Progress in the understanding of bulk solids attrition in dilute phase pneumatic conveying

Powder Technology 143 – 144 (2004) 308 – 320 www.elsevier.com/locate/powtec

Progress in the understanding of bulk solids attrition in dilute phase pneumatic conveying Lars Frye a,*, Wolfgang Peukert b a

b

Institute of Particle Technology, TU Mu¨nchen, Boltzmannstr. 15, 85748 Garching, Germany Institute of Particle Technology, Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnberg, Cauerstr. 4, 91058 Erlangen, Germany

Abstract To investigate attrition processes in pneumatic conveying, it is distinguished between process parameters, determining the stress conditions (SC) the particles are subjected to during conveying (process function), and material properties, being responsible for the individual reaction of different materials to these stress conditions (material function). For dilute phase conveying, the process function was determined for a pipe bend preceded by a straight pipe by employing computational fluid dynamics (CFD). The influence of the main parameters as obtained by dimensional analysis, namely, Stokes parameter, Froude number, Reynolds number and the ratio of bend radius to pipe diameter, was investigated and discussed. The results showed that the impact conditions were different from what is commonly expected. The impact angles in a pipe bend (rB/D = 5; D = 80 mm) were determined to lie between 5j and 35j. Consequently, the tangential impact velocity components are considerably higher than the normal ones. The experiments carried out to determine the material function revealed that the dominating attrition mechanisms differ between polypropylene (PP) particles on one hand and polymethylmethacrylates (PMMA) and polystyrenes (PS) on the other. By applying dynamic mechanical analysis (DMA), the glass transition temperature of the polymers was identified to be a key factor in the determination of the prevailing attrition mechanism. Based on these findings, a qualitative three-level model of the attrition process, involving stress mode, material-specific attrition mechanisms and basic (microscopic) attrition mechanisms, was developed. D 2004 Published by Elsevier B.V. Keywords: Pneumatic conveying; Polymers; Process function; Material function; Dynamic mechanical analysis (DMA); Attrition mechanisms

1. Introduction Due to their complexity, attrition processes are not very well understood to date. One reason for this is that in many experimental studies no clear differentiation between the stress conditions generated by the respective process (e.g., friction in bearings, pneumatic conveying or fluidized bed) and the material-specific reaction to these stresses is made. Furthermore, as Meng and Ludema [1] state in an extensive review of wear modeling, many authors appear to select material property variables for their models in an arbitrary manner or without apparent connection to real modes of material loss. Attrition in pneumatic conveying, like in other industrial processes, is an undesired and yet nonpreventable side effect. To address attrition phenomena, different approaches * Corresponding author. Lehrstuhl fuer Feststoff- u., Grenzflaechenverfahrenstechnik (LFG), Technische Universitaet Mu¨nchen, Boltzmannstr. 15, 85748 Garching, Germany. Tel.: +49-89-289-15656; fax: +49-89-28915674. E-mail address: [email protected] (L. Frye). 0032-5910/$ - see front matter D 2004 Published by Elsevier B.V. doi:10.1016/j.powtec.2004.04.023

have been followed. On one hand, experiments are carried out in comparatively complex test rigs providing stress conditions closely related to industrial processes [2], which in turn usually are not well defined. The second approach is to carry out experiments under well-defined stress conditions in simple setups to identify basic attrition mechanisms [3 – 5]. This of course bears the danger that the obtained results might not be directly transferable to industrial processes due to differing stress conditions. To overcome this uncertainty for pneumatic conveying, a detailed analysis of conveying processes with respect to attrition was conducted. Based on this, a concept was developed in which it is rigidly distinguished between process parameters determining the stress conditions the particles are subjected to during conveying and material properties being responsible for the individual reaction of different materials to these stress conditions. In order to identify these, experiments were carried out under defined stress conditions whose values were set as close to those obtained from the process parameters as possible.

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Consequently, attrition formation in pneumatic conveying is interpreted as the result of a process function describing the stress conditions the particles are subjected to in the conveying pipelines and a material function summarizing the material-specific response to the process function in terms of intrinsic material properties. Both functions are of course not fully independent, because particle properties like for example size or air retention capability are of great influence on the mode of conveying. Nevertheless, we assume that the influence of process parameters and material properties on attrition can be separated with satisfying accuracy. Details on both process and material function will be given posterior to the description of the materials used for the model experiments.

2. Test material Pneumatic conveying is largely applied to transport granular polymers where usually even smallest amounts of attrition cannot be tolerated. Therefore, the current study is focused on polymers of four chemically different classes. Polypropylene (PP) and polyethylene (PE) belong to the semicrystalline polymers, which possess both an amorphous phase and a crystalline phase. The polymethylmethacrylates (PMMA) and polystyrenes (PS) are fully amorphous. Some material properties of the polymers are summarized in Table 1. The particle shape was determined by visual inspection. To obtain the particle diameter xp, the volume of individual particles was measured in a He-pycnometer, and the diameter of the sphere possessing the same volume was calculated. The solid density qp was measured in the Hepycnometer as well. The Vicker’s hardness HV was determined in a microhardness tester, while Young’s modulus E and yield stress ry were given by the manufacturer. Finally, the J-integral value JQd, which corresponds to the critical energy release rate Gc for materials with a nonlinear deformation curve, was measured at the Institute of Polymeric Materials, Martin-Luther University Halle-Wittenberg by employing a modified Charpy notched impact test. Table 1 Overview of different material properties Name

Shape

xp/ min

qp/ Hv/ (kg/m3) MPa

E/ MPa

ry/ JQd/ MPa (kJ/m2)

PP 1040 N PP 1100 RC PP 1148 RC PP 2500 H PE 2420 H PE 5031 L PMMA G7 PMMA G55 PS 144 C PS 158 K

Elliptical Elliptical Elliptical Elliptical Elliptical Elliptical Cylindrical Cylindrical Cylindrical Cylindrical

4.04 4.00 4.11 4.06 3.28 3.46 3.20 3.03 3.46 3.46

869.9 869.7 867.8 896.3 919.3 946.3 1191.8 1203.9 1053.1 1059.8

2000 1500 1650 1100 260 1000 3200 3100 3300 3300

40 34 35 23 11 26 n.a. n.a. n.a. n.a.

95.5 85.0 90.0 68.0 61.5 84.5 208.9 178.0 177.7 178.8

2.04 2.09 1.92 n.a. n.a. 4.00 0.77 0.65 1.54 1.99

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3. Determination of the process function for dilute phase conveying In general, the bulk solids mass flow ratio l, defined as the ratio of the mass flow of solids to that of conveying gas, is low for dilute phase conveying. According to Klinzing et al. [6], l ranges from 0 to 15. Therefore, Computational Fluid Dynamics (CFD) can be employed to determine the stress conditions the particles are subjected to. Here, a commercial code—CFX Tascflow by AEA Technology— was used. 3.1. Identification of key parameters by dimensional analysis The first step in the determination of the process function was to perform a dimensional analysis to identify the properties most relevant with respect to the emerging stress conditions. This was done for the general case of a straight pipe being connected to a bend. In the analysis, the particles were regarded as spheres, the influence of turbulence was neglected due to the large particle diameters xp and particle wall impacts were modeled in a simplified form by using the coefficient of restitution e. If the dimensional analysis is carried out according to Lo¨ffler [7], the stress conditions (SC) can be expressed as a function of the following independent nondimensional coefficients: SC ¼ f

Re ¼

w¼

uqf D ; gf

Fr ¼

u2 qf ; xp gðqp  qf Þ !

qp x2p u rB qp lE ; ; ; ;e gf D D qf D

ð1Þ

Here, u is the median gas velocity, qf and qp are the fluid and particle densities, gf is the fluid viscosity, D the pipe diameter, lE the length of the straight pipe, rB the radius of curvature of the pipe bend and g the gravitational constant. Besides the coefficient of restitution, the density ratio and two geometrical ratios, some well-known dimensionless numbers were found. They are the Reynolds number Re, the Froude number Fr, in this case defined in its extended version as it is commonly done for fluidized beds, and the Stokes parameter w. Due to the approximately 1000 times higher density of the disperse phase, the influence of the density ratio can be neglected. The same holds for the lE/D ratio because neither the length lE of the straight pipe nor the pipe diameter D was varied throughout this study. The influence of the coefficient of restitution is not discussed because it was assumed that only the first particle wall impact in the pipe bend contributes significantly to attrition. Therefore, only the influences of Reynolds number, Froude number, Stokes parameter and rB/D ratio on the stress conditions are discussed in the results section.

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3.2. Computational domain Based on the results of the dimensional analysis, the computational domain for the numerical simulations was defined. This geometry had to serve several purposes. First of all, it had to be closely related to an industrial conveying process. Because a test rig of identical geometry was built and used in parallel to carry out attrition experiments as well as to verify the simulation results, it had to be ensured that significant attrition rates could be obtained. Based on these requirements, it was decided to model a pipe bend preceded by a straight pipe because bends show the highest attrition rates per unit length. The exact setup is shown in Fig. 1. Gas and particles enter the domain at the right hand side of the straight pipe and leave it through the pipe bend. Due to its simple setup, defined stress conditions which are yet closely related to industrial conveying setups are guaranteed in the attrition experiments. It is the scope of the numerical simulations to determine those stress conditions by applying accurate models. 3.3. Setup of numerical simulations For the simulations, the approach by Euler –Lagrange as described by Ebert [8] or Huber and Sommerfeld [9] was used. The fluid phase is modeled as a continuum by solving the conservation equations for mass and momentum, which are given in Eqs. (2) and (3), for an incompressible Newtonian fluid using the Einstein summation convention. Herein, p denotes the pressure and Sui is the so-called particle source term, which takes into account the influence of the disperse phase on the fluid phase. qf

Bui ¼0 Bxi

ð2Þ

qf

Bui B Bp B 2 ui þ qf ðuj ui Þ ¼  þ gf Sui Bxj Bxi Bt Bx2j

ð3Þ

The conservation of energy was disregarded in this context because the conveying process was modeled as

isothermal. Turbulence was incorporated into the above equations through the Reynolds Stress averaging leading to the so-called Reynolds-Averaged Navier-Stokes (RANS) equations. To solve the resulting system of equations which is not closed, the standard k –e turbulence model as described by Launder and Spalding [10] was applied. In contrast to the fluid phase, the particles of the disperse phase are modeled separately (Lagrange). They are assumed to be spherical and inert. Particle –particle interactions are neglected, and no particle source terms were included in the turbulence equations. The particle motion is calculated by applying the well-known Basset – Boussinesq – Oseen (BBO) equation [11]. Because the density of the polymers is approximately three orders of magnitude larger than that of the continuous phase, the terms for virtual mass, pressure gradient and Basset force were disregarded. qp

p 3 dvp p xp ¼ 3pgf xp Ccor ðu  vp Þ þ qp x3p g 6 6 dt

ð4Þ

The first term on the right hand side denotes the drag force according to the Stokes law. The corrective drag coefficient CCor can be interpreted as the ratio of drag coefficient CD and Stokes drag coefficient CD,Stokes. It accounts for the experimental results on the viscous drag of a solid sphere [11]. The second term is the gravitational force and vp is the particle velocity. 3.4. Determination of stress conditions One problem associated with the numerical simulations is that it is possible to calculate particle trajectories, but that with the common commercial codes, no information about the particle wall impact locations and conditions could be gained. Therefore, an external Fortran routine was programmed, which determines where particle wall impacts take place and computes the distributions of impact relevant quantities like impact angle and normal as well as tangential impact velocity components. The points of impact are determined by monitoring the smallest distance between a particle and the wall, as well as

Fig. 1. Geometry and dimensions of the computational domain used for the CFD simulations.

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the angle a defined in Fig. 1. If both change above a certain threshold value, a particle wall impact has taken place. This usually occurs between two timesteps so that the real point of impact has to be approximated. For this purpose, the pipe wall was expressed in cylindrical coordinates, and the original coordinate system was transferred into the xV, yV, zV system. As shown in Fig. 2 and !Eq. (5), the assumed point of impact on the pipe surface S is derived from the particle coordinates right before impact. 1 0 rB cosu1 þ D=2cosu1 cosu2 C B C B ! C ð5Þ r sinu þ D=2sinu cosu S ¼B 1 1 2 C B B A @ D=2sinu2 If a particle wall impact has taken place, the coordinates of the impact point and the particle velocity are recorded. From these, the wall impact angles awall as well as the normal (vn) and tangential (vt) impact velocity components of all particles are determined for their first respective impact in the pipe bend. Based on the maximum and minimum values, the cumulative number distributions of these quantities, denoted by Q0, are calculated. Details on this procedure can be found in Ref. [12]. 3.5. Results of the numerical simulations In Table 2, the values of the nondimensional coefficients used to study their influence on the stress conditions are shown. For the reference simulation (index: ref), experimentally determined material properties and entrance velocities of both disperse and fluid phase were used. The material used was PP 1040 N, because its particles are almost spherical. For particle density and diameter, the values of Table 1 were taken. The measured initial particle velocity was 41.03 m/s, which is approximately equal to the fluid velocity of 40.77 m/s. The bulk solids mass flow ratio was set to 1, and all particle wall collisions were modeled as fully elastic (e = 1). In the simulations, the particles entered the domain evenly distributed over the inlet face. The distribution of the stress conditions, namely, the cumulative number distributions of wall impact angle and

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Table 2 Values of the non-dimensional coefficients for study of their respective influence on the stress conditions Simulation

Variable Non-dimensional coefficients

ref Re1 Re2 Fr1 Fr2 w1 w2 (rB/D)1 (rB/D)2

Re

Fr

w

rB/D

qp/qf

lE/D

e

208,142 92,011 709,969 208,142 208,141 208,142 208,142 208,142 208,142

56.3 56.3 56.3 30.5 84.7 56.3 56.3 56.3 56.3

394,735 394,735 394,735 394,735 394,735 218,745 607,625 394,735 394,735

5 5 5 5 5 5 5 2 10

747 747 747 747 747 747 747 747 747

30 30 30 30 30 30 30 30 30

1 1 1 1 1 1 1 1 1

the normal and tangential velocity components as a function of Stokes parameter are shown in Fig. 3. It can be seen that awall decreases with increasing w, while both impact velocity components increase. This is in agreement with what was expected, because higher particle inertia forces or a decrease in the stopping distance leads to a reduced ability of the particles to follow the fluid flow in the bend. The particles therefore proceed more directly to the outer pipe wall, where they impact with a higher total velocity under a lower angle. A similar dependence was found for the Froude number. If particle sedimentation dominates over inertia forces (Fr #), the particles enter the pipe bend at a lower position and consequently impact under increased impact angles. Furthermore, the particles travel a longer distance through the pipe bend and are therefore slowed down, which results in decreased impact velocity components (see trajectory of particle 2 in Fig. 1). For the Reynolds number, the dependence of the impact conditions is the other way round. High Reynolds numbers lead to high impact angles and low impact velocity components. This can be explained with the higher asymmetry of the fluid flow field in the vicinity of the bend for higher Reynolds numbers, which keeps the particles from directly proceeding to the bend wall. Consequently, the particle wall impacts take place later under increased angles and reduced velocities. If the absolute values of the impact parameters are considered, it is striking that the values of the impact angles

Fig. 2. Procedure for determination of approximate particle wall impact locations.

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Fig. 3. Cumulative number distributions of wall impact angle awall, normal (vt) and tangential (vn) impact velocity component as a function of inertial parameter w.

are very low, which results in lower normal impact velocity components as well as higher tangential ones. A detailed explanation for this was given in Ref.[13]. The main reason is that not only the bend geometry is of influence on the impact conditions. The second factor is the pipe curvature, which gives rise to a shift in the tangential plane in the point of impact when the particles do not hit the bend wall close to the symmetry plane of the pipe (see Fig. 1). This is also the reason for the differences between our calculated angles and those obtained by Salman et al. [3], who found angles of up to 75j. Because the authors performed two-dimensional simulations, the influence of pipe curvature was not accounted for. To study the influence of bend geometry, the rB/D ratio was varied. The results are shown in Fig. 4.

As expected, the impact angle increases with decreasing rB/D ratios, which leads to increased normal and tangential velocity components. It is, however, noticeable that the normal impact component is affected much stronger than the tangential one. Finally, the stress conditions for the materials shown in Table 1 were calculated by using their respective material properties and experimentally determined initial velocities. In all cases, the stress conditions were similar to those of the reference simulation. Only for the tangential velocity component, a slight scatter was observed [13], which can be attributed to slightly varying experimental conditions. With respect to attrition, several conclusions can be drawn. First of all, in dilute phase conveying, the impact angles appear to be much smaller than it is usually assumed.

Fig. 4. Cumulative number distributions of wall impact angle awall, normal (vt) and tangential (vn) impact velocity component as a function of rB/D ratio.

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This means that the distribution of impact energy (as denoted by the normal and tangential impact velocity components for instance), and with it the governing attrition mechanisms, are subject to change. Based on the above results, sliding friction is likely to play a significant role in particle degradation, which has to be borne in mind for the determination of the material function. Furthermore, not only is the bend geometry of great influence on the stresses the particles experience, the influence of pipe curvature cannot be neglected as well. This is of importance for the case that two-dimensional simulations are carried out to determine the stress conditions in which this effect is not considered. The identical stress conditions in the pipe bend for the different materials are a prerequisite to extract the material function by carrying out attrition experiments, which is discussed in the following section.

4. The material function 4.1. General approach Based on the analysis of the different modes of conveying, two stress modes were identified. In dilute phase conveying, the particles are mainly attrited by impacts with the pipe wall. In dense phase conveying, most of the attrition is caused by particles sliding against the pipe wall or against each other. A rigid separation of these two modes leads to the fundamental modes of normal impacts on one side of the scale and sliding friction with a constant contact pressure on the other. In an industrial conveying system however, the stress modes will always coexist with a wide range of corresponding stress conditions. Nevertheless, the fundamental stress modes provide an opportunity to find out which mode is responsible for the major part of attrition and which attrition mechanisms are in effect as a consequence. Thus, the first step in the determination of the material function was the simulation of the two fundamental stress

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modes normal impact and sliding friction under well-defined stress conditions. These were—wherever possible— set according to the results obtained from the process function to ensure that the obtained results can be transferred to the conditions in conveying processes. The second step was to stress particles in a similar way that they are stressed in a pneumatic conveying system, without sacrificing the controlled stress conditions. This was achieved by carrying out experiments in a test rig possessing the geometry, which was already used for the numerical simulations (see Fig. 1). In order to verify whether the obtained results can be transferred to pneumatic conveying processes, experiments were carried out in a pilot plant scale conveying installation. In parallel, various material properties were evaluated and measured to find out which are of relevance in attrition processes. This knowledge, together with the results of the attrition experiments and the findings from the process function, was intended to serve as a basis for the modeling of attrition processes—qualitatively as a first step and hopefully quantitatively at a later stage. 4.2. Experimental setup and parameters The setups of the different installations used for the attrition experiments are shown in Fig. 5. All installations have been described in detail elsewhere [13], hence only the main features are stated here. Fig. 5(a) shows the installation for normal impacts, which was originally developed by Scho¨nert. Details on its operation can be found in Marktscheffel and Scho¨nert [14]. Particles are fed by a vibratory feeder (1) into a rotor (2) which possesses two radial channels. The particles are accelerated in these channels and hit the impact ring (3). Its geometry ensures normal impacts. The whole impact chamber (4) can be evacuated in order to eliminate any effects due to viscous drag. Fig. 5(b) shows the sliding friction apparatus. Here, particles possessing a rectangular shape to maintain a constant contact pressure are pressed onto a rotating disc

Fig. 5. Design of test rigs for normal impacts (a), sliding friction (b) and process-oriented particle stressing (c).

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simulating the wall material. With the normal load F, the number of revolutions n, the distance r and the contact time tc, the stress conditions sliding velocity vs and distance s as well as contact pressure pc are controlled. In the pipe bend installation (Fig. 5(c)), the particles are stressed under conditions that are closely related to those in industrial conveying setups. The particle velocity is approximately equal to the gas velocity and was set comparatively high in order to obtain measurable attrition rates. The normal impacts were carried out with an impact velocity of 40 m/s. Due to the low attrition rates, these were measured after three, six and nine consecutive particle wall impacts. The same procedure was applied in the pipe bend installation. Here, the particle and gas velocities normal to the inlet face were approximately 41 m/s. The sliding friction experiments were carried out either for a contact pressure of 0.61 MPa and a sliding distance of 200 m, or for a pressure of 61 kPa and a distance of 1500 m. The sliding velocities were varied between 4 and 8 m/s. For the polypropylenes, additional experiments were conducted to study the influence of varying normal loads, sliding distances and wall materials. In all cases, the attrition rate was determined as the relative loss of mass, i.e., the difference between initial particle mass Mi and that of the attrited particles Ma divided by the initial mass. A¼

Mi  Ma Mi

ð6Þ

4.3. Experimental results In Figs. 6 and 7, the results of attrition experiments, conducted in the three setups shown in Fig. 5, are presented for polymethylmethacrylate, polystyrene and polypropyl-

ene. The experimental conditions are given in the legends of the respective diagrams. Those of the sliding friction experiments were changed between PMMA and PS on one hand and PP on the other, because as the middle diagram in Fig. 6 shows, the conditions used lead to hardly detectable attrition rates for the polypropylenes. Therefore, instead of a disc possessing the same surface topography as the pipe bend material (ST-bend), a sandblasted steel disc (ST-sb) was used in conjunction with a reduced contact pressure and an increased sliding distance. If only the experiments simulating the fundamental stress modes impact and friction are regarded, it can be seen that the relative attrition behavior of the polymers changes between these two modes. While for example, PMMA G55 is the second most degraded under normal impact conditions; it is the least attrited of the tested PMMA and PS granules in the sliding friction experiments. The same behavior is observed for PP. Apparently, the governing material properties and thus the material-specific reaction differs with the stress mode. If the results obtained in the normal impact and sliding friction experiments are compared with those of the pipe bend installation, it can be seen that in the case of PMMA and PS, the relative attrition behavior of the impact experiments corresponds to that observed in the pipe bend. For PP, the relative attrition behavior of the pipe bend corresponds to that of the sliding friction experiments. As the numerical simulations have shown, oblique impacts are the stress mode the particles are subjected to in the pipe bend, it can be concluded that although as stated before, the stress conditions are very similar for all polymers, the materials react with different material-specific attrition mechanisms. Apparently, for PMMA and PS, the attrition mechanisms observed under pure normal impact conditions also domi-

Fig. 6. Comparison of the attrition rates for different PMMA and PS granules as obtained from normal impact and pipe bend experiments.

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315

Fig. 7. Comparison of the attrition rates for different polypropylenes as obtained from experiments in the sliding friction and pipe bend installations.

nate attrition formation caused by oblique impacts, while for PP, the mechanisms observed under sliding friction conditions dominate. Because the exact nature of these material-specific attrition mechanisms is unknown, they were named after the fundamental stress modes, i.e., Impact and Friction. The above conclusion is corroborated by a comparison of the normal impact experiments between PMMA and PS on one hand, and PP on the other. Both PMMA and PS are much more susceptible to impact stresses than PP, which in comparison shows almost negligible attrition rates. The interpretation of the sliding friction experiments is a little more complex. If Friction is assumed to be dominating for PP and not for PMMA and PS, negligible attrition rates in the sliding friction experiments would be expected for the latter two material classes. As the middle diagram in Fig. 6 shows, this is not the case. One possible explanation for this is the different form of the stress field, which develops as a consequence stress mode and material properties. Details on this will be given in the discussion of the qualitative attrition model. For polyethylene, no conclusions concerning the material-specific attrition mechanisms could be deduced from the experiments. 4.4. Determination of material properties with relevance to attrition behavior One of the most important tasks in the determination of the material function is to identify those material properties relevant to attrition formation. A comparison of the above results to classic mechanical material properties, e.g., Young’s modulus E or Vicker’s hardness Hv as given in Table 1, suggests that these are not suitable to describe attrition formation. This is due to the fact that the respective

measurement procedures for their determination do not take into account the dynamic nature of the attrition process. Therefore, standard tensile tests were carried out to obtain experimental stress strain curves for the above materials. The stress velocity was set as high as possible to account for the dynamic nature of attrition. But the test velocities of 350 mm/min for PP and PE, and 60 mm/min for PMMA and PS were still below the stress velocities encountered in dilute phase pneumatic conveying. The stress velocity had to be reduced for PMMA and PS, which broke almost immediately when higher velocities were used. Despite these shortcomings, an important difference between the PP and the PMMA and PS granules can be observed when analyzing the stress strain curves in Fig. 8. It is noteworthy, that both polypropylenes show a regime of plastic flow before breakage, which is neither observed for PMMA nor for PS 144 C. Only PS 158 K exhibits a very small flow regime. This difference in material behavior might be a quick and easy test to evaluate whether a certain bulk solid is more apt to be attrited by the mechanism of Impact or Friction. Of course, this observation still has to be verified for further materials. As can be seen in Fig. 8, both polyethylenes show a regime of viscous flow. It can thus be concluded that they are likely to be attrited by Friction as well. With dynamic mechanical analysis (DMA), a material characterization method was applied which quantifies the material reaction to dynamic stresses. The measurements were carried out in single cantilever flexure mode. For this, rectangular polymer samples of 32  6  2 mm had to be produced. This was done by injection molding of the original polymers. These samples are fixed between two clamps with the sample dimensions being measured carefully. One of the two clamps is fixed, while the other can be

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Fig. 8. Comparison of the stress strain curves for the different polymers; vstress,PP/PE = 350 mm/min, vstress,PMMA/PS = 60 mm/min.

moved up and down. To this clamp, a sinusoidal deformation e is applied at a defined frequency, and the resulting strain r is measured. By applying a defined temperature program, the complex modulus which can be divided into the storage modulus EV (amount of energy stored elastically) during one load cycle, and the loss modulus EU (amount of dissipated energy) is measured as a function of temperature and stress velocity. Characteristic for polymers is the glass transition, which can be identified by a steep decline of the storage modulus and a corresponding increase in loss modulus. The reason for this is that below the glass transition, no movement of the polymer molecule chains relative to each other is possible, and the material responds stiffly to a deformation. When the glass transition is reached, relative movement of

the polymer chains becomes possible, and the material reacts viscoelastic to a deformation. The energy that can be stored elastically decreases (EV #), while the amount of dissipated energy increases (EU z). Details on the measurement method can be found in Ref. [15], while the experimental parameters and results have been presented in Ref. [13]. With respect to the single-particle experiments, it was observed that the polypropylenes which are attrited by Friction are stressed in their glass transition regimes, whereas the glass transition temperature of PMMA and PS lies well above the stress temperature. For PP, it was found that the attrition rate decreases with decreasing values of both storage and loss modulus [13]. A possible explanation for this behavior can be found in the microscopic attrition

Fig. 9. Comparison of the attrition rates obtained from pipe bend experiments for nine impacts with gas and particle velocities of approximately 40 m/s with storage (EV) and loss modulus (EU) values measured at 10 Hz and 25 jC.

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mechanisms known from tribology and was discussed in Ref. [16]. If the attrition rates obtained in the pipe bend installation are plotted against the respective storage and loss modulus values at 25 jC, which corresponds to the macroscopic stress temperature for the attrition experiments in the pipe bend installation, the diagrams shown in Fig. 9 are obtained. When only the polypropylenes are regarded, the trend of decreasing attrition rates with both decreasing storage and loss modulus values observed in the sliding friction experiments can be found here as well. The scatter of course gets larger because in the pipe bend installation, although Friction is the most prominent attrition mechanism, Impact also contributes to overall attrition. With respect to the other materials, a differentiated analysis has to be carried out. In the case of the polyethylenes, which are both stressed in the glass transition regime, and which consequently should be mostly attrited by sliding friction, it can be observed that PE 5031 L fits into the trend described for the polypropylenes, while PE 2420 H deviates considerably. This might be attributed to the fact that this polymer is very soft, possessing a storage modulus of only 192 MPa, and that therefore, the influence of other attrition mechanisms like adhesion might not be neglected. Although a qualitative theoretical explanation for the above correlation between attrition rate and dynamic modulus values was developed only for cases in which Friction is the dominating attrition mechanism, the PMMA granules also appear to fit in, while the PS particles do not. It still has to be resolved what causes the differences in the behavior of PMMA and PS.

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5. Qualitative model of the attrition process for dilute phase conveying Based on the conclusions drawn from the results for the determination of the process and material functions, a qualitative three-level model of the attrition process was developed, which is outlined in Fig. 10 for the case of dilute phase conveying. In this case, the particles are subjected to oblique impacts against the pipe wall with a certain wall impact angle awall and an impact velocity vimpact, which can be divided into a normal (vn) and a tangential (vt) component. Thus, stresses induced by both components coexist under these conditions. This so-called stress mode can be deduced from the process function. As the single-particle experiments have shown, attrition formation and thus the material-specific reaction to the stresses discussed above varies with the materials used, i.e., the material properties. The single-particle experiments clarified that in the pipe bend and thus presumably in dilute phase conveying the polypropylenes, as well as PE 5031 L, are mainly attrited by the same mechanisms in effect under pure sliding friction conditions, which in this case were subsumed in the term Friction. PMMA and PS 144 C on the other hand are attrited by mechanisms observed under normal impact conditions, thus termed Impact. PS 158 K is a special case because based on the results of the tensile tests, it is likely to be attrited by Impact, although Friction might also contribute on a small scale. It has to be stated at this point that the material-specific attrition mechanisms shown in Fig. 10 can only be considered as boundaries of a spectrum. Depending on the material properties, both mechanisms contribute to attrition on varying scales. With the

Fig. 10. Three-level model of the attrition process (stress mode exemplary given for dilute phase conveying).

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procedure discussed above, only qualitative conclusions concerning the dominating material-specific attrition mechanism can be drawn. By applying dynamic mechanical analysis, it was possible to show that the glass transition temperature is a key parameter in the identification of the dominating material-specific attrition mechanisms. Materials stressed in their glass transition regimes are attrited by Friction, while Impact is dominating for materials whose glass transition temperature lies above the stress temperature. These findings can be explained with the temperature-dependent material behavior of the bulk solids. The materials are brittle below their glass transition, and thus most of the impact energy is stored elastically in the particles. This leads to the emergence of a three dimensional stress distribution, which reaches far into the particles. These stresses lead to the formation of attrition fragments due to growth of microcracks, accumulation of internal flaws or just by locally exceeding the material strength. Due to only minor plastic deformation, the surface asperities of the pipe wall do not penetrate far into the material. Consequently, the tangential impact velocity component is of minor importance because its main effect results in an asymmetry of the stress distribution. If the materials are stressed in their glass transition regime, they react viscoelastic. Here, the three dimensional stress distribution develops in the immediate vicinity of the contact region. Due to plastic deformation by relative motion of the polymer chains, no stresses reaching into the material develop, but the wall surface asperities penetrate into the polymer and remove attrition fragments due to the acting vt. These differences in the stress field, in dependence of the material behavior, are a possible expla-

nation why brittle materials also exhibit high attrition under pure sliding friction conditions. In this case, as for the normal impacts stresses reaching into the material develop due to the acting contact pressure, leading to similar mechanisms of material removal. These differ from those of viscoelastic materials. The third level of the model involves the basic or microscopic attrition mechanisms. Here, the exact formation of attrition fragments is described. In the case of Impact, chipping and fragmentation, as described in Refs. [4,5] and in Ref. [17], are observed. For Friction, there are basically three different mechanisms known from tribology [18,19]. These are abrasion, surface disruption and adhesion. In the top part of Fig. 11(a), an original PMMA G55 particle is shown, while in the bottom part the same particle is depicted after nine impacts in the pipe bend installation. Here, chipping can be clearly observed. Fig. 11(b) shows the surface of a PP 1040 N particle before (top) and after (bottom) sliding it against a steel disc of identical topography to that of the pipe bend material with a velocity of 6 m/s for 200 m under a contact pressure of 0.61 MPa. Fig. 11(c) shows the initial and after sliding surfaces of PMMA G55, obtained under identical sliding conditions. While for PP 1040 N, the sliding surface contains considerably large deformations, which can be attributed to either abrasion or surface disruption; hardly any change can be seen for PMMA G55. This is an indication that the attrition mechanisms are different for brittle materials. Under the given conditions, it is likely that subsurface cracks lead to material removal. The fact that in this case no penetration of surface asperities occurs, explains the smooth surface topography.

Fig. 11. Initial PMMA G55 particle (a—top) and chipping (a—bottom) observed after nine impacts in the pipe bend, and surfaces of a PP 1040 N (b) and a PMMA G55 (c) particle before (top) and after (bottom) sliding, 200 m against a steel surface of identical topography to the pipe bend material with 6 m/s and a contact pressure of 0.61 MPa.

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6. Conclusions In this research project, the problem of attrition in pneumatic conveying was addressed by regarding it as the result of a process and a material function. The process function summarizes the influence of all process parameters, and as a result, provides the stress conditions in terms of stress mode, intensity and number of stress events. The material function on the other hand, contains material properties which govern the attrition behavior of individual bulk solids, and as a result, supplies an attrition function. With the knowledge of these two functions, it should be possible to distinguish between materials and estimate the governing attrition mechanism and the approximate attrition rate. The process function for dilute phase conveying was determined by numerical simulations with a commercial computational fluid dynamics code. The analysis of particle wall impact conditions in a pipe bend showed that they take place under low wall impact angles of 5j to 35j, which results in low normal (5– 25 m/s) and high tangential (33 – 44 m/s) impact velocity components. These findings lead to the conclusion that not only stresses caused by the normal impact velocity component are important in oblique impact observed in dilute phase conveying, but that stresses induced by the tangential component play an important role as well. The results of the attrition experiments carried out for the determination of the material function showed that for polymethylmethacrylate and polystyrene, the relative attrition behavior observed in the stress mode of normal impact corresponds to that observed in the pipe bend, whereas deviations were found for the stress mode sliding friction. For polypropylene, on the other hand, the relative attrition behavior in the pipe bend corresponds to that of the sliding friction stress mode. An explanation for this was deduced from material properties obtained by dynamic mechanical analysis (DMA). It was found that the glass transition temperature or glass transition regime is a key factor in the determination of the mechanism the polymer particles are attrited by. If the stress temperature, i.e., the conveying temperature lies below the glass transition temperature, the material-specific attrition mechanism Impact is responsible for attrition formation, while in the other case, Friction is the dominating mechanism. These findings provide a possibility to at least qualitatively predict the attrition rates that will be encountered by measurement of the dynamic mechanical properties. It was furthermore found that if Friction is the dominant mechanism, decreasing values of storage and loss modulus lead to lower attrition rates. Unfortunately, as the polypropylenes show, this does not hold for all materials under investigation. While PE 5031 L fits into the above scheme, PE 2420 H, which has an extremely low storage modulus, does not. Here, additional attrition mechanisms have to be taken into account.

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Whether these findings can be transferred to further polymer classes has yet to be resolved. Based on the results presented, a qualitative three-level model of the attrition process was developed. The top level is the stress mode, which has to be known if the problem of attrition is to be addressed successfully. This can be derived from the process function. The second level contains the material-specific attrition mechanism, which is identified by pursuing the presented approach for the determination of the material function. Finally, the basic or microscopic attrition mechanisms describing exactly how attrition fragments are formed constitute the bottom level of this model.

Acknowledgements This project is sponsored by the German Federal Ministry of Economics and Technology, grant AiF-No. 13252 N/1. The authors appreciate the financial support.

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