Experimental and computational studies of gas–particle flow in a ‘sand-blast’ type of erosion tester

Powder Technology 160 (2005) 93 – 102 www.elsevier.com/locate/powtec

Experimental and computational studies of gas–particle flow in a Fsand-blast_ type of erosion tester Qianpu Wang, Morten Chr. Melaaen *, Sunil R. De Silva T, Guifang Tong Telemark University College (HiT-TF) and Tel-Tek, Kjølnes Ring, N-3914 Porsgrunn, Norway Received 11 February 2003; received in revised form 5 May 2005 Available online 4 October 2005

Abstract Experimental and computational studies of gas – particle flow in a Fsand-blast_ type of erosion tester are described. Values of the particle velocity distribution have been obtained under various set-up conditions for three abrasives: glass beads, crushed glass, and olivine sand, each in two size ranges. The particle velocities were measured using laser Doppler anemometry (LDA). The divergence of the particle plume was investigated with a video camera. A computational fluid dynamics model has been developed using the Fluent package. Both the Euler – Lagrangian approach and the Euler – Euler approach are used to calculate the particle velocity distribution and plume divergence. Discussions and analyses of the experimental as well as the computational results are included. The simulations show altogether good agreement with experimental data. The experimental observations together with the computed results should increase the depth of understanding of the underlying physics. D 2005 Elsevier B.V. All rights reserved. Keywords: Sand-blast erosion tester; Modelling; Particle velocity; Plume divergence

1. Introduction The Fsand-blast_ type of erosion tester, in which particles are accelerated in a gas stream along a nozzle before striking the specimen, is widely used for quantifying particle impact erosion against a solid surface. There are several difficulties in relating the data obtained from these test rigs to erosion in actual operating plants. One of the reasons is due to the complexity of the solid– gas flow, while a second is due to a lack of understanding of the operational differences between the different laboratory erosion testers [1]. The erosion wear rates of materials are strongly dependent on the particle flux, impact velocity and impact angle [2– 5]. So it is important to know the particle velocity distribution accurately in an erosion tester. Both theoretical and experimental research have been carried out by many researchers. Several methods have been used to measure the particle velocity. These include the photographic techniques of multiple flash photography, high* Corresponding author. Tel.: +47 35 575286; fax: +47 35 57 5001. E-mail address: [email protected] (M.C. Melaaen). T Professor Dr. Sunil R. De Silva passed away on April 29, 2002. 0032-5910/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2005.08.006

speed framing photography, laser Doppler velocimeter, and so on. A number of researchers [6 –12] have, over the years, carried out investigations into solid – gas flow dynamics and developed models to relate the particle velocities and plume divergence with the particle properties and operational conditions. But these models are limited, and some important parameters like particle concentration and shape effect have not been included. In the present work, a two-dimensional computational fluid dynamics model has been developed using the Fluent package. Both Euler –Lagrangian approach and Euler – Euler approach were used to model the particle velocity distribution and plume divergence. The first model is based on the Euler – Lagrangian approach to predict the particle velocities and particle trajectories under different boundary conditions. Coupling between the discrete phase and continuous phases was included to consider the effect of powder concentration. For the sake of difficulties modelling high solid concentration with the Euler – Lagrangian approach, the Euler –Euler model is used to include the effect of particle – particle collisions. Experimental values of the particle velocity have been obtained under various set-up conditions for three abrasives:

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Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

Fig. 1. Schematic diagram of the sand-blast type of erosion rig at POSTEC.

glass beads, crushed glass, and olivine sand, each in two size ranges to compare with the simulation results. The particle velocities were measured using laser Doppler anemometry (LDA). The divergence of the particle plume was investigated with a video camera. 2. Experimental work The Fsand-blast_ erosion tester at POSTEC (Department of POwder Science and TEChnology at the Telemark Technological R&D Center), see Fig. 1, uses a K-Tron Soder T-20 double screw feeder to supply a constant steady flow of powder to the mixing chamber. On the POSTEC erosion rig, the screw feeder is mounted on top of a balance in order that the loss in weight can be calculated and the mass of abrasive used can be known. The constantly agitated powder container above the twin

Glass beads

screws is also connected to the top of the mixing chamber by a thin air pipe. This is used to prevent blow back from the mixing chamber. The driving airflow is fed into the mixing chamber via a supersonic nozzle. The supersonic nozzle is a venturi nozzle with an upstream diameter of 3 mm and a throat diameter of 0.85 mm. The acceleration tube (see Fig. 1) is made from boron carbide and is 3 mm in inner diameter and 90 mm long. The abrasive is accelerated along the tube due to the drag force supplied by the fast flowing air. For all experiments in this paper, the stand off distance which is the distance from the end of the acceleration tube to the target center is 23 mm. In the present experiments, the air supply for gas –particle mixture control is not used (Fig. 1). All the erosion test materials were supplied by the Wolfson Center for Bulk Solids Handling Technology at the University of Greenwich from sources within the UK. The three materials

Olivine sand Fig. 2. Particle shape under microscope.

Crushed glass

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102 Table 1 Specification of erosion materials Material Glass beads Crushed glass Olivine sand

Coarse fraction Fine fraction Coarse fraction Fine fraction Coarse fraction Fine fraction

Diameter range (Am)

Mean diameter (Am)

Density (kg/m3)

150 – 250 75 – 150 150 – 300 75 – 150 160 – 315 75 – 190

185 130 170 95 190 140

2500 2500 2500 2500 3300 3300

selected for these experiments were olivine sand, glass beads and crushed glass each in two size ranges. The representative shapes of these materials are shown in Fig. 2. The particle size and density are provided in Table 1. The non-intrusive laser Doppler anemometer (LDA) has become a commonly used experimental tool in single and multiphase flows. The general features of LDA are nonintrusive, very high accuracy, very high spatial resolution with a fast dynamic response. LDA is used to simultaneously measure the mean and the fluctuating velocities. In this experiment, only the mean particle velocity has been measured. The angular distribution of the particle plume was investigated with a video camera as shown in Fig. 3. The digital picture produced was next analysed by imagine analysis software [13], and the darkness in the picture is used when defining the plume edge. It is assumed that the plume edge is at 1% darkness relative to the center value. The length H and width S of the particle angular distribution were used for calculating the angle of divergence, while the actual acceleration tube external diameter D was used to scale all the pictures. The following assumptions as justified by Shipway and Hutchings [10] were made: the angular distribution of particle trajectories with respect to the nozzle axis was axially symmetrical. The angle of divergence could then be calculated using trigonometry with the acceleration tube internal diameter and the normalized values of S and H. 3. Numerical approach The development of a reliable model of the erosion test apparatus at POSTEC has some important advantages. With a reliable model, the amount of experimentation required to obtain a set of desired results can be considerably reduced. Also the ability to accurately predict the velocity and velocity distribution at the target is important as it means that the erosion rig can be set-up to work under the desired conditions without the need for lengthy tests using laser Doppler anemometry to confirm the particle velocity.

95

phase is solved by tracking a large number of particles through the calculated flow field. The gas and particle phase coupling is accomplished by an iterative coupled solution of the fluid phase and the dispersed phase. The particle velocities are obtained by carrying out calculations based on Newton’s laws. The equation of motion of an individual particle was given by  Y
duYp
Y Y g qp  q ¼ F D u  up Þ þ qp dt dxYp Y ¼ up dt

ð1Þ

The acceleration-dependent drag terms (the added mass and Basset history integral terms) and the lift forces (such as the Magnus and Saffman terms) were negligible due to the large density ratio of solid to gas (about 2500). The second equation is the trajectory equation which is solved by stepwise integration over discrete time steps. By solving Eq. (1), the velocity and position of all particles at each time step could be calculated.   In Eq. (1), FD uY  uYp is the drag force per unit particle mass and: 18l CD Re ð2Þ FD ¼ qp dp2 24 Re ¼

dp qj uYp  uY j

ð3Þ

l

The drag coefficient C D in Eq. (2) is a function of the relative Reynolds number of the following general form: a2 a3 CD ¼ a1 þ þ ð4Þ Re Re2 where a’s are constants that depend on different models. In this paper, the model of Morsi and Alexander [14] for smooth spherical particles was used for simulating glass beads. For non-spherical particles, olivine sand and crushed glass, the model of Haider and Levenspiel [15] was used:  24
b3 Re CD ¼ 1 þ b1 Reb2 þ ð5Þ Re b4 þ Re The values of b 1, b 2, b 3, and b 4 in Eq. (5) are functions of the particle shape factor.

D

3.1. The Euler – Lagrangian approach

H For simulating turbulent gas –particle flow, currently there are two approaches in Fluent: the Euler – Lagrangian approach and the Euler – Euler approach. In the Euler – Lagrangian approach, the fluid phase is treated as a continuum by solving the time averaged continuity and momentum equations (as given by Eqs. (6) and (7) when k = gas), while the dispersed

S Fig. 3. Plume divergence measurement.

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Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

These ordinary differential equations (Eq. (1)) were integrated along the trajectories of individual particles of different sizes and the gas velocity field was provided by the solution of the equations governing the conservation of mass and momentum. In the case of solid particles, collisions between particles and tube wall were assumed to be elastic. This is a simplification, and it is also assumed that the tube wall surface is smooth. It is also possible to include particle –particle collisions in the Euler – Lagrangian model, however this is not possible in Fluent’s Euler –Lagrangian model so far. The disadvantage of using the Euler – Lagrangian model when the particle –particle collisions are considered is the need for large computer memory size and computational time. When the particle number is above a certain level, it is hard to use the Euler – Lagrangian model because of computer limitations.

The fluid solid exchange coefficient, K sg, is defined as Ksg ¼

as q s f ss

ð10Þ

The ‘‘particulate relaxation time’’, s s, is defined as qs ds2 18lg

ss ¼

ð11Þ

f is defined differently for the different exchange coefficient models [21], f ¼

CD Res a1:7 g 24

Res ¼

ð12Þ

qg ds j uYs  uYg j

ð13Þ

lg

3.2. The Euler– Euler (granular) approach

The drag coefficient [21,22]: h
0:687 i CD ¼ ag w24Res 1 þ 0:15 ag Res s CD ¼ 0:44

When particle –particle collisions have an important effect on the plume divergence and particle velocities in the erosion tester, the Euler – Euler (granular) multiphase model is used in this work. The Eulerian multiphase model solves a set of momentum and continuity equations for each phase. Phase coupling is achieved through the pressure and viscosity and the interphase exchange coefficients. The solid phase pressure, bulk viscosity and shear viscosity are deduced from the kinetic theory for granular flow given by Syamlal et al. [16,17] and Gidaspow [19]. The mass conservation and momentum balance for phase k (k = gas or solid) are given by:  B B
ð6Þ ðak qk Þ þ ak qk uj;k ¼ 0 Bt Bxj

where w s is the shape factor which is unit for spherical particles and between zero and unit for all other particles. The collisional and kinetic parts are added to give the solids shear viscosity:

  B
B
ak qk ui;k þ ak qk uj;k ui;k Bt Bxj

lkin;s

¼  ak þ


 Bsij;k BP þ þ ak qk gi þ Fi;k Bxi Bxj

n X


 Kkq ui;q  ui;k

ls ¼ lcol;s þ lkin;s

ð15Þ 

lcol;s ¼

ð14Þ

4 hs as qs dp goss ð1 þ ess Þ 5 p

 12 ð16Þ

pffiffiffiffiffiffiffi  as dp qs hs p 2 1 þ ð1 þ ess Þð3ess  1Þas goss ¼ 5 6ð3  ess Þ

ð17Þ

The solids bulk viscosity is:

ð7Þ

q¼1

In order to solve the above governing equations, more constitutive equations are needed. The solid phase pressure, P s, which includes both kinetic and collisional pressures, is given by Chapman and Cowling [20] as: Ps ¼ as qs ð1 þ 2ð1 þ ess Þas goss Þhs

for Res V1000 for Res > 1000

 1=2 4 hs ks ¼ as qs ds goss ð1 þ ess Þ 3 p

ð18Þ

Conservation of the solid fluctuation energy is:

  3 B B
ð qs a s h s Þ þ qs as uj;s hs 2 Bt Bxj  
 Bui;s B Bhs þ jhs ¼  Ps dij þ sij;s  chs þ /gs Bxj Bxj Bxj ð19Þ

ð8Þ

In this case, the coefficient of restitution e ss is assumed to be equal to 0.8. h s is the granular temperature for the solid phase, which is proportional to the kinetic energy of the random motion of the particles. The radial distribution coefficient g oss is "   13 #1 3 es 1 goss ¼ ð9Þ 5 es;max

Table 2 Inlet air pressure, airflow and air velocity Air pressure (bar)

Airflow (m3/h)

Air velocity in the acceleration tube (m/s)

2 3 4 5 6

1.09 1.51 1.88 2.31 2.67

42.8 59.4 73.9 90.8 104.9

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

2

3

Glass beads Olivine sand Crushed glass

3

0.5 kg/m 5 kg/m3

4

5

Particle velocity [m/s]

Particle velocity [m/s]

3

0.1 kg/m 2.5 kg/m3

40 35 30 25 20 15 10

6

97

40 35 30 25 20 15 10 2

3

Inlet air pressure [bar]

4 5 Inlet air pressure [bar]

6

Fig. 4. Effect of particle concentration on the particle velocity (glass beads, coarse fraction).

Fig. 6. Effect of particle shape on the particle velocity (coarse fraction, particle concentration 0.5 kg/m3).

The collisional dissipation of energy is:
 3 12 1  e2ss goss pffiffiffi ch s ¼ qs a2s hs2 ds p

To achieve an understanding of particle behaviour in the sand-blast type of erosion tester, a comprehensive analysis of particle dynamics within the tester was carried out. In the present work, the particle velocities, particle velocity distribution and plume divergence were measured under various set-up conditions. The first velocity component was in the vertical direction which is parallel to the acceleration tube, while the second component was the horizontal particle velocity perpendicular to the acceleration tube. The experimental results are discussed below only with the first velocity in the vertical direction.

ð20Þ

The energy exchange between the fluid and solid phase is: /gs ¼  3Kgs hs

ð21Þ

The diffusion coefficient for granular energy j 0s is: jhs ¼

pffiffiffiffiffiffiffi 15ds qs as hs p 12 1 þ g2 ð4g  3Þas goss 4ð41  33gÞ 5  16 ð41  33gÞgas goss þ 15p

where g ¼

ð22Þ

1 ð1 þ ess Þ 2

ð23Þ

4. Results and discussion 4.1. Experimental results and discussion

Fine fraction

35 30 25 20 15 10 5 0

Coarse fraction Jet divergence [°]

Particle velocity [m/s]

In the experimental as well as in the computational study, particular emphasis was given to the flow condition with inlet air pressures of 2, 3, 4, 5 and 6 bar and particle concentrations of 0.1, 0.5, 2.5, 5 and 8 kg/m3. The inlet air pressure is the pressure upstream of the air injection tube (Fig. 1). The relation between the inlet air pressure and airflow rate is listed in Table 2. All measurements were obtained at a distance of 23 mm from the tube outlet.

4.1.1. Mean particle velocity The particle velocities were examined at different inlet air pressures (hence, airflow rates), particle concentrations, particle sizes and particle shapes in order to understand the effect of each factor. The results are illustrated in Figs. 4 –6. The results show definite relations between the various investigated parameters and the particle velocity. It can be seen from Figs. 4– 6 that as the inlet air pressure and hence airflow rate increases, the particle velocity also increases. It is known that the relation between the particle velocity and the driving air pressure can be given by the power law [3]. The power law fit made for the data from the particle concentration of 0.1 kg/ m3 gave an exponent of 0.62 (V ” P 0.62) and the fit was good (R = 0.996). This is comparable to the power law fits reported by Stevenson and Hutchings [3]. The same curve fitting has been done for the other data points in Figs. 4 –6, and the exponents are between 0.36 and 0.62. Figs. 4 and 5 also show that the particle velocity decreases as the particle concentration and particle size increase at the Glass beads Olivine sand Crushed glass

8 6 4 2 0

2

3

4

5

6

Inlet air pressure [bar] Fig. 5. Effect of particle size on the particle velocity (glass beads, particle concentration 0.5 kg/m3).

2

3

4 5 Inlet air pressure [bar]

6

Fig. 7. Effect of particle shape on the plume divergence (fine fraction, particle concentration 2.5 kg/m3).

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Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

Jet divergence [°]

2.5 kg/m3 8 kg/m3

Particle Velocity [m/s]

0.5 kg/m3 5 kg/m3

10 8 6 4 2 0 2

2.5

3

3.5

35 25 15 5 -4

Fig. 8. Effect of particle concentration on jet divergence (olivine sand, 75 – 150 Am).

same inlet air pressure. These trends can be explained by the number of particle – particle and particle –wall collisions. The average particle – particle distance will decrease as the particle concentration increases, so the number of collisions increases as the particle concentration increases, and as a result the particle velocity decreases due to the particle kinetic energy lost during collisions. It may be observed in Fig. 6 that the crushed glass and olivine sand have a higher mean velocity than the glass beads. It is believed that the shape effect is very important. As the particle shape becomes less spherical at same inlet air pressure, the particle velocity increases markedly, especially at high inlet air pressure. This marked effect can be explained by drag coefficient. Particles experience higher drag coefficient and drag force as they become less spherical [15].

75-150 µm 160-315 µm

6 4 2 4 5 Inlet air pressure [bar]

-1

0

1

2

3

4

5

Fig. 10. Measured particle velocity distribution with inlet air pressure (glass beads, 150 – 250 Am, 0.5 kg/m3).

understand the sand-blast type of erosion tester, it is very important to know the plume divergence. It can be concluded from the results of this investigation that the amount of divergence varies depending on the particle shape, particle concentration, particle size, and inlet air pressure. The particle divergence after leaving the accelerating tube in the sand-blast erosion tester can be attributed to two effects, first because of the inter-particle and particle –wall collisions and second because the particles suffer dynamic phase interaction with the fluid. A similar trend regarding particle shape effects has been previously reported by Shipway and Hutchings [10] and explained on the basis of the effect of wall roughness in the nozzle. The particle velocity profiles in Figs. 10 and 11 illustrate that the profile for each inlet air pressure is similar. The profiles for low particle concentrations are however slightly steeper than for high particle concentration. The non-uniform particle velocity distribution can be explained by the air velocity profiles. 4.2. Euler –Lagrangian model results The Euler – Lagrangian model was first used to predict the particle velocity. The calculation domain included the mixing chamber, acceleration tube and erosion chamber as shown in Fig. 1, and simulation were carried out in a two-dimensional axisymmetric coordinate system. The supersonic nozzle and the target are not included so far in the simulation. The inlet air velocity which is calculated by the measured volume flow rate is set as the inlet boundary condition. The particle trajectory equation was solved for a number of particle sizes to obtain the average particle velocity.

-5

0 3

-2

Particle velocity [m/s]

Jet divergence [°]

4.1.2. Plume divergence The results summarised in Figs. 7 – 9 indicate that the extent of the divergence of the particle jet is related to the variables investigated. Figs. 7 –9 show the effects of particle shape, particle concentration, particle size and inlet air pressure on the plume divergence. The results from the investigation of plume divergence show that as the inlet air pressure increases, the divergence angle also increases. It was also observed that when the particle concentration increases, the divergence angle increases. The spherical glass beads have the largest divergence angle, then olivine sand, and finally crushed glass. The particle size also is an important factor in the observed jet divergence. The plume divergence of fine particles is larger than that of the coarse ones. It is known that the erosion performance of the materials in a tester is largely dependent on the particle flux at impact [2]. To

2

-3

Traverse Position [mm]

Inlet air pressure [bar]

8

5 Bar 3 Bar

45

-5

4

6 Bar 4 Bar 2 Bar

55

6

Fig. 9. Effect of particle size on jet divergence (olivine sand, 2.5 kg/m3).

-4

-3

-2

35 30 25 20 15 10 5 -1 0

0.1 kg/m3 0.5 kg/m3 2.5 kg/m3

1

2

3

4

5

Traverse position [mm] Fig. 11. Measured particle velocity distribution with particle concentration (glass beads, 150 – 250 Am, 2 bar).

Measurement (F)

Fluent (F)

Measurement (C)

Fluent (C)

99

0.1 kg/m3 LDA 2.5 kg/m3 LDA

60

0.1 kg/m3 Fluent 2.5 kg/m3 Fluent

40

50 40 30 20 10 0 2

3

4

5

6

Particle velocity [m/s]

Particle velocity [m/s]

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

Inlet air pressure [bar]

35 30 25 20 15 10 2

Fig. 12. Particle velocity with inlet air pressure (glass beads, 0.1 kg/m3).

3

4

5

6

Inlet air pressure [bar]

Figs. 12 and 13 show the comparison of results between simulation and measurement for the particle concentration of 0.1 kg/m3 (corresponding volume fraction is about 0.004%). The one-way coupling was applied in this dilute flow. For spherical glass beads, shown in Fig. 12, the measurements and numerical predictions are in very good agreement for both coarse and fine dispersed particles. Fig. 13 shows the particle velocity of non-spherical particles (olivine sand). It can be found that the model overpredicted the particle velocity compared with the measurement. The calculation for nonspherical particles is difficult because even a small deviation of shape from the sphere causes considerable irregular motion [18]. It is impossible to consider each particle shape effect when a number of non-spherical particles are used in the simulation. The drag coefficient used in the present calculation is derived from experiments, which may have a significant discrepancy to the present particles, and hence the model may produce uncertainties with simulation of non-spherical particles. At a low particle concentration, the particle – particle collisions can be neglected in the Euler –Lagrangian model. It is clear in this case that the drag coefficient model of Morsi and Alexander is very good for the prediction of the spherical particle velocity, while the drag coefficient model of Haider and Levenspiel overpredicted the non-spherical particle velocity by more than 50%. Fig. 14 shows the effect of particle concentration on the particle velocity with both measurements and simulations. No large difference was observed in the simulation when increasing the particle concentration from 0.1 to 2.5 kg/m3. In the measurements, the particle velocity decreased significantly with increasing particle concentration. However, the

Fig. 14. Effect of particle concentration on particle velocity (glass beads, 150 – 250 Am).

Euler – Lagrangian simulation results do not show the particle velocity difference between different particle concentration. As the particle concentration increases, the inter-particle collisions become important to particle velocity and plume divergence. However, the Euler – Lagrangian model in the Fluent code so far does not allow the inclusion of the particle – particle collision. The calculation of the plume divergence angle from the experimental study is presented in Section 2. About the calculation of the divergence angle in the simulation, the particle concentration is used. The plume edge is where the particle volume fraction is 1% of the volume fraction at plume center. The simulated plume divergence angles, shown in Fig. 15, compared to the experimentally measured divergence angles, showed that the model predicts lower plume divergence at all driving pressures. This is almost certainly due to the system being modelled without particle – particle interactions at present. This cannot be included in the model used so far and so the Euler – Euler model was used to consider the interaction of particles. 4.3. Euler– Euler model results In this section, the mean particle velocity, particle velocity distribution and plume divergence calculated for different inlet air pressures and particle concentrations by using the Euler – Euler multiphase model are presented and compared with the LDA measurements. Only the acceleration tube with the erosion chamber is modelled and simulated in a two-

Simulation

100 80 60 40 20 0 2

3

4

5

6

Inlet air pressure [bar]

Jet divergence [°]

Particle velocity [m/s]

Measurement Measurement Simulation

10 8 6 4 2 0 2

3

4

5

6

Inlet air pressure [bar] Fig. 13. Particle velocity with inlet air pressure (olivine sand, coarse fraction, 0.1 kg/m3).

Fig. 15. Plume divergence angle (glass beads, 75 – 150 Am, 2.5 kg/m3).

100

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102 3

Particle velocity [m/s]

0.5 kg/m Fluent

3

0.5 kg/m LDA

30 25 20 15 10 5 -7 -6 -5 -4 -3 -2 -1 0

1

2

3 4

5

6

7

Traverse position [mm] Fig. 18. Particle velocity distribution (glass beads, 75 – 150 Am, 2 bar).

Fig. 16. Air velocity distribution (2 bar).

dimensional Cartesian coordinate system. The inlet air velocities and volume fractions are defined for air and particle phases as the inlet boundary conditions. Figs. 16 and 17 show the air and particle velocity distributions in the sand-blast type of erosion tester using the Euler – Euler model. It is clear that the particle velocity is not uniform in the axial direction. The particles have a radial velocity when they leave the acceleration tube. This is mainly due to the particle – particle and particle – wall interactions inside the tube. Because the collisions may lead to a rotation movement and a radial velocity component, the particles were forced to move in radial direction leading to the divergence. Figs. 18 and 19 present the comparison of particle velocity distribution between model predictions and measurements for spherical particles at particle concentrations of 0.5 kg/m3 and 2.5 kg/m3, respectively. It is observed that the predicted velocity profiles under both particle concentration conditions are in good agreement with the experimental data.

Fig. 20 presents the comparison of mean particle velocity between measurements and calculations. The agreement of the simulation results with the experiments is very good when using the Euler – Euler model to predict the spherical particle velocity under various particle concentrations. Fig. 21 shows the comparison of plume divergence angle between video camera measurements (explained in Section 2) and Euler – Euler model predictions. For the Euler –Euler predictions, the edge of the simulated particle volume fraction is used when calculating the divergence angle. The plume edge is where the particle volume fraction is 1% of the particle volume fraction at center. It is observed that the experimental and simulated results are in reasonable agreement. Comparing with the Euler – Lagrangian model result in Fig. 15, it shows that the Euler – Euler model can predict the plume divergence more closely to the experimental result because of the particle –particle interactions. The simulation results are slightly larger than that in the experiment. One reason may be that the simulations use a single particle size representing the wide range of particle size distribution in measurements. The multiphase models are also at present not so mature. Another reason may be that the video camera cannot be used to exactly define the dilute particle plume edge. The simulation results of non-spherical particles (crushed glass and olivine sand) using the Euler –Euler model are illustrated in Figs. 22 and 23. Fig. 22 shows that the particle velocity of crushed glass modelled by the Euler –Euler model reasonably accords with the experimental results. The plume divergence angle calculated by the Euler –Euler model is about 15– 20% higher than the measurement results, see Fig. 23. This

Particle velocity [m/s]

2.5 kg/m3 Fluent

2.5 kg/m3 LDA

25 20 15 10 5 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

Traverse position [mm] Fig. 17. Particle velocity distribution (2 bar, glass beads, 150 – 250 Am, 0.5 kg/m3).

Fig. 19. Particle velocity distribution (glass beads, 75 – 150 Am, 2 bar).

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

0.5 kg/m3 LDA 3

0.5 kg/m3 Fluent

0.5 kg/m3 LDA

3

0.5 kg/m3 Fluent

2.5 kg/m Fluent

40

2.5 kg/m3 LDA

50

30 20 10 0 2

3

4

5

Inlet air pressure [bar]

Particle velocity [m/s]

Particle velocity [m/s]

2.5 kg/m LDA

101

2.5 kg/m3 Fluent

40 30 20 10

Fig. 20. Mean particle velocity with inlet air pressure (Glass beads, 75 – 150 Am).

0 2

3

4

5

6

Inlet air pressure [bar]

indicates that the shape of angular particles is a very important factor and need to be studied in the future. 5. Conclusions The results presented on the particle dynamics within a Fsand-blast_ type of erosion tester have enabled a better understanding of the erosion tester. The results have enabled the relations between the particle velocity and the various system parameters including particle shape, size, concentration and air pressure. The effect of these parameters upon the angle of plume divergence has also been investigated and discussed. The results between measurement and simulation were compared. Based on the presented results, the following conclusions can be drawn: & The model predictions for spherical particle velocities at low concentration were in very good agreement with the LDA measurements in both Euler – Lagrangian and Euler –Euler models. With high particle concentrations, the Euler –Euler model is usable while Euler –Lagrangian model is not. For non-spherical particles, the Euler –Lagrangain model overpredicted the particle velocity by about 50% probably because of the selected drag model. There is a definite effect of non-spherical particle shape on the particle velocities and plume divergence in a Fsand-blast_ erosion tester. & The model prediction for plume divergence of spherical particles is in quite reasonable agreement with the measurements when using the Euler – Euler model. The Euler – Lagrangian model underestimated the plume divergence because particles and wall collisions cannot be included. It is impossible so far to predict the plume divergence

Fig. 22. Mean particle velocity with inlet air pressure (crushed glass, 150–300 Am).

accurately for non-spherical particles in both the Euler – Euler model and Euler – Largrangian model. This is because the shape coefficient of non-spherical particles is not yet well developed. & The particle size has the effect of reducing the particle velocity under given operating conditions. The investigation also confirmed the effect of particle concentration on the velocity. It can be concluded from the results that the higher particle concentration is, the lower the particle velocities are under the same operating conditions. & The extent of the particle divergence is mainly attributed to the particle collisions (including the particle – wall collision) and fluid dynamic forces acting on the particles. Nomenclature CD Drag coefficient dp Particle diameter e ss Coefficient of restitution gi Gravity acceleration g oss Radial distribution coefficient K sg or K gs Fluid solid exchange coefficient j 0s Diffusion coefficient for granular energy P Pressure Re Reynolds number t Time u Velocity Y u Fluid phase velocity vector uYp Particle velocity vector Simulation

Measurement

Measurement Simulation

8

Jet divergence [°]

Jet divergence [°]

8

7 6 5 4 3

6 4 2 0

2

3

4

5

Inlet air pressure [bar] Fig. 21. Plume divergence angle (glass beads, 75 – 150 Am, 2.5 kg/m3).

2

3

4 5 Inlet air pressure [bar]

6

Fig. 23. Plume divergence angle (olivine sand, 75 – 150 Am, 2.5 kg/m3).

102

Q. Wang et al. / Powder Technology 160 (2005) 93 – 102

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