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Comminution of material particles by water jets — Influence of the inner shape of the mixing chamber
International Journal of Mineral Processing 95 (2010) 25–29
Contents lists available at ScienceDirect
International Journal of Mineral Processing j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j m i n p r o
Comminution of material particles by water jets — Influence of the inner shape of the mixing chamber Libor M. Hlaváč a,⁎, Irena M. Hlaváčová a, Petr Jandačka a, Jiří Zegzulka b, Jana Viliamsová a, Jaroslav Vašek c, Vilém Mádr a a b c
Institute of Physics, Faculty of Mining and Geology, VŠB – Technical University of Ostrava, 17.listopadu 15/2172, Ostrava – Poruba, Czech Republic Institute of Transport, Faculty of Mechanical Engineering, VŠB – Technical University of Ostrava, 17.listopadu 15/2172, Ostrava – Poruba, Czech Republic Institute of Geonics, Czech Academy of Sciences, Studentská 1768, Ostrava – Poruba, Czech Republic
a r t i c l e
i n f o
Article history: Received 22 April 2009 Received in revised form 10 February 2010 Accepted 15 March 2010 Available online 27 March 2010 Keywords: Industrial minerals Comminution Water jet Mineral processing Particle size
a b s t r a c t Material comminution is one of the typical processes present during the injection abrasive water jet generation inside the mixing chamber and the focussing tube of the abrasive water jet cutting head. The determination of an extent of changes in the size of particles induced in the cutting head is the main objective of this contribution. Knowledge of the particle size at the exit from the cutting head is necessary for studying of the subsequent processes, e.g. the impingement of water jet with industrial mineral particles on a solid-state target or collision of such water jet with liquid barrier or opposite flowing jet of the same type. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Previous research works have revealed that generation of the abrasive water jet in the entrainment system inherently includes not only acceleration or focussing of abrasive particles (Tazibt et al., 1994a, b; Dong et al., 2004), but also their partial destruction, e.g. grinding, splitting, internal distortion. Hashish (1983, 1989) or Hlaváč (1996) and Hlaváč et al. (1999) studied these processes both experimentally and theoretically. The experimental results of particle sizes obtained around the year 1996 were based on sedimentation techniques. The capture of particles, better said slurry, after the mixing process was also worse than today, because the abrasive water jet was directed to the special water-filled container (Vašek et al., 1993). Therefore, the particle destruction was effected by this subsequent impact on water medium and even on the container bottom, for higher pressures of water used for jet generation. The container was an open system and so some smaller particles were lost — they were taken away by overflowing water. Nevertheless, the observed reduction in the weight of individual particles and, subsequently, the detriment of the cutting process lead to the theoretical and experimental works of Raissi et al. (1996), Nanduri et al. (1996), Weule and Suchy (2000) and Suchy
⁎ Corresponding author. Tel.: +420 597323147. E-mail address: [email protected] (L.M. Hlaváč). 0301-7516/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2010.03.003
(2001) all of them trying to improve the internal geometry of the cutting head and focussing tube towards suppressing the mineral deterioration. Opposite to these efforts, the disintegration of particles in the mixing process provoked the idea of the intentional use of water jets for mineral particles comminution (Mazurkiewicz, 1992; Hlaváč and Vašek, 1996; Guo and Dong, 2007). The influence of an internal shape of the cutting head on the particle disintegration in the mixing process with water jet was studied experimentally just now with a connection with the opposite jet comminution of materials (Hlaváč et al., 2008) and some results and theoretical reasons are presented in this paper.
2. Description of the experimental layout Two configurations (marked A and B) of mixing chambers were tested (see Fig. 1). They represent two usual commercial cutting heads used in experiments. The product of the mixing process – the mixed jet – was picked up in such a manner that reduced influence of any of the additional disintegration processes acting at particles to the lowest possible values. Namely, interaction of water jet containing the particles with the rigid or liquid target could cause a substantial increase in the amount of disintegrated particles thus depreciating the results of the experimental analysis of the mixing product itself. Therefore, after passing through the mixing chamber and the focusing tube (after the suction process), the mixed water jet was directed
26
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29
Nomenclature α angle between the inlet direction of the sucked material and water jet axis...[–] γ the compressibility of water at the pressure po...[Pa− 1] the symbol substituting for the bracket (1 − γpo)...[–] γo the discharge coefficient of the water nozzle...[–] μo the density of material intended for grinding...[kg m− 3] ρm the density of water under the standard conditions... ρo [kg m− 3] the mean size of the original material particles...[m] ao the mean size of the particles produced in the course an of a mixing process...[m] c the velocity of sound in a material of the sucked particles...[m s− 1] the velocity of sound in water...[m s− 1] co the drag coefficient of a material particle in the flowing CD water...[–] the diameter of the water nozzle...[m] do the specific energy needed for the formation of a unit EP free surface in material of the sucked particles − the specific surface (fracture) energy of the sucked material...[J m− 2] the pressure of water before the nozzle, i.e. in the po pumping system...[Pa] the new surface produced by disintegration of partiPN cles into smaller ones...[m2] the velocity of the sucked material...[m s− 1] vm the velocity of water jet without admixtures at the exit vo from the water nozzle...[m s− 1]
along the axis of a tube with the diameter 0.15 m and the length 2 m (Fig. 2), where it was damped by interaction with the air naturally to such an extent that in the bent part directing the stream into the catch tank no substantial destruction of particles took place any more. The axis of the jet and the axis of the tube delimiting space for the jet flow are parallel to the earth surface plane. The slurry was flowing from the tube into the container. This part of the system was closed so that no water or slurry is lost. The tests were performed with the identical sucked materials of the identical particle mean size and the identical water jet and outlet mixed water jet parameters: the water pressure, the water orifice diameter, the focussing tube diameter and the focusing tube length.
Fig. 1. Diagrammatical sections through the configurations of the mixing chambers used in experiments for generation of the abrasive water jet: 1 — water jet; 2 — mix of sucked air and material particles; 3 — outflow of the mixed jet; A — mixing chamber with the perpendicular inlets, B — mixing chamber with the inclined inlets.
Thus, the only differing parameter was the internal shape of the mixing chamber. Parameters constant in experiments were as follows: Water pressure 380 MPa ± 5% Water orifice diameter 0.25 mm ± 5% Focusing tube inner diameter 0.51 mm ± 5% Focusing tube length 51 mm ± 5% Disintegrated material Australian garnet 80 mesh (average particle size 0.27 mm) The experimental work was performed with the non-porous almandine powder with commercial mark “Australian garnet”. This is an abrasive mineral with declared hardness 8.5 on the Mohs scale (unverified by self tests), with mineralogical purity of 97%, chemical composition Fe3Al2Si3O12. The size interval of the original uncrushed particles was (0.1–0.8) mm with the average particle size 0.27 mm. The grains are monocrystallic, therefore, the transcrystallic breaks during crushing can be assumed. The specific heat capacity is 720 J kg− 1 K− 1 and density of the mineral is 4084 kg m− 3. The values were determined by calorimetric measurements and measurements in pycnometer respectively. The specific surface energy of this mineral was determined from various experiments and calculations. Starting from values around 20 J m− 2 calculated in nineties of the 20th century (presented by Hlaváč et al. 1999) through the values close to 5.5 J m− 2, determined from the preliminary data obtained from experiments with a new arrangement last year, the most recent value presented by Jandačka et al. (2009) is applied — EP = 2.835 J m− 2. 3. Discussion of experimental results Basic shift of particle sizes from the input state to the outlet one is evident from the graph presented in Fig. 3 and photos of inlet and outlet particles presented in Fig. 4. Comparison of the distribution curves determined from laser particle size analysers for the products obtained from the both types of mixing chambers show that product from the chamber with normal inlets is more comminuted (Fig. 5). Nevertheless, this result is matching the anticipation. The surprise can be the difference of the resulting particle sizes from both chamber types. The modal values determined from experiments differ one from another more than 50% (difference between average values obtained for both tested pieces of mixing chambers with individual configurations is 51.85%). The theoretical model for calculation of the interaction between the water jet and material particles in the mixing chamber and the focusing tube published by Hlaváč in 1996 does not internally contain the dependence of the particle size on the angle between water jet axis and axis of the sucked particles inlet. The model was derived for particle inlet direction perpendicular to the water jet axis that was common at those days. The interactions can be examined on the basis of several physical approaches. The attention is focused on a collision process between the jet and the material particle. Physical studies indicate that at these collisions, a sharp increase in the stress in the material particle takes place and thus the particle may be damaged or broken (Hlaváč and Sochor, 1994; Hlaváč, 1996). Experiments aimed at research of the abrasive water jets have really confirmed that the original particle size of the abrasive material changes already in the mixing chamber and the focusing tube (Hlaváč and Martinec, 1998). In the subsequent theoretical and experimental analysis it has been found that the behaviour of materials in the course of suction into the water jet, interaction between the water stream and material particles and particle disintegration can be modelled. Physical relationships describing the origin of new particles due to interaction between the water jet and particles of material in the course of ejector-based suction are presented as Eqs. (1) and (2) (based on the theory presented by Hlaváč et al. 2008). The newly produced surface, which is
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29
27
Fig. 2. A sketch of the experimental set-up for entrapment of the mixed water jet.
of the newly formed particles can be calculated from this equation 3
an =
24ρo EP ao co c : + CD πao d2o μ 2o p2o γ2o
24ρo EP a2o co c
ð2Þ
Eq. (3) makes possible to calculate the momentum difference in the impact of water jet onto the mineral particle sucked into the mixing chamber. This momentum difference depends on the angle between the axis of the water jet and the axis of the feeder tube. Subsequently, the reduced impact force and respective energy absorption can be determined from the momentum difference and the change can be reflected on the average size of particles produced in the mixing chamber calculated from Eq. (2).
2 2
Fig. 3. Comparison of input particle size distribution and average output particle size distributions from both tested cutting head configurations.
formed by transformation of the interaction energy into the material damage, can be calculated from the equation
PN =
CD πao d2o μ 2o p2o γ2o : 4ρo EP co c
ð1Þ
Considering the physical simplification that both the original and the newly formed particles are approximated as cubes, the mean size
Δ mvm = CD πρm ao vo
ao πa3o ρ v cos α: − co 6 m m
ð3Þ
Since the relationship of the particle size calculated from Eq. (2) on the jet impact force (momentum transfer) is linear, the percentage degree reduction of the force causes corresponding increase of the average size of broken particles. The shift in the modus of the particle size caused by change of the feeder tube axis from the direction perpendicular to the water jet axis to the angle value close to 45° is evident in the graph presented in Fig. 5. Considering usual values for tested abrasive material the increase of the grain size modus is determined from the Eq. (2) using momentum decrease calculated from Eq. (3) (48.75%). This momentum decrease implies the increase of the modal value 51.25%. This value is in a good agreement with presented experimental data that yield the ratio close to 51.85%
Fig. 4. An example of input (left hand side photo) and outlet (right hand side photo) garnet particles used in presented experiments.
28
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29 Table 1 Comparison of experimentally and theoretically determined modal values.
Value for chamber type A Value for chamber type B Difference between results for chamber types
Experimentally set modus
Theoretically set modus
Difference between experiment and theory
16.2 μm
16.0 μm
1.24%
24.6 μm
24.2 μm
1.63%
51.85%
51.25%
with a larger size influencing thus not only the result of the one certain measurement (see Fig. 5) but also the average value of more measurements. Fig. 5. Volumetric particle size distribution of the mixed water jet from the two mixing chamber shapes, two tested conformable pieces.
determined from the modus of the particle size (see Fig. 5 and Table 1). The modus of the experimentally determined grain size distribution for particle inlet perpendicular to the water jet axis is about 16.2 μm, while the modus of the experimentally determined grain size distribution for particle inlet including 45° with the water jet axis is about 24.6 μm. The maximum (modus) of the distribution evaluated from the Eq. (2) for the usual garnet properties and experimental conditions as above is 16 μm. This value was calculated for the average specific surface energy 2.835 J m− 2 that was determined from the work necessary for disintegration of particles inside the special chamber put into the pressure machine (Jandačka et al., 2009). The shifted value of the distribution modus calculated for the particle inlet declined to 45° from the Eqs. (3) and (2) is 24.2 μm. Comparison of the theoretically derived curves based on the calculated value with the ones determined from experimental values is evident observing curves in Fig. 6 where the calculated “theoretical” curves are prepared using presented Eqs. (1) through (3). The higher values determined experimentally for particle sizes in the range from about 0.5 μm up to 10 μm can be explained in a few ways. The higher amount of smaller particles can be caused by the internal defects in the original particles (as the theoretical model does not imply such a relationship yet), by the agglomeration of smaller particles into some greater objects or by the adsorption of the very small particles onto the greater ones producing in that way objects of greater sizes. The two last mentioned phenomena are not sufficiently recognizable in the process of particle size analyses in the commercial laser-based particle analysers. The higher values round the particle size 130 μm can be caused by few particles or even just one particle
Fig. 6. Comparison of the volumetric particle size distribution of the mixed water jet from the two mixing chamber shapes with theoretical curve calculated for both cases.
4. Conclusions The results presented in this article show that the inlet particle suction perpendicular to the water jet axis causes larger damage of particles and produces smaller average particle size. This phenomenon can be used for intentional disintegration of brittle materials, especially minerals. The elementary theoretical set of equations can be used for partial analysis of the product flowing out of the mixing process — the average particle size can be determined quite well. The distribution of the particles and its variation caused by internal particle damage or some other phenomena cannot be determined from this theoretical base and need further deeper investigation. Nevertheless, the mixing process inside the cutting head of the entrained water jet constitutes a good base for utilization of the water jet as the tool for intentional particle softening in subsequent processes. Acknowledgements The authors thank the Ministry of Industry and Trade (project 1H-PK2/22), the Grant Agency of the Czech Republic (project 105/06/ 1516), the Grant Agency of the Czech Academy of Sciences (project AV0Z30860518) and the company PTV spol. s r.o. Hostivice for financial support provided to the presented research. References Dong, Y., Tyler, L.J., Summers, D.A., Johnson, M., 2004. Experimental study of particle velocity measurement in abrasive water jet cutting in the nozzle and jet stream using multiple sensing elements. In: Gee, C. (Ed.), Proc. Water Jetting. BHR Group, Mainz, Germany, pp. 137–147. Guo, Ch., Dong, L., 2007. Energy consumptions in comminution of mica with cavitation abrasive water jet. Journal of China University of Mining and Technology 17 (2), 251–254. Hashish, M., 1983. Experimental studies of cutting with abrasive waterjets. Proc. 2nd U.S. Water Jet Symposium. Rolla, Missouri, U.S.A, pp. 379–389. Hashish, M., 1989. A model for abrasive-waterjet (AWJ) machining. Trans. of the ASME. Journal of Engineering Materials and Technology 111, 154–162. Hlaváč, L.M., 1996. Interaction of grains with water jet — the base of the physical derivation of complex equation for jet cutting of rock materials. In: Gee, C. (Ed.), Proc. Jetting Technology. BHR Group, Mech. Eng. Pub. Ltd, Cagliari, Italy, pp. 471–485. Hlaváč, L.M., Martinec, P., 1998. Almandine garnets as abrasive material in high-energy waterjet — physical modelling of interaction, experiment, and prediction. Jetting Technology. BHR Group, Prof. Eng. Pub. Ltd, Bury StEdmunds/London, pp. 211–223. Hlaváč, L.M., Sochor, T., 1994. A contribution to the physics of a high velocity abrasive particle interaction with brittle non-homogeneous materials. Jet Cutting Technology. BHR Group, Mech. Eng. Pub. Ltd, London, pp. 117–126. Hlaváč, L.M., Vašek, J., 1996. Physical aspects of the H.E.L.J. use in clean coal technologies. Proc. Environmental Issues and Waste Management in Energy and Mineral Production SWEMP '96. DIGITA, Cagliari, pp. 1305–1312. Hlaváč, L.M., Sosnovec, L., Martinec, P., 1999. Abrasives for high energy water jet: investigation of properties. In: Hashish, M. (Ed.), Proc. 10th American Waterjet Conference. WJTA, Houston, Texas, pp. 409–418. Hlaváč, L.M., Vašek, J., Hlaváčová, I.M., Jandačka, P., 2008. Potential of liquid jets for preparation of micro and nano particles. In: Muir, A. (Ed.), Green Chemistry & Engineering Proc. International Conference on Process Intensification & Nanotechnology. BHR Group, Albany, New York State, pp. 205–218.
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29 Jandačka, P., Hlaváč, L.M., Mádr, V., Šancer, J., Staněk, F., 2009. Measurement of specific fracture energy and surface tension of brittle materials in powder form. International Journal of Fracture 159 (1), 103–110. doi:10.1007/s10704-009-9376-x. Mazurkiewicz, M., 1992. Coal and minerals excavation and disintegration by high pressure waterjet. In: Rakowski, Z. (Ed.), Proc. Geomechanics 91. Balkema, Rotterdam, pp. 249–257. Nanduri, M., Taggart, D.G., Kim, T.J., Ness, E., Haney, C.N., Bartkowiak, C., 1996. Wear patterns in abrasive waterjet nozzles. In: Gee, C. (Ed.), Proc. Jetting Technology. BHR Group, Mech. Eng. Pub. Ltd, Cagliari, Italy, pp. 27–43. Raissi, K., Cornier, A., Kremer, D., Simonin, O., 1996. Mixing tube geometry influence on abrasive water jet flow. In: Gee, C. (Ed.), Proc. Jetting Technology. BHR Group, Mech. Eng. Pub. Ltd, Cagliari, Italy, pp. 247–261. Suchy, U., 2001. Investigation of a new cutting head concept based on an annular driving jet. In: Hashish, M. (Ed.), Proc. 2001 WJTA American Waterjet Conference. WJTA, Minnesota, Minneapolis, pp. 175–191.
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Tazibt, A., Schmitt, A., Parsy, F., Abriak, H., Thery, B., 1994a. Effect of air on acceleration process in AWJ entrainment system. In: Allen, N.G. (Ed.), Proc. Jet Cutting Technology. BHR Group, Mech. Eng. Pub. Ltd, Rouen, France, pp. 47–58. Tazibt, A., Parsy, F., Schmitt, A., Abriak, H., Thery, B., 1994b. Hydrodynamic investigation and prediction of abrasive acceleration process in abrasive water jet cutting. In: Allen, N.G. (Ed.), Proc. Jet Cutting Technology. BHR Group, Mech. Eng. Pub. Ltd, Rouen, France, pp. 67–80. Vašek, J., Martinec, P., Foldyna, J., Hlaváč, L., 1993. Influence of properties of garnet on cutting process. Proc. 7th American Water Jet Conference. WJTA, Seattle, Washington, pp. 375–387. Weule, H., Suchy, U., 2000. Mixing head for abrasive-water-jet cutting with an annular driving jet. In: Ciccu, R. (Ed.), Proc. Jetting Technology. BHR Group, Prof. Eng. Pub. Ltd, Ronneby, Sweden, pp. 47–56.
Contents lists available at ScienceDirect
International Journal of Mineral Processing j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j m i n p r o
Comminution of material particles by water jets — Influence of the inner shape of the mixing chamber Libor M. Hlaváč a,⁎, Irena M. Hlaváčová a, Petr Jandačka a, Jiří Zegzulka b, Jana Viliamsová a, Jaroslav Vašek c, Vilém Mádr a a b c
Institute of Physics, Faculty of Mining and Geology, VŠB – Technical University of Ostrava, 17.listopadu 15/2172, Ostrava – Poruba, Czech Republic Institute of Transport, Faculty of Mechanical Engineering, VŠB – Technical University of Ostrava, 17.listopadu 15/2172, Ostrava – Poruba, Czech Republic Institute of Geonics, Czech Academy of Sciences, Studentská 1768, Ostrava – Poruba, Czech Republic
a r t i c l e
i n f o
Article history: Received 22 April 2009 Received in revised form 10 February 2010 Accepted 15 March 2010 Available online 27 March 2010 Keywords: Industrial minerals Comminution Water jet Mineral processing Particle size
a b s t r a c t Material comminution is one of the typical processes present during the injection abrasive water jet generation inside the mixing chamber and the focussing tube of the abrasive water jet cutting head. The determination of an extent of changes in the size of particles induced in the cutting head is the main objective of this contribution. Knowledge of the particle size at the exit from the cutting head is necessary for studying of the subsequent processes, e.g. the impingement of water jet with industrial mineral particles on a solid-state target or collision of such water jet with liquid barrier or opposite flowing jet of the same type. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Previous research works have revealed that generation of the abrasive water jet in the entrainment system inherently includes not only acceleration or focussing of abrasive particles (Tazibt et al., 1994a, b; Dong et al., 2004), but also their partial destruction, e.g. grinding, splitting, internal distortion. Hashish (1983, 1989) or Hlaváč (1996) and Hlaváč et al. (1999) studied these processes both experimentally and theoretically. The experimental results of particle sizes obtained around the year 1996 were based on sedimentation techniques. The capture of particles, better said slurry, after the mixing process was also worse than today, because the abrasive water jet was directed to the special water-filled container (Vašek et al., 1993). Therefore, the particle destruction was effected by this subsequent impact on water medium and even on the container bottom, for higher pressures of water used for jet generation. The container was an open system and so some smaller particles were lost — they were taken away by overflowing water. Nevertheless, the observed reduction in the weight of individual particles and, subsequently, the detriment of the cutting process lead to the theoretical and experimental works of Raissi et al. (1996), Nanduri et al. (1996), Weule and Suchy (2000) and Suchy
⁎ Corresponding author. Tel.: +420 597323147. E-mail address: [email protected] (L.M. Hlaváč). 0301-7516/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2010.03.003
(2001) all of them trying to improve the internal geometry of the cutting head and focussing tube towards suppressing the mineral deterioration. Opposite to these efforts, the disintegration of particles in the mixing process provoked the idea of the intentional use of water jets for mineral particles comminution (Mazurkiewicz, 1992; Hlaváč and Vašek, 1996; Guo and Dong, 2007). The influence of an internal shape of the cutting head on the particle disintegration in the mixing process with water jet was studied experimentally just now with a connection with the opposite jet comminution of materials (Hlaváč et al., 2008) and some results and theoretical reasons are presented in this paper.
2. Description of the experimental layout Two configurations (marked A and B) of mixing chambers were tested (see Fig. 1). They represent two usual commercial cutting heads used in experiments. The product of the mixing process – the mixed jet – was picked up in such a manner that reduced influence of any of the additional disintegration processes acting at particles to the lowest possible values. Namely, interaction of water jet containing the particles with the rigid or liquid target could cause a substantial increase in the amount of disintegrated particles thus depreciating the results of the experimental analysis of the mixing product itself. Therefore, after passing through the mixing chamber and the focusing tube (after the suction process), the mixed water jet was directed
26
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29
Nomenclature α angle between the inlet direction of the sucked material and water jet axis...[–] γ the compressibility of water at the pressure po...[Pa− 1] the symbol substituting for the bracket (1 − γpo)...[–] γo the discharge coefficient of the water nozzle...[–] μo the density of material intended for grinding...[kg m− 3] ρm the density of water under the standard conditions... ρo [kg m− 3] the mean size of the original material particles...[m] ao the mean size of the particles produced in the course an of a mixing process...[m] c the velocity of sound in a material of the sucked particles...[m s− 1] the velocity of sound in water...[m s− 1] co the drag coefficient of a material particle in the flowing CD water...[–] the diameter of the water nozzle...[m] do the specific energy needed for the formation of a unit EP free surface in material of the sucked particles − the specific surface (fracture) energy of the sucked material...[J m− 2] the pressure of water before the nozzle, i.e. in the po pumping system...[Pa] the new surface produced by disintegration of partiPN cles into smaller ones...[m2] the velocity of the sucked material...[m s− 1] vm the velocity of water jet without admixtures at the exit vo from the water nozzle...[m s− 1]
along the axis of a tube with the diameter 0.15 m and the length 2 m (Fig. 2), where it was damped by interaction with the air naturally to such an extent that in the bent part directing the stream into the catch tank no substantial destruction of particles took place any more. The axis of the jet and the axis of the tube delimiting space for the jet flow are parallel to the earth surface plane. The slurry was flowing from the tube into the container. This part of the system was closed so that no water or slurry is lost. The tests were performed with the identical sucked materials of the identical particle mean size and the identical water jet and outlet mixed water jet parameters: the water pressure, the water orifice diameter, the focussing tube diameter and the focusing tube length.
Fig. 1. Diagrammatical sections through the configurations of the mixing chambers used in experiments for generation of the abrasive water jet: 1 — water jet; 2 — mix of sucked air and material particles; 3 — outflow of the mixed jet; A — mixing chamber with the perpendicular inlets, B — mixing chamber with the inclined inlets.
Thus, the only differing parameter was the internal shape of the mixing chamber. Parameters constant in experiments were as follows: Water pressure 380 MPa ± 5% Water orifice diameter 0.25 mm ± 5% Focusing tube inner diameter 0.51 mm ± 5% Focusing tube length 51 mm ± 5% Disintegrated material Australian garnet 80 mesh (average particle size 0.27 mm) The experimental work was performed with the non-porous almandine powder with commercial mark “Australian garnet”. This is an abrasive mineral with declared hardness 8.5 on the Mohs scale (unverified by self tests), with mineralogical purity of 97%, chemical composition Fe3Al2Si3O12. The size interval of the original uncrushed particles was (0.1–0.8) mm with the average particle size 0.27 mm. The grains are monocrystallic, therefore, the transcrystallic breaks during crushing can be assumed. The specific heat capacity is 720 J kg− 1 K− 1 and density of the mineral is 4084 kg m− 3. The values were determined by calorimetric measurements and measurements in pycnometer respectively. The specific surface energy of this mineral was determined from various experiments and calculations. Starting from values around 20 J m− 2 calculated in nineties of the 20th century (presented by Hlaváč et al. 1999) through the values close to 5.5 J m− 2, determined from the preliminary data obtained from experiments with a new arrangement last year, the most recent value presented by Jandačka et al. (2009) is applied — EP = 2.835 J m− 2. 3. Discussion of experimental results Basic shift of particle sizes from the input state to the outlet one is evident from the graph presented in Fig. 3 and photos of inlet and outlet particles presented in Fig. 4. Comparison of the distribution curves determined from laser particle size analysers for the products obtained from the both types of mixing chambers show that product from the chamber with normal inlets is more comminuted (Fig. 5). Nevertheless, this result is matching the anticipation. The surprise can be the difference of the resulting particle sizes from both chamber types. The modal values determined from experiments differ one from another more than 50% (difference between average values obtained for both tested pieces of mixing chambers with individual configurations is 51.85%). The theoretical model for calculation of the interaction between the water jet and material particles in the mixing chamber and the focusing tube published by Hlaváč in 1996 does not internally contain the dependence of the particle size on the angle between water jet axis and axis of the sucked particles inlet. The model was derived for particle inlet direction perpendicular to the water jet axis that was common at those days. The interactions can be examined on the basis of several physical approaches. The attention is focused on a collision process between the jet and the material particle. Physical studies indicate that at these collisions, a sharp increase in the stress in the material particle takes place and thus the particle may be damaged or broken (Hlaváč and Sochor, 1994; Hlaváč, 1996). Experiments aimed at research of the abrasive water jets have really confirmed that the original particle size of the abrasive material changes already in the mixing chamber and the focusing tube (Hlaváč and Martinec, 1998). In the subsequent theoretical and experimental analysis it has been found that the behaviour of materials in the course of suction into the water jet, interaction between the water stream and material particles and particle disintegration can be modelled. Physical relationships describing the origin of new particles due to interaction between the water jet and particles of material in the course of ejector-based suction are presented as Eqs. (1) and (2) (based on the theory presented by Hlaváč et al. 2008). The newly produced surface, which is
L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29
27
Fig. 2. A sketch of the experimental set-up for entrapment of the mixed water jet.
of the newly formed particles can be calculated from this equation 3
an =
24ρo EP ao co c : + CD πao d2o μ 2o p2o γ2o
24ρo EP a2o co c
ð2Þ
Eq. (3) makes possible to calculate the momentum difference in the impact of water jet onto the mineral particle sucked into the mixing chamber. This momentum difference depends on the angle between the axis of the water jet and the axis of the feeder tube. Subsequently, the reduced impact force and respective energy absorption can be determined from the momentum difference and the change can be reflected on the average size of particles produced in the mixing chamber calculated from Eq. (2).
2 2
Fig. 3. Comparison of input particle size distribution and average output particle size distributions from both tested cutting head configurations.
formed by transformation of the interaction energy into the material damage, can be calculated from the equation
PN =
CD πao d2o μ 2o p2o γ2o : 4ρo EP co c
ð1Þ
Considering the physical simplification that both the original and the newly formed particles are approximated as cubes, the mean size
Δ mvm = CD πρm ao vo
ao πa3o ρ v cos α: − co 6 m m
ð3Þ
Since the relationship of the particle size calculated from Eq. (2) on the jet impact force (momentum transfer) is linear, the percentage degree reduction of the force causes corresponding increase of the average size of broken particles. The shift in the modus of the particle size caused by change of the feeder tube axis from the direction perpendicular to the water jet axis to the angle value close to 45° is evident in the graph presented in Fig. 5. Considering usual values for tested abrasive material the increase of the grain size modus is determined from the Eq. (2) using momentum decrease calculated from Eq. (3) (48.75%). This momentum decrease implies the increase of the modal value 51.25%. This value is in a good agreement with presented experimental data that yield the ratio close to 51.85%
Fig. 4. An example of input (left hand side photo) and outlet (right hand side photo) garnet particles used in presented experiments.
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L.M. Hlaváč et al. / International Journal of Mineral Processing 95 (2010) 25–29 Table 1 Comparison of experimentally and theoretically determined modal values.
Value for chamber type A Value for chamber type B Difference between results for chamber types
Experimentally set modus
Theoretically set modus
Difference between experiment and theory
16.2 μm
16.0 μm
1.24%
24.6 μm
24.2 μm
1.63%
51.85%
51.25%
with a larger size influencing thus not only the result of the one certain measurement (see Fig. 5) but also the average value of more measurements. Fig. 5. Volumetric particle size distribution of the mixed water jet from the two mixing chamber shapes, two tested conformable pieces.
determined from the modus of the particle size (see Fig. 5 and Table 1). The modus of the experimentally determined grain size distribution for particle inlet perpendicular to the water jet axis is about 16.2 μm, while the modus of the experimentally determined grain size distribution for particle inlet including 45° with the water jet axis is about 24.6 μm. The maximum (modus) of the distribution evaluated from the Eq. (2) for the usual garnet properties and experimental conditions as above is 16 μm. This value was calculated for the average specific surface energy 2.835 J m− 2 that was determined from the work necessary for disintegration of particles inside the special chamber put into the pressure machine (Jandačka et al., 2009). The shifted value of the distribution modus calculated for the particle inlet declined to 45° from the Eqs. (3) and (2) is 24.2 μm. Comparison of the theoretically derived curves based on the calculated value with the ones determined from experimental values is evident observing curves in Fig. 6 where the calculated “theoretical” curves are prepared using presented Eqs. (1) through (3). The higher values determined experimentally for particle sizes in the range from about 0.5 μm up to 10 μm can be explained in a few ways. The higher amount of smaller particles can be caused by the internal defects in the original particles (as the theoretical model does not imply such a relationship yet), by the agglomeration of smaller particles into some greater objects or by the adsorption of the very small particles onto the greater ones producing in that way objects of greater sizes. The two last mentioned phenomena are not sufficiently recognizable in the process of particle size analyses in the commercial laser-based particle analysers. The higher values round the particle size 130 μm can be caused by few particles or even just one particle
Fig. 6. Comparison of the volumetric particle size distribution of the mixed water jet from the two mixing chamber shapes with theoretical curve calculated for both cases.
4. Conclusions The results presented in this article show that the inlet particle suction perpendicular to the water jet axis causes larger damage of particles and produces smaller average particle size. This phenomenon can be used for intentional disintegration of brittle materials, especially minerals. The elementary theoretical set of equations can be used for partial analysis of the product flowing out of the mixing process — the average particle size can be determined quite well. The distribution of the particles and its variation caused by internal particle damage or some other phenomena cannot be determined from this theoretical base and need further deeper investigation. Nevertheless, the mixing process inside the cutting head of the entrained water jet constitutes a good base for utilization of the water jet as the tool for intentional particle softening in subsequent processes. Acknowledgements The authors thank the Ministry of Industry and Trade (project 1H-PK2/22), the Grant Agency of the Czech Republic (project 105/06/ 1516), the Grant Agency of the Czech Academy of Sciences (project AV0Z30860518) and the company PTV spol. s r.o. Hostivice for financial support provided to the presented research. References Dong, Y., Tyler, L.J., Summers, D.A., Johnson, M., 2004. Experimental study of particle velocity measurement in abrasive water jet cutting in the nozzle and jet stream using multiple sensing elements. In: Gee, C. (Ed.), Proc. Water Jetting. BHR Group, Mainz, Germany, pp. 137–147. Guo, Ch., Dong, L., 2007. Energy consumptions in comminution of mica with cavitation abrasive water jet. Journal of China University of Mining and Technology 17 (2), 251–254. Hashish, M., 1983. Experimental studies of cutting with abrasive waterjets. Proc. 2nd U.S. Water Jet Symposium. Rolla, Missouri, U.S.A, pp. 379–389. Hashish, M., 1989. A model for abrasive-waterjet (AWJ) machining. Trans. of the ASME. Journal of Engineering Materials and Technology 111, 154–162. Hlaváč, L.M., 1996. Interaction of grains with water jet — the base of the physical derivation of complex equation for jet cutting of rock materials. In: Gee, C. (Ed.), Proc. Jetting Technology. BHR Group, Mech. Eng. Pub. Ltd, Cagliari, Italy, pp. 471–485. Hlaváč, L.M., Martinec, P., 1998. Almandine garnets as abrasive material in high-energy waterjet — physical modelling of interaction, experiment, and prediction. Jetting Technology. BHR Group, Prof. Eng. Pub. Ltd, Bury StEdmunds/London, pp. 211–223. Hlaváč, L.M., Sochor, T., 1994. A contribution to the physics of a high velocity abrasive particle interaction with brittle non-homogeneous materials. Jet Cutting Technology. BHR Group, Mech. Eng. Pub. Ltd, London, pp. 117–126. Hlaváč, L.M., Vašek, J., 1996. Physical aspects of the H.E.L.J. use in clean coal technologies. Proc. Environmental Issues and Waste Management in Energy and Mineral Production SWEMP '96. DIGITA, Cagliari, pp. 1305–1312. Hlaváč, L.M., Sosnovec, L., Martinec, P., 1999. Abrasives for high energy water jet: investigation of properties. In: Hashish, M. (Ed.), Proc. 10th American Waterjet Conference. WJTA, Houston, Texas, pp. 409–418. Hlaváč, L.M., Vašek, J., Hlaváčová, I.M., Jandačka, P., 2008. Potential of liquid jets for preparation of micro and nano particles. In: Muir, A. (Ed.), Green Chemistry & Engineering Proc. International Conference on Process Intensification & Nanotechnology. BHR Group, Albany, New York State, pp. 205–218.
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