ARTICLE IN PRESS

Optics & Laser Technology 41 (2009) 94– 98

Contents lists available at ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

E-m

journal homepage: www.elsevier.com/locate/optlastec

Concentration model based on movement model of powder flow in coaxiallaser cladding

Nan Yang

Laser Process Center, Tianjin Polytechnic University, Tianjin 300160, China

a r t i c l e i n f o

Article history:

Received 13 November 2007

Received in revised form

14 March 2008

Accepted 23 March 2008Available online 4 June 2008

Keywords:

Concentration

Powder

Nozzle

92/$ - see front matter & 2008 Elsevier Ltd. A

016/j.optlastec.2008.03.008

ail address: gracey79n@yahoo.com.cn

a b s t r a c t

The structure below the coaxial nozzle is critical since the spatial distribution of metal powder particles

determines the laser attenuation as well as catchment efficiency. It is difficult to simulate the powder

concentration distribution, because the complex phenomena involved in the two-phase turbulence

flow. In this paper, the air-powder flow is studied along with powder properties, nozzle geometries and

shielding gas setting. A Gaussian model is established to quantitatively predict the powder stream

concentration in order to facilitate coaxial nozzle design optimizations. An experimental setup is design

to measure the powder concentration for this process. The simulated results are compared with the

experimental results. This study shows that the powder concentration mode is influenced significantly

by powder properties, nozzle geometries and shielding gas setting.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The quality and efficiency of laser-aided direct metal deposi-tion largely depends on the powder flow structure below thenozzle. Operating parameters such as powder properties, nozzlegeometries and shielding gas setting should be optimized basedon the understanding of the powder concentration distribution.

Some researches were done in this field. Model of effects ofpowder concentration distribution on fabrication of thin-wallparts in coaxial laser cladding was developed by Liu et al. [1]. Theydefined the static model of powder mass concentration distribu-tion at cold-stream conditions in coaxial single-pass cladding witha low-power laser as a Gaussian function [2]. They alsoinvestigated formation mechanism of cross-sectional profile of aclad bead in coaxial laser cladding [3], and presented in-timeadjustment in laser cladding manufacturing process as a means toimprove dimensional accuracy and surface finish of the built part[4]. An experimental investigation of the influence of processingparameters on clad angle in laser cladding by powder waspresented by Onwubolu et al. [5], and the movement model andthermal model of powder particle in coaxial laser cladding isproposed by Lin [6,8].

In this paper, an investigational approach is described whichincludes simulation method and experimental setup. This simula-tion methodology considers more general conditions and has thepotential for optimization of powder flow for coaxial lasercladding. A precise and low-cost optical measuring system andits application are also included.

ll rights reserved.

2. Movement model

The powder stream with shield gas output from the annularnozzle can be divided into three regions by AA0 and BB0. Thelongitudinal section of the annular nozzle and the powder streamare shown in Fig. 1, where w is the nozzle exit width, r is thenozzle inward wall radius, a is nozzle angle and f is powderdivergence angle. In order to establish powder particle movementmodel, some assumptions should be illustrated [8–11]:

(1)

A powder particle is moving in a uniform gas flow, and itsinitial spray angle from the nozzle exit is a.

(2)

The velocity of shield gas is constant in a short stand-offdistance.

The velocity of particle can be solved by

dvx

dt¼

18mð1þ 0:15Re0:687Þðux � vxÞ

rpd2p

dvy

dt¼

18mð1þ 0:15Re0:687Þðuy � vyÞ

rpd2p

þ g

Re ¼rdp

m

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðux � vxÞ

2þ ðuy � vyÞ

2qvx0 ¼ v0 cos a

vy0 ¼ v0 sin a

ux ¼ u0 cos a

uy ¼ u0 sin a

vðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2

x þ v2y

q

8>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>:

(1)

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Nomenclature

w nozzle exit width (m)r nozzle inward wall radius (m)a nozzle anglef powder divergence angleg gravitational acceleration (m/s2)v particle velocity component (m/s)u gas velocity component (m/s)v0 initial velocity of particle at nozzle exit (m/s)u0 initial velocity of gas at nozzle exit (m/s)t time (s)m gas viscosity (kg/s m)r gas density (kg/m3)d diameter (m)r density (kg/m3)Re Reynold number

e velocity recovery ratiomp powder mass flow rate (kg/s)f(x, y, z) powder particles number 3D distribution function

(particles/m3)m(y) powder particles number vertical distribution func-

tion (particles/m)d Gaussian parameter (m)N particle number flow rate (particles/s)R powder stream radius

Subscripts

p particleg gasx, y, z directions in Cartesian coordinatesA, A0 point A, A0

N. Yang / Optics & Laser Technology 41 (2009) 94–98 95

where v is particle velocity, u is shield gas (argon) velocity, v0 isinitial particle velocity at nozzle exit, u0 is initial gas velocity atnozzle exit, v(t) is velocity of the particle at moment t, m and r aregas viscosity and density, dp and rp are particle diameter anddensity, Re is the Reynold number.

The spraying angle f of powder flow at point A (Fig. 1) can beestimated by the collision reflect angle of two particles M and N. M

comes from the outward wall exit of the nozzle’s left side and N

comes from the inward wall exit of nozzle’s right side. Based onthe constant momentum principle at the collision moment, thereflect angle of M can be used to estimate the spraying angle by

f ¼ arctan evpx

vpy

� �(2)

Where e is velocity recovery ratio of the particles (M, N) aftercollision, vpx and vpy are velocity component in X- and Y-axes of M

before collision. The constant parameters can be seen in Table 1.

3. Concentration model

In this paper, the powder flow concentration distribution inregions 2 and 3 is more concerned than region 1, as shown inFig. 1, and the concentration of powder is expressed by volumefraction. We suppose that the 3D distribution of the powder

Fig. 1. The three regions of gas-powder flow.

particles’ number in regions 2 and 3 could be expressed by theGaussian function [12]:

f ðx; y; zÞ ¼mðyÞ

2pd2exp �

x2 þ z2

2d2

� �(3)

where f(x, y, z) is powder particles number 3D distributionfunction, m(y) is powder particles number vertical distributionfunction: the number of particles in the powder stream indifferent cross-section along stand off distance, d is Gaussianparameter.

The powder particles in regions 2 and 3 come from the annularnozzle, so

mðyÞ ¼N

vy(4)

where vy can be solved by Eq. (1), N is the number of particlessprayed by the nozzle in one second, the relationship of N andpowder mass flow rate mp is

N ¼3mp

4pðdp=2Þ3rp

(5)

Based on 73d principle, more than 99% of the particles in theregion x2+z2+p9d2, so the radius of powder stream can beestimated by 3d:

3d ¼ RðyÞ (6)

where R(y) is the radius of powder stream in regions 2 and 3.Substituting Eqs. (4)–(6) with Eq. (3), the powder 3D volume

fraction function is given by

cðx; y; zÞ ¼4

3p � ðdp=2Þ3 � f ðx; y; zÞ

¼9mp

2p � RðyÞ2 � vy � rp

exp �9ðx2 þ z2Þ

2RðyÞ2

" #(7)

In region 2,

RðyÞ ¼ r þw� xðyÞ (8)

where x(y) is the horizontal displacement of the particle sprayedfrom the outward wall of nozzle, it could be solved by Eq. (1).

In region 3,

RðyÞ ¼ xA0 þ ðy� yA0 Þ tan f (9)

where (xA0 , yA0) is the coordinate of point A0 , it could be solved byEq. (1). f could be solved by Eq. (2).

When z ¼ 0, the results of Eq. (7) can be shown as 2D figuresfrom Figs. 2–5. The curve 1, 2 and 3 in Fig. 2 are, respectively, the

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Table 1The constant parameters

Fluid density r (kg/m3) Particle density r(kg/m3)

Gas viscosity m (kg/

m s)

Collision recovery

ratio e

Nozzle inward wall radius

r (mm)

Particle diameter dp

(mm)

1.225 8000 1.789�10�5 0.56 2 75

Fig. 2. Volume fraction distribution stand-off distances: (1) y ¼ 5.45 mm, (2)

y ¼ 6.22 mm and (3) y ¼ 25.77 mm.Fig. 3. Volume fraction distribution along the nozzle’s central line under different

mp: (1) mp ¼ 500 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601. (2)

mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

Fig. 4. Volume fraction distribution along the nozzle’s central line under different

w: (1) mp ¼ 300 mg/s; w ¼ 2 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601. (2)

mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

Fig. 5. Volume fraction distribution along the nozzle’s central line under different

v0: (1) mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601. (2)

mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

N. Yang / Optics & Laser Technology 41 (2009) 94–9896

volume fraction distribution at y ¼ 5.45 mm (between BB0 and AA0

in Fig. 1), y ¼ 6.22 mm (AA0), y ¼ 25.77 mm(between AA0 and thesubstrate). The peak values(C, D and E) of each curve (2, 1 and 3)are the powder volume fraction values on the nozzle’s central line(at radius distance 0 mm); the distance of the two extreme pointsof each curve (for example, FG) is the diameter of the powderstream at corresponding stand-off distance. Fig. 2 shows thatpowder volume fraction along AA0 has the biggest peak value andthe smallest powder stream diameter value among the threecases.

Fig. 3 shows the volume fraction distribution along the nozzle’scentral line under different powder mass flow rate in a shortstand-off distance (30 mm). At first, the volume fraction of powderincreases because of the diameter of powder stream decreasing.Each curve’s peak value is at point (0, 6.22 mm) which is the cross-over point of AA0 and the nozzle’s central line. Then, the volumefraction of powder decreases due to the stream diameter andparticle velocity increasing. Moreover, the powder mass flow rate(mp) is an important parameter to influence all the concentrationvalues, but it does not influence the peak position in stand offdistance obviously. The ratio of each concentration value at thesame stand-off distance of curve 1 and 2 is about 5:3.

Fig. 4 shows the volume fraction distribution along the nozzle’scentral line under different nozzle exit width. It is shown that winfluences the concentration peak value. The bigger w value is, thesmaller the concentration values are. This is because under givenpowder mass flow rate, the bigger the diameter of powder streamis, the bigger intervals between particles are. w also influences thepeak value position in stand off distance. For the bigger w (thelower line AA0 in Fig. 1), the lower the peak value position is seen.

Fig. 5 shows the volume fraction distribution along the nozzle’scentral line under different initial particle velocity. It is shownthat v0 influence the concentration peak value, because theintervals between particles is larger in the powder stream withhigher velocity. v0 also influences the concentration peak valueposition in stand off distance. This is because the curvature ofparticle trajectory is bigger with higher particle velocity. In Fig. 6,focused regions 1 and 2 are, respectively, in fast and slow powderstream. The focused region 2 in slow powder stream is lower;therefore, the concentration peak position is lower.

Fig. 7 shows the gas velocity influence the concentration peakvalue and its position. The reason is similar to the effect of particlevelocity.

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Fig. 6. The focused region in fast and slow powder stream.

Fig. 7. Volume fraction distribution along the nozzle’s central line under different

u0: (1) mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601. (2)

mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

Fig. 8. Volume fraction distribution along the nozzle’s central line under different

a: (1) mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8m/s; u0 ¼ 0.8 m/s; a ¼ 451. (2)

mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

N. Yang / Optics & Laser Technology 41 (2009) 94–98 97

Fig. 8 shows the nozzle angle influences the concentrationpeak value and its position. This is because the nozzle angleinfluences the particle velocity and direction. The nozzle angle canfocus the powder; so the stream can be switched from lessfocused stream to a focused one.

4. Experimental research

Direct measurement of powder concentration is impossible.Therefore, the powder volume fraction could be measured by animage processing technique. Typical image-based technique forstudying small particle motions in carrier gas is PIV [13]. Theprinciple and devices of experiment are shown in Figs. 9(a) and(b). The image of powder stream taken by CCD camera is shown inFig. 9(c). The parts of measurement system are as follows: YAGpulse laser, 2D sheet of light lens, CCD camera, etc.

Double sets Q switch pulse Nd+:YAG laser were selected forthis case to replace the expensive high-powder laser source. Itswavelength is 532 nm, single pulse energy is 220 mJ, pulse repeatfrequency is 10 Hz, and pulse width is 6 ns. Nd+:YAG laser beam istransformed into a 2D light sheet by a quartz cylindrical lens. Thelight sheet depth can be adjusted from 1 to 2.5 mm; its width canbe adjusted from 15 to 35 mm, so that the image of particle flow

longitudinal section could be taken by CCD camera. Dots of thehigh-speed CCD is 1000�1000, 12 bit (provide 4096 class greyscale), 50 frame/s. Synchronous monitor is used to make CCDcamera and double pulse laser work synchronously. UsingDELPHI7.0 based on Windows 2000, visualized imaged processingsoftware is successfully developed, and it consists of imagecollect, image record, image show timely, image processing andimage correction.

The 316L stainless steel powder particles (diameters areabout 45–150mm) are output with an average mass flow rateof 300 mg/s, delivered with argon with a velocity of 0.8 m/sfrom the nozzle with the exit width of 3 mm and the nozzle angleof 601.

Fig. 10 shows the comparison of simulated and measuredpowder concentration distribution. The predicted concentrationvariation along the central axis is compared with experimentaldata. Two data reach their peak value at the focus spot and thendecrease obviously. The concentration level and position of focusspot (at 6 mm) are good predicted.

5. Conclusions

Based on movement model, a Gaussian concentration model inmore general conditions is proposed to simulate the volumefraction distribution of powder particle stream under differentprocess parameters in coaxial laser cladding.

It is found that the powder parameters such as particle velocityand mass flow rate influence the powder stream configura-tion and concentration distribution. The nozzle geometriesinfluence powder flow structure and concentration distribution.The nozzle exit width influences the concentration peak valueand its position. Smaller exit width of the nozzle give smallerpowder flow diameter and higher peak values at focus poison.The nozzle angle influences the focused character characteristics.Smaller nozzle angle tends to give better focused properties.This is helpful in increasing the catchment efficiency betweenlaser and powder. The gas setting such as gas velocity alsoinfluences the flow structure and concentration distribution.Smaller gas velocity could give higher peak values at focusposition.

Experimental research of the powder stream concentrationunder given nozzle and gas settings are carried out. Measuredresults are found to agree with calculated data.

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Fig. 9. (a) Principle of DPIV measurement; (b) devices of experiment and (c) the picture of powder stream.

Fig. 10. Comparison of volume fraction distribution of measured value and

simulated value along the nozzle’s central line under the same process

parameters: mp ¼ 300 mg/s; w ¼ 3 mm; v0 ¼ 0.8 m/s; u0 ¼ 0.8 m/s; a ¼ 601.

N. Yang / Optics & Laser Technology 41 (2009) 94–9898

Acknowledgments

This project was supported by National Natural Science Fund ofChina (No. 6047804) and Key Project of Tianjin Science andTechnology Committee (No. 033188011).

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