders ofthe image or the ligament structure at the atomizer edge and were removed for the analysis (Figure 3). With thisit was possible to determine the droplet sizes, positions, and counts as well as the ligament sizes and positions.Furthermore, unlike PDA measurements it was possible to estimate the diameter of non-spherical droplets,which is a great advantage especially in the primary atomization region near the atomizer edge.A comparison of the MATLAB code to commercially available shadow sizing codes can be found in [8].PIVCameracuevette diffuser expansionlenswith dyediscmeasurementvolume587 nm532 nmFigure 2. Optical setup for shadowgraphic images2dualNd:YAGlaser

ILASS – Europe 2010Pre-filming primary atomization: Experiments and #526#377#427(b)(c)(a)Figure 3. Examples of back light images. Fluid is Shellsol D70, V/b 25 mm²/s, (a) ūg 20 m/s,(b) ūg 40 m/s, (c) ūg 60 m/sExperimental resultsShadowgraphyFigure 4 shows D10, D32, and DV90 measured using the shadowgraphic technique as a function of mean airvelocity for a film flow rate of V/b 25 mm²/s. Liquid physical properties appear to have a relatively minoreffect on final drop sizes. This is theorized to be due to the opposing effects on fluid properties on film development and primary atomization. For example, fluid viscosity specifies the inner frictional forces of the liquidfilm such that higher viscosity results in a lower film velocity. Likewise, larger inertial forces are required toaccelerate a film of higher density. As a result, increased fluid density is expected to lower the film speed. Dueto these effects the relative velocity between the liquid and the gaseous phase will increase with increasing fluidviscosity and density, and it is well known that an increase in relative velocity enhances the atomization efficiency. However, it is also well known that high fluid viscosity and density act to stabilize a fluid against atomization [9]. Therefore, as a result of these offsetting effects the final change in drop sizes with fluid properties appears to be relatively minor and is likely within experimental uncertainty. Future investigations will be neededto reduce the experimental uncertainty such that these effects can be better quantified.Contrary to the minor effects observed due to liquid physical properties, the gas phase velocity appears tohave a major effect on the outcome of primary atomization. Mean diameters decrease with increasing air speed,which can be explained by the increasing aerodynamic forces acting on the surface of the ligaments.In addition to the influence of the liquid properties on the breakup of the liquid film, Figure 4 shows a comparison of the shadowgraphic measurement at the atomizer edge and PDA measurements taken 50 mm downstream of the atomizer edge for Shellsol D70. D10 from the PDA measurements is approximately 60% smallerthan that measured with shadowgraphy, and for D32 the difference is around 100%. The largest discrepancy between the PDA and the shadowgraphic measurements is for DV90 (approximately 130-230%). These differencesare due to the fact that the shadowgraphic measurements only cover the primary breakup zone whereas the PDAmeasurements were taken downstream of the atomizer edge where secondary breakup of the largest droplets hasoccurred. Consequently, the shadowgraphic measurements provide more complete information about the dropletsizes in the primary breakup region. As mentioned in the introduction, initial droplet sizes and positions have asignificant impact on the accuracy of numerical simulations, thus the improved knowledge provided here couldbe used to enhance the accuracy of future simulations.The same shadowgraphic measurements were performed at a film flow rate V/b 75 mm²/s and are shownin Figure 5. Comparing the results for D10, D32, and DV90 with the ones at V/b 25 mm²/s (Figure 4) revealssmall changes in the mean diameters which are likely within the experimental uncertainty of the measurementtechnique. Future investigations will attempt to quantify and reduce these uncertainties to enable a more detailedinvestigation on the influence of the film flow rate on primary breakup.High speed videosTo better understand the breakup process, high speed videos were recorded at frame rates up to 5 kHz usingthe shadowgraphic technique shown in Figure 2. Due to reduced resolution, fragment sizes could not be accurately determined from these videos. Nevertheless, they provide valuable insight into the atomization physics.Figure 6 shows typical results for two fluids. In both cases, a mass of liquid, referred to as a ligament, accelerates away from the atomizing edge while indentations appear in the perpendicular direction. The averagelength of the indentations is given the symbol lig, and was estimated manually from the high speed videos.Eventually these indentations form bag like structures which break into fine drops in a manner similar to bagbreakup observed during secondary atomization [10]. Events such as this appear to occur rather periodically,and manual analysis of the high speed videos was used to estimate the mean breakup frequency, f.Results for lig and f are shown in Figure 10 when discussing the new atomization model.3

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modeling(b)(c)(a)Figure 4. Variation of (a) D10, (b) D32, and (c) DV90 for varying mean air velocities and V/b 25 mm2/s(b)(c)(a)Figure 5. Variation of (a) D10, (b) D32, and (c) DV90 for varying mean air velocities and V/b 75 mm2/sFilm thickness measurementsAvailable models of pre-filming atomization require knowledge of the film thickness [5], which was measured here using a model LT-8100 laser focus displacement meter (LFDM) from Keyence Corporation. In thisdevice, the focusing lens of a 670 nm laser vibrates with a known displacement. Intensity of backscattered lightis recorded as a function of time, and it is assumed that peak intensity occurs when the laser focal point coincideswith the film surface. To prevent signal corruption due to light reflection from the aluminum pre-filmer, its surface was anodized using a black dye. With this it was possible to measure surface heights within a range of 1 mm and a resolution of 0.1 m. Further details on this device and its application to the measurement of filmsurface heights can be found in [11, 12].1 mmatomizing edge1 mmatomizing edge lig lig(a)(b)Figure 6. Typical high speed videos for ūg 40 m/s, V/b 25 mm2/s, time between images is 0.4 ms.(a) Shellsol D70 and (b) 50% propanediol4

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modelingThe LFDM principle assumes that the surface to be measured is a diffuse reflector, such that a backscatteredsignal is achieved regardless of surface angle. Unfortunately, the liquid surface measured here is specularly reflective, and, as a result, liquid height could only be measured when the surface was approximately perpendicularto the laser. Consequently, only the crests and troughs of the wavy film were detectable, and the signal qualitywas insufficient to calculate the wave frequency. Nevertheless, averaging the signal over time produced a goodestimate of the mean film height.Figure 7 shows the recorded mean film heights. These results are spatially averaged from measurementstaken between 15 to 35 mm after the film injection and 4 mm about the atomizer centerline. In all cases thestandard deviation is within 7% of the mean. As expected, film height decreases with increasing gas velocityand decreasing liquid loading.Theoretical modelingIn [5] Dombrowski presents a model for atomization of a liquid sheet acted upon by high speed air flowingover its top and bottom surface. A linear stability analysis is used to calculate the most unstable wavelength fora given sheet thickness, and growth of this wave is assumed to eventually lead to break up into streamwise ligaments. Finally, these ligaments are assumed to form drops due to capillary instabilities.Having measured the initial film thickness, this model can be applied here. Figure 8 compares the predictions of Dombrowski for a constant sheet thickness [5] with the downstream PDA measurements shown in Figure 4(b). Agreement between measurement and prediction is quite good. Here it should be noted that Dombrowski’s original work reports a model uncertainty as high as 20% [5]. Therefore, it is expected that experiments at other operating conditions may reveal larger uncertainties than those shown in Figure 8. Nevertheless,these results show that the Dombrowski model accurately predicts the downstream drop sizes measured here.Unfortunately, use of this model requires knowledge of the mean film height, a quantity which has provendifficult to predict or measure in realistic gas turbine injectors such as that shown in Figure 1(a). Furthermore,the model predictions do not agree with the upstream drop size measurements reported above. Therefore, toimprove upon this, the remainder of this work discusses the development of a new atomization model whichdoes not require film height as an input and is optimized to predict upstream drop sizes.Figure 9 outlines the proposed process. First, waves develop on the film and periodically transport mass tothe atomizing edge. This is assumed to result in the formation of cylindrical ligaments of diameter, Dlig, andfrequency, f. These ligaments are unstable due to capillary effects and break apart to form large drops of diameter Dd. Finally, these large drops are assumed to undergo secondary atomization via the bag breakup mechanism. In what follows, each process is considered in detail and models are presented to describe their effects.Film flowIn [4] Bhayaraju presents visualizations of the wavy film on a planar pre-filming atomizer similar to thatused in the current investigation. Large amplitude surface waves were observed which contributed significantlyto the breakup at the atomizing edge. Here it is assumed that these waves result from the Kelvin-Helmholtz instability wherein aerodynamic forces from the high speed, co-flowing gas destabilize the liquid film.Due to the inlet length, xinlet, shown in Figure 1(b), a boundary layer will develop in the air flow before contacting the film surface. As discussed in [13], the presence of such boundary layers dominate the KelvinHelmholtz instability whenever We ( l/ g) 1 where We is the Weber number based on the gas phase boundarylayer and is the vorticity thickness.(b)(c)(a)Figure 7. Mean film height for (a) V/b 15 mm2/s, (b) V/b 25 mm2/s, and (c) V/b 50 mm2/s5

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modelingFor all conditions considered here Reinlet 5x105such that laminar boundary layer development can be assumed, and from the analysis of Blasius [14] xinlet 3.012Reinlet.(1)Using Eq. (1) it can be shown that We ( l/ g) 1 for all testconditions. Therefore, based on the analysis presented in [13] theinitial wave frequency can be approximated by f (uc/ )( g/ l)1/2where uc is the initial wave convection velocity approximated byuc ūg( g/ l)1/2. Combining this with Eq. (1) yields:Figure 8. Comparison betweenpredictions of Dombrowski [5] anddownstream measurements forShellsol D70 at V/b 25 mm2/sf 0.331ugxinlet gReinlet l . (2)If it is assumed that all initial waves accelerate downstream at anequal rate, then Eq. (2) can be used to estimate the frequency ofwaves reaching the atomizing edge. By further assuming that onespanwise ligament forms from each wave, Eq. (2) can also be used topredict the atomization frequency.Figure 10(a) compares the measured frequency from the high speed videos to that predicted by Eq. (2). Thesolid black line represents the best fit between measurements and prediction. From this it can be concluded thatEq. (2) should be multiplied by a constant 1.45 to account for non-linear effects which cannot be predicted by thelinear stability analysis used here. Once this is done reasonable agreement is achieved between theory and experiment.Ligament formation and breakupAssuming the spanwise ligaments are initially cylindrical, mass conservation yields: Dlig2/4 (V/b)/f. Because aerodynamic forces are negligible in the parallel direction, it is reasonable to assume these cylinders breakup due to capillary instabilities. For this case, Rayleigh’s analysis predicts the most unstable wavelength, lig 4.508Dlig [15]. Combining this with Eq. (2) including the 1.45 factor yields: lig 7.342 V b xinlet lug1 2 1 Reinlet 4 . g (3)Figure 10(b) compares the observed breakup wavelengths with those predicted by Eq. (3). The solid blackline represents the best fit between measurements and prediction. On average the agreement between experiment and theory is quite good and practically no correction is needed. It is supposed that the large scatter in thedata is due to measurement uncertainties, and improved measurement techniques are needed to reduce this uncertainty.Oligfilmflow1mmatomizing ligamentformation RayleighbreakupOligDdDlig(a)(b)Figure 9. Atomization model: (a) typical experimental observations and (b) proposed model6bagbreakup

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modelingIgnoring satellite drops and assuming that one drop of diameter, Dd, forms from each wavelength, mass conservation yields, Dlig2 ig/4 Dd3/6. Combining this with Eq. (3), results in a prediction for the large initialdroplets:Dd 3.130 V b xinlet lug1 2 1 Reinlet 4 . g (4)Droplet breakupAccording to the proposed model, these large drops immediately undergo further breakup due to aerodynamic effects. This is referred to as secondary atomization, and for drops of low viscosity (Ohd 0.1) previous experimental investigations have shown that breakup occurs when Wed 11 where Wed is the Weber number basedon the drop diameter [10]. Note that Ohd 0.1 for all cases considered here.Observations of secondary atomization have shown that various breakup modes are possible depending onthe level of aerodynamic loading. Bag breakup occurs for 11 Wed 35, wherein the center of the drop isblown downstream and the periphery forms a thick torodial rim [10]. A similar breakup process is observed inthe high speed videos shown in Figure 6 and Figure 9(a). For this case, Wert provides a model which predictsthe fragment D32 based on the initial Weber number [16],D32 0.324 g ug2 Wed Ttot Tini 23.(5)Here Ttot is the non-dimensional total breakup time and Tini is the initiation time, which Hsiang approximates as 5and 1.6 respectively for Ohd 0.1 [17].When applying Eq. (5), special attention must be paid to the relative gas velocity. In the current model thedrops are assumed to break up at the atomizing edge where boundary layers result in a local gas velocity, ug, thatis significantly less than the mean gas velocity, ūg. To approximate this, the gas phase boundary layer is modeled using a flat plate solution ignoring the effect of the liquid film. In that case, the appropriate boundary layerdevelopment length is xedge (Figure 1). Using this it can be shown that Reedge 5x105 for all conditions considered here. Therefore, the boundary layer remains laminar, and the relative gas velocity is approximated fromthe Blasius solution at y Dd/2.Figure 10(c) compares D32 calculated using Eq. (5) with the measured values shown in Figure 4 and Figure5. At the lowest air velocities it was occasionally found that Wed 11, such that bag breakup is not expected andEq. (5) could not be applied. For these situations it was found that D32 Dd/2.The solid black line in Figure 10(c) represents the best fit between theory and the experimental measurements. For all conditions considered here, agreement is within 30%, indicating that the proposed model hasadequately captured the most important physics.(b)(c)(a)Figure 10. Theoretical predictions compared to measurements for (a) breakup frequency, (b) spanwisewavelength, and (c) D32 after primary atomization7

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modelingFuture investigations will attempt to reduce the model uncertainty using more precise measurements and incorporating additional physical effects. For example, knowledge of the film flow is currently limited and it isunclear if the model has accurately predicted the actual wave frequency. To address this, future investigationswill attempt to measure the wave frequency. Furthermore, Figure 10(a) reveals that the accuracy of the predictedfrequency is a function of the material properties, and it seems likely that the uncertainty could be reduced if Eq.(2) were to include the stabilizing effect of liquid phase viscosity.For practical applications of the proposed model, Eq. (4) would be used to estimate the initial droplet size.Then atomization of these droplets would be predicted using either experimental correlations such as Eq. (5) ornumerical atomization models such as the TAB [18] or DDB [19] methods. Therefore, as currently constructed,this model could be incorporated into Lagrangian droplet tracking codes which include computation of secondary atomization. This would then allow for simulation of spray drop sizes and dispersion for a practical atomizersuch as that shown in Figure 1(a) without the need to measure initial droplet sizes. Of course, validation is required before this is recommended for design proposes.ConclusionThis work considered liquid atomization in a planar pre-filming air blast atomizer. The influence of liquidphysical properties, air velocity, and film flow rate were studied by means of shadowgraphy, PDA measurements, high speed visualization and film thickness measurements. Particular attention was paid to the meandroplet diameters in the primary breakup zone.For the range of conditions considered here, changes in the mean air velocity resulted in the most significanteffect on mean diameters while modification of the liquid physical properties or flow rate produced relativelyminor effects.Based on the experimental results, a new physics based model was derived to predict D32. The accuracy iswithin 30% of the measured values. The main advantages of this model are: prediction of the droplet sizes inthe near region of the atomizer edge and no reliance on unknown flow properties, such as the film thickness.To validate the results presented here, future work is planned to improve the accuracy of the experimentaltechniques and measure the frequency and size of waves on the film surface.NomenclatureDdrop diameter [m]fwave or atomization frequency [s-1]hmean film height [m]Oh Ohnesorge number, l/( l D)1/2Re Reynolds number, ugx/ gTini non-dimensional initiation timeTtot non-dimensional total breakup timeuvelocity in the x-direction [m s-1]ūmean u through a yz-plane [m s-1]V/b volumetric film flow rate per unit length in the z-direction [m2 s-1]We Weber number, gug2D/ vorticity thickness, ūg/(dug/dy)max [m] lig spanwise wavelength [m] dynamic viscosity [kg m-1 s-1] kinematic viscosity [m2 s-1]ρdensity [kg m-3] surface tension [kg/s2]SubscriptsggaslliquidAcknowledgementThe research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n ACP8-GA-2009-234009.This study is part of the 4-year KIAI project started in May 2009, a European initiative financed under theFP7 and which addresses innovative solutions for the development of new combustors in aero-engines. It aims atproviding low NOx methodologies to be applied to design these combustors.8

ILASS – Europe 2010Pre-filming primary atomization: Experiments and modelingReferences[1] Lefebvre, A. H., Atomization and Sprays 10(3-5): 251-276 (2000).[2] Lazik, W., Doerr, T., Bake, S., Bank, R. v. d., Rachwitz, L., ASME Turbo Expo, Berlin, Germany (2008).[3] El-Shanawany, M. S., Lefebvre, A. H., Journal of Energy 4(4): 184-189 (1980).[4] Bhayaraju, U., Hassa, C., Atomization and Sprays 19(12): 1147-1169 (2009).[5] Dombrowski, N., Johns, W. R., Chemical Engineering Science 18(3): 203-214 (1963).[6] Müller, A., Koch, R., Bauer, H. J., Hehle, M., Schäfer, O., ASME Turbo Expo, Barcelona, Spain (2006).[7] Müller, A., Dullenkopf, K., Bauer, H.-J., 14th International Symposium on Applications of LaserTechniques to Fluid Mechanics, Lisbon, Portugal (2008).[8] Kapulla, R., Tuchtenhagen, J., Müller, A., Dullenkopf, K., Bauer, H.-J., 16 GALA-Fachtagung, (2008).[9] Weber, C., Zeitschrift für angewandte Mathematik und Mechanik 11(2): 136-154 (1931).[10] Guildenbecher, D., López-Rivera, C., Sojka, P., Experiments in Fluids 46(3): 371-402 (2009).[11] Ebner, J., Gerendas, M., Schäfer, O., Wittig, S., Journal of Engineering for Gas Turbines and Power124(4): 874-880 (2002).[12] Kneer, J., Eastwick, C., Müller, A., Johnson, G., Robinson, A., Bauer, H.-J., ASME Turbo Expo, Berlin,Germany (2008).[13] Villermaux, E., Physics of Fluids 10(2): 368-373 (1998).[14] White, F. M., Viscous Fluid Flow, McGraw-Hill Book Co. (1991).[15] Rayleigh, L., Proceedings of the London Mathematical Society s1-10(1): 4-13 (1878).[16] Wert, K. L., International Journal of Multiphase Flow 21(6): 1063-1071 (1995).[17] Hsiang, L. P., Faeth, G. M., International Journal of Multiphase Flow 19(5): 721-735 (1993).[18] O'Rourke, P. J., Amsden, A. A., International Fuels and Lubricants Meeting and Exposition, Toronto,Ontario (1987).[19] Ibrahim, E. A., Yangt, H. Q., Przekwas, A. J., Journal of Propulsion 9(4): 651-654 (1993).9

Karlsruhe Institute of Technology (KIT) Campus Süd, 76131 Karlsruhe, Germany . investigated for use in lean burn combustors which promise the additional advantages of fuel efficiency and low . paid to ensuring that the model is well suited to future implementation in