A Numerical Study on Metallic Powder Flow in Coaxial Laser Cladding

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1 Journal of Appled Flud Mechancs, Vol. 9, No. 5, pp , Avalable onlne at ISSN , EISSN DOI: /acadpub.afm A Numercal Study on Metallc Powder Flow n Coaxal Laser Claddng H. Lu 1,2, J. B. Hao 1, G. Yu 3, H. F. Yang 1, L. W. Wang 4 and Z. T. Han 1 1 School of Mechancal and Electrcal Engneerng, Chna Unversty of Mnng and Technology, Xuzhou, Jangsu, , Chna 2 Jangsu Key Laboratory of Mne Mechancal and Electrcal Equpment, Chna Unversty of Mnng & Technology, Xuzhou, Jangsu , Chna 3 Key Laboratory of Mechancs n Advanced Manufacturng, Insttute of Mechancs, Chnese Academy of Scence, Beng, , Chna 4 School of Cvl Engneerng, Beng Jaotong Unversty, Beng, , Chna Correspondng Author Emal: luhao56@cumt.edu.cn (Receved September 20, 2015; accepted November 11, 2015) ABSTRACT In coaxal laser claddng, the qualty and property of deposton products are greatly nfluenced by the powder flow, whch s responsble to transport addtve materals to the deposton pont on a substrate precsely. The metallc powder flow n coaxal laser claddng s smulated by a numercal model based on the gas-sold flow theory. The characterstcs of powder concentraton dstrbuton between coaxal nozzle and deposton pont for a nd of ncel based alloy powder are studed by the proposed model. The relatonshp between the process parameters and powder flow characterstcs, such as focus dstance from the nozzle ext and maxmum powder concentraton, s analyzed to optmze the powder feedng process. In addton, the nfluence of substrate wth dfferent surface shapes on the powder flow s nvestgated. The results can be used as a gudelne for the locaton of the substrate and the selecton of proper processng parameters for coaxal laser claddng. Keywords: Coaxal laser claddng; Gas-sold flow; Powder concentraton dstrbuton; Substrate shape. NOMENCLATURE a1, a2, a3 constants for sphercal partcles C1ε, C2ε emprcal constants n -ε model CD drag coeffcent CL tme scale constant Cμ constant n the turbulent vscosty dc dameter of carrer gas nlet de dameter of nozzle ext d dameter of nner gas nlet dm partcle sze constant do dameter of outer gas nlet dp partcle dameter dt tme step en resttuton coeffcent F powder feed rate FD drag force per unt partcle mass and unt velocty dfference Fd mass fracton of partcles wth dameter greater than d F addtonal force per unt partcle mass Gb generaton of turbulence netc energy due to buoyancy G rate producton of turbulence netc energy owng to the mean velocty gradent Re S tc u, u u1p, u2p up u, v, w v vc v vo wm wo relatve Reynolds number sectonal area of the nozzle nlet tme for the partcle to cross the vortex, component of the gas velocty partcle velocty before and after collson component of the partcle velocty random velocty fluctuaton gas velocty at nozzle nlet velocty of carrer gas flow at the nozzle nlet velocty of nner gas flow at the nozzle nlet velocty of outer gas flow at the nozzle nlet wdth of mddle annular channel wdth of outer annular channel x, x poston n, drecton δ ronecer delta ε dsspaton of netc energy of turbulence ζ normally dstrbuted random number θm angle of mddle annular channel

2 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , g component of the gravtatonal acceleraton h heght below the nozzle ext netc energy of turbulence Le vortex length scale n spread parameter Prt turbulent Prandtl number p pressure Q gas volume per unt tme θo μ μt ρ ρp σ, σε τ τe τ angle of outer annular channel molecular vscosty turbulent vscosty gas densty partcle densty emprcal constants n -ε model partcle relaxaton tme vortex lfe vscous stress 1. INTRODUCTION In laser claddng process, a hgh-performance coatng can be produced by addng metallc materals nto a movng melt pool through sequental deposton tracs. Each trac s created by rapd soldfcaton of the melt pool that s formed by meltng the addtve materals and a thn layer of the substrate employng a laser beam. Combnng wth a computer-aded desgn model of an obect, ths technology can also be used to create a three-dmensonal component by mult-layer deposton (Dnda et al. 2012). The addtve materal usually s n the form of metallc powder, whch can be nected laterally or coaxally to the laser beam (Zeovc et al. 2007). Between the two dfferent ways of powder feedng, coaxal laser claddng s easer to realze automaton because of ts ndependence from the drecton of moton (Pnerton and L 2004). The coaxal laser claddng process can be classfed nto three stages. In the frst stage, metallc powder partcles are delvered nto the substrate by a carrer gas flow. Laser beam, powder flow, and gas flow nteract wth each other before these partcles reach a substrate. In the second stage, laser energy s absorbed by the surface of the substrate, so a melt pool s formed by molten metal and the powder partcles. When the substrate or the laser beam moves, the melt pool soldfes rapdly and then a thn layer s produced on the substrate surface n the thrd stage. The powder flow characterstcs n the frst stage of coaxal laser claddng, such as the powder focal dstance and the maxmum powder concentraton, not only domnate the total mass of powder partcles reached the melt pool, but also have a great nfluence on the laser power attenuaton (Pnerton 2007). The clad qualtes are nfluenced by the powder concentraton dstrbuton between the coaxal nozzle and the substrate (Lu and L 2005). Therefore, t s essental to study the powder flow characterstcs to buld a coatng on substrate wth accurate dmensons and hgh powder usng effcency. The powder flow characterstcs are determned by many factors, ncludng the structure and the sze of coaxal nozzle, sheldng gas flow rate, carrer gas flow rate, powder feed rate, the propertes of powder partcles and envronmental condtons. There are complex relatonshps between these nput varables and the powder concentraton dstrbuton. Ln (2000) studed the focused and columnar powder streams of a coaxal nozzle wth varous arrangements of the nozzle ext, provng that the nozzle arrangements play a crtcal role n concentraton mode of the powder flow. Pan and Lou (2005) presented a stochastc model consderng powder partcles shape effects to smulate the powder flow n the nozzle. They studed the effect of the wdth of the powder outlet passage on the powder flow shape. Yang (2009) developed a concentraton model of powder partcle stream for coaxal laser claddng, and found that the ext wdth of the coaxal nozzle had a postve relatonshp wth powder stream dameter and a negatve relatonshp wth pea powder concentraton at focus poston. Tabernero et al. (2010) nvestgated the powder flux dstrbuton evoluton for three dfferent nds of metallc powder usng a 3-D numercal model. Balu et al. (2012) conducted a parametrc study on a coaxal mult-materal powder flow, and measured some ey powder flow characterstcs, such as the standoff dstance, the dameter of the powder stream at the stand-off dstance, and the velocty of the powder partcles. Lu et al. (2015) studed the collson behavor of partcles wth the nternal wall of a coaxal nozzle, and revealed the effect of powder propertes on the powder flow through a gas-sold model. However, process parameters such as sheldng and carrer gas flow rate, powder feed rate, the shape of substrate, have barely dscussed n those wors. In ths paper, a 3-D numercal model of metallc powder flow s developed based on a gven coaxal nozzle, whch has the ablty to predct the powder concentraton dstrbuton, partcle veloctes and traectores between the coaxal nozzle and the deposton pont. The relatonshp between the gas flow rate and powder concentraton dstrbuton s nvestgated. Further, the effect of substrate on the powder flow s also dscussed. 2. POWDER FLOW MODEL 2.1 Descrpton and Assumptons Laser claddng process and a typcal coaxal nozzle s shown n Fg. 1. There are three dfferent nd of gas flow n the coaxal nozzle. At the center, the gas flow s parallel to the laser beam and the man purpose of ths nner gas flow s to protect the lenses from the hot powder partcles that rcocheted from the substrate. Another nd of gas flow called carrer gas flow s to transport the powder partcles to the deposton pont. The outer gas flow generates protectve atmosphere n perpheral of 2248

3 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , powder flow to prevent powder partcles from oxdaton. All these gas flows and ther nteractons affect the powder concentraton dstrbuton below the ext of coaxal nozzle. Fg. 1. Setch of laser claddng process and geometry structure of coaxal nozzle. In the powder stream, sheldng and carrer gas should be consdered as contnuous phase whle powder partcles should be treated as dscrete phase nto the contnuous phase. Hence, the model of powder stream conssts of two dfferent modules. The proposed model s based on the followng assumptons (Zeovc et al. 2007): 1. The gas flow s consdered as a steady-state turbulent flow wth constant velocty dstrbuton at the nlet boundary. The ntal veloctes of powder partcles are constant and perpendcular to the nlet surface of the nozzle. 2. The forces of drag, nerta and gravty are consdered n the model, whle other forces, ncludng pressure and surroundng flow acceleraton, are neglected. 3. The collson between partcles s not consdered, because the probablty s too low. 4. The powder partcles are sphercal, and the partcle sze s assumed to follow the general Rossn-Rammler dstrbuton expresson. 5. Heat transfer by laser radaton s neglected. 6. Powder partcles flow represented as a dscrete phase does not affect the contnuous phase due to the low mass and concentraton of the partcles. 2.2 Contnuous Phase Modelng The contnuous phase modelng s based on Naver- Stoes dfferental equatons wth the Reynolds method of averagng tme-dependent equatons, together wth the standard -ε turbulent model. Snce the gas flow s consdered to be steady, ncompressble, sothermal and chemcally homogeneous, the tme-averaged, governng equatons for turbulent flow are expressed as follows (Zhao et al. 2015). Conservaton of mass: x ( u ) 0 (1) where ρ s gas densty, and the vectors u and x represent the velocty and poston n drecton. Conservaton of momentum: p ( uu ) g x x x (2) where p, g and τ s pressure, gravtatonal acceleraton, vscous stress tensor, respectvely. The τ s gven by u [( t )( x u 2 u )] t x 3 x (3) where μ s the molecular vscosty, δ s the Kronecer delta that δ=1 for =, otherwse δ=0, and μt s the turbulent vscosty defned by C t 2 (4) where Cμ=0.09 s a constant, the netc energy of turbulence, and ε the dsspaton of netc energy of turbulence, whch s defned n standard -ε turbulent model as follows: Conservaton of netc energy of turbulence: x ( u) x t ( ) G G x b (5) Conservaton of dsspaton of netc energy of turbulence: 2 t ( u ) ( ) C1 ( G Gb ) C2 (6) x x x G u t ( ) x x t u ut Gb g Pr x u x (7) (8) where C1ε=1.44, C2ε=1.92, σ=1.0 and σε=1.3 are emprcal constants, Prt s the turbulent Prandtl number, G s the rate producton of turbulence netc energy owng to the mean velocty gradents, Gb s the generaton of turbulence netc energy due to buoyancy (Tabernero et al. 2010). Standard wall functons are employed for the turbulent model, consderng the low gas vscosty and the relatvely low Reynolds number of the powder flow n the laser claddng. There s no need to refne the grds near the wall n the model usng standard wall functons, whch assocate the physcal quanttes n the wall wth these n the turbulent core. Thus a hgh calculaton effcency wth suffcent accuracy s acqured. 2.3 Dscrete Phase Modelng In ths study, powder partcles as a dscrete phase are consdered to be dspersed n the gas flow, whose governng equatons are gven n the 2249

4 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , standard flud dynamcs above. The traectory of each powder partcle s descrbed n a Lagrangan reference frame based on a force balance that s wrtten as: du dt ( ) g FD ( u up) F (9) P P where up s the velocty of partcle, ρp s the partcle densty, and FD(u - up) represents the drag force per unt partcle mass expressed as: F D 18 CD Re (10) d 24 2 P P where dp s the partcle dameter, Re s relatve Reynolds number gven by dp u up Re (11) and CD s the drag coeffcent that can be calculated as: a2 a3 CD a1 (12) 2 Re Re where a1,a2,a3 are constants wthn a certan range of relatve Reynolds number for sphercal partcles, see Mors and Alexander. (1972). Rosn-Rammler dstrbuton s used to represent the sze dstrbuton of powder partcles. In ths method, the whole range of partcle szes s dvded nto a number of dscrete ntervals. Each of these ntervals s descrbed by a mean dameter d for traectory calculatons. Accordng to Rosn-Rammler dstrbuton, the mass fracton of partcles wth dameter greater than d s expressed by: F d d n exp( ( ) ) (13) d m where dm s the partcle sze constant, and n s the spread parameter. The effect of velocty fluctuaton on the partcle n the turbulence flow s consdered for partcle traectory calculaton by the dscrete random wal model. The turbulence s modeled by eddes defned by a Gaussan dstrbuted random velocty fluctuaton u, v, w and a vortex lfe τe: 2 u' v' w' (14) 3 e 2C (15) L where ζ s a normally dstrbuted random number used for the three drectons due to the assumpton of sotropc turbulence, and CL s the tme scale constant. The tme for the partcle to cross the vortex tc can be calculated as: P Le t c ln 1 (16) u up where τ s the partcle relaxaton tme, Le s the vortex length scale, and u-up s the magntude of the relatve velocty. The partcle s consdered to nteract wth the flud phase vortex over the smaller one among the vortex lfe τe and the crossng tme tc. When ths tme s reached, a new value of nstantaneous velocty s obtaned by usng a new value of ζ n Eq.(14). Wth the tme ntegral of the force balance dfferental equaton, the partcle velocty at each pont along ts traectory s obtaned. The partcle traectory can be predcted by the nematc equaton as follow: dx u (17) p dt where x represents the poston of the partcle. The collson between the partcles and the nternal wall of the coaxal nozzle s consdered n ths model. The resttuton coeffcent s used to evaluate the momentum loss of partcle collson wth the nternal wall: e u 2P n (18) u1p where en s the resttuton coeffcent, and u1p, u2p s the partcle velocty before and after collson. Generally, the resttuton coeffcent depends on the powder and nozzle materal, mpact velocty, hardness rato, nozzle wall roughness. In ths study, the resttuton coeffcent s consdered as a constant when the materal of coaxal nozzle and powder are selected to smplfy the model. The contnuous phase s consdered as a contnuous homogeneous medum and solved by Naver-Stoes equatons for each tme step. The dscrete phase s smulated by tracng a great quantty of partcles n the calculated flud feld. The mass, momentum and energy n ths dscrete phase can be exchanged wth the flud phase. 2.4 Model Descrpton The soluton technque used n ths study s based on the FLUENT software, whch solves the governng equatons of contnuous phase and dscrete phase lsted above by a specfed fntevolume method. In order to explore the complete powder feedng process, a 3D geometry model of the whole coaxal nozzle together wth the cylndrcal space below the ext of nozzle as computatonal doman s bult (Fg. 2). The geometry model has four carrer gas and powder partcle nlets, and those four carrer gas path connect wth an annular channel. The nner sheldng gas nlet s located above the ext of the nozzle. There are two outer sheldng gas nlets that delver gas nto the outer annular channel. The man structural parameters of the computatonal doman are lsted n Table

5 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , velocty v, and outer sheldng gas at a velocty vo (Fg. 3). The three nds of gas nlet surface are defned as velocty nlet boundary condton, and the computatonal doman of coaxal nozzle s bounded by the wall boundary condton. The cylndrcal computatonal doman below the nozzle, whch has 20 mm n heght and 14.2 mm n dameter, s large enough to capture gas-sold flow characterstcs of nterest, and defned as pressure outlet boundary condton at the sde and the bottom surface. Fg. 2. The geometry model of the computatonal doman. (a) sometrc vew; (b) sectonal vew; (c) bac vew. Table 1 Man structural parameters of the computatonal doman Structural parameters Symbol Value Inner gas nlet dameter (mm) d 6 Carrer gas nlet dameter (mm) dc 4 Outer gas nlet dameter (mm) do 2 Mddle channel wdth (mm) wm 2.2 Mddle channel angle ( ) θm 60 Outer channel wdth (mm) wo 1.2 Outer channel angle ( ) θo 50 Nozzle ext dameter (mm) de 14.2 Heght below the nozzle (mm) h 20 The mesh s bult n the bass of the 3-D geometry usng GAMBIT software. Snce the geometry s complex, the body ftted coordnate (BFC) grd system, whch allows the non-standard geometry of the coaxal nozzle to be mapped nto Cartesan or cylndrcal geometry, s used to accurately predct the structure of the powder flow. The grd ndependency s performed for the smulaton cases n ths study. The mean element sze s selected n the range of 0.3 mm to 1.0 mm wth a step sze of 0.5 mm. The results show that the powder concentraton dstrbuton s ndependent wth the element densty when the mean element sze s less than 0.75 mm. Therefore, a mean element sze of 0.7 mm s used consderng computatonal effcency. In ths stuaton, there are elements for a cm 3 doman of Fg. 2. The representatve cases n the coaxal laser claddng are free gas-sold flow and gas-sold flow at the start of the deposton on the substrate wth varous shapes. The boundary condtons of the free gas flow are shown n Fg. 3. Metallc powder s delvered by gas flow at a carrer gas velocty vc. The nner sheldng gas flows from the nlet at a Fg. 3. Boundary condtons of the free gas flow. (a) front vew; (b) vertcal vew. The boundary condtons of the gas-sold flow at the start of the deposton on the substrate wth varous shapes are shown n Fg. 4. The coaxal nozzle geometry and the boundary condtons on t are the same as the case of free gas-sold flow. The geometry of the computatonal doman below the nozzle ext s modfed accordng to the substrate shape. The wall boundary condton s defned at the bottom surface of the computatonal doman. For the cases wth dfferent substrate shape, the dstance from the center of the nozzle ext to the deposton pont on the substrate s set as a constant of 10 mm, so as to detect the powder flow varaton. Fg. 4. Boundary condtons of the gas-sold flow wth varous substrates. (a) flat surface; (b) convex surface; (c) concave surface. The gas veloctes at the coaxal nozzle nlets are nput parameters of the gas-sold model, whle gas flow rates are processng parameters n laser 2251

6 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , claddng experments. To relate the expermental process parameters wth numercal computaton, the followng equaton s used: Q v (18) S where v s the gas velocty at nozzle nlet, Q s the gas volume per unt tme, and S s the sectonal area of the nozzle nlet. The nput parameters used n ths study are summarzed n Table 2. Table 2 Input parameters of the smulatons Input parameters Value F (g/mn) 1.75, 2.95, 4.15, 5.35, 6.55 v (m/s) 9, 2.5, 5, 7.5, 10 vc (m/s) 1, 3, 5, 7, 9 vo (m/s) 9, 2.5, 5, 7.5, 10 nozzle was valdated by our prevous wor (Lu et al. 2015). In laser claddng, the powder flow below the nozzle plays an mportant role n the clad qualty. Fg. 6 shows powder concentraton dstrbuton below the nozzle smulated by the model when the nner sheldng gas and outer sheldng gas s at velocty of 5 m/s, carrer gas s at velocty of 1 m/s at the nlets and powder feed rate s 4.1 g/mn. The powder flow s annular when t s delvered from the coaxal nozzle. The powder flow converges below the coaxal nozzle tp under the effect of sheldng gas and nerta of partcles, generatng an ellpsodal hgh concentraton zone. After the powder flow merged, t gradually dverges. The carrer gas and sheldng gas used n ths study s argon, and the powder s ncel based alloy powder wth a powder sze dstrbuton of 45 µm µm dameter. The partcle sze dstrbuton of the powder s measured by seve analyss. The measured and the approxmated partcle sze dstrbuton are shown n Fg. 5. The property parameters of the powder that are used n the smulatons are lsted n Table 3. Fg. 5. The measured and assumed partcle sze dstrbuton of ncel based alloy powder. Table 3 Basc smulaton parameters of partcle phase Parameters of partcle pahse Value Densty (g/m 3 ) 8350 Mnmum dameter (μm) 40 Maxmum dameter (μm) 130 Mean dameter (μm) 90 Number of dscrete ntervals 9 Spread parameter 4.7 Resttuton coeffcent 0.9 Gravty acceleraton (m/s 2 ) RESULTS AND DISCUSSION 3.1 Characterstcs of Powder Flow The proposed gas-sold model of the coaxal Fg. 6. Powder concentraton dstrbuton below the coaxal nozzle n longtudnal secton. To obtan more nformaton about the powder flow, powder concentraton at dfferent horzontal planes below the coaxal nozzle s shown n Fg. 7. The Z coordnate values of these planes are 2.5 mm, 8 mm, 15 mm and 18 mm, respectvely. The powder flow below the coaxal nozzle tp can be classfed nto three dfferent zones based on the powder concentraton dstrbuton: annular zone, consoldaton zone and dspersed zone. The annular zone s ust below the ext of nozzle (Fg. 7 (a)), and the powder concentraton n the center ncreases wth the standoff dstance ncreasng n ths zone. In the consoldaton zone, the powder concentraton s hghest at the center of the horzontal plane (Fg. 7 (b)(c)), and t s located n the range of 4 mm to 15 mm away from the nozzle ext. The powder partcles dsperse from the center under the consoldaton zone, so the dspersed zone s formed, the powder dstrbuton of whch s smlar to that of the annular zone (Fg. 7(d)). Obvously, the substrate should be placed n the consoldaton zone to mprove powder effcency and clad qualty n laser claddng. As s seen n Fg. 7 (b) and (c), the powder concentraton n the consoldaton zone s approxmately symmetrcal, whch s the reason that coaxal laser claddng s ndependent from moton drecton. 2252

7 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , The plane where the powder concentraton reaches ts maxmum s defned as focal plane, whch s located 7.9 mm below the ext of coaxal nozzle n ths case. Fg. 8 shows the powder concentraton profles along the nozzle axs and the radal axs n the focal plane, respectvely. The powder concentraton along the nozzle axs shows a rse frst followed by a declne, and the pea powder concentraton s about 3.5 g/m3 n focal plane (Fg. 8 (a)). In the focal plane, t also can be seen that the powder concentraton decreases rapdly from 3.5 g/m3 to 1.0 g/m3 wthn 2 mm of the nozzle axs, presentng a Gaussan or near-gaussan shape. Ths downward trend slows down when t s 2 mm to 3mm away from nozzle axs (Fg. 8 (b)). Fg. 8. Powder concentraton profles (a) along the nozzle axs and (b) the radal axs n the focal plane. 3.2 Effect of Process Parameters The numercal results are summarzed wth varatons of nner sheldng gas rate, carrer gas rate, outer sheldng gas rate and powder feed rate. The nner sheldng gas rate plays an mportant role n powder flow convergence (Fg. 9). The powder concentraton reaches ts hghest value of 6.6 g/m3 at the dstance of 3.9 mm away from the nozzle ext when the nner sheldng gas s not used. Wth the nner sheldng gas rate ncreasng, the powder focal dstance from nozzle ext ncreases and the maxmum powder concentraton decreases. It becomes more dffcult for powder flow to converge wth hgher nner gas flow rate. But the focus of powder flow could be controlled wth the nner sheldng gas flow. Consderng the man purpose of nner sheldng gas s to prevent Fg. 7. Powder concentraton dstrbuton n transverse secton wth nozzle ext dsplacement of (a) 2.5 mm, (b) 8 mm, (c) 15 mm, and (d) 18 mm. 2253

8 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , powder partcles from reboundng to the nozzle, nner gas sheldng rate should reman n a relatvely moderate range. especally when the carrer gas rate ncreases from 3 m/s to 5 m/s. The decrease of the maxmum powder concentraton could be explaned by a hgher partcle velocty, whch maes the powder partcle scatter under the nozzle ext. Ths ndcates that good convergence characterstcs of powder flow, whch are sutable for coaxal laser claddng, can be obtaned at a relatvely low flow rate of carrer gas. Fg. 9. Powder concentraton along the nozzle axs wth varous nner sheldng gas rate when carrer gas rate s 1m/s, outer sheldng gas rate s 5m/s, and powder feed rate s 4.1g/mn. The effect of outer sheldng gas on the powder flow s shown n Fg. 10. The maxmum concentraton of powder flow s only about 2.5 g/m 3 wthout the help of outer sheldng gas flow. The powder concentraton profles are dentcal when the outer gas flow rate s n the range of 2.5 m/s to 10 m/s, wth the maxmum concentraton ncreasng to about 3.5 g/m 3. It also can be seen from Fg. 10 that the outer gas flow does not have any nfluence on the focus of the powder flow. Ths result demonstrates that the outer gas flow could mprove the maxmum concentraton of powder flow wthout alterng ts focus. However, ths mprovement s lmted. Fg. 11. Powder concentraton along the nozzle axs wth varous carrer gas rate when nner sheldng gas rate s 5m/s, outer sheldng gas rate s 5m/s, and powder feed rate s 4.1g/mn. The powder concentraton profles along the nozzle axs under dfferent powder feed rates are shown n Fg. 12. The focus of the powder flow s 7.9 mm at any powder feed rate. When the powder s transported at 1.75 g/mn, 2.95 g/mn, 4.15 g/mn, 5.35 g/mn, 6.55 g/mn, the maxmum concentraton of powder flow s 1.5 g/m 3, 2.6 g/m 3, 3.5 g/m 3, 4.4 g/m 3, 5.4 g/m 3, respectvely. Thus a strong postve lnear relatonshp between the maxmum powder concentraton and the powder feed rate s detected. Ths s because the sold phase has lttle nfluence on the gas flow due to ts low volume fracton durng the laser claddng process. It could be deduced that a certan range of powder feed rate could be used at a proper combnaton of sheldng gas flow and carrer gas flow, and the focus of powder flow s guaranteed. Fg. 10. Powder concentraton along the nozzle axs wth varous outer sheldng gas rate when carrer gas rate s 1m/s, nner sheldng gas rate s 5m/s, and powder feed rate s 4.1g/mn. The nfluence of carrer gas on the powder flow s shown n Fg. 11. By ncreasng the carrer gas rate from 1 m/s to 5 m/s, the powder flow focal dstance decreases from 7.9 mm to 4.9 mm. However, the focus of powder flow stays the same wth the carrer gas flow rate n the range of 5 m/s to 9 m/s. Meanwhle, the maxmum powder concentraton has a remarable downward trend Fg. 12. Powder concentraton along the nozzle axs wth varous powder feed rate when nner sheldng gas rate s 5m/s, carrer gas rate s 1m/s, and outer sheldng gas rate s 5m/s. 2254

9 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , Effect of Substrate In ths study, a case of flat substrate placed 10 mm under the coaxal nozzle s dscussed frst. The locaton of the substrate s determned by the calculaton results descrbed above. The powder concentraton dstrbuton wth the flat substrate s shown n Fg. 13. Comparng to the result wthout a substrate, the powder concentraton above the substrate ncreases more than two tmes. Ths can be explaned by two reasons. One s that a hghpressure and low-velocty gas mass s formed n the center due to the blocng effect of the substrate, whch maes the powder partcles decelerate and the number of partcles ncreases n that space under a steady state of powder feedng process. The other s that partcles ht the substrate and bounce nto the calculaton doman. Most of the partcles n the center have much lower radal velocty than ther axal velocty when they ht the substrate, so usually they rebound from the substrate many tmes wthn the center space (Fg.13(b)), whch s a great contrbuton to the concentraton of powder flow. Substrate wth cylndrcal surface, as well as flat surface, s also used n laser claddng. The powder concentraton dstrbuton wth cylndrcal surface s shown n Fg. 14 under two cases: convex surface and concave surface wth radus of 5 mm. In order to compare wth the result wth flat substrate, the same powder feedng process parameters s appled and the dstance from the nozzle ext to the substrate surface remans 10 mm. It can be seen that the powder concentraton wth convex surface s smaller than the result wth flat surface as a whole. The gas flow downward along the convex surface maes the nfluence of the hgh-pressure and lowvelocty gas mass weaer so that the hgh powder concentraton zone becomes smaller. On the contrary, the concave surface leads to the role of hgh-pressure and low-velocty gas mass stronger n the powder convergence. On the other sde, partcles can rebound wthn the space more tmes on the concave surface than on the convex surface. As a result, powder concentraton wth the concave surface s much greater near the surface as s shown n Fg. 14. Fg. 14. The powder concentraton dstrbuton below the coaxal nozzle wth cylndrcal substrate of (a) convex surface or (b) concave surface. 4. CONCLUSIONS Fg. 13. The effect of flat substrate on the powder flow: (a) the powder concentraton dstrbuton below the coaxal nozzle; (b) rebound of a partcle on the substrate. It s mportant to delver the powder partcles to the deposton pont n an optmal process parameters n coaxal laser claddng. Usng the gas-sold model of a gven coaxal nozzle proposed by ths paper, t can be observed that the metallc powder flow converges from an annular dstrbuton below the nozzle ext to a Gaussan dstrbuton on the focus plane. The effect of powder feedng parameters on the metallc powder flow has been nvestgated by the model. Wth the nner sheldng gas rate ncreasng, the powder focal dstance from nozzle ext ncreases and the maxmum powder concentraton decreases. The outer gas flow could mprove the maxmum concentraton of powder flow wthout alterng ts focus. Wth the ncrease of carrer gas flow rate, the maxmum powder concentraton has a remarable downward trend especally when the carrer gas rate ncreases from 3 m/s to 5 m/s. The maxmum 2255

10 H. Lu et al. / JAFM, Vol. 9, No. 5, pp , powder concentraton shows a strong postve lnear relatonshp wth the powder feed rate. The substrate and ts shape have an mportant nfluence on the metallc powder flow by the means of changng the gas flow and bounce of the partcles. ACKNOWLEDGEMENTS Ths research was supported by the Chna Postdoctoral Scence Foundaton Funded Proect (Grant No. 2015M581881), Natonal Natural Scence Foundaton of Chna (Grant No ), Natural Scence Foundaton of Jangsu Provnce (Grant No. b ), and a Proect Funded by the Prorty Academc Program Development of Jangsu Hgher Educaton Insttutons (PAPD). REFERENCES Balu P., P. Leggett and R. Kovacevc (2012). Parametrc study on a coaxal mult-materal powder flow n laser-based powder deposton process. J. Mater. Process. Tech. 212(7), Dnda, G. P., A. K. Dasgupta and J. Mazumder (2012). Texture control durng laser deposton of ncel-based superalloy, Scrpta Mater. 67(5), Ln, J. (2000). Numercal smulaton of the focused powder streams n coaxal laser claddng, J. Mater. Process. Tech. 105(1-2), Lu, H., X. L. He, Y. Gang, Z. B. Wang, S. X. L, C. Y. Zheng and W. J. Nng (2015). Numercal smulaton of powder transport behavor n laser claddng wth coaxal powder feedng, Sc. Chna-Phys. Mech. Astron. 58(10), Lu, J. C. and L. J. L (2005). Effects of powder concentraton dstrbuton on fabrcaton of thn-wall parts n coaxal laser claddng, Opt. Laser. Technol. 37(4), Mors, S. A. and A. J. Alexander (1972). An nvestgaton of partcle traectores n twophase flow systems. J. Flud. Mech. 55(2), Pan, H. and F. Lou (2005). Numercal smulaton of metallc powder flow n a coaxal nozzle for the laser aded deposton process, J. Mater. Process. Tech. 168(2), Pnerton, A. J. (2007). An analytcal model of beam attenuaton and powder heatng durng coaxal laser drect metal deposton, J. Phys. D: Appl. Phys. 40(23), Pnerton, A. J. and L. L (2004). Modellng powder concentraton dstrbuton from a coaxal deposton nozzle for laser-based rapd toolng, J. Manuf. Sc. E.-T. Asme. 126(1), Tabernero, I., A. Lamz, E. Uar, L. N. López de Lacalle, C. Angulo and G. Urban (2010). Numercal smulaton and expermental valdaton of powder flux dstrbuton n coaxal laser claddng, J Mater Process Tech 210(15), Yang, N. (2009). Concentraton model based on movement model of powder flow n coaxal laser claddng. Opt Laser Technol, 41(1), Zeovc, S., R. Dwved and R. Kovacevc (2007), Numercal smulaton and expermental nvestgaton of gas powder flow from radally symmetrcal nozzles n laser-based drect metal deposton, Int. J. Mach. Tool. Manu. 47(1), Zhao, T., Z. Wang, M. Tae, K. Lu and Y. Cu (2015). Investgaton of the dsperson behavor of nertal partcles wthn accelerated doman, J. Appl. Flud. Mech. 8(1),