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A numerical 3D simulation for prediction of wear caused by solid particle impact
Wear 276–277 (2012) 75–84
Contents lists available at SciVerse ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
A numerical 3D simulation for prediction of wear caused by solid particle impact Hossein Ashrafizadeh a,∗ , Fakhreddin Ashrafizadeh b a b
Department of Mechanical Engineering, Isfahan University of Technology, P.O. Box 8415683111 Isfahan, Iran Department of Materials Engineering, Isfahan University of Technology, Isfahan, Iran
a r t i c l e
i n f o
Article history: Received 26 June 2011 Received in revised form 29 October 2011 Accepted 14 December 2011 Available online 22 December 2011 Keywords: Erosion wear Impact energy Collision angle Discrete element method
a b s t r a c t Discrete element method has been used to simulate the behavior of particles interacting with a flat plate in order to define a relationship between shear-normal impact energy and wear rate during mechanical erosion. The analysis was performed for various collision angles, velocities and particle concentrations and, it was found that the shear impact energy of particles with the plate was maximized at collision angles near 30◦ where the wear rate had its maximum value. To investigate the influence of particles accumulation on the surface, a similar simulation procedure for a single particle impacting a plate was carried out and the results demonstrated the role of particles interactions on normal-shear impact energy and consequently on the erosion mechanism. Comparison of the simulation data with experimental data indicated that the shear impact energy was mainly relevant to cutting and cracking erosion mechanism while normal impact energy was related to forging and extrusion mechanisms. The results obtained suggest that this numerical simulation method may be used in a predictive way to study practical design problems and to explain some phenomena associated with solid particle impact erosion. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Solid particle interaction is a process by which material is removed from a surface impacted by a stream of particles. The damage caused by erosion has been reported in many components including helicopter blades, turbine blades, transport of solid particles through pipes and boiler tubes exposed to fly ash [1]. A possible solution to decrease the erosion wear is by changing the material properties and surface characteristics. A number of research works have focused on erosion resistance of materials for improvement of protective coatings that are resistant to harsh environments caused by ash, dust, smoke and airborne particles [2–8]. These researches have mostly relied on the surface strength of the component for a certain operational condition. Based on some experimental techniques, many models have been proposed to evaluate the wear rate in different modes of erosion due to solid particle interactions [9–13]. Talia et al. performed a theoretical analysis on a new laboratory technique for solid particle erosion. Using this technique, he could evaluate the effect of particle velocity components (normal and tangential) on wear rate, separately [1]. Zhang et al. used an experimental approach to identify the material removal mechanisms and defined a relationship between the erosion variables and acoustic emission and applied the results to evaluate the erosion mechanism in metal tubes of
∗ Corresponding author. Tel.: +98 311 3913039; fax: +98 311 3913039. E-mail address: sh.ashrafi[email protected] (H. Ashrafizadeh). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.12.003
a boiler [14]. Mazur et al. performed a 3D numerical simulation using finite volume method, looking for reduction of the erosion process [15]. On the other hand, Bielawski and Beres employed finite element method to investigate tensile stresses at the surface of multilayered coatings under single particle impact, simulating specific mechanical erosion conditions [16]. These numerical
Fig. 1. Schematic view of the simulation setup.
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Fig. 2. Schematic view of finite element simulation for determining coefficient of restitution of ash particle impacting a stainless steel plate.
Fig. 3. The meshed model of the spherical ash particle and stainless steel plate.
Fig. 4. Variation of velocity of ash sphere as a function of time during impact (initial velocity 20 m/s).
Fig. 5. The arrangement of particles and flat plate in the beginning of simulation.
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Fig. 6. Impact energy as a function of time (initial velocity 20 m/s, collision angle 30◦ , particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
simulations can be used in a predictive manner to solve practical design problems as they are easier and less expensive compared to experimental setup. Recently, discrete element method (DEM) has found applications as a reliable method in predicting particles behavior in granular flows. Using DEM, it is possible to calculate the normalshear impact energy between particles and containers wall. As the grinding quality is proportional to impact energy between balls and ground substances, several types of mills have been modeled by this technique [17–19]. Sato used DEM and performed several experiments to find the correlation between impact energy of balls and their abrasion rate in a planetary ball mill. He could predict the wear rate constant by DEM simulation and it appears that these simulations help the producers to optimize their present designs [20].
To the best of our knowledge, DEM has not been used so far for evaluation of erosion wear caused by solid particle impacts. In this research, using C computer language, a numerical 3D simulation based on discrete element method has been developed for predicting the wear rate and erosion mechanism of solid particle impacts. The boundary condition and analysis were set according to the experimental data reported by Zhang et al. and the simulation results were compared with the data available in the literature [14]. The influence of process parameters including impact angle, particle concentration and initial speed on the normal-shear impact energy has been analyzed. The simulation was also performed for a single particle and has been compared to a group of particles; the interactions and mechanisms are described and discussed in the present article.
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Fig. 7. Particles colliding the flat plate; (a) collision angle 90◦ , (b) collision angle 30◦ .
2. Simulation 2.1. Simulation conditions Fig. 1 shows a schematic view of the simulation setup. As indicated, particles with an initial speed and concentration, leave the nozzle and hit the tube at an angle with respect to the longitudinal axis of the tube (␣). The tube material was assumed stainless steel and the particles made from ash and, in simulation, density and other parameters were set according to the physical properties of tube and ash particles. Several basic assumptions were made for this simulation;
I. The particles have spherical shape. II. The particles diameter is 200 m and all of them have the same size. III. The jet diameter (6 mm) is small compared to the tube diameter and the impact area. As a result, the particles were assumed to impact a flat plate. IV. The effect of air drag on particles motion is neglected. 2.2. Simulation formulation In DEM simulation, the motion of each particle is calculated through a cyclic process of small time step (t). Each particle may
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Fig. 8. Impact energy as a function of collision angle (initial velocity 20 m/s, particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
collide with many other particles as well as the container walls [21]. The general DEM methodology and its variants are well established and have been described in the review article by Walton [22]. The particles are allowed to overlap with an average typically less than 0.5%. The amount of overlap (x), normal (vn ) and tangential (vt ) velocities determine the collision forces via a contact force law. There are several types of contact forces that are used for solving dynamic equations in DEM [23]. However, in granular flow simulations often simple models (linear) are used [24]. In the present work, a linear spring-dashpot model was employed as the DEM formulation and central difference method was used for numerical integration. Eqs. (1) and (2) show the linear spring dashpot model; Fn = −Kn x + Cn vn
(1)
Ft = min{Fn , Kt
vt dt + Ct vt }
(2)
where Fn is normal force, Ft is tangential force, Kn is normal stiffness, Kt is tangential stiffness, Cn is normal damping and Ct is tangential damping. Considering the size of particles, the time step was chosen very small (0.1 s) for stability reasons. Obviously, such a small time step imposed a high level of computations. Consequently, to speed up the calculations and to reduce the processing time, parallel computing techniques were employed and the program was run on a computer with multiprocessors. DEM simulation parameters were defined based on Venugopal and Mishra findings [25,26]. The coefficient of friction was chosen 0.3 and in order to find the coefficient of restitution of spherical
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Fig. 9. Wear of stainless steel flat plate as a function of collision angle, based on data obtained from Ref. [14] (initial velocity 20 m/s, particle concentration 464 g/m3 , time duration 52 min).
ash particle with steel plate, a simulation based on finite element method was utilized. This nonlinear finite element code, modeled the dynamic process of the collision between a deformable sphere made from ash and deformable planar surface made from stainless steel. The simulation was setup based on the data of a previous published research [24]. Fig. 2 demonstrates a schematic view of the simulation for determination of the coefficient of restitution. In this model, explicit dynamic was set as the step type and elastoperfectly plastic with von Mises yield criterion was employed to describe the material behavior. The number of elements was increased to ensure that the problem is not mesh dependent and Fig. 3 shows the final meshed model. The boundary condition was set by attaching one side of the plate to ground and the penalty contact between the other side of the plate and the particle was defined. The initial condition was that the particle had an initial normal velocity toward the steel plate. Further, it was assumed that the plate remained flat throughout the process and consequently the coefficient of restitution did not vary. Considering Fig. 4 and by using Eq. (3), the coefficient of restitution between a spherical ash and steel plate for an initial velocity of 20 m/s was obtained 0.81. e=
vout vin
(3)
calculate the normal and shear impact energy of particles with flat plane, the following equations were used [27]; Enormal =
m
Fn Vn
(4)
1
Eshear =
m
Ft Vt
(5)
1
where E indicates impact energy and m is the number of particles having interactions with the plane on that moment. As an example, Fig. 6 demonstrates the normal and shear impact energy as a function of time for the condition of impact angle equal to 30◦ and initial speed of 20 m/s. It can be seen that in this time span (after 0.01 s), the response is stabilized and a periodic behavior is observed. Fig. 7 presents the particle interactions with angles of 90◦ and 30◦ after 0.015 s. It can be seen that for the 90◦ collision angle, particles tend to accumulate near the contact area while in the case of 30◦ , particles move at a path along reverse direction of the impact. The data collection was carried out within the range of 0.01–0.015 s where the stabilization of the system was ensured; the average value of normal-shear impact energy was determined through this time span and used to evaluate the influence of various parameters. 3. Results and discussion
At the beginning of the simulation, the particles were positioned in a circular format by having a distinct span between them in longitudinal direction, as indicated in Fig. 5. It should be mentioned that for visual purposes, the particles are magnified twice their real size in Figs. 5 and 7. As the initial condition of the simulation, the particles have an initial velocity toward the impact plane with a defined impact angle. It was assumed that the particles are colliding a flat plate and, consequently, the only boundary condition in this simulation is a plate where the particles make collision. In each time step, the distance of every single particle from the flat plate is calculated, and when the particle is in contact with the plate, the reaction forces are calculated using the relevant equations. The analysis was performed for the time duration of 0.015 s and to
3.1. Effect of collision angle In order to study the effect of collision angle on normal and shear impact energies, particle diameters, initial speed and particle concentration were kept constant. It can be seen in Fig. 8 that both the normal and shear impact energies have a maximum point; the maximum point of the shear impact energy is positioned exactly where the maximum wear has occurred, i.e. around 30◦ . The collision angle of the particles is an important issue in the erosion process. It has been shown that for a given velocity, particles concentration and particles diameter, there is a collision angle (˛) that maximizes the wear rate. This angle has been reported near 20–30◦ ;
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Fig. 10. Impact energy as a function of collision angle for a single particle (initial velocity 20 m/s); (a) shear impact energy, (b) normal impact energy.
when the angle increased further, the wear decreased steadily until ˛ reached 80◦ and, at higher angles, the wear increased again [14]. The variation in Fig. 8a confirms that the shear impact energy curve has a maximum value close to 30◦ , decreasing uniformly until ˛ approaches 80◦ and then increases slightly toward 90◦ . Based on scanning electron micrographs of the eroded specimens, it has been stated that the most dominant material removal mode in mechanical erosion is cutting together with cracking happened at 20–30◦ [14]. Hence, considering the similarities between shear impact energy graph and wear rate (Fig. 9), it appears that this parameter is related to cutting and cracking mechanisms and, by considering the shear impact energy, it would be possible to estimate the conditions for the maximum wear. Similar fractography examinations have revealed that on the span of collision angle 60–80◦ the major mechanism is deformation of the surface by particle impacts. This is described as a forging and normal extrusion mechanism, producing deep surface pits that contribute to the erosion process. As demonstrated in Fig. 8b, the maximum normal impact energy occurs around 80◦ . Therefore, it can be concluded that the normal impact energy defines the level of deformation and forging mechanism. Further, considering the fact that the normal impact energy curve did not reveal any particular feature around
30◦ , it can be stated that it is not directly related to the wear rate. The 3D simulation performed in the present research can explain the reason of increasing of shear impact energy at ˛ = 90◦ ; at this angle the particles have the tendency to accumulate on the impact area (Fig. 7a). Subsequently, new particles collide and push the existent particles into the plate while, at the same time, forcing them to move. This explanation clarifies the reason of increase in shear impact energy and also the wear rate that occur at 90◦ . It should be noted that the same explanation can be used for the decrease in normal impact energy at ˛ = 90◦ . In fact, the presence of other particles in the impact area, leads to a reduction in the normal impact energy of new particles leaving the nozzle. This happens because only part of their energy is transmitted to the plate and part of that is absorbed by the existent particles. Comparing Fig. 8 with Fig. 9, it can be seen that the curves showing the amount of wear and the shear impact energy versus the collision angle almost have the same trend. As a result, it can be stated that there exists a linear correlation between these two parameters. The small difference in the shape of the curves may be explained considering the assumptions that have been made
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Fig. 11. Impact energy as a function of initial velocity (particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
for simplicity. The air drag that was neglected in this simulation could affect the particles motion. In addition, the wear test was performed for 52 min during which the surface of the plate is eroded and this could change the coefficient of restitution and, therefore, the particles motions. To investigate the influence of particles accumulation on the surface, a similar simulation procedure for a single particle impacting a plate was carried out. Fig. 10 presents variation of shear and normal
impact energies as a function of impact angle for a single particle. It can be observed that the normal impact energy increases continuously until it reaches a maximum at ˛ = 90◦ . On the other hand, the shear impact energy shows, after a peak value, a steady decreasing trend till ˛ reaches 90◦ . Comparison of the data for single particle with the results presented in Fig. 8 confirms the role of particles interactions on normal-shear impact energy and consequently on the erosion mechanism.
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Fig. 12. Impact energy as a function of particle concentration (initial velocity 20 m/s); (a) shear impact energy, (b) normal impact energy.
3.2. Effect of particles velocity The effect of particles initial velocity after leaving the nozzle has been evaluated for a constant value of particle concentration. The analysis was performed for several collision angles and the calculated normal and shear impact energies are summarized in Fig. 11 As expected, by increasing the speed, both the normal and
shear impact energies increase. This is obvious considering the fact that a particle with higher speed contains more energy. Again, it is observed that the increasing rate and the slope in the shear impact energy for collision are higher at angles in the range 20–30◦ and this is in agreement with the experimental results reported for wear rate as a function of nozzle initial speed [14]. On the other hand, normal impact energy increases approximately as a third
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order function of initial velocity for all the measured collision angles and the maximum does not occur at 90◦ , instead, it shows a higher value around 60–80◦ . Therefore, it is expected that the forging and penetration of particles into the surface to be higher in this range.
main effects exerted by multi particles impact are that the maximum normal impact energy occurs at ˛ = 80◦ and an increasing trend in shear impact energy for collision angles above 80◦ . References
3.3. Effect of particles concentration The particle concentration is defined as the mass of particles per unit volume in the air stream. It is well established that higher particle concentration will lead to more collisions for a constant velocity in a given time interval. Experimental results have indicated that, in general, increase in particle concentration leads to higher wear and, in addition, the rate of increase is higher for angles in the range 20–30◦ . The same result was obtained by DEM simulation for shear impact energy. As shown in Fig. 12, both the normal and shear impact energies increase by increasing particle concentration. However, it can be seen that for collision angles between 20 and 30◦ , the rate of increase in shear impact energy is higher. The variation of normal impact energy versus particle concentration in Fig. 12b shows that although it increases for all the impact angles, the slope of the curve is comparatively higher at ˛ = 80◦ . Hence, considering the relationship between normal impact energy and forging mechanism, it is expected by increasing the particle concentration, forging and penetration of surface increase for all angles, while it would be more intense for collision angle of 80◦ . 4. Conclusion In this research, discrete element method (DEM) was used to simulate the behavior of a jet of particles that exit a nozzle and hit a flat plate for various impact angles, particle velocities and particle concentrations. The main goal was to evaluate DEM as a reliable method for predicting wear rate and erosion mechanism in problems associated with solid particle interactions and a numerical technique to explain some phenomena that are observed during experimentation. Comparing the simulation results with reported experimental data, it was confirmed that there is a correlation between shear impact energy and the wear rate. In other words, shear impact energy is relevant to cutting and cracking erosion mechanism while the normal impact energy is more related to forging mechanism and does not directly affect the wear rate. It was found that for a given velocity and particle concentration, the shear impact energy became a maximum value around collision angle 30◦ and the normal impact energy near 80◦ . It was also realized that increasing the velocity or particle concentration lead to a higher shear and normal impact energies; the rate of increase of the shear impact energy was higher at 20–30◦ and that of the normal impact energy at 60–80◦ . The results of simulation are in well agreement with previous experimental data and, in addition, they explain the increase in shear impact energy and, thus, the wear rate observed at 90◦ impact angle. Moreover, comparison of the behavior of a single particle with a group of particles impacting a surface, employing DEM, demonstrated the influence of accumulation and particles interactions on normal and shear impact energies. The
[1] M. Talia, H. Lankarani, J.E. Talia, New experimental technique for the study and analysis of solid particle erosion mechanisms, Wear 225–229 (1999) 1070–1077. [2] E. Quesnel, Y. Pauleau, P. Monge-Cadet, M. Brun, Tungsten and tungstencarbon PVD multilayered structures as erosion-resistant coatings, Surf. Coat. Technol. 62 (1993) 474–479. [3] Y. Gachon, P. Ienny, A. Forner, G. Farges, M.C. Sainte Catherine, A.B. Vannes, Erosion by solid particles of W/W–N multilayer coatings obtained by PVD process, Surf. Coat. Technol. 113 (1999) 140–148. [4] D.W. Wheeler, R.J.K. Wood, Solid particle erosion of diamond coatings under non-normal impact angles, Wear 250 (2001) 795–801. [5] A. Leyland, A. Matthews, Thick Ti/TiN multilayered coatings for abrasive and erosive wear resistance, Surf. Coat. Technol. 70 (1994) 19–25. [6] Q. Yang, D.Y. Seo, L.R. Zhao, X.T. Zeng, Erosion resistance performance of magnetron sputtering deposited TiAlN coatings, Surf. Coat. Technol. 188–189 (2004) 168–173. [7] H.J. Kolkman, Effect of TiN/Ti gas turbine compressor coatings on the fatigue strength of Ti–6Al–4 V base metal, Surf. Coat. Technol. 72 (1995) 30–36. [8] X. Chen, J.W. Hutchinson, Particle impact on metal substrates with application to foreign object damage to aircraft engines, J. Mech. Phys. Solids 50 (2002) 2669–2690. [9] A. Levy, The erosion–corrosion of tubing steels in combustion boiler environments, Corros. Sci. 35 (1993) 1035–1056. [10] R. Bellman, A. Levy, Erosion mechanism in ductile metals, Wear 70 (1981) 1–27. [11] B.A. Lindsley, A.R. Marder, The effect of velocity on the solid particle erosion rate of alloys, Wear 225–229 (1999) 510–516. [12] W.J. Head, M.E. Harr, The development of a model to predict the erosion of materials by natural contaminants, Wear 15 (1970) 1–46. [13] Y. Xie, H.McI. Clark, H.M. Hawthorne, Modelling slurry particle dynamics in the Coriolis erosion tester, Wear 225–229 (1999) 405–416. [14] L. Zhang, V. Sazonov, J. Kent, T. Dixon, V. Novozhilov, Analysis of boiler-tube erosion by the technique of acoustic emission part I. Mechanical erosion, Wear 250 (2001) 762–769. [15] Z. Mazur, R. Campos-Amezcua, G. Urquiza-Beltran, A. Garcia-Gutierrez, Numerical 3D simulation of the erosion due to solid particle impact in the main stop valve of a steam turbine, Appl. Therm. Eng. 24 (2004) 1877–1891. [16] M. Bielawski, W. Beres, FE modeling of surface stresses in erosion-resistant coatings under single particle impact, Wear 262 (2007) 167–175. [17] R.D. Morrison, P.W. Cleary, M.D. Sinnott, Using DEM to compare the energy efficiency of pilot scale ball and tower mills, Miner. Eng. 22 (2009) 665–672. [18] P.W. Cleary, Ball motion, axial segregation and power consumption in a full scale two chamber cement mill, Miner. Eng. 22 (2009) 809–820. [19] N. Djordjevic, F.N. Shi, R. Morrison, Determination of lifter design, speed and filling effects in AG mills by 3D DEM, Miner. Eng. 17 (2004) 1135–1142. [20] A. Sato, J. Kano, F. Saito, Analysis of abrasion mechanism of grinding media in a planetary mill with DEM simulation, Adv. Powder Technol. 21 (2010) 212–216. [21] K. Maoa, M.Y. Wangb, Z. Xuc, T. Chend, DEM simulation of particles damping, Powder Technol. 142 (2004) 154–165. [22] O.R. Walton, Numerical simulation of inelastic frictional particles–particles interaction, in: M.C. Roco (Ed.), Particulate Two-Phase Flow, 1994, pp. 884–911. [23] A. Di Renzo, F.P. Di Maio, Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes, Chem. Eng. Sci. 59 (2004) 525–541. [24] X. Zhang, L. Vu-Quoc, Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions, Int. J. Impact Eng. 27 (2002) 317–341. [25] B.K. Mishra, C.V.R. Murty, On the determination of contact parameters for realistic DEM simulations of ball mills, Powder Technol. 115 (2001) 290–297. [26] R. Venugopal, R.K. Rajamani, 3D simulation of charge motion in tumbling mills by the discrete element method, Powder Technol. 115 (2001) 157–166. [27] E. Tugcan Tuzcu, Raj K. Rajamani, Modeling breakage rates in mills with impact energy spectra and ultra fast load cell data, Miner. Eng. 24 (2011) 252–260.
Contents lists available at SciVerse ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
A numerical 3D simulation for prediction of wear caused by solid particle impact Hossein Ashrafizadeh a,∗ , Fakhreddin Ashrafizadeh b a b
Department of Mechanical Engineering, Isfahan University of Technology, P.O. Box 8415683111 Isfahan, Iran Department of Materials Engineering, Isfahan University of Technology, Isfahan, Iran
a r t i c l e
i n f o
Article history: Received 26 June 2011 Received in revised form 29 October 2011 Accepted 14 December 2011 Available online 22 December 2011 Keywords: Erosion wear Impact energy Collision angle Discrete element method
a b s t r a c t Discrete element method has been used to simulate the behavior of particles interacting with a flat plate in order to define a relationship between shear-normal impact energy and wear rate during mechanical erosion. The analysis was performed for various collision angles, velocities and particle concentrations and, it was found that the shear impact energy of particles with the plate was maximized at collision angles near 30◦ where the wear rate had its maximum value. To investigate the influence of particles accumulation on the surface, a similar simulation procedure for a single particle impacting a plate was carried out and the results demonstrated the role of particles interactions on normal-shear impact energy and consequently on the erosion mechanism. Comparison of the simulation data with experimental data indicated that the shear impact energy was mainly relevant to cutting and cracking erosion mechanism while normal impact energy was related to forging and extrusion mechanisms. The results obtained suggest that this numerical simulation method may be used in a predictive way to study practical design problems and to explain some phenomena associated with solid particle impact erosion. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Solid particle interaction is a process by which material is removed from a surface impacted by a stream of particles. The damage caused by erosion has been reported in many components including helicopter blades, turbine blades, transport of solid particles through pipes and boiler tubes exposed to fly ash [1]. A possible solution to decrease the erosion wear is by changing the material properties and surface characteristics. A number of research works have focused on erosion resistance of materials for improvement of protective coatings that are resistant to harsh environments caused by ash, dust, smoke and airborne particles [2–8]. These researches have mostly relied on the surface strength of the component for a certain operational condition. Based on some experimental techniques, many models have been proposed to evaluate the wear rate in different modes of erosion due to solid particle interactions [9–13]. Talia et al. performed a theoretical analysis on a new laboratory technique for solid particle erosion. Using this technique, he could evaluate the effect of particle velocity components (normal and tangential) on wear rate, separately [1]. Zhang et al. used an experimental approach to identify the material removal mechanisms and defined a relationship between the erosion variables and acoustic emission and applied the results to evaluate the erosion mechanism in metal tubes of
∗ Corresponding author. Tel.: +98 311 3913039; fax: +98 311 3913039. E-mail address: sh.ashrafi[email protected] (H. Ashrafizadeh). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.12.003
a boiler [14]. Mazur et al. performed a 3D numerical simulation using finite volume method, looking for reduction of the erosion process [15]. On the other hand, Bielawski and Beres employed finite element method to investigate tensile stresses at the surface of multilayered coatings under single particle impact, simulating specific mechanical erosion conditions [16]. These numerical
Fig. 1. Schematic view of the simulation setup.
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Fig. 2. Schematic view of finite element simulation for determining coefficient of restitution of ash particle impacting a stainless steel plate.
Fig. 3. The meshed model of the spherical ash particle and stainless steel plate.
Fig. 4. Variation of velocity of ash sphere as a function of time during impact (initial velocity 20 m/s).
Fig. 5. The arrangement of particles and flat plate in the beginning of simulation.
H. Ashrafizadeh, F. Ashrafizadeh / Wear 276–277 (2012) 75–84
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Fig. 6. Impact energy as a function of time (initial velocity 20 m/s, collision angle 30◦ , particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
simulations can be used in a predictive manner to solve practical design problems as they are easier and less expensive compared to experimental setup. Recently, discrete element method (DEM) has found applications as a reliable method in predicting particles behavior in granular flows. Using DEM, it is possible to calculate the normalshear impact energy between particles and containers wall. As the grinding quality is proportional to impact energy between balls and ground substances, several types of mills have been modeled by this technique [17–19]. Sato used DEM and performed several experiments to find the correlation between impact energy of balls and their abrasion rate in a planetary ball mill. He could predict the wear rate constant by DEM simulation and it appears that these simulations help the producers to optimize their present designs [20].
To the best of our knowledge, DEM has not been used so far for evaluation of erosion wear caused by solid particle impacts. In this research, using C computer language, a numerical 3D simulation based on discrete element method has been developed for predicting the wear rate and erosion mechanism of solid particle impacts. The boundary condition and analysis were set according to the experimental data reported by Zhang et al. and the simulation results were compared with the data available in the literature [14]. The influence of process parameters including impact angle, particle concentration and initial speed on the normal-shear impact energy has been analyzed. The simulation was also performed for a single particle and has been compared to a group of particles; the interactions and mechanisms are described and discussed in the present article.
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Fig. 7. Particles colliding the flat plate; (a) collision angle 90◦ , (b) collision angle 30◦ .
2. Simulation 2.1. Simulation conditions Fig. 1 shows a schematic view of the simulation setup. As indicated, particles with an initial speed and concentration, leave the nozzle and hit the tube at an angle with respect to the longitudinal axis of the tube (␣). The tube material was assumed stainless steel and the particles made from ash and, in simulation, density and other parameters were set according to the physical properties of tube and ash particles. Several basic assumptions were made for this simulation;
I. The particles have spherical shape. II. The particles diameter is 200 m and all of them have the same size. III. The jet diameter (6 mm) is small compared to the tube diameter and the impact area. As a result, the particles were assumed to impact a flat plate. IV. The effect of air drag on particles motion is neglected. 2.2. Simulation formulation In DEM simulation, the motion of each particle is calculated through a cyclic process of small time step (t). Each particle may
H. Ashrafizadeh, F. Ashrafizadeh / Wear 276–277 (2012) 75–84
79
Fig. 8. Impact energy as a function of collision angle (initial velocity 20 m/s, particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
collide with many other particles as well as the container walls [21]. The general DEM methodology and its variants are well established and have been described in the review article by Walton [22]. The particles are allowed to overlap with an average typically less than 0.5%. The amount of overlap (x), normal (vn ) and tangential (vt ) velocities determine the collision forces via a contact force law. There are several types of contact forces that are used for solving dynamic equations in DEM [23]. However, in granular flow simulations often simple models (linear) are used [24]. In the present work, a linear spring-dashpot model was employed as the DEM formulation and central difference method was used for numerical integration. Eqs. (1) and (2) show the linear spring dashpot model; Fn = −Kn x + Cn vn
(1)
Ft = min{Fn , Kt
vt dt + Ct vt }
(2)
where Fn is normal force, Ft is tangential force, Kn is normal stiffness, Kt is tangential stiffness, Cn is normal damping and Ct is tangential damping. Considering the size of particles, the time step was chosen very small (0.1 s) for stability reasons. Obviously, such a small time step imposed a high level of computations. Consequently, to speed up the calculations and to reduce the processing time, parallel computing techniques were employed and the program was run on a computer with multiprocessors. DEM simulation parameters were defined based on Venugopal and Mishra findings [25,26]. The coefficient of friction was chosen 0.3 and in order to find the coefficient of restitution of spherical
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Fig. 9. Wear of stainless steel flat plate as a function of collision angle, based on data obtained from Ref. [14] (initial velocity 20 m/s, particle concentration 464 g/m3 , time duration 52 min).
ash particle with steel plate, a simulation based on finite element method was utilized. This nonlinear finite element code, modeled the dynamic process of the collision between a deformable sphere made from ash and deformable planar surface made from stainless steel. The simulation was setup based on the data of a previous published research [24]. Fig. 2 demonstrates a schematic view of the simulation for determination of the coefficient of restitution. In this model, explicit dynamic was set as the step type and elastoperfectly plastic with von Mises yield criterion was employed to describe the material behavior. The number of elements was increased to ensure that the problem is not mesh dependent and Fig. 3 shows the final meshed model. The boundary condition was set by attaching one side of the plate to ground and the penalty contact between the other side of the plate and the particle was defined. The initial condition was that the particle had an initial normal velocity toward the steel plate. Further, it was assumed that the plate remained flat throughout the process and consequently the coefficient of restitution did not vary. Considering Fig. 4 and by using Eq. (3), the coefficient of restitution between a spherical ash and steel plate for an initial velocity of 20 m/s was obtained 0.81. e=
vout vin
(3)
calculate the normal and shear impact energy of particles with flat plane, the following equations were used [27]; Enormal =
m
Fn Vn
(4)
1
Eshear =
m
Ft Vt
(5)
1
where E indicates impact energy and m is the number of particles having interactions with the plane on that moment. As an example, Fig. 6 demonstrates the normal and shear impact energy as a function of time for the condition of impact angle equal to 30◦ and initial speed of 20 m/s. It can be seen that in this time span (after 0.01 s), the response is stabilized and a periodic behavior is observed. Fig. 7 presents the particle interactions with angles of 90◦ and 30◦ after 0.015 s. It can be seen that for the 90◦ collision angle, particles tend to accumulate near the contact area while in the case of 30◦ , particles move at a path along reverse direction of the impact. The data collection was carried out within the range of 0.01–0.015 s where the stabilization of the system was ensured; the average value of normal-shear impact energy was determined through this time span and used to evaluate the influence of various parameters. 3. Results and discussion
At the beginning of the simulation, the particles were positioned in a circular format by having a distinct span between them in longitudinal direction, as indicated in Fig. 5. It should be mentioned that for visual purposes, the particles are magnified twice their real size in Figs. 5 and 7. As the initial condition of the simulation, the particles have an initial velocity toward the impact plane with a defined impact angle. It was assumed that the particles are colliding a flat plate and, consequently, the only boundary condition in this simulation is a plate where the particles make collision. In each time step, the distance of every single particle from the flat plate is calculated, and when the particle is in contact with the plate, the reaction forces are calculated using the relevant equations. The analysis was performed for the time duration of 0.015 s and to
3.1. Effect of collision angle In order to study the effect of collision angle on normal and shear impact energies, particle diameters, initial speed and particle concentration were kept constant. It can be seen in Fig. 8 that both the normal and shear impact energies have a maximum point; the maximum point of the shear impact energy is positioned exactly where the maximum wear has occurred, i.e. around 30◦ . The collision angle of the particles is an important issue in the erosion process. It has been shown that for a given velocity, particles concentration and particles diameter, there is a collision angle (˛) that maximizes the wear rate. This angle has been reported near 20–30◦ ;
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Fig. 10. Impact energy as a function of collision angle for a single particle (initial velocity 20 m/s); (a) shear impact energy, (b) normal impact energy.
when the angle increased further, the wear decreased steadily until ˛ reached 80◦ and, at higher angles, the wear increased again [14]. The variation in Fig. 8a confirms that the shear impact energy curve has a maximum value close to 30◦ , decreasing uniformly until ˛ approaches 80◦ and then increases slightly toward 90◦ . Based on scanning electron micrographs of the eroded specimens, it has been stated that the most dominant material removal mode in mechanical erosion is cutting together with cracking happened at 20–30◦ [14]. Hence, considering the similarities between shear impact energy graph and wear rate (Fig. 9), it appears that this parameter is related to cutting and cracking mechanisms and, by considering the shear impact energy, it would be possible to estimate the conditions for the maximum wear. Similar fractography examinations have revealed that on the span of collision angle 60–80◦ the major mechanism is deformation of the surface by particle impacts. This is described as a forging and normal extrusion mechanism, producing deep surface pits that contribute to the erosion process. As demonstrated in Fig. 8b, the maximum normal impact energy occurs around 80◦ . Therefore, it can be concluded that the normal impact energy defines the level of deformation and forging mechanism. Further, considering the fact that the normal impact energy curve did not reveal any particular feature around
30◦ , it can be stated that it is not directly related to the wear rate. The 3D simulation performed in the present research can explain the reason of increasing of shear impact energy at ˛ = 90◦ ; at this angle the particles have the tendency to accumulate on the impact area (Fig. 7a). Subsequently, new particles collide and push the existent particles into the plate while, at the same time, forcing them to move. This explanation clarifies the reason of increase in shear impact energy and also the wear rate that occur at 90◦ . It should be noted that the same explanation can be used for the decrease in normal impact energy at ˛ = 90◦ . In fact, the presence of other particles in the impact area, leads to a reduction in the normal impact energy of new particles leaving the nozzle. This happens because only part of their energy is transmitted to the plate and part of that is absorbed by the existent particles. Comparing Fig. 8 with Fig. 9, it can be seen that the curves showing the amount of wear and the shear impact energy versus the collision angle almost have the same trend. As a result, it can be stated that there exists a linear correlation between these two parameters. The small difference in the shape of the curves may be explained considering the assumptions that have been made
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Fig. 11. Impact energy as a function of initial velocity (particle concentration 500 g/m3 ); (a) shear impact energy, (b) normal impact energy.
for simplicity. The air drag that was neglected in this simulation could affect the particles motion. In addition, the wear test was performed for 52 min during which the surface of the plate is eroded and this could change the coefficient of restitution and, therefore, the particles motions. To investigate the influence of particles accumulation on the surface, a similar simulation procedure for a single particle impacting a plate was carried out. Fig. 10 presents variation of shear and normal
impact energies as a function of impact angle for a single particle. It can be observed that the normal impact energy increases continuously until it reaches a maximum at ˛ = 90◦ . On the other hand, the shear impact energy shows, after a peak value, a steady decreasing trend till ˛ reaches 90◦ . Comparison of the data for single particle with the results presented in Fig. 8 confirms the role of particles interactions on normal-shear impact energy and consequently on the erosion mechanism.
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Fig. 12. Impact energy as a function of particle concentration (initial velocity 20 m/s); (a) shear impact energy, (b) normal impact energy.
3.2. Effect of particles velocity The effect of particles initial velocity after leaving the nozzle has been evaluated for a constant value of particle concentration. The analysis was performed for several collision angles and the calculated normal and shear impact energies are summarized in Fig. 11 As expected, by increasing the speed, both the normal and
shear impact energies increase. This is obvious considering the fact that a particle with higher speed contains more energy. Again, it is observed that the increasing rate and the slope in the shear impact energy for collision are higher at angles in the range 20–30◦ and this is in agreement with the experimental results reported for wear rate as a function of nozzle initial speed [14]. On the other hand, normal impact energy increases approximately as a third
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order function of initial velocity for all the measured collision angles and the maximum does not occur at 90◦ , instead, it shows a higher value around 60–80◦ . Therefore, it is expected that the forging and penetration of particles into the surface to be higher in this range.
main effects exerted by multi particles impact are that the maximum normal impact energy occurs at ˛ = 80◦ and an increasing trend in shear impact energy for collision angles above 80◦ . References
3.3. Effect of particles concentration The particle concentration is defined as the mass of particles per unit volume in the air stream. It is well established that higher particle concentration will lead to more collisions for a constant velocity in a given time interval. Experimental results have indicated that, in general, increase in particle concentration leads to higher wear and, in addition, the rate of increase is higher for angles in the range 20–30◦ . The same result was obtained by DEM simulation for shear impact energy. As shown in Fig. 12, both the normal and shear impact energies increase by increasing particle concentration. However, it can be seen that for collision angles between 20 and 30◦ , the rate of increase in shear impact energy is higher. The variation of normal impact energy versus particle concentration in Fig. 12b shows that although it increases for all the impact angles, the slope of the curve is comparatively higher at ˛ = 80◦ . Hence, considering the relationship between normal impact energy and forging mechanism, it is expected by increasing the particle concentration, forging and penetration of surface increase for all angles, while it would be more intense for collision angle of 80◦ . 4. Conclusion In this research, discrete element method (DEM) was used to simulate the behavior of a jet of particles that exit a nozzle and hit a flat plate for various impact angles, particle velocities and particle concentrations. The main goal was to evaluate DEM as a reliable method for predicting wear rate and erosion mechanism in problems associated with solid particle interactions and a numerical technique to explain some phenomena that are observed during experimentation. Comparing the simulation results with reported experimental data, it was confirmed that there is a correlation between shear impact energy and the wear rate. In other words, shear impact energy is relevant to cutting and cracking erosion mechanism while the normal impact energy is more related to forging mechanism and does not directly affect the wear rate. It was found that for a given velocity and particle concentration, the shear impact energy became a maximum value around collision angle 30◦ and the normal impact energy near 80◦ . It was also realized that increasing the velocity or particle concentration lead to a higher shear and normal impact energies; the rate of increase of the shear impact energy was higher at 20–30◦ and that of the normal impact energy at 60–80◦ . The results of simulation are in well agreement with previous experimental data and, in addition, they explain the increase in shear impact energy and, thus, the wear rate observed at 90◦ impact angle. Moreover, comparison of the behavior of a single particle with a group of particles impacting a surface, employing DEM, demonstrated the influence of accumulation and particles interactions on normal and shear impact energies. The
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