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Improvements in hydrocyclone design flow lines stabilization
Powder Technology 176 (2007) 1 – 8 www.elsevier.com/locate/powtec
Improvements in hydrocyclone design flow lines stabilization Lucía Fernández Martínez ⁎, Antonio Gutiérrez Lavín, Manuel María Mahamud, Julio L. Bueno Department of Chemical Engineering and Environmental Technology, University of Oviedo.C/ Julián Clavería 8. 33006 Oviedo, Spain Received 6 September 2006; received in revised form 24 January 2007; accepted 5 February 2007 Available online 14 February 2007
Abstract Pressure distribution field within the separation chamber of hydrocyclones is qualitatively and quantitatively analyzed in the context of the design of compact plants for the on-board treatment of ballast water. Once the qualitative analysis has been carried out, the conclusions arising from this analysis have been evaluated by defining a parameter termed “asymmetry coefficient”, which provides quantitative information about the behaviour within the hydrocyclone. The influence of the vortex finder both on flow patterns and on air-core precession is successfully studied. As well as giving an insight into hydrocyclone flow lines behaviour, this article attempts to improve operational efficiency by modifying several design parameters in order to provide a stabilization of flow lines (reducing turbulence). © 2007 Elsevier B.V. All rights reserved. Keywords: Hydrocyclones; Pressure patterns; Flow field; Length increasing; Design; Separation
1. Hydrocyclones as separation unit operations Hydrocyclones are inertial devices that allow the separation or concentration of macrofluids as suspensions because of the difference between inertial forces that govern the movement of suspended solids in a liquid bulk. Unlike centrifuges, which use the same separation principle, hydrocyclones possess a number of advantages [1–4] such as the absence of moving parts, high capacity, low maintenance requirements, low energy consumption and short residence time. A hydrocyclone body consists of a chamber integrated by a cylindrical and a conical part as shown in Fig. 1. Hydrocyclone design parameters following Rietema [5] criterion are calculated based on semi-empirical equations and dimensionless numbers proposed by Svarovsky [6] and Castilho and Medronho [7] and Medronho [8]. Therefore, it is important to understand the relative flow pattern and its inherent mechanism that enables separation within the hydrocyclone in order to improve operation performance [9]. The feed slurry enters the hydrocyclone tangentially in the cylindrical upper zone, allowing a progressive separation of the suspended solids from the feed stream. The separation principle is ⁎ Corresponding author. Tel.: +34 985102997; fax: +34 985103434. E-mail address: [email protected] (L.F. Martínez). 0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.02.001
due to the centrifugal forces generated by the tangential motion of the liquid: the circular screw-like trajectory creates a radial acceleration. If the density of solid particles is higher than the fluid density, these particles are impelled to the wall, where they collapse and leave the hydrocyclone through the lower exit, being separated. If the particles are lighter than the liquid phase, these
Fig. 1. Some typical views of a hydrocyclone.
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L.F. Martínez et al. / Powder Technology 176 (2007) 1–8
Fig. 3. Simplified flow sheet of the experimental plant. Fig. 2. Schematic diagram of a conventional hydrocyclone.
are differentially carried to the upper exit. The basic flow pattern of a hydrocyclone, the usual nomenclature and some characteristic terms are shown in Fig. 2. Although the separation principle is well defined and hydrocyclones do not require a complex design, the actual separation mechanism within them is still not well known. Several authors have attempted to model the anisotropic flow [10–18] and complementary research has been carried out related to flow patterns within cyclones [19], providing interesting conclusions in order to understand hydrocyclone behaviour. Prior to these studies, it had been assumed for the purpose of modelling that the flow patterns within a cyclone or hydrocyclone were axisymmetric. This is the proposal of Dyakowski and Williams [20], basing their study on the application of a learning model which takes into consideration mass and momentum principles to predict flow patterns within a hydrocyclone and the regions of high solid concentration. Dwari et al. [3] also consider that turbulent eddy diffusion has a negligible effect on separation. Petty and Parks [21] assumed a non-turbulent flow for hydrocyclones used for oil–water separation. In this study it is stated by measuring the pressure drop along the axial and radial coordinates of a 18 cm internal diameter hydrocyclone that the flow pattern is asymmetric. Moreover, this paper focuses on how the vortex finder length influences the pressure patterns and air-core precession, with the aim of Table 1 Dimensions of the hydrocyclone used in the experiment Parameters
Di/Dc
Do/Dc
W/Dc
Du/Dc
L/Dc
Θ
Rietema Dc(Internal) 5 cm 10 cm 18 cm
0.28
0.34
0.40
0.2
5
10°–20°
0.28 0.29 0.3
0.34 0.3 0.33
0.8 0.8 0.67 1.67 3.3
0.2 0.2 0.17
5 5 4.17 5.17 6.83
11.4° 11.4° 16.3°
trying to choose the hydrocyclone configuration with the minimum pressure drop. In order to widen the effect of geometry configuration on pressure patterns, the total cylindrical length on the hydrocyclone has been studied, and its influence has been combined with effects of changing vortex finder length. 2. Experimental set up Three sizes of hydrocyclone are used to carry out this study, their internal diameters being 5, 10, 18 cm. These have been designed according to Rietema [5] and their dimensions indicated in Fig. 2 are shown in Table 1. Water at room temperature (15 °C) is fed using a 3 kW centrifugal pump P050/30T, passing through a by-pass that regulates the flow, which is measured by a Khrone Aquaflux 090 K/D DN40 PN 40 electromagnetic flow meter. The hydrocyclones are placed in parallel, allowing independent operation. The suspension contained in the tank is continuously stirred to maintain the concentration at a constant value, being conducted through a recirculation system. A flow sheet of the experimental device is shown in Fig. 3. Results obtained with the 18 cm hydrocyclone, which is provided with fifteen gaps, are described here. With three operating body lengths: 75, 93 and 123 cm, obtained by adding rings to the cylindrical body, the pressure pattern within the hydrocyclone has been determined in the axial and radial coordinates. The vortex finder is introduced inside the hydrocyclone at different heights to prove its effect on separation performance. 3. Materials and methods The pressure measurements inside the hydrocyclone were carried out using a probe which is introduced within the hydrocyclone and is connected to a U-tube-shaped differential manometer. The pressure drop is measured both in the radial and axial coordinates. In Fig. 4, a schematic diagram of the
L.F. Martínez et al. / Powder Technology 176 (2007) 1–8
3
Fig. 4. Schematic diagram of the pressure measuring equipment.
measuring equipment and details of the pressure probe and Ushaped manometer are shown. 4. Flow layout within a hydrocyclone The different approaches followed to understand hydrocyclone flow patterns were supported by computer software. Turbulence models for the prediction of high swirl are still being developed and entail a very high computing cost [14]. Due to this limitation, and in order to clarify the real behaviour of turbulence flow in a hydrocyclone, this study attempts to clarify experimentally the real particle and flow patterns within. The first step that has been followed by other authors in order to solve this dilemma is to model the fluid flow [10], due to the fact that hydrocyclones operate with high flow velocities (turbulent fluid flow regime), the generation term should be higher than the dissipation term [12]. The following step was to model the particle dynamics to determine the separation efficiency. The trajectory of each
Fig. 5. Schematic diagram of the pressure measured vs. hydrocyclone diameter.
Fig. 6. Pressure gaps location.
particle is tracked from the moment it enters the hydrocyclone to when it is drained out via the downflow or upflow. It is necessary to point out that, when a collision of the particle with the wall takes place, many factors affect the particle reentrainment [19], such as the shape and size of the particle, the physical aspect of the wall, the velocity and direction of the
Fig. 7. Asymmetric flow zones.
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Fig. 8. Effect of the vortex finder length on the pressure patterns.
particle and the number of particles deposited before. During the sedimentation process, small particles move at almost identical velocities to the larger ones, smaller particles appearing to be dragged by the larger ones. Separation as well as the static pressure drop are determined by the centrifugal acceleration field within the hydrocyclone [22]. All this phenomena are quite difficult to analyse computationally so this makes necessary an experimental approach. 5. Results and discussion Further studies have devoted a great deal of time to focusing on modelling pressure distribution inside the hydrocyclone. At the same cross-section, the pressure near the wall decreases, first gently and then sharply near the air-core [11]. This result has been also achieved in the present research. For a random fixed axial coordinate (z = 0.425 m) in the hydrocyclone of 75 cm total length, this behaviour is shown in Fig. 5. It is necessary to point out that there is no symmetry across the radial coordinate and there is no need to place the locus of minimum pressure in the centre of the hydrocyclone. Several sources of anomaly must be explained a priori: The pressure probes are not placed along the same vertical line as Fig. 6 indicates. Once the probe is introduced in the body of the hydrocyclone there appear flow perturbations, more intense in the zones closer to the spigot, where the space between the flow lines is narrow.
It has been observed that the flow is not either symmetric in the axial coordinate. It has been demonstrated that there exist regions of high turbulence, where recirculation movements can be noticed in the conical upper part in the cylinder and in the inlet due to the generation of the well-known short-circuit. These results are in accordance with those exposed by Yang et al. [15] and Doby et al. [23]. There is also a change in flow patterns, close to the spigot, due to the existing strong swirl in this zone. Fig. 7 shows all these anomalies in the hydrocyclone of 75 cm total length without the presence of the vortex finder. 5.1. Qualitative analysis of flow fields within a hydrocyclone 5.1.1. Effect of the vortex finder length on the pressure patterns In the outer part of the vortex finder an eddy is generated [12]. On the contrary to that expressed in the equilibrium orbit theory [6], this causes a small amount of liquid to be moved from the upper part of the hydrocylone to the bottom of the vortex finder, entering in the overflow forming the so-called short-circuit flow. The bulk flow of the liquid moves down helicoidally to the underflow exit. The highest values of dissipation rate occur near the inlet of the vortex finder, eddies are created and dissipated violently, so turbulence is very high. The dissipation rate depends on changes in flow pattern, so the flow in the cylindrical part should be modified in order to avoid this flow pattern [12]. This has also been stated experimentally (see Fig. 8), not
Fig. 9. Effect of the vortex finder length on the air-core precession.
L.F. Martínez et al. / Powder Technology 176 (2007) 1–8
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Fig. 10. Stabilization of flow pressure patterns thanks to increasing length.
computationally, in this study. Possible amendments are proposed later, in order to modify the intensity and scale of turbulence. In Fig. 8 is observed that the most stable behaviour, that is to say, the most symmetric flow lines are obtained when the introduction of the vortex finder is placed at 5 cm, as reported by Haas et al. [24]. The highest variation is found when the length of the vortex finder inside the hydrocyclone is 7.5 cm, due to the fact that the pressure gap is really close to the tip of the vortex finder and so the measurements are taken quite close to the turbulence caused. 5.1.2. Effect of the vortex finder length on air-core precession It was assumed that the presence of an air-core (due to swirl) takes place as the result of the pressure being below atmospheric pressure. This difference in pressure leads to the development of
Fig. 11. Stabilization of air-core precession thanks to increasing length.
Fig. 12. Stabilization of air-core precession thanks the increasing length (ratio between introduced length of vortex finder and total length of 0.1).
the air-core, and is maintained when the outlets are opened to the atmosphere. It is observed that the air-core is developed from the underflow. Contrary to this theory, Cullivan et al. [13] point out that the air-core is not pressure-driven but is rather transport-driven, because the axial pressure is below atmospheric conditions only close to the underflow stream. It is also pointed out that near the underflow stream there exists a reversal flow that interrupts the continuity of the air-core. Several authors have made great efforts in trying to model the air-core. Olson and Van Ommen [25] have concluded that the hydrocyclone flow split is a function of the air-core. Slack et al. [2] consider that the low pressure air-core shape and size is a function of the swirl velocity field and the localised slurry density. The shape depends on the slurry concentration and the predicted swirl. Due to the difference of velocities between the solid and liquid phase, the air-core is unstable and, the larger the particle, the more obvious this phenomenon becomes [11]. The instability of the precession of the air-core makes such a movement not to
Fig. 13. Calculus of the asymmetry coefficient.
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Fig. 14. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 75 cm (asymmetry coefficient).
be assumed as completely certain (Figs. 9, 11, 12). These results agree with Cullivan et al. [13]. In this study, to determine air-core precession, the minimum pressure point is plotted as shown in Fig. 9, where it can be seen that this minimum pressure point is not placed in the centre of the hydrocyclone due to the eddies generated within. This trend is similar to that found in the pressure patterns, the most symmetric patterns being found far from the inlet and the spigot. There are also asymmetric zones in the upper part of the conical zone. The turbulence caused by the vortex finder is also represented in Fig. 9. If the vortex finder is introduced in the cylindrical region, this causes a perturbation in the flow lines and the point of minimum pressure is displaced from the centre. On the contrary, if the vortex finder is introduced inside the conical part of the hydrocyclone, this causes a stabilization of flow lines. 5.1.3. Modification of the hydrocyclone length and its influence on turbulence associated to the vortex finder In order to improve the hydrocyclone performance, when used as centrifugal solid–liquid separator, an in the same way that occurs in unidirectional sedimentation, the modification of the length of the cylindrical part has been here considered, as a possible amendment of minimizing turbulence effects. The hydrocyclone total length increases from a starting total length of 75 cm to 93 cm and 123 cm. Fig. 10 shows the pressure patterns when there is no introduction of the vortex finder for the different lengths considered. The stabilization of flow lines in the cylindrical zone is clearly plotted; showing that in this part of the cyclone there is no such turbulence. It is also corroborated that when the length of the cylindrical part increases the pressure drop decreases [26]. The same behaviour is shown for the air-core precession, where the point of minimum pressure is also placed in the centre of the hydrocyclone if the length of the cylindrical zone is increased (Fig. 11). Although the flow is more symmetric in this zone it is necessary to point out that the turbulences in the inlet and spigot still persist. The same asymmetric behaviour is found in the top
part, of the cone part but less marked when the total length increases. The influence of a vortex finder in the velocity field deformation is reported by Dyakowski and Williams [20]. Other models such as those proposed by Svarovsky [6] do not take into account the effect of the vortex finder on particle separation. For a given ratio between the introduced length of the vortex finder and the total length of 0.1 (see Fig. 12), it can be seen that when the length of the cylindrical part increases, the vortex finder influence over the flow patterns decreases. In this study, the operation has been carried out without suspended solids load, but several authors such as Doby et al. [23] have proposed that high solids concentration hinder the formation of low pressure near the centre of the spigot, due to the sediment accumulation. 5.2. Quantitative analysis of the flow fields within a hydrocyclone 5.2.1. Effect of the vortex finder length on the pressure patterns In order to determine the quantitative analysis of the pressure patterns within a hydrocyclone, a new coefficient is introduced termed “asymmetry coefficient” and represented by “AS”. AS ¼ j
A2 −A1 j A2 þ A1
ð1Þ
This is obtained (see Fig. 13) by the calculus of the areas obtained at both sides of the normalised pressure curve. The absolute value of the ratio between its subtraction and its addition, gives us the value of this coefficient.
Fig. 15. Detail of the interferences caused by the vortex finder.
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Fig. 16. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 123 cm (asymmetry coefficient).
Once the asymmetry coefficient has been defined, it is expected to achieve coherent results with those obtained in the qualitative analysis. In Fig. 14, a representation of the values obtained for AS when the total length of the hydrocyclone is 75 cm at different introduction lengths of the vortex finder can be seen. This is also demonstrated by the rise of the values of the asymmetry coefficient; the high turbulences generated near the spigot (see Fig. 14). As previously said, the vortex finder introduces turbulence in a hydrocyclone, as can be seen when the pressure gaps are placed near the tip of the vortex finder. This phenomenon is observed when the depth of the vortex finder tip is 5 cm and 7.5 cm, as the upper pressure gaps are placed quite close to the vortex finder tip. Indeed, if the values of AS at these two points are compared, we can observe that the asymmetry coefficient increases as the tip of the vortex finder moves closer to the pressure gaps (see Fig. 15). However, the introduction of the vortex finder in the conical region, instead of showing higher turbulence, causes a stabilization of the flow lines as shown by the lower values of AS. Regarding air-core precession, we previously reported that there exists a region of instability near the spigot and near the inlet; the high values of the asymmetry coefficient corroborate this assumption obtained by qualitative analysis.
5.2.2. Effect on the flow lines when the cylindrical length is increased Qualitative analysis reveals a stabilization of the flow lines by increasing the total length (increasing cylindrical length). In the cylindrical region, flow lines seem to be more stable when the vortex finder tip is situated far from this region (see Figs. 16 and 17). This is proved by the close values between the parameter AS. In summary, this quantitative analysis allows us to observe stabilization. When the total length is increased, AS values are found to be closer to one another. The increasing of the total length by the increment of the cylindrical length produces a stabilization of the flow lines (closer values of AS), this stabilization is more noticeable, the further away the vortex finder tip is. 6. Conclusions By their structural, mechanical, hydrodynamics robustness and separation efficiency, Hydrocyclones are solid–liquidseparation unit operations particularly useful to be integrated as a part of compact plants able to be carried, housed or stowed. Hydrodynamic mechanism inside hydrocyclones is far from being well defined and predicted. Influence of some design
Fig. 17. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 93 cm (asymmetry coefficient).
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parameters such as vortex finder position on the stabilization of flow lines is pointed out, introducing the so-called “asymmetry coefficient” as a means of quantifying turbulences within hydrocyclones. Possible amendments such as increasing cylindrical length are proposed, in order to modify the intensity and scale of turbulence. From this paper the following conclusions can be drawn in order to understand a bit more hydrocyclone behaviour: Flow patterns in the hydrocyclone are asymmetric, emphasizing regions near the inlet and spigot and it is the top part of the cone. Minimum pressure point is not always placed in the centre of the hydrocyclone due to the eddies generated within. Hydrocyclone geometry heavily influences pressure patterns. Modification of geometrical parameters such as the introduction of the vortex finder and increasing cylindrical body length causes a modification in the pressure patterns, which has also influences air-core precession. Regarding vortex finder experiments from our experimental setup, the highest stabilization of flow lines is obtained when vortex finder tip is placed at 5 cm within the hydrocyclone. With regards to cylindrical body length, it is observed that there exists a stabilization of pressure pattern if the length of the cylindrical part increases. It is also shown that the minimum pressure point tends to be placed in the centre if the cylindrical part increases. To compare flow patterns between different geometries, an adimensional coefficient termed “asymmetry coefficient” is introduced. This coefficient shows higher values in high turbulence regions above mentioned. It also shown how the asymmetry coefficient increases as the tip of the vortex finder moves closer to the pressure gaps. Nomenclature Dc Hydrocyclone cylindrical section diameter (m) Di Hydrocyclone inlet diameter (m) Do Hydrocyclone vortex finder diameter (m) Du Hydrocyclone apex diameter (m) ℓ Cylindrical part length (m) L Total length (m) A1, A2 areas obtained at both sides of the normalised pressure curve (m2) AS asymmetry coefficient (–) Greek symbols Θ Cone angle ΔP Pressure drop (N/m2) Acknowledgments The authors would like to acknowledge the financial support from the “Ministerio de Educación y Ciencia” (Spain) for this investigation within the Project (REN2003–09389). References [1] S. Schuetz, G. Mayer, M. Bierdel, M. Piesche, Investigations on the flow and separation behaviour of hydrocyclones using computational fluid dynamics, Int. J. Miner. Process. 73 (2004) 229–237.
[2] M.D. Slack, S. Del Porte, M.S. Engelman, Designing automated computational fluid dynamics modelling tools for hydrocyclone design, Miner. Eng. 17 (2004) 705–711. [3] R.K. Dwari, M.N. Biswas, B.C. Meikap, Performance characteristics for particles of sand FCC and fly ash in a novel hydrocyclone, Chem. Eng. Sci. 59 (2004) 671–684. [4] K.U. Bhaskar, B. Govindarajan, J.P. Barnwal, K.K. Rao, B.K. Gupta, T.C. Rao, Classification studies of lead–zinc ore fines using water-injection cyclone, Int. J. Miner. Process. 77 (2005) 80–94. [5] K. Rietema, Performance and design of hydrocyclones, Parts I–IV, Chem. Eng. Sci. 15 (1961) 298–325. [6] L. Svarovsky, Efficiency of separation of particle from fluids (chapter 3) and hydrocyclones (chapter 6), In: Solid-Liquid separation, London, (1990) 43–73 & 202–50. [7] I.R. Castilho, R.A. Medronho, A simple procedure for design and performance prediction of Bradley and Rietema Hydrocyclones, Miner. Eng. 13 (2000) 183–191. [8] R.A. Medronho, Scale-up of hydrocyclones at low feed concentrations, Ph.D. Thesis, University of Bradford, (1985). [9] L.F. Martínez, A.G. Lavín, M.M. Mahamud, J.L. Bueno, Hydrocyclones in water depuration (Spain), Tecnología del Agua (in press). [10] P. He, M. Salcudean, I.S. Gartshore, A numerical simulation of hydrocyclones, Chem. Eng. Res. Des. 77 (1999) 429–441. [11] G.Q. Dai, W.M. Chen, J.M. Li, L.Y. Chu, Experimental study of solid– liquid two-phase flow in a hydrocyclone, Chem. Eng. J. 74 (1999) 211–216. [12] G.Q. Dai, J.M. Li, W.M. Chen, Numerical prediction of the liquid flow within a hydrocyclone, Chem. Eng. J. 74 (1999) 217–223. [13] J.C. Cullivan, R.A. Williams, T. Dyakowski, C.R. Cross, New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics, Miner. Eng. 17 (2004) 651–660. [14] A.F. Nowakowski, J.C. Cullivan, R.A. Williams, T. Dyakowski, Application of CFD to modelling of the flow in hydrocyclones. Is this a realizable option or still a research challenge, Miner. Eng. 17 (2004) 661–669. [15] I.H. Yang, C.B. Shin, T.-H. Kim, S. Kim, A three-dimensional simulation of a hydrocyclone for the sludge separation in water purifying plants and comparison with experimental data, Miner. Eng. 17 (2004) 637–641. [16] J.A. Delgadillo, R.K. Rajamani, A comparative study of three turbulenceclosure models for the hydrocyclone problem, Int. J. Miner. Process. 77 (2005) 217–230. [17] E. Ovalle, R. Araya, F. Concha, The role of wave propagation in hydrocyclone operations I: an axisymmetric stream function formulation for a conical hydrocyclone, Chem. Eng. J. 111 (2005) 205–211. [18] E. Ovalle, F. Concha, The role of wave propagation in hydrocyclone operations II: wave propagation in the air–water interface of a conical hydrocyclone, Chem. Eng. J. 111 (2005) 213–223. [19] L. Ma, D.B. Ingham, X. Wen, Numerical modelling of the fluid and particle penetration through small sampling cyclones, J. Aerosol Sci. 31 (2000) 1097–1119. [20] T. Dyakowski, R.A. Williams, Prediction of high solids concentration regions within a hydrocyclone, Powder Technol. 87 (1996) 43–47. [21] C.A. Petty, S.M. Parks, Flow structures within miniature hydrocyclones, Miner. Eng. 17 (2004) 615–624. [22] K.T. Hsieh, K. Rajamani, Phenomenological model of the hydrocyclone: model development and verification for single-phase flow, Int. J. Miner. Process. 22 (1988) 223. [23] M.J. Doby, W. Kraipech, A.F. Nowakowski, Numerical prediction of outlet velocity patterns in solid–liquid separators, Chem. Eng. J. 111 (2005) 173–180. [24] P.A. Haas, E.O. Nurmi, M.E. Whatley, J.R. Engel, Midget hydrocyclones remove micron particles, Chem. Eng. Progr. 53 (1957) 203–207. [25] T.J. Olson, R. Van Ommen, Optimizing hydrocyclone design using advanced CFD model, Miner. Eng. 17 (2004) 713–720. [26] B. Wang, A.B. Yu, Numerical study of particle–fluid flow in hydrocyclones with different body dimensions, Miner. Eng. 19 (2006) 1022–1033.
Improvements in hydrocyclone design flow lines stabilization Lucía Fernández Martínez ⁎, Antonio Gutiérrez Lavín, Manuel María Mahamud, Julio L. Bueno Department of Chemical Engineering and Environmental Technology, University of Oviedo.C/ Julián Clavería 8. 33006 Oviedo, Spain Received 6 September 2006; received in revised form 24 January 2007; accepted 5 February 2007 Available online 14 February 2007
Abstract Pressure distribution field within the separation chamber of hydrocyclones is qualitatively and quantitatively analyzed in the context of the design of compact plants for the on-board treatment of ballast water. Once the qualitative analysis has been carried out, the conclusions arising from this analysis have been evaluated by defining a parameter termed “asymmetry coefficient”, which provides quantitative information about the behaviour within the hydrocyclone. The influence of the vortex finder both on flow patterns and on air-core precession is successfully studied. As well as giving an insight into hydrocyclone flow lines behaviour, this article attempts to improve operational efficiency by modifying several design parameters in order to provide a stabilization of flow lines (reducing turbulence). © 2007 Elsevier B.V. All rights reserved. Keywords: Hydrocyclones; Pressure patterns; Flow field; Length increasing; Design; Separation
1. Hydrocyclones as separation unit operations Hydrocyclones are inertial devices that allow the separation or concentration of macrofluids as suspensions because of the difference between inertial forces that govern the movement of suspended solids in a liquid bulk. Unlike centrifuges, which use the same separation principle, hydrocyclones possess a number of advantages [1–4] such as the absence of moving parts, high capacity, low maintenance requirements, low energy consumption and short residence time. A hydrocyclone body consists of a chamber integrated by a cylindrical and a conical part as shown in Fig. 1. Hydrocyclone design parameters following Rietema [5] criterion are calculated based on semi-empirical equations and dimensionless numbers proposed by Svarovsky [6] and Castilho and Medronho [7] and Medronho [8]. Therefore, it is important to understand the relative flow pattern and its inherent mechanism that enables separation within the hydrocyclone in order to improve operation performance [9]. The feed slurry enters the hydrocyclone tangentially in the cylindrical upper zone, allowing a progressive separation of the suspended solids from the feed stream. The separation principle is ⁎ Corresponding author. Tel.: +34 985102997; fax: +34 985103434. E-mail address: [email protected] (L.F. Martínez). 0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.02.001
due to the centrifugal forces generated by the tangential motion of the liquid: the circular screw-like trajectory creates a radial acceleration. If the density of solid particles is higher than the fluid density, these particles are impelled to the wall, where they collapse and leave the hydrocyclone through the lower exit, being separated. If the particles are lighter than the liquid phase, these
Fig. 1. Some typical views of a hydrocyclone.
2
L.F. Martínez et al. / Powder Technology 176 (2007) 1–8
Fig. 3. Simplified flow sheet of the experimental plant. Fig. 2. Schematic diagram of a conventional hydrocyclone.
are differentially carried to the upper exit. The basic flow pattern of a hydrocyclone, the usual nomenclature and some characteristic terms are shown in Fig. 2. Although the separation principle is well defined and hydrocyclones do not require a complex design, the actual separation mechanism within them is still not well known. Several authors have attempted to model the anisotropic flow [10–18] and complementary research has been carried out related to flow patterns within cyclones [19], providing interesting conclusions in order to understand hydrocyclone behaviour. Prior to these studies, it had been assumed for the purpose of modelling that the flow patterns within a cyclone or hydrocyclone were axisymmetric. This is the proposal of Dyakowski and Williams [20], basing their study on the application of a learning model which takes into consideration mass and momentum principles to predict flow patterns within a hydrocyclone and the regions of high solid concentration. Dwari et al. [3] also consider that turbulent eddy diffusion has a negligible effect on separation. Petty and Parks [21] assumed a non-turbulent flow for hydrocyclones used for oil–water separation. In this study it is stated by measuring the pressure drop along the axial and radial coordinates of a 18 cm internal diameter hydrocyclone that the flow pattern is asymmetric. Moreover, this paper focuses on how the vortex finder length influences the pressure patterns and air-core precession, with the aim of Table 1 Dimensions of the hydrocyclone used in the experiment Parameters
Di/Dc
Do/Dc
W/Dc
Du/Dc
L/Dc
Θ
Rietema Dc(Internal) 5 cm 10 cm 18 cm
0.28
0.34
0.40
0.2
5
10°–20°
0.28 0.29 0.3
0.34 0.3 0.33
0.8 0.8 0.67 1.67 3.3
0.2 0.2 0.17
5 5 4.17 5.17 6.83
11.4° 11.4° 16.3°
trying to choose the hydrocyclone configuration with the minimum pressure drop. In order to widen the effect of geometry configuration on pressure patterns, the total cylindrical length on the hydrocyclone has been studied, and its influence has been combined with effects of changing vortex finder length. 2. Experimental set up Three sizes of hydrocyclone are used to carry out this study, their internal diameters being 5, 10, 18 cm. These have been designed according to Rietema [5] and their dimensions indicated in Fig. 2 are shown in Table 1. Water at room temperature (15 °C) is fed using a 3 kW centrifugal pump P050/30T, passing through a by-pass that regulates the flow, which is measured by a Khrone Aquaflux 090 K/D DN40 PN 40 electromagnetic flow meter. The hydrocyclones are placed in parallel, allowing independent operation. The suspension contained in the tank is continuously stirred to maintain the concentration at a constant value, being conducted through a recirculation system. A flow sheet of the experimental device is shown in Fig. 3. Results obtained with the 18 cm hydrocyclone, which is provided with fifteen gaps, are described here. With three operating body lengths: 75, 93 and 123 cm, obtained by adding rings to the cylindrical body, the pressure pattern within the hydrocyclone has been determined in the axial and radial coordinates. The vortex finder is introduced inside the hydrocyclone at different heights to prove its effect on separation performance. 3. Materials and methods The pressure measurements inside the hydrocyclone were carried out using a probe which is introduced within the hydrocyclone and is connected to a U-tube-shaped differential manometer. The pressure drop is measured both in the radial and axial coordinates. In Fig. 4, a schematic diagram of the
L.F. Martínez et al. / Powder Technology 176 (2007) 1–8
3
Fig. 4. Schematic diagram of the pressure measuring equipment.
measuring equipment and details of the pressure probe and Ushaped manometer are shown. 4. Flow layout within a hydrocyclone The different approaches followed to understand hydrocyclone flow patterns were supported by computer software. Turbulence models for the prediction of high swirl are still being developed and entail a very high computing cost [14]. Due to this limitation, and in order to clarify the real behaviour of turbulence flow in a hydrocyclone, this study attempts to clarify experimentally the real particle and flow patterns within. The first step that has been followed by other authors in order to solve this dilemma is to model the fluid flow [10], due to the fact that hydrocyclones operate with high flow velocities (turbulent fluid flow regime), the generation term should be higher than the dissipation term [12]. The following step was to model the particle dynamics to determine the separation efficiency. The trajectory of each
Fig. 5. Schematic diagram of the pressure measured vs. hydrocyclone diameter.
Fig. 6. Pressure gaps location.
particle is tracked from the moment it enters the hydrocyclone to when it is drained out via the downflow or upflow. It is necessary to point out that, when a collision of the particle with the wall takes place, many factors affect the particle reentrainment [19], such as the shape and size of the particle, the physical aspect of the wall, the velocity and direction of the
Fig. 7. Asymmetric flow zones.
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Fig. 8. Effect of the vortex finder length on the pressure patterns.
particle and the number of particles deposited before. During the sedimentation process, small particles move at almost identical velocities to the larger ones, smaller particles appearing to be dragged by the larger ones. Separation as well as the static pressure drop are determined by the centrifugal acceleration field within the hydrocyclone [22]. All this phenomena are quite difficult to analyse computationally so this makes necessary an experimental approach. 5. Results and discussion Further studies have devoted a great deal of time to focusing on modelling pressure distribution inside the hydrocyclone. At the same cross-section, the pressure near the wall decreases, first gently and then sharply near the air-core [11]. This result has been also achieved in the present research. For a random fixed axial coordinate (z = 0.425 m) in the hydrocyclone of 75 cm total length, this behaviour is shown in Fig. 5. It is necessary to point out that there is no symmetry across the radial coordinate and there is no need to place the locus of minimum pressure in the centre of the hydrocyclone. Several sources of anomaly must be explained a priori: The pressure probes are not placed along the same vertical line as Fig. 6 indicates. Once the probe is introduced in the body of the hydrocyclone there appear flow perturbations, more intense in the zones closer to the spigot, where the space between the flow lines is narrow.
It has been observed that the flow is not either symmetric in the axial coordinate. It has been demonstrated that there exist regions of high turbulence, where recirculation movements can be noticed in the conical upper part in the cylinder and in the inlet due to the generation of the well-known short-circuit. These results are in accordance with those exposed by Yang et al. [15] and Doby et al. [23]. There is also a change in flow patterns, close to the spigot, due to the existing strong swirl in this zone. Fig. 7 shows all these anomalies in the hydrocyclone of 75 cm total length without the presence of the vortex finder. 5.1. Qualitative analysis of flow fields within a hydrocyclone 5.1.1. Effect of the vortex finder length on the pressure patterns In the outer part of the vortex finder an eddy is generated [12]. On the contrary to that expressed in the equilibrium orbit theory [6], this causes a small amount of liquid to be moved from the upper part of the hydrocylone to the bottom of the vortex finder, entering in the overflow forming the so-called short-circuit flow. The bulk flow of the liquid moves down helicoidally to the underflow exit. The highest values of dissipation rate occur near the inlet of the vortex finder, eddies are created and dissipated violently, so turbulence is very high. The dissipation rate depends on changes in flow pattern, so the flow in the cylindrical part should be modified in order to avoid this flow pattern [12]. This has also been stated experimentally (see Fig. 8), not
Fig. 9. Effect of the vortex finder length on the air-core precession.
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Fig. 10. Stabilization of flow pressure patterns thanks to increasing length.
computationally, in this study. Possible amendments are proposed later, in order to modify the intensity and scale of turbulence. In Fig. 8 is observed that the most stable behaviour, that is to say, the most symmetric flow lines are obtained when the introduction of the vortex finder is placed at 5 cm, as reported by Haas et al. [24]. The highest variation is found when the length of the vortex finder inside the hydrocyclone is 7.5 cm, due to the fact that the pressure gap is really close to the tip of the vortex finder and so the measurements are taken quite close to the turbulence caused. 5.1.2. Effect of the vortex finder length on air-core precession It was assumed that the presence of an air-core (due to swirl) takes place as the result of the pressure being below atmospheric pressure. This difference in pressure leads to the development of
Fig. 11. Stabilization of air-core precession thanks to increasing length.
Fig. 12. Stabilization of air-core precession thanks the increasing length (ratio between introduced length of vortex finder and total length of 0.1).
the air-core, and is maintained when the outlets are opened to the atmosphere. It is observed that the air-core is developed from the underflow. Contrary to this theory, Cullivan et al. [13] point out that the air-core is not pressure-driven but is rather transport-driven, because the axial pressure is below atmospheric conditions only close to the underflow stream. It is also pointed out that near the underflow stream there exists a reversal flow that interrupts the continuity of the air-core. Several authors have made great efforts in trying to model the air-core. Olson and Van Ommen [25] have concluded that the hydrocyclone flow split is a function of the air-core. Slack et al. [2] consider that the low pressure air-core shape and size is a function of the swirl velocity field and the localised slurry density. The shape depends on the slurry concentration and the predicted swirl. Due to the difference of velocities between the solid and liquid phase, the air-core is unstable and, the larger the particle, the more obvious this phenomenon becomes [11]. The instability of the precession of the air-core makes such a movement not to
Fig. 13. Calculus of the asymmetry coefficient.
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Fig. 14. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 75 cm (asymmetry coefficient).
be assumed as completely certain (Figs. 9, 11, 12). These results agree with Cullivan et al. [13]. In this study, to determine air-core precession, the minimum pressure point is plotted as shown in Fig. 9, where it can be seen that this minimum pressure point is not placed in the centre of the hydrocyclone due to the eddies generated within. This trend is similar to that found in the pressure patterns, the most symmetric patterns being found far from the inlet and the spigot. There are also asymmetric zones in the upper part of the conical zone. The turbulence caused by the vortex finder is also represented in Fig. 9. If the vortex finder is introduced in the cylindrical region, this causes a perturbation in the flow lines and the point of minimum pressure is displaced from the centre. On the contrary, if the vortex finder is introduced inside the conical part of the hydrocyclone, this causes a stabilization of flow lines. 5.1.3. Modification of the hydrocyclone length and its influence on turbulence associated to the vortex finder In order to improve the hydrocyclone performance, when used as centrifugal solid–liquid separator, an in the same way that occurs in unidirectional sedimentation, the modification of the length of the cylindrical part has been here considered, as a possible amendment of minimizing turbulence effects. The hydrocyclone total length increases from a starting total length of 75 cm to 93 cm and 123 cm. Fig. 10 shows the pressure patterns when there is no introduction of the vortex finder for the different lengths considered. The stabilization of flow lines in the cylindrical zone is clearly plotted; showing that in this part of the cyclone there is no such turbulence. It is also corroborated that when the length of the cylindrical part increases the pressure drop decreases [26]. The same behaviour is shown for the air-core precession, where the point of minimum pressure is also placed in the centre of the hydrocyclone if the length of the cylindrical zone is increased (Fig. 11). Although the flow is more symmetric in this zone it is necessary to point out that the turbulences in the inlet and spigot still persist. The same asymmetric behaviour is found in the top
part, of the cone part but less marked when the total length increases. The influence of a vortex finder in the velocity field deformation is reported by Dyakowski and Williams [20]. Other models such as those proposed by Svarovsky [6] do not take into account the effect of the vortex finder on particle separation. For a given ratio between the introduced length of the vortex finder and the total length of 0.1 (see Fig. 12), it can be seen that when the length of the cylindrical part increases, the vortex finder influence over the flow patterns decreases. In this study, the operation has been carried out without suspended solids load, but several authors such as Doby et al. [23] have proposed that high solids concentration hinder the formation of low pressure near the centre of the spigot, due to the sediment accumulation. 5.2. Quantitative analysis of the flow fields within a hydrocyclone 5.2.1. Effect of the vortex finder length on the pressure patterns In order to determine the quantitative analysis of the pressure patterns within a hydrocyclone, a new coefficient is introduced termed “asymmetry coefficient” and represented by “AS”. AS ¼ j
A2 −A1 j A2 þ A1
ð1Þ
This is obtained (see Fig. 13) by the calculus of the areas obtained at both sides of the normalised pressure curve. The absolute value of the ratio between its subtraction and its addition, gives us the value of this coefficient.
Fig. 15. Detail of the interferences caused by the vortex finder.
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Fig. 16. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 123 cm (asymmetry coefficient).
Once the asymmetry coefficient has been defined, it is expected to achieve coherent results with those obtained in the qualitative analysis. In Fig. 14, a representation of the values obtained for AS when the total length of the hydrocyclone is 75 cm at different introduction lengths of the vortex finder can be seen. This is also demonstrated by the rise of the values of the asymmetry coefficient; the high turbulences generated near the spigot (see Fig. 14). As previously said, the vortex finder introduces turbulence in a hydrocyclone, as can be seen when the pressure gaps are placed near the tip of the vortex finder. This phenomenon is observed when the depth of the vortex finder tip is 5 cm and 7.5 cm, as the upper pressure gaps are placed quite close to the vortex finder tip. Indeed, if the values of AS at these two points are compared, we can observe that the asymmetry coefficient increases as the tip of the vortex finder moves closer to the pressure gaps (see Fig. 15). However, the introduction of the vortex finder in the conical region, instead of showing higher turbulence, causes a stabilization of the flow lines as shown by the lower values of AS. Regarding air-core precession, we previously reported that there exists a region of instability near the spigot and near the inlet; the high values of the asymmetry coefficient corroborate this assumption obtained by qualitative analysis.
5.2.2. Effect on the flow lines when the cylindrical length is increased Qualitative analysis reveals a stabilization of the flow lines by increasing the total length (increasing cylindrical length). In the cylindrical region, flow lines seem to be more stable when the vortex finder tip is situated far from this region (see Figs. 16 and 17). This is proved by the close values between the parameter AS. In summary, this quantitative analysis allows us to observe stabilization. When the total length is increased, AS values are found to be closer to one another. The increasing of the total length by the increment of the cylindrical length produces a stabilization of the flow lines (closer values of AS), this stabilization is more noticeable, the further away the vortex finder tip is. 6. Conclusions By their structural, mechanical, hydrodynamics robustness and separation efficiency, Hydrocyclones are solid–liquidseparation unit operations particularly useful to be integrated as a part of compact plants able to be carried, housed or stowed. Hydrodynamic mechanism inside hydrocyclones is far from being well defined and predicted. Influence of some design
Fig. 17. Effect of the vortex finder length on pressure patterns for a hydrocyclone length of 93 cm (asymmetry coefficient).
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parameters such as vortex finder position on the stabilization of flow lines is pointed out, introducing the so-called “asymmetry coefficient” as a means of quantifying turbulences within hydrocyclones. Possible amendments such as increasing cylindrical length are proposed, in order to modify the intensity and scale of turbulence. From this paper the following conclusions can be drawn in order to understand a bit more hydrocyclone behaviour: Flow patterns in the hydrocyclone are asymmetric, emphasizing regions near the inlet and spigot and it is the top part of the cone. Minimum pressure point is not always placed in the centre of the hydrocyclone due to the eddies generated within. Hydrocyclone geometry heavily influences pressure patterns. Modification of geometrical parameters such as the introduction of the vortex finder and increasing cylindrical body length causes a modification in the pressure patterns, which has also influences air-core precession. Regarding vortex finder experiments from our experimental setup, the highest stabilization of flow lines is obtained when vortex finder tip is placed at 5 cm within the hydrocyclone. With regards to cylindrical body length, it is observed that there exists a stabilization of pressure pattern if the length of the cylindrical part increases. It is also shown that the minimum pressure point tends to be placed in the centre if the cylindrical part increases. To compare flow patterns between different geometries, an adimensional coefficient termed “asymmetry coefficient” is introduced. This coefficient shows higher values in high turbulence regions above mentioned. It also shown how the asymmetry coefficient increases as the tip of the vortex finder moves closer to the pressure gaps. Nomenclature Dc Hydrocyclone cylindrical section diameter (m) Di Hydrocyclone inlet diameter (m) Do Hydrocyclone vortex finder diameter (m) Du Hydrocyclone apex diameter (m) ℓ Cylindrical part length (m) L Total length (m) A1, A2 areas obtained at both sides of the normalised pressure curve (m2) AS asymmetry coefficient (–) Greek symbols Θ Cone angle ΔP Pressure drop (N/m2) Acknowledgments The authors would like to acknowledge the financial support from the “Ministerio de Educación y Ciencia” (Spain) for this investigation within the Project (REN2003–09389). References [1] S. Schuetz, G. Mayer, M. Bierdel, M. Piesche, Investigations on the flow and separation behaviour of hydrocyclones using computational fluid dynamics, Int. J. Miner. Process. 73 (2004) 229–237.
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