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Keywords:Abrasive jet machiningParticle orientationParticle embeddingPulsed laser shadowgraphySolid particle erosion

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lve damparticlex pro

the orientation of the particles at the moment of impact can

ransfer rate mayd particles [15].le embedment intiguous contactd throughout theic friction forcessized to strongly

vertex to the center of mass aligned with the velocity vector upon

Contents lists available at ScienceDirect

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Wear 336-337 (2015) 920http://dx.doi.org/10.1016/j.wear.2015.04.016of the particles remaining embedded into the target material. impact. While the model of Getu et al. [11] predicted that certainparticle orientations are more favorable to particle embedment,the particle orientations within an actual abrasive jet were notmeasured. The present study is thus mainly motivated by the

0043-1648/& 2015 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: 1 416 979 5000x7655; fax: 1 416 979 5265.E-mail address: mpapini@ryerson.ca (M. Papini).strongly affect the resulting erosion mechanism. Getu et al. [11]have shown that particle orientation may also affect the likelihood

depend on particle orientation, i.e. angular particles were morelikely to embed when their major axis connecting the leadingmaterial removal from the target surface [13]. Examples of suchsolid particle erosion processes include erosion in dust collectors,particle transportation in pipes and channels, and abrasive jetmachining processes. Erosion on brittle materials generally involvesfracture and crack propagation, while ductile materials are usuallyeroded through cutting, plowing and chip separation mechanisms[4,5]. As shown by Hutchings [6], and Papini and coworkers [710],

the surface roughness, thus affecting uid ow [1of micro-heat exchanger applications, the heat talso be reduced due to the presence of embedde

Getu et al. [11] identied two criteria for particsolid particle erosion processes: (i) that conbetween the particle and the target be maintaineimpact, and (ii) that the magnitude of the statreach a critical value. Both of these were hypothecessive impact of abrasive particles on a target that results in a similar mechanism reduces the etch rate [12], and also increases3,14]. In the AJM1. Introduction

Many industrial applications invogement of a jet of fast moving solidow. Solid particle erosion is a compsizes, and nozzle standoff distances. A particle orientation angle was dened as the angle between theparticle linear velocity vector (approximately parallel to the jet centerline axis) and the line connectingthe center of mass to the furthest downstream particle vertex. Particles were considered to be oriented,i.e. in a conguration favorable to embedding, if this angle was between 0 and 10. The measurementsrevealed that, at all pressures (i) between 24% and 29.5% of the particles were oriented at the nozzle exit;(ii) the percentage of oriented particles increased slowly with standoff distance; (iii) larger particles hada stronger tendency to orient than smaller ones; (iv) particles having larger aspect ratios had a strongertendency to aerodynamically align with the jet, and (v) although not all particles that were orientedactually embedded, the measured percentage of embedded particles on Al 6061-T6 surfaces neverthelesscorrelated with the percentage of oriented particles. A model capable of predicting the instantaneousparticle orientation and velocity within and downstream of the nozzle was presented and shown toagree well with measurements. To the knowledge of the authors, these are the rst measurements of theinstantaneous orientation of abrasive particles under conditions that are typical of abrasive air jets. Theresults may have important implications for optimizing solid particle erosion tests and in abrasive jetmachining applications.

& 2015 Elsevier B.V. All rights reserved.

age due to the impin-les propelled by a uidcess involving the suc-

Particle embedding can be undesirable in a variety of applica-tions. For example, it may cloud the results of solid particle erosiontesting of polymers and other soft materials since the embeddedparticles may shield the target surface from further impacts. In theabrasive jet micro-machining (AJM) of polymer microuidic chips,Accepted 26 April 2015Available online 5 May 2015Measurements and modeling of instantwithin abrasive air jets and implication

Vahid Hadavi, Bjrn Michaelsen, Marcello Papini n

Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria

a r t i c l e i n f o

Article history:Received 8 February 2015Received in revised form11 April 2015

a b s t r a c t

Previous theoretical studieembedding in solid particlimpact. The present studytaneous orientation distrib

journal homepage: wwweous particle orientationor particle embedding

et, Toronto, ON, Canada M5B 2K3

dicate that the material removal mechanism and the likelihood of particleosion processes strongly depend on instantaneous particle orientation atlized pulsed laser shadowgraphy to measure the size, shape, and instan-ns of particles within a micro-abrasive jet at various pressures, particle

lsevier.com/locate/wear

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V. Hadavi et al. / Wear 336-337 (2015) 92010unanswered question of which process parameters lead to theorientations favorable for embedding.

There are few existing analytical models capable of predictingthe inuence of the process parameters such as jet pressure andtravel distance on the rotation of particles in an air jet. Most stu-dies have focused on the behavior of spherical particles in a gassolid ow, which, due to their symmetry, are simpler to analyzeand measure. In these cases, the effect of parameters such asparticle density and size, and the viscosity and regime of the owon the behavior of the particles have been studied by investigatorssuch as Marchioli et al. [16], Kuerten [17] and Kulick et al. [18].Most actual applications, however, involve the use of irregularlyshaped particles, rather than idealized spherical ones.

A number of researchers have dened parameters to describenon-spherical particle shape, in order to assess their behavior in auid. For example, Wadell [19] introduced a sphericity factor, ,dened as the ratio of the surface area of an equivalent spherehaving the same volume as the actual particle, to the surface areaof the actual particle. Hzler et al. [20] utilized two measures ofsphericity, one in the lengthwise direction and the other in thecrosswise direction, in order to relate the drag force to theorientation of particles traveling in a uid. On the other hand, Lothet al. [21] suggested that the shape of a particle is best describedby its aspect ratio.

Because of the forces and moments that act on non-sphericalparticles in uid ows, their direction of motion can potentially beinuenced by their orientation. Generally, the rotational motion ofnon-spherical particles and their likelihood of orientation withuid ow depends on the shape of particle and the Reynoldsnumber regime of the ow. The behavior of elongated ellipsoidalparticles has been analytically studied by several investigators.Jeffery was one of the rst [22], while Brenner [23,24] and Harperand Chang [25] also further developed the theoretical models. Thebehavior of non-spherical particles has also been studiednumerically and experimentally by several investigators such asFan and Ahmadi [26], Zhang et al. [27] and Parsheh et al. [28]during the past two decades. However, most of these investiga-tions focused on Stokes ow in which case large aspect ratio hasbeen found to be most likely to align with the ow direction [29].Other Stokes ow studies such the one by Fan and Ahmadi [26]discuss the types of forces acting on a particle such as the shearinduced lift. Studies in the realm of Stokes ow are useful inapplications such as those describing blood ow or in the paperindustry to analyze ber ow, rather than the presently con-sidered high speed turbulent abrasive jet ow.

Particles in a turbulent ow may exhibit quite complex beha-vior which is dramatically different from that in Stokes ow. Ingeneral, not only may the motion of particles be inuenced by theturbulent ow, but also the characteristics of the ow may bealtered by the motion of the particles. For example, depending onthe ow regime and the shape of particles, non-spherical particlesare often subject to an irregular or wobbling behavior in a tur-bulent ow [30]. This implies that the particle secondary motionmay weaken the turbulent phase of the ow as a portion of theirlinear kinetic energy is transformed to particle rotational motion.Depending on the particle shape and size, the interaction betweennon-spherical particles and the ow can potentially intensify orweaken the turbulence.

Most models of the interaction between non-spherical particlesand uid ow focus on idealized disks, cylinders, long bers andellipsoids, for which a large variety of shapes can be describedusing few geometrical parameters. In their review of the literatureon the behavior of non-spherical particles in high Reynold'snumber ows, Mando and Rosendahl [31] noted that aky (asopposed to blocky) particles have been modeled using at ellip-

soids and disks of various aspect ratios. Depending on the regimeof uid ow and the aspect ratio, the particles may experience apreferred orientation [31]. For example, Christiansen and Barker[32] and Clift et al. [33] claim that particles above an aspect ratio of1.7 result in signicant secondary (i.e. rotational) motion. How-ever, Zhang et al. numerically modeled the behavior of elongatedellipsoidal particles in a turbulent uid ow, and found that onlyparticles with an aspect ratio greater than 5 are likely to rotate andalign with the ow direction [27]. Mortensen et al. [34] applieddirect numerical simulation (DNS) to study the behavior of ellip-soidal particles in a turbulent ow and also reported that thetendency for alignment increases with aspect ratio. In another DNSmodel, Paschkewitz et al. [35] found that rigid slender bers aremost likely to be aligned. They also calculated reductions in drag(up to 26%) depending on the aspect ratio and reported that par-ticle shape can signicantly affect the turbulence. Finally, Zas-tawny et al. [36] used DNS to estimate the lift, drag forces andtorques that act on four different non-spherical particles in a gasow.

A major difculty associated with modeling the secondarymotion of non-spherical particles is the determination of anappropriate drag coefcient, which in general depends on both theparticle shape and instantaneous alignment. While t parametershave been used to derive drag coefcients [36], this has been doneonly for a limited range of particle geometries and ow regimes,and most studies ignore the inuence of the instantaneous particlealignment relative to the ow direction.

Many techniques have been developed to measure particlebehavior in uidparticle ows. The earliest experimental studiesof the orientation of particles appear to have been conducted bymonitoring macroscopic particles in viscous uids [37]. Later on,Salem and Fuller [38] studied the behavior of particles using anoptical technique that captured the two-dimensional distributionof the small angle light scattering of particles in a ow. Bernsteinet al. [29] applied a coupled system of microscopic video-photo-graphy and image analysis to determine the orientation ofcylindrical particles both in laminar and turbulent water ows.They reported that the orientation of cylindrical particles wasinuenced by the particle rotational diffusion coefcient and owvelocity gradient. For ows more typical of abrasive jets, Ruff andIves [39] developed a rotating double disk apparatus that appliedthe time of ight principle to measure the average abrasive velo-city. Andrews and Horseld [3] utilized a single-frame longexposure camera with a halogen light lamp in order to measureabrasive particle trajectory and velocity. Andrews also developed aparticle correlation method that utilized an optical sensor in orderto determine the distribution of sand grain velocity in a sand-blastoperation [40]. Ghobeity et al. [41] applied a phase-Doppler par-ticle analyzer (PDPA), and Dehnadfar et al. [42] utilized double-pulse laser shadowgraphy in order to measure abrasive velocitydistribution. No attempt at measuring particle orientation wasmade in any of these studies.

In summary, although the behavior of spherical and non-spherical particles in uids has been measured and modeled inpast investigations, the studies mostly focused on Stokes ow.Very few considered ow regimes approaching those present insolid particle erosion testing and AJM applications, and noneconducted measurements of instantaneous particle orientation insuch ows. While previous studies have identied initial orienta-tions of angular particles that are most likely to give rise toembedding, none considered what process parameters are likelyto result in these particular orientations. The aims of this paperwere to address this question, by, for the rst time, measuring andmodeling the distribution of instantaneous angular particleorientations in an abrasive air jet under conditions that are typicalof solid particle erosion testing and abrasive jet machining

applications.

2. Experiments

2.1. Particle characterization

Four sizes of angular silicon carbide (SiC) powders (Gritsize60, 90, 120, and 180) were used in the experiments. Anoptical particle sizing system (Clemex PSA Research Unit, ClemexTechnologies Inc., Longueuil, Quebec, Canada) was used to obtainthe in-plane distribution of area, circular diameter(DCircular2 area/ ), and roundness (R 4 area 2

). Fig. 1 shows a

V. Hadavi et al. / Wear 336-337 (2015) 920 11perimeter

sample image of the particles obtained using this system.The distribution of the average particle out of plane thicknesses

was calculated based on non-contact optical prolometer (Nano-vea ST400, Micro Photonics Inc., Allentown, PA, USA) measure-ments of the ratio of the volume to the in-plane area. Parametersdescribing the obtained distributions of these parameters for allthe powders utilized in the experiments are provided in AppendixA. As an example, Fig. 2 shows the distribution of the DCircular, area,R, thickness and aspect ratio for three particle samples (90 grit)containing approximately 1000 particles.

For all grit sizes, the average thickness was 34 times less thanthe average circular diameter, indicating that the particles wereaky, rather than blocky.

2.2. Shadowgraphy measurements

2.2.1. ApparatusThe behavior of the airborne particles within the jet was studied

using images obtained from double-pulsed laser shadowgraphy.The jet was formed by a commercial micro-abrasive blaster (Accu-o, Comco Inc., Burbank, CA, USA) operating between 100 and500 kPa, utilizing a 40 mm long, 1.5 mm diameter round nozzle. Themass ow rate for each set of conditions was measured by col-lecting and weighing the particles exiting from the nozzle during ameasured time interval, and ranged from 0.41 g/min for the smal-lest particles (grit 180) to 3.12 g/min for the largest particles (grit60). Under these conditions, the average distance between theparticles in ight varied between 2 mm and 10 mm, thus ensuringthat there was very little, if any, interaction between them.

The details of the shadowgraphy apparatus can be found in Ref.[42]. Briey, a double-pulsed frequency-double Nd: YAG (neody-mium:yttrium aluminum garnet) laser, capable of generating amaximum 0.3 J/pulse pair at 1000 Hz was coupled to a high ef-ciency diffuser (Item No.: 1108417, Lavision, Gmbh, Goettingen,Germany). As shown in Fig. 3, the diffuser was placed directlyopposite a high speed CCD camera (Imager Pro PlusX, LavisionGmbH, Goettingen, Germany) tted with a high magnicationzoom lens (Navitar zoom 12 , Navitar Inc., Rochester, New York,USA) such that the axis of the diffuser and lens of the CCD camerawere aligned. The jet of particles was made to pass in a poly-carbonate chamber placed between the diffuser and CCD camerasuch that the particles on the focal plane of the lens were illu-minated by the laser pulses. The laser pulse duration was 1 ns, and,Fig. 1. Geometry of 90 grit SiC particles.depending on experimental conditions, the time intervals betweenpulses were generally in the range of 14 ms. For measurements ofrotation angle (Section 2.2), the time interval was increased to15 ms. In this manner, multiple sets of two images of the particlesin ight were obtained and used to determine the particle velocityand orientation.

Shadowgraphic measurements were made on airborne parti-cles within abrasive jets utilizing the four sizes of SiC particlesdescribed in Section 2.1, each using 5 different pressures and at5 different standoff distances from the nozzle exit (Table 1). Allmeasurements at a given combination of particle size, air pressureand standoff were repeated at least twice. Analyses were per-formed based on 2000 image pairs, since comparison to analysesusing 3000 images yielded differences in measured quantities thatwere at most 6.8%.

2.2.2. Analysis of the shadowgraphy imagesThe particle linear velocity distribution was measured from the

image pairs using Davis Software (Lavision GmbH, Goettingen,Germany) and, in order to evaluate the instantaneous angularposition of the particles within the jet, the images were alsoimported into Clemex PSA Professional Research Particle Size andShape Image Analysis software (Clemex Technologies Inc., Long-ueuil, Quebec). Two different measures of the angular positionwere used, the alignment angle and the orientation angle. Thealignment angle was dened as the angle between the line alongthe longest orthogonal distance between any two points on theedge of the particle (longest feret in Fig. 4a) and the velocityvector, which was approximately parallel to the jet axis. Thealignment angle reects the likelihood of aerodynamic alignmentsince it is dened based on the direction of the longest particledimension relative to the ow direction. Particle embedment, onthe other hand, depends more on the location of the particlecenter of mass relative to its leading vertex (the assumed targetimpact point), rather than the location of the longest feret. Toreect this, an orientation angle (Fig. 4b) was measured as theangle between the jet axis, i.e. the particle velocity vector, and theline connecting the furthest downstream particle vertex and theparticle centroid. In this scheme, a zero orientation angle indicatesa perfectly oriented particle with its velocity vector parallel to theline connecting the leading vertex and the center of mass. Thisdenition is consistent with that used by Getu et al. [11] in theiranalytical studies of embedding.

The X and Y coordinates of points dening the perimeters(Section 3), centers of mass, longest ferets, and leading vertices ofthe particles were obtained from analysis of the shadowgraphyimages using the Clemex software. A Matlab R2013a (Mathworks)routine was developed to determine the resulting distribution oforientation and alignment angles. Measurement of orientation andalignment angle distributions were based on their absolute values,i.e. direction of rotation was not considered, and the optimum binsize was chosen based on the FreedmanDiaconis rule [43].

The angular position distributions represent an instantaneoussnapshot at a given standoff and cannot be used to infer whetherthe particles were rotating. Therefore, for grit 60 particles at thenozzle exit, 20 and 40 mm standoff, the particle angular dis-placements (rotation angle) about their centers of mass thatoccurred during the interval between laser pulses were alsomeasured by considering the double pulse image pairs. To ensurethat particle rotations were only measured in the plane parallel tothe velocity vector, only particles with less than 20% variation inplanar area measured in successive images were used. To ensurethat the rotation of particle could be detected, the time intervalbetween the two laser pulses was set at 15 ms so that the distancetraveled by the particle was 34 times larger than the particle

dimensions.

V. Hadavi et al. / Wear 336-337 (2015) 920122.3. Particle embedment experiments

In order to determine whether orientation could be correlatedwith particle embedment, 5.5 mm thick Al 6061-T6 (90 BHN) sampleswere subjected to short bursts of the SiC abrasive powders using thesame setup described in Section 2.1 at a pressure of 300 kPa (Table 1).The samples were polished to a roughness of 0.02 mm and a

Fig. 2. Distribution of (a) in-plane area; (b) circular diameter; (c) roundne

Fig. 3. Shadowgraphy setup for measurement of particles velocity and orientation.programmable shutter device was utilized so that the substrate wouldbe exposed to the burst of abrasives for less than 12.5 ms to ensurethat individual embedded particles and impact craters could be

ss; (d) average thickness; and (e) aspect ratio for 90 grit SiC abrasive.

Table 1Combination of process parameters used in the shadowgraphy and embeddingmeasurements. Each condition was used for all four particles sizes described inAppendix A.

Distance from nozzle exit (mm) Jet pressure (kPa)

100 200 300 400 500

0 a a a a a

10 a a a a a

20 a a a a a

30 a a a a a

40 a a a a a

a Shadowgraphy experiment. Embedding experiment.

identied. All blasting was performed with the jet incident perpen-dicular to the target. After being exposed to the burst, the sampleswere cleaned with distilled water and dried using compressed air toensure that all the dust and/or deposited abrasives were removed.

Scanning electron micrographs (SEMs) were taken of theblasted surfaces, and the embedded particles were identied andcounted using energy dispersive x-ray spectroscopy (EDX) toconrm the presence of Si. The number of launched particles wasdetermined in a similar manner, except that the number of impactsites (sum of the identied impact craters and embedded parti-cles) were counted. The percentage of embedded particles wasdetermined as the ratio of the number of embedded particles tothe total number of launched particles. A calculation of the num-ber of blasted particles based on the average particle size, themeasured particle mass ow rate, the particle density, and theexposure time, typically yielded results that were within 8% of themanually counted impact sites. Fig. 5 indicates that most of theembedded particles penetrated into the target in the directionperpendicular to their thickness.

3. Model to predict particle orientation

Li et al. [44] developed a model that predicts the linear velocityof spherical particles in an abrasive ow, based on steady and

one-dimensional compressible airparticle ow in a frictionlessnozzle, ignoring the collisions between abrasive particles or with thenozzle. The model utilizes the particle and nozzle dimensions, theinput pressure and the air ow rate in order to determine the air andparticle velocities inside the nozzle and in the free jet. The distancefromwhere the particles are fed into the nozzle to the desired nozzlestandoff is divided into cells, and in each cell, the air velocity andresulting particle drag force are used to calculate the acceleration,and thus the linear velocity of the particles. The equations of motionare solved in each cell, until the air and particle velocity are obtained

orientation as the particle rotated and the frontal area changed.Theencsimcen

bypospar

(1)

(2)

V. Hadavi et al. / Wear 336-337 (2015) 920 13Fig. 4. Denition of (a) alignment angle , and (b) orientation angle for a typicalparticle.

Fig. 5. SEMshowing embedded SiC particles (solid lines) and impact craters

without embedded particles (dashed lines) in Al6061-T6.than 1% difference in calculated average velocity when 2500cells were used. In the cell that was furthest upstream withinthe nozzle, a random alignment angle (Fig. 4a) was assigned toeach particle which was assumed initially stationary.

(3) The forces acting on the particle in rst cell inside nozzle werefound. The equations of motion were solved and the linearvelocity, torque and resulting angular acceleration determined,along with the rotation angle and position of center of mass.The torque (T) in any given cell was calculated as

T F X 1n cp= ( )

where Fn is the net drag force and Xcp is the distance from thecenter of mass to the center of pressure of the particle, assumed tobe located at the mid-point of the instantaneous length of theparticle in the Y direction (Fig. 6). Fn was assumed to act along thejet axis, and be constant in a given cell as [44]determined from the analysis of the shadowgraphic images ofparticles at the nozzle exit (Section 2.2.2). For each particle,between 150 and 250 points were used to dene the particleperimeter. Therefore, the shapes of the particles used in thesimulation were two-dimensional projections of actual particles.The interior of the nozzle and the region between the nozzleexit and the desired standoff distance were divided into 2000cells, so chosen based on convergence studies that ensured a lessthe resultant drag force was calculated based on the relativeition of the center of mass and the center of pressure of theticles (Fig. 6). The model was executed using the following steps:

The skeleton point representation of the particle geometries, i.e.the X and Y coordinates of the perimeter of the particles, wereanyse variations in instantaneous drag coefcient not only inu-ed the rotational particle motion, but also the translational. Forplicity, it was assumed that all particles traveled with theirter of mass on the jet centerline. The translation and rotation ofgiven particle about its center of mass in any given cell causedat any position both within and after exiting the nozzle.The approach of Li et al. [44], developed for nonrotating sphe-

rical particles, was modied in the present work to take intoaccount angular particle shape, and rotational motion. The maincomplication in introducing rotating angular particles was in thecalculation of the drag coefcient, which not only depended on theindividual particle shape, but also changed instantaneously withFig. 6. Schematic dening particle parameters used in the model.

where I is the moment of inertia of the particle and dt is the time it

for spherical particles, and a modication of this model introducedby Dehnadfar et al. [42] for non-rotating angular particles.

4.2. Particle rotation angle

As a representative case, the distribution of measured particlerotation angles at three standoff distances are shown in Fig. 8 forgrit 60 particles.

The distributions follow typical log-normal patterns, with thevast majority of particles rotating less than 20 over the 1.11.3 mmrange of distances over which the measurements were made. Therewas an approximately 11% increase (from 58% to 69%) in particlesrotating less than 20 as the standoff increased from the nozzle exitto 40 mm. This implies a decreased rotational kinetic energy as theparticles travel in the jet and became more aligned with the ow.Assuming that particles travel an average distance of 1.2 mmduring the measurements, then, despite the fact that the average

120 100 74 78 80 86 94200 93 101 104 105 112300 108 114 131 140 150400 130 134 146 156 169500 148 168 175 180 187

180 100 93 101 104 106 109200 120 128 131 136 142300 136 141 155 165 177400 159 166 180 187 196500 167 185 194 201 208

Fig. 7. Predicted and measured average particle linear velocities for grit 60 and 90particles at 300 kPa.

V. Hadavi et al. / Wear 336-337 (2015) 92014takes for the particle to travel the very small length of one cell.In each cell, the skeleton point representation of the particle

periphery was updated considering the rotation occurring in theprevious cell by multiplying by an appropriate rotation matrix. Theupdated instantaneous alignment angle and projected area wereutilized at the beginning of next cell to calculate (step iii) the dragforce, linear velocity and corresponding rotation angle for that cell.This nested loop was repeated for all the cells to a standoff dis-tance of 40 mm to obtain the orientation and alignment angles,and the linear and rotational velocities and accelerations in eachcell for 200 particles, each of grit size 60 and 90.

The orientation angle of a given particle as dened in Fig. 4bwas predicted by determining, at the cell corresponding to thedesired standoff, the positions of the most downstream vertex andcenter of mass of the particle. The predicted orientation angles atdifferent standoffs could then be compared with the correspond-ing shadowgraphic measurements.

4. Results and discussion

4.1. Particle linear velocity

The measured average linear particle velocities at differentstandoffs and pressures are given in Table 2. For the 040 mmrange of standoff distances, the particle velocity increased with thestandoff distance in most cases, implying that the net drag forceacted furthest upstream side of the particle, tending to accelerateand rotate the particles. Fig. 7 shows the trend for two particlesizes at 300 kPa, together with the results from the model ofSection 3. For all particle sizes, the model was able to predict thelinear velocities to within a maximum error of 15%. The error islikely due to the fact that the same calibration factor for dragcoefcient (Appendix B) was used for both grit 60 and grit 90particles, resulting in over-estimates for the larger particle size andunderestimates for the smaller.

As expected, increases in pressure led to increases in particlelinear velocity; e.g., the average velocity of grit 90 particles at300 kPa increased from 110 m/s to 136 m/s as the standoff chan-ged from 10 mm to 40 mm. At the same pressure and standoff, asexpected, the particle velocity increased with decreasing particleF V V A C0.5 2n air air particle particle D2( )= ( )

where air is the air density. The air and particle velocities,V Vandair particle, were calculated following the procedure Li et al. [44],except that the instantaneous alignment-dependent equations fordrag coefcient, CD, presented in Appendix B were used rather thana constant drag coefcient. The instantaneous projected frontal areaof the particle, Aparticle, was determined as the product of themeasured average particle thickness (Section 2.3) and the instanta-neous height, calculated from the skeleton point representation ofthe particle which, as discussed below, was updated in each cell,according to the instantaneous alignment angle ( ), between theparticle major axis (i.e. longest feret of particle), L, and the jet axis.The particle angular acceleration , velocity and rotation angle about the center of mass were calculated using

T I 3= ( )

t dt

t dt tdt t

2 4 ( + ) = ( + ) + ( ) + ( )

( )

dt 5 = ( )size. These trends generally agree with the model of Li et al. [44]Table 2Average particle linear velocity (m/s) of particles at different standoffs and jetpressures.

Grit size Pressure (kPa) Average particle velocity (m/s)

Standoff (mm)

0 (Nozzle exit) 10 20 30 40

60 100 34 36 38 41 39200 60 66 67 69 67300 76 83 87 89 89400 87 96 100 106 106500 67 108 112 116 115

90 100 64 69 71 81 89200 88 90 96 101 106300 101 110 120 128 136400 110 116 125 131 141500 122 136 147 152 159rotational velocity is very high (25,000 rad/s), it can be concluded

material removal mechanism and likelihood of particle embeddingin the solid particle erosion of ductile materials [68,11]. As arepresentative example, Fig. 10 shows the distribution of orientationangle at a 20 mm standoff for grit 90 particles at 5 different pres-sures. Similar distributions were obtained for all other particles sizesand standoffs. There was a clear tendency for particles to orientthemselves with the jet axis at all pressures, i.e. the peaks occurredat low orientation angles. In all cases (i.e., all particles sizes, pres-sures, and standoffs), the differences in percentages of particles inthe rst three adjacent bins were all statistically signicant (t-test, Pvalue o0.05). In most cases, the differences in the relatively smallpercentage of particles traveling with orientations between 30 and90 were also statistically signicant. As can be seen in the examplegiven in Fig. 10, in all cases there was also no signicant effect (t-test,P value o0.05) of pressure on the percentage of the particles at anygiven range of orientations.

Fig. 11 gives the average percentage of the oriented particles(orientation angle between 0 and 10) at all air pressures for eachparticle size and standoff. It shows that larger particles are gen-

V. Hadavi et al. / Wear 336-337 (2015) 920 15that most (64%) of the particles rotate less than one full revolutionas they travel 20 mm.

4.3. Distribution of alignment angle

Fig. 9 shows that, consistent with Mortensen et al. [34], particlesthat have larger aspect ratios (AR, the ratio of longest to shortestferet) are more likely to align with the direction of uid ow. Forexample, there was approximately double the number of particles inthe left-most (most aligned) bin for particles having AR42.5 thanthose having ARo1.5. This increase is statistically signicant (t-test,P value o0.05). There was no statistically signicant effect of aspectratio on alignment when the aspect ratio was less than 1.5.

4.4. Inuence of process parameters on the distribution of orienta-tion angle

As mentioned in Section 2.2.2, the orientation angle at themoment of impact has been previously shown to strongly affect the

erally more likely to be oriented with the jet direction at a givenstandoff than small ones. At all standoffs, the percentage of

Fig. 8. Distribution of angular displacements of grit 60 particles at 300 kPa at thefollowing standoffs (a) nozzle exit; (b) 20 mm; and (c) 40 mm. The average lineardistance traveled by the particles whilst rotating through these angles was between1.1 and 1.3 mm.Fig. 9. Variation of the alignment angle with aspect ratio at P300 kPa and 20 mmstandoff for (a): grit 90; and (b): grit 60 particles. Scatter bars show the standarddeviation.

Fig. 10. Distribution of orientation angle at the standoff of 20 mm for grit 90 SiC

abrasives. Scatter bars show the standard deviation.

oriented particles was signicantly lower for grit 180 compared togrit 90 and 60, and also grit 120 compared to grit 90 and 60 (t-test,P value o0.05).

Fig. 11 also demonstrates that, for all particle sizes, particlestend to become more oriented with the jet as the standoff isincreased. The increase in percentage oriented was statisticallysignicant for any two standoffs with at least 20 mm difference (t-test, P value o0.05). The increase in the number of orientedparticles with standoff is expected and consistent with the dis-cussion of the measurements of rotation presented in Section 4.2,i.e., the orienting torques due to the drag forces have a longer timeto act on the particles.

4.5. Comparison between predicted and measured particleorientation

that the number of embedded particles also would increase with Fig. 12. Predicted and measured distribution of particle orientation angles atnozzle exit and 40 mm standoff for (a) grit 90, and (b) grit 60 particles at 300 kPa.

Fig. 13. Predicted and measured percentages of oriented particles (010) at dif-ferent standoffs for (a) grit 90, and (b) grit 60 particles at 300 kPa. Scatter bars onpredicted values show standard deviation of multiple runs of the model using 200particles.

V. Hadavi et al. / Wear 336-337 (2015) 92016standoff. Indeed, Fig. 14 shows that the measured percentage ofembedded particles from the experiments of Section 2.3 at 300 kPaincreased with standoff. This increase was statistically signicant forany two standoffs with at least 20 mm difference (t-test, P valueo0.05). For example, the percentage of the embedded particles forgrit 60 abrasives utilizing 300 kPa jet pressure was 1.2 times higher atstandoff of 40 mm than at 10 mm. This increase was due to a 14.7%increase in the average kinetic energy of the particle and a 24%increase in the percentage of the oriented particles. Fig. 14 also showsthat the percentage of embedded particles at a typical standoffincreased with particle size. For example, the percentage of embed-ded particles at a 30 mm standoff for grit 90 abrasives, was 1.25 timeshigher than that for grit 180 abrasives under the same test conditions.

Fig. 11. Average percentage of oriented particles for different particle sizes at dif-ferent stand offs. Each bar shows the average of all tested pressures, and scatterbars show the standard deviation.Fig. 12 shows the predicted (model of Section 3) and measuredorientation distributions of grit 90 and 60 particles at the nozzleexit and at a 40 mm standoff. The predicted and measured trendsare highly consistent, although there was a tendency to slightlyover predict the percentage of oriented particles.

Furthermore, Fig. 13 also shows that the model of Section 3.0was able to quite accurately predict the percentage of orientedparticles at any standoff distance. For example, Fig. 13 shows that,in the worst case, the model predicted approximately 39% of grit90 particles oriented with the jet axis at a 40 mm standoff, whilethe corresponding measured value was a 36%, i.e. the predictedwas 1.08 times the measured.

5. Inuence of particle orientation on particle embedding

Since it was shown in Section 4 that increased standoff distancesresulted in higher percentages of oriented particles, it was expected

Fig. 15 shows a correlation between the percentage of launchedparticles that embedded, and the percentage that were oriented(between 0 and 10 orientation angle) for all particle sizes andstandoffs at a 300 kPa pressure. The approximately linear corre-lation in Fig. 15 indicates that approximately 50% of the orientedparticles actually embedded.

The shortcoming of the above comparison, based on mea-surements made at different standoffs for a single pressure, is thatthe increase in standoff not only leads to a higher percentage oforiented particles, but also to a higher abrasive kinetic energy.Therefore, the correlation in Fig. 15 cannot be said to be due toorientation alone. Recalling that pressure had a negligible effect onorientation (Section 4.4), another set of experiments was per-formed in which the pressure was adjusted so that equal average

embedded to oriented grit 120 particles in the present study. WhileGetu et al. [11] did not establish whether particles meeting this rstcriteria were necessarily those which were oriented, the presentresults support that view. Finally, Getu et al. [11] also reported aninsignicant inuence of particle size on particle embedment inpolymers; although the abrasive sizes utilized in that work were in arelatively narrow size range (103136 mm). The present work is morein agreement with the experiments of Ref. [46] in which a directcorrelation between increasing particle size and increasing percen-tage of embedded particles was reported. A possible reason for thiscorrelation could be the fragmentation of large particles upon initialor subsequent impacts that has been reported by, e.g., Walley andField [47].

6. Conclusions

Double-pulsed laser shadowgraphy and image analysis wereused to study the instantaneous orientation of abrasive particleswithin an air jet. The results of this study may nd application inthe optimization of abrasive jet machining process parameters,and in solid particle erosion studies. The main conclusions can besummarized as follows:

(1) At all pressures, between 26% and 37% of the particles werefound to be oriented (orientation angle between 0 and 10)with the jet axis.

(2) There was a tendency for high aspect ratio particles to alignwith jet direction.

(3) Although up to 30% of the particles were oriented with the

Fig. 15. Correlation between percentage of embedded and oriented particles at300 kPa. The dashed line indicates a linear t to all data. Scatter bars show standard

Fig. 16. Comparison of percentage of oriented particles and embedded particles forthe tests at 10 mm standoff and 500 kPa pressure with 40 mm standoff and 300 kPa(grit 90). In both cases, the average particle velocity was 135 m/s.

V. Hadavi et al. / Wear 336-337 (2015) 920 17particle velocity was obtained at two different standoffs. Fig. 16shows that, for the same particle velocity, the percentage ofembedded particles at 40 mm standoff was 1.095 times higherthan at 10 mm, due entirely to the 1.15 times higher percentage ofparticle orientation at 40 mm. It also shows that, even at a con-stant velocity, similar to the correlation in Fig. 15, around 56% oforiented particles actually embed.

While these experiments are preliminary since they wereperformed on only a single material, should this correlation proveto be typical for a class of metals, or were there a method toestimate the correlation, then the demonstrated ability of themodel to accurately predict instantaneous orientation suggests aprocedure whereby estimates of embedding percentage could beobtained for a wide variety of applications. Measurement andmodeling of such orientation/embedding correlations is a topic forcontinued study.

Getu et al. [11] modeled embedding by assuming randomlyorientated idealized angular particles impacting polymeric targetsdescribed by a rigid-plastic material model. While the target is dif-ferent, some useful conclusions can be drawn by comparison withtheir work. For example, they reported that there was a preferredorientation for particles to embed with a minimum impact velocity,i.e., at a given incident velocity, particles with preferred orientationwere more likely to embed. Their conclusion is that preferredorientation occurs when the sum of impact angle and orientationangle is near 90, which is consistent with the present study, whichfound that orientations between 0 and 10 are likely to embed at a90 impact angle. Getu et al. [11] also reported that approximately25% of 136 mm garnet particles in their rigid-plastic model met anecessary, but not sufcient condition for embedment, i.e. the par-ticles maintained contiguous contact with the target during impact.This compares well with the 28% of oriented grit 120 particles foundin the present study at the same 20 mm standoff distance andsimilar pressures. The ratio between the embedded particles to thosemeeting this criteria in Getu et al.'s work [11] was 0.34, which isroughly comparable with the 0.42 ratio between the percentage of

Fig. 14. Percentage of embedded particles at different standoffs for different par-

ticles sizes at 300 kPa. Scatter bars show the standard deviation.deviations.jet axis at the nozzle exit, a statistically signicant tendency

was found for the likelihood of orientation to increase by up to1.24 times at a distance of 40 mm from the jet exit.

(4) The inuence of pressure on particle orientation at a givenstandoff was found to be insignicant.

(5) Larger particles were more likely to orient themselves in the jetdirection than smaller ones. At the same test condition (pressureand standoff), larger particles were more likely to embed.

(6) Although particles rotated rapidly, a large portion of them(64%) did not rotate for more than a full revolution over a20 mm distance.

(7) Orientation was correlated with embedding on virgin surfaces;i.e., approximately 50% of the oriented abrasives actuallyembedded. In terms of embedding, particle velocity was foundto be much less important than orientation.

(8) The model presented in this paper that took into account angularparticle rotation in the calculation of instantaneous drag forcewas able to accurately predict measured particle linear velocityand orientation distribution for a wide variety of process con-

Appendix A. Particle size and shape distributions

b 1

Finally, the thicknesses followed a log-normal distribution:

f xx

e,12 A-3

xLn

2

2

2

( | ) =( )

( ( ) )

Appendix B. Modeling of instantaneous drag force

Rosendahl [45] suggested that the drag coefcient of non-spherical particles could be based on their alignment in a ow(Fig. B1) as follows:

C C C C sin B-1D D D D, 0 , 90 , 03( ) ( ) = + ( ) ( ) = = =

In the present work, the angular particles were approximated astwo differently shaped ellipsoids for the purposes of the calculationof drag coefcient, based on the expressions for ellipsoids derived byZastawny et al. [36] in their direct numerical simulation (DNS) fra-mework for turbulent ow at Reynold's Numbers Reo1000. Shapes1 and 2 (Fig. B1) were used for particles with aspect ratios larger andsmaller, respectively, than 1.75. The drag coefcient at a giveninstantaneous was thus calculated using [36]

C C C C sin B-2D D D Da

, 0 , 90 , 00( ) ( ) = + ( ) ( ) = = =

where

CaRe

aRe B-3D a a, 0

1 32 4 = + ( )=

CaRe

aRe B-4D a a, 0

5 76 8 = + ( )=

TablDistr

3

1

al1

D 219.2 151.9 88.8

l a

ll aTh

mal

V. Hadavi et al. / Wear 336-337 (2015) 92018ickness Mean (lm) 94.9Standard deviation (lm) 31.6Distribution (thickness) Log normal m4.48 0.41 Log norundness Mean 0.60Standard deviation 0.11

Distribution (roundness) Weibull a0.64 b 6.51 WeibuRoparameters 2.8210 circular Mean (m) 362.9

Standard deviation (lm) 70.6Distribution Weibull a386.34 b7.03 WeibulStandard deviation

( m2 )32,629

Distribution and Normal m1.071054

Norm60

Area Mean ( m2 ) 107,357a a

e A1ibution of various characterizing parameters for the utilized SiC particles. f x a b

b xe,

A-2x a/ b( | ) = ( )

( )As shown in Table A1, the particle areas were found to follow anormal distribution:

f x e,12 A-1

x

2

2

2

( | ) =( )

( )

The circular diameters and roundness were found to best t aWeibull distribution of the following form:ditions. The model may be used in the future to aid in the pre-diction of particle embedding for a wide variety of applications.

Acknowledgments

The authors gratefully acknowledge the nancial support of theNatural Sciences and Engineering Council Research of Canada(NSERC) (le number: RGPIN - 2014-03895) and the CanadaResearch Chairs Program (le number: 950-228028).38.7 21.8 27.723387 b6.89 Weibull a161.26 b7.58 Weibull a98.66 b3.500.59 0.58 0.560.11 0.12 0.120.63 b5.94 Weibull a0.62 b5.94 Weibull a0.61 b5.0764.5 39.44 27.8623.2 12.2 10.48m4.09 0.40 Log normal m3.61 0.33 Log normal m3.28 0.36Grit size

90 120 180

8,909 18,507 6791

2,085 5183 4008

m3.89104.21104

Normal m1.77 1046.35103

Normal m6.801034.04103

Fig. B1. Two forms of simplied non-spherical shapes utilized in this study:(a) ellipsoid 1 and (b) ellipsoid 2 [33].

lipso

2.05.10.415.51.024.60.93.10.2

Table B2

)

ent

V. Hadavi et al. / Wear 336-337 (2015) 920 19are the drag coefcients at 0 and 90 respectively, anda a a, ,0 1 2, a3, a4, a5, a6, a7, a8 are the t parameters from Ref. [36],listed in Table B1 for the two assumed shapes.

Eqs. (B-3) and (B-4) were developed for Reo1000, while Re inthe present research could be as high as 15,000. Unfortunately,

Variations of drag coefcient versus traveled distance for 3 sample particles.

Particle number CD Distance from nozzle entrance (mm

0 10 20

1 a 0.69 1.42 2.22b 0.78 0.75 0.76

2 a 0.81 1.54 7.90b 1.45 1.41 3.61

3 a 1.35 1.81 1.55b 1.44 1.37 1.41

a Drag coefcient based on calculations of the present study (alignment dependb Drag coefcient based on calculations of Ref. [42].Table B1Value of t parameters used in Eqs. (B-2), (B-3) and (B-4) [36].

Fit parameter El

a0a1a2a3a4a5a6a7a8there is no data available in the literature for this range. Therefore,the CD in Eq. (B-2) was scaled for a best t of linear velocity withmeasured results. It was found that a constant factor of 3.75resulted in predicted linear velocities that agreed fairly well withmeasured ones for all standoffs, pressures and particle sizes.Comparison between the calibrated drag coefcient used in thepresent study and the term utilized by Dehnadfar et al. [42] fornon-rotating angular particles showed that variations of CD atdifferent standoffs followed the same pattern, and that overall,they were typically within 30% of each other (Table B.2). This lendscondence to the CD utilized in the present study.

An example of the t of measured and predicted velocitiesutilizing this correction was shown in Fig. 7.

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V. Hadavi et al. / Wear 336-337 (2015) 92020

Measurements and modeling of instantaneous particle orientation within abrasive air jets and implications for particle...IntroductionExperimentsParticle characterizationShadowgraphy measurementsApparatusAnalysis of the shadowgraphy images

Particle embedment experiments

Model to predict particle orientationResults and discussionParticle linear velocityParticle rotation angleDistribution of alignment angleInfluence of process parameters on the distribution of orientation angleComparison between predicted and measured particle orientation

Influence of particle orientation on particle embeddingConclusionsAcknowledgmentsParticle size and shape distributionsModeling of instantaneous drag forceReferences