Measurement of Velocity Field of Powder Fluid in Laser Fabrication

The digital image processing method based on DPIV technique was developed to measure the gas-powder two-phase flow velocity field in laser fabrication. The powder flow image measurement process is composed of image collecting, image saving, velocity vector field and flow line group construction. Two adjacent instantaneous images of the same powder flow have been collected by CCD camera. Based on interrelated algorithm, the displacement vector field and the velocity vector field have been calculated. The data of the whole velocity field have been fitted to construct a group of flow line. Under the same process parameters as measurement, the velocity distribution is simulated by FLUENT software, and the simulated result agrees with the measured result. Results show that, the measurement method can be used to obtain the powder flow field velocity distribution online and further design the nozzle size.


Introduction
Laser cladding was developed to become an efficient laser manufacturing technique, and it was able to fabricate and repair 3D metal part (Yang,2002,pp. 234-238).In laser manufacturing, high power laser, metal powder and gas are output from coaxial nozzle.The powder flow is a complicate process, velocity field of the two-phase flow (powder and gas) can obviously affect the shape and function of laser cladding casing.Therefore, the velocity field measurement of the powder flow is important.However, the powder particle is too small and moves too fast to be distinguished using direct measurement method.Up to now, the reasonable and quantitative evaluation method is not complete.Digital Particle Image Velocimetry (DPIV) technique is developed to measure the powder flow field in our work.It could provide almost all information of moving particles in flow field conveniently.Comparing with traditional velocity measurement methods, it is a quick and quantitative method.Measurement of concentration field in powder flow is reported in other paper (Yang,2006,pp.993-997).This paper will lay emphasis on the digital image processing method for construction of velocity field in the powder flow.

Measurement of Velocity Field in Powder Flow by DPIV
DPIV measurement system of powder flow field mainly consists of double pulse Nd + : YAG laser, sheet light, CCD camera, synchronous monitor, image plate and computer.Double pulse Nd + : YAG laser was used to illuminate the powder fluid field, its parameters are: λ=532nm, single pulse energy 220mJ, pulse repeat frequency 10Hz, pulse duration 6μs.Special quartz cylindrical lens are selected to transform Nd + : YAG laser beam into a 2D sheet light, which have adjustable thickness from 1mm to 2.5mm and a length from 5mm to 35mm.Frame straddle CCD camera with double-exposure function is used to catch two frame images with the exposure time duration of 1μs~40ms.The picture of measurement device of powder flow velocity field is shown as Fig. 1.

Reconstruction of Velocity Field
Reconstruction of velocity field mainly consists of image collect, image record, image show timely, image processing and image correction.The visualized image processing software has been developed with DELPHI package.Cross correlation algorithm (as shown in Fig. 2) are used to calculate the displacement Δd of powder particles in two images (Wang,2000,pp.302-306,Wu,2002,pp.594-598), velocity of particles are obtained from Δd /Δt where Δt is the double pulse duration.

Pretreatment
The aim of pretreatment is to distinguish powder region and non-powder region with concentration criterion.Two CCD original images (format: bmp, size: 1004 pixels × 1004 pixels, exposure duration: t Δ =1μs) of the same powder flow field are shown as Fig. 3 (a) and (b).
The white region has metal powder and the black region hasn't because of no light reflection.It is not necessary to process the black region, because the calculating time and the wrong distinguishing probability will be increased.So, the black region must be filtered.The concentration of a small area A in the image of powder flow field can be defined as follows: Where is the number of the pixel in area A whose grey value > G (a given value), py px× is the number of all the pixel of A.
If c> * c (a given value), A can be regarded as an area with powder, otherwise, A is non-powder region.The pretreatment computing program flow can be seen in Fig. 4 .

Cross Correlated Coefficient
Cross correlated coefficient is used to describe the similar characteristic about two small regions.The cross correlated coefficient of two same size grey matrixes is defined as (Sun, 2000, pp.364-367,Wu,2004,pp.623-628): ( Where ) , ( y x G k is the grey value of the pixel point(x,y)in grey matrix k G (k=1,2), m and n are the differences between 1 G and 2 G in x and y direction respectively, Rs is the cross correlated coefficient of grey matrix ∈ n m Rs .

Velocity Vector Field
The velocity field can be expressed as: (3) Where uv E is the velocity field at moment t,

Fitting the Velocity Data
In order to draw velocity vector flow lines, consecutive function can be built up from ] , [ j i u and ] , [ j i v . Let: Where The fitting errorδ is expressed as: In order to get the minimum of u δ and v δ , let: Where: [ ] The coefficients in ) , ( j i u can be obtained by:

Velocity Vector Flow Line Group
Velocity vector flow line is to describe the flow direction of a flow field (Tian,2001,pp.211-213,Wei,2001,pp.14-19).At a point in the velocity vector flow line, the directions of tangent and velocity vector (at the same point) are identical.
The velocity vector flow line equation can be express as: Where (x,y) is a point in the flow field.

Measured Result and Calculated Result
Under the process parameters: initial powder volume fraction at the nozzle entrance c=0.1 and initial gas velocity u=3m/s, the experimental results are obtained from Fig. 6 to Fig. 8.
As shown in Fig. 6, velocity vector field can be obtained in about 375 s μ by this software.The small arrows' lengths stand for velocity magnitudes, and the arrows' directions stand for velocity vector direction.Above the focused region, powder from two sides of nozzle moves face to face.Below the focused region, the powders of two roads leave each other duo to collision.Velocity increases gradually along the gravity direction (the direction of stand-off distance).And Fig.3 (b) which is the most similar to the sub-region in Fig.3 (a) whose head position is ) , ( ai ai y x .This can be

Figure 2 .Figure 3 .
Figure 2. Cross correlation algorithm for calculating velocity of powder particles by DPIV

Figure 8 .
Figure 8.Comparison between calculated value and measured value of the velocity distribution on the nozzle's center line