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Enhancement of hydrocyclone separation performance by eliminating the air core
Chemical Engineering and Processing 43 (2004) 1441–1448
Enhancement of hydrocyclone separation performance by eliminating the air core Liang-Yin Chu a,∗ , Wei Yu a , Guang-Jin Wang a , Xian-Tao Zhou a , Wen-Mei Chen a , Guang-Qing Dai b b
a School of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065, China State Key Laboratory of Hydraulics on High-Speed Flows, Chengdu, Sichuan 610065, China
Received 21 July 2003; received in revised form2613February January 2004 2004; accepted 13 January 2004 Available online
Abstract A new hydrocyclone was designed with a solid core fixed along the central axis in this study. By introducing the solid core, the air core inside the hydrocyclone could be eliminated effectively. Comprehensive effects of eliminating the air core by the solid core on the hydrocyclone performance indices were experimentally investigated. To examine the influence mechanism of air core on the separation performance, a Laser Doppler Anemometer (LDA) was used to investigate the turbulent flow field inside hydrocyclones with and without air cores. The results showed that the radial and axial velocity components in the area near the entrance of the vortex finder, and the radial and axial turbulence components were all reduced by eliminating the air core, i.e. the flow field characteristics inside the hydrocyclone with solid core became more suitable for the separation process. By replacing the air core with solid core, the hydrocyclone separation performance was improved effectively. Comparing the hydrocyclones with air core and solid core, it was proved to be featured with higher total separation efficiency, larger reduced separation efficiency, smaller corrected cut size and higher separation sharpness, although the hydrocyclone cone shape changed from common type, to parabola type, and to hyperbola type. By increasing the inner space of the hydrocyclone cone, the improvement of separation performance became more remarkable. © 2004 Elsevier B.V. All rights reserved. Keywords: Hydrocyclone; Separation; Turbulence; Powder technology; Hydrodynamics
1. Introduction Hydrocyclones are getting more and more interest from various industries, because of their obvious advantages such as simple structure, low cost, large capacity and small volume. Besides a large amount of applications in mineral processing, hydrocyclone separation technique has been used in an increasing number of applications recently in environmental engineering, petrochemical engineering, food engineering, electrochemical engineering, bioengineering, pulping process and so on. It is well known that the hydrocyclone separation performance is determined by the fluid flow characteristics inside the hydrocyclone. Because of the inherent fluid flow characteristics inside the common hydrocyclone, the separation ∗ Corresponding author. Tel.: +86-28-8546-0682; fax: +86-28-8540-4976. E-mail address: [email protected] (L.-Y. Chu).
0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.01.002
process in the common hydrocyclone is always accompanied by some inherent disadvantages, such as unsatisfactory separation efficiency and sharpness [1]. Although the geometry and operation of hydrocyclones is simple in nature, explaining the detailed mechanisms by which they work has proved to be extremely complicated [2–4]. In the conventional hydrocyclone, there generally exist outer and inner helical flows, a circulation flow, a short-circuit flow and an air core. The air core has a large effect on the hydrocyclone flow field and the separation performance; consequently a lot of researches have been made on it previously [5–15]. Among the previous investigations, most of them were just concerned with the prediction and measurement of the air-core diameter and shape [5–11]. Only a few studies have been made on the influence of the air core on hydrocyclone separation performance. Xu et al. [12] reported that the hydrocyclone efficiency could be improved by eliminating the forced vortex (the forced vortex inside the hydrocyclone including air core and liquid forced vortex) with a
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solid rod inserted from the vortex finder into the hydrocyclone; however, Lee and Williams [13] reported an opposite result that the solid rod degraded the hydrocyclone efficiency. Recently, the authors have investigated the effects of various central inserts on hydrocyclone separation efficiency [14,15]. The results also showed that the insertion of a cylindrical rod could improve the separation efficiency [14]. Why two opposite results came out about the effect of replacing the air core with a solid rod on the hydrocyclone efficiency? To answer the question, a further systematical investigation should be carried out on both the flow field and the separation performance of the hydrocyclone. However, a comprehensive understanding of the influence of the air core on both the flow field characteristics inside the hydrocyclone and the hydrocyclone separation performance is still lacking. The objective of this study is to understand the comprehensive effect of the air core on both the flow field and the separation performance of hydrocyclones by replacing the air core with a solid core. The structure design of the solid core will be different from those reported previously. Hydrocyclones with different cone shapes will be also introduced in this study to ascertain the influence behavior of the air core on the performance. A Laser Doppler Anemometer (LDA) will be used to investigate the turbulent flow field inside hydrocyclones with and without air cores, in order to probe into the influence mechanism of the existence of air core on the performance. The hydrocyclone performance indices will include total separation efficiency, reduced separation efficiency, cut size, separation sharpness, flow ratio and capacity, so that useful guidance could be obtained for designing efficient hydrocyclones.
2. Experimental 2.1. Apparatus A conventional type hydrocyclone was designed according to Rietema’s optimum geometry for separation [16]. The hydrocyclone geometry is shown in Fig. 1. With the same geometric parameters, a new hydrocyclone was designed with a solid core as shown in Fig. 2(b). The fixation of the solid core here was designed different from those reported in previous investigations. Previously two main fixation methods were reported as follows. (1) The solid core was just inserting into the hydrocyclone from the vortex finder and then fixing the solid core outside the vortex finder, that is, the solid core was fixed in the manner of a cantilever [12]; and (2) the solid core was positioned along the central axis aided by vortex finder and body supports inside the hydrocyclone, in which the body supports were used to hold the solid rod centrally and reduce excessive vibration of the rod at lower parts of the hydrocyclone [13]. Using the first method, it might be difficult to ensure the solid core acting as a stationary core rod because of the serious vibration; however, the
Fig. 1. Geometry of the common type hydrocyclone.
body supports in the second method might certainly destroy the regular flow field inside the hydrocyclone. Therefore, a new fixation method was developed in this study. The solid core was inserted through the hydrocyclone via the vortex finder and the underflow pipe, and then fixed outside the overflow and underflow chambers as illustrated in Fig. 2(b), so that the rod could be fixed stably and the main flow field inside the hydrocyclone will not be disturbed. The diameter of the solid rod was selected as 6 mm to ensure no air core existed any more. To investigate the influence behavior of the air core on the hydrocyclone performance in more details, hydrocyclones with common type cone, parabola type cone and hyperbola type cone were designed as illustrated in Fig. 2. Except the shape of the cone, other geometric parameters of these hydrocyclones were all the same. The lengths of the cone sections were all 177.2 mm. For the parabola type cone, the generatrix equation was designed as follows: Z = 0.003272r 3 − 0.823
(1)
where, the coordinate center was chosen at the center of the smaller end of cone part; Z stands for the axial position (mm); and r for the radial position (mm). For the hyperbola type cone, the equation of the generatrix was designed as Z = 1259.58r −0.1 − 876.67
(2)
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Fig. 2. Schematic diagram of hydrocyclones. (a) Common type hydrocyclone (No. C10); (b) new type hydrocyclone designed with a solid core (No. C11); (c) hydrocyclone with a parabola type cone (No. C20); (d) hydrocyclone with a parabola type cone and a solid core (No. C21); (e) hydrocyclone with a hyperbola type cone (No. C30); and (f) hydrocyclone with a hyperbola type cone and a solid core (No. C31).
where, the coordinate center was at the center of the larger end of cone part, and Z and r are the same as those in Eq. (1). To observe the air core condition inside the hydrocyclones, the hydrocyclones were all made of transparent Perspex. The solid rods were made of stainless steel, and the diameters were all 6 mm. 2.2. Measurement of the flow field inside hydrocyclones A laser Doppler anemometer (2D-LDA-10, Dantec Elektronik, Denmark) was used to measure the flow fields inside hydrocyclones with and without air core, in order to provide some fundamental data for investigating the influence of the air core on hydrocyclone performance. The velocity was measured from the frequency of the Doppler burst. In the measurements, an optical compensating box was fixed around the hydrocyclone. The optical compensating boxing was of rectangular cross section and was filled with water. The hydrocyclone and the compensating box were both made of transparent Perspex and polished. The optical error was rectified during the measuring. The radial and axial components of time-averaged velocity and turbulence at certain positions inside hydrocyclones with and without air core were measured. Liquid used in the experiments was water, in which some special tracing particles were added. The measured points inside the hydrocyclone were a series of netted points. The axial position of the measured points or the axial distance from top was 10, 35, 60, 85, 110, 145, 170, 195, and 220 mm. The radial step of the measured points in the hydrocyclone
was 3 mm. Constant inlet pressure of 80 kPa was maintained in the whole experiments. 2.3. Separation experiments Solid particles were made of quartz with density of 2650 kg/m3 . The liquid phase was water. Particle size distribution was measured by a particle size analyzer (MARVERN 2000, UK), and that of the feed is shown in Fig. 3. The solid weight concentration of the feed slurry was 0.8 wt.% in all the separation experiments. Before the separation process, feed slurry with 0.8 wt.% solid concentration was prepared by adding 1.6 kg of solid particles of quartz into 200 kg of water. To maintain the solid concentration constantly in the separation process, samples were taken from both underflow and overflow with the same time
Fig. 3. Particle size distribution of the feed slurry.
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interval. A centrifugal pump was used in the experiments. The inlet pressure was also kept at 80 kPa constantly. The mass flow rates and volume flow rates of the feed slurry, overflow and underflow of hydrocyclone were measured simultaneously. To minimize the experimental errors, the measurements carried out 3–5 times and the arithmetically averaged values were taken as the results. To check the reliability of the mass balance, samples were simultaneously taken from all the feed, underflow and overflow, and then the solid weight concentrations and the particle size distributions of the samples were measured.
2.4. Definition of hydrocyclone performance indices 2.4.1. Separation efficiency Total separation efficiency is defined by the following equation: Et =
Gu Cu G e Ce
(3)
where Gu and Ge are the mass flows of underflow and feed, respectively, and Cu and Ce are the solid weight concentrations of underflow and feed.
Fig. 4. Comparison of flow field characteristics inside hydrocyclones with and without air core. (䊊) With air core; (䊉) with solid core.
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Reduced separation efficiency is defined as Et =
Et − Rf 1 − Rf
(4)
where, Et is the reduced separation efficiency, Rf is called the flow ratio that is the ratio of volume flow of underflow to that of feed, and Et is the total separation efficiency. 2.4.2. Corrected cut size Grade efficiency is featured with probability characteristics, and the grade efficiency curve is also called as probability distribution curve because the curve stands for the probability that the particles with a certain size grade could be separated into underflow from the feed of hydrocyclone. Therefore, according to the grade efficiency curve, the particle size grade related to the grade efficiency of 50% is a size grade of the particles with 50% separation probability, which is called cut size d50 [2]. The corresponding particle size related to the reduced grade efficiency is called corrected cut size d50C . 2.4.3. Separation sharpness Separation sharpness or so-called classification sharpness depends on the steepness of the grade efficiency curve. A quite common way to measure the separation sharpness is to take a ratio of two sizes corresponding to two different percentages (symmetrical around 50%) on the grade efficiency curve. In this study, the separation sharpness is defined as follows: d30C H(30/70) = (5) d70C stands for the separation sharpness, and d30C where H(30/70) and d70C for the two sizes corresponding to 30 and 70% on the reduced grade efficiency curve, respectively. The larger the separation sharpness, the better the separation or classification process.
2.4.4. Capacity Capacity or so-called throughput is the feed flow rate of the hydrocyclone.
3. Results and discussion 3.1. Flow field characteristics inside hydrocyclones with and without air core The comparison of the time-averaged velocity and turbulence profiles inside the hydrocyclones with air core and with solid core is shown in Fig. 4. With eliminating the air core by solid core, the axial velocity components in the central area nearby the entrance of the vortex finder become smaller, while those in other areas almost remains at the same magnitude level. Fig. 5 shows the schematic illustration of flow patterns inside hydrocyclones with air core and
Fig. 5. Schematic illustration of flow patterns inside hydrocyclones with and without air core. (a) With air core; (b) with solid core.
with solid core. The air in the air core always moved upwards, therefore, an upward drag force was acted on the liquid at the liquid/air interface by the air; on the other hand, when the air core was replaced by a solid core, not only was the above-mentioned upward drag force disappeared, but also a downward friction force was acted on the liquid at the liquid/solid interface by the solid core. As a result, the upward axial velocity of liquid in the central area decreased when the air core was replaced with a solid core. The decrease of the axial velocity of fluid nearby the entrance of vortex finder is beneficial to reducing the mixing of coarse particles in overflow products. Compared with that in the conventional hydrocyclone with air core, the magnitude of the radial velocity components in the hydrocyclone with solid core is obviously smaller, although the distribution profiles are similar. Because the overflow discharge velocity of liquid was heavily dependent on the upward axial velocity of liquid at the entrance of the vortex finder, the solid core reduced the overflow discharge rate because of the decrease of the upward axial velocity of liquid at the entrance of the vortex finder. As a result, the radial velocity of liquid near the entrance of vortex finder decreased. The reduction in radial velocity components is advantageous for separating fine particles, because the drag forces, which act towards the center, are reduced. Compared with those in the hydrocyclone with air core, both the radial and axial turbulence components in the hydrocyclone with solid core reduced generally. Especially in the cone section of hydrocyclone, the radial turbulence components reduced remarkably. Because of the shaking and rocking of the air core inside the conventional hydrocyclone, the symmetry and the equilibrium of the flow field for separation is negatively affected. By replacing the air core with solid core, the flow field characteristics inside
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Fig. 6. Reduced grade efficiency curves of different hydrocyclones.
the hydrocyclone was stabilized, and then the turbulence reduced. In a more stable flow field, the separation process would be sharper. That is to say, the separation performance could be enhanced by eliminating the air core. 3.2. Effect of the air core on hydrocyclone separation performance The reduced grade efficiency curves of different hydrocyclones with and without air core are illustrated in Fig. 6, and the effects of air core on hydrocyclone performance indices are shown in Fig. 7. Compared with those hydrocyclones with air core, the hydrocyclones with solid core were all featured with higher total separation efficiency, higher reduced separation efficiency, smaller corrected cut size, and higher separation sharpness, no matter what kind of cone shape was introduced. That is the experimental results showed that the replacement of the air core by the solid core improved the hydrocyclone separation performance. Compared with that of the hydrocyclone with common type cone, the performance improvement degree of the hydrocyclone with parabola type cone was more remarkable; on the other hand, that of the hydrocyclone with hyperbola cone was lower. This verified that the improvement of the hydrocyclone separation performance indices was resulted from replacing the air core by the solid core. In the hydrocyclone with parabola cone, the inner space of the lower part was larger, therefore, the fluctuation of the size and position of the air core was more serious, i.e. the rocking and shape changing of the air core were more remarkable. With the inner space of the hydrocyclone cone section decreasing, the shape and size fluctuation and the rocking of the air core weakened. The rocking and shaking of the air core might cause the instability and degrade the asymmetry and equilibrium of the liquid flow field inside the hydrocyclone. After eliminating the air
core by inserting solid core, the flow field inside the hydrocyclone could be stabilized. That is to say, the negative effect of the air core on the separation performance of the hydrocyclone with parabola cone should be the largest, that of the hydrocyclone with hyperbola cone should be the smallest, and that of the hydrocyclone with common cone should lay in the middle. Consequently, the improvement degree of the separation performance indices of the hydrocyclone with parabola cone should be the largest by removing the air core, and that with common cone should take the second place, and that with hyperbola cone should be the lowest. Why did an opposite result come out in the previous experimental investigations reported by Lee and Williams [13]? A most probable explanation could be made as follows. The negative effect on the separation efficiency might be mainly due to their “body supports” designed for fixing the solid rod. The main flow field inside the hydrocyclone might be disturbed by the body supports, and the negative effect of this on the separation efficiency might be more remarkable than the positive effect of eliminating the air core. As a result, the hydrocyclone separation efficiency was not improved, but deteriorated. This indicates that, in order to improve the separation efficiency by replacing the air core with solid insert, the main nature of the liquid flow field should not be disturbed. The experimental results showed that, the replacement of the air core by solid core always led to larger flow ratio and lower capacity in this study. In the central area, both the radial and axial velocity components of liquid flowing towards the vortex finder were reduced by replacing the air core with solid core. As a result, the overflow flowrate decreased. Correspondingly, the relative volume flowrate ratio of underflow to feed increased. The increase in the flow ratio verified again that the flow field inside the hydrocyclone was stabilized by eliminating the air core but not by reducing the cross section of the underflow, because more underflow discharged when the air core was replaced by the solid core. In fact, the solid core did not decrease the cross section area for the overflow and underflow discharges remarkably, because the solid core just occupied the space where the air core existed (as illustrated in Fig. 5). The reasons for the lower capacity might be explained as follows. The overflow rate, which occupied the main part of the total liquid flow, decreased due to the above-mentioned cause, i.e. the overflow discharge velocity was decreased by the solid core. Therefore, a lower capacity was resulted from the decrease of the overflow rate. As to the influence degree of replacing the air core by a solid core on the flow rates, it was the most remarkable in the hydrocyclone with a common type cone, and the smallest in that with a parabola type cone. In summary, by replacing the air core with solid core, the flow field characteristics inside the hydrocyclone became more suitable for separation, which resulted in higher separation efficiency and sharpness.
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Fig. 7. Performance comparison between hydrocyclones with and without air core. (a) Total separation efficiency; (b) reduced separation efficiency; (c) corrected cut size; (d) separation sharpness; (e) flow ratio; and (f) capacity.
4. Conclusions By introducing a solid core, the air core inside the hydrocyclone was eliminated effectively. By eliminating the air core, the radial and axial velocity components in the area that just under the vortex finder, and the radial and axial
turbulence components were all reduced, i.e. the flow field characteristics inside the hydrocyclone became more beneficial for the separation process. The separation performance of the hydrocyclone was improved effectively by eliminating the air core with a solid core. Compared with the common type hydrocyclone with air core, the hydrocyclone
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with solid core was proven to be featured with higher total separation efficiency, larger reduced separation efficiency, smaller corrected cut size, and higher separation sharpness. With increasing the inner space of the hydrocyclone cone, the separation performance improvement became more remarkable.
Acknowledgements The research was supported by the Scientific Foundation of State Key Laboratory of Hydraulics on High-Speed Flows (Grant No. 0104).
Appendix A. Nomenclature Ce Cu d d30C d50 d50C d70C Et Et Ge Gu G (d) H(30/70) r Rf Z
solid weight concentration of feed (%) solid weight concentration of underflow (%) particle size (m) particle size corresponding to 30% on the reduced grade efficiency curve (m) cut size (m) corrected cut size (m) particle size corresponding to 70% on the reduced grade efficiency curve (m) total separation efficiency (%) reduced separation efficiency (%) mass flow of feed (kg/s) mass flow of underflow (kg/s) reduced grade efficiency (%) separation sharpness (–) radial position (mm) flow ratio (%) axial position (mm)
References [1] L.Y. Chu, Q. Luo, Hydrocyclone with high sharpness of separation, Filtr. Sep. 31 (1994) 733. [2] L. Svarovsky, Hydrocyclones, Holt, Rinehart and Winston Ltd, London, 1984. [3] L.Y. Chu, W.M. Chen, Research on the motion of solid particles in a hydrocyclone, Sep. Sci. Technol. 28 (1993) 1875. [4] L.Y. Chu, W.M. Chen, X.Z. Lee, Effects of geometric and operating parameters and feed characters on the motion of solid particles in hydrocyclones, Sep. Purif. Technol. 26 (2002) 237. [5] M.R. Davidson, An adaptive method of predicting the air-core diameter for numerical-models of hydrocyclone flow, Int. J. Miner. Process. 43 (1995) 167. [6] T. Dyakowski, R.A. Williams, Prediction of air-core size and shape in a hydrocyclone, Int. J. Miner. Process. 43 (1995) 1. [7] J. Romero, R. Sampaio, A numerical model for prediction of the air-core shape of hydrocyclone flow, Mechan. Res. Commun. 26 (1999) 379. [8] F.J.W. Podd, H.I. Schlaberg, B.S. Hoyle, Model-based parameterisation of a hydrocyclone air-core, Ultrasonics 38 (2000) 804. [9] F. Concha, A. Barrientos, J. Montero, R. Sampaio, Air core and roping in Hydrocyclones, Int. J. Miner. Process. 44–45 (1996) 743. [10] R.A. Williams, O.M. Ilyas, T. Dyakowski, F.J. Dickin, J.A. Gutierrez, M. Wang, M.S. Beck, C. Shah, A. Rushton, Air-core imaging in cyclonic separators—implications for separator design and modeling, Chem. Eng. J. Biochem. Eng. J. 56 (1995) 135. [11] P.R. Steffens, W.J. Whiten, S. Appleby, J. Hitchins, Prediction of air-core diameters for hydrocyclones, Int. J. Miner. Process. 39 (1993) 61. [12] J.R. Xu, Q. Luo, J.C. Qiu, Studying the flow field in a hydrocyclone with no forced vortex, Part I: Average velocity, Filtr. Sep. 27 (1990) 276. [13] M.S. Lee, R.A. Williams, Performance-characteristics within a modified hydrocyclone, Miner. Eng. 6 (1993) 743. [14] L.Y. Chu, W.M. Chen, X.Z. Lee, Effect of structural modification on hydrocyclone performance, Sep. Purif. Technol. 21 (2000) 71. [15] L.Y. Chu, W.M. Chen, X.Z. Lee, Enhancement of hydrocyclone performance by controlling the inside turbulence structure, Chem. Eng. Sci. 57 (2002) 207. [16] K. Rietema, Performance and design of hydrocyclones. IV: Design of hydrocyclones, Chem. Eng. Sci 15 (1961) 320.
Enhancement of hydrocyclone separation performance by eliminating the air core Liang-Yin Chu a,∗ , Wei Yu a , Guang-Jin Wang a , Xian-Tao Zhou a , Wen-Mei Chen a , Guang-Qing Dai b b
a School of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065, China State Key Laboratory of Hydraulics on High-Speed Flows, Chengdu, Sichuan 610065, China
Received 21 July 2003; received in revised form2613February January 2004 2004; accepted 13 January 2004 Available online
Abstract A new hydrocyclone was designed with a solid core fixed along the central axis in this study. By introducing the solid core, the air core inside the hydrocyclone could be eliminated effectively. Comprehensive effects of eliminating the air core by the solid core on the hydrocyclone performance indices were experimentally investigated. To examine the influence mechanism of air core on the separation performance, a Laser Doppler Anemometer (LDA) was used to investigate the turbulent flow field inside hydrocyclones with and without air cores. The results showed that the radial and axial velocity components in the area near the entrance of the vortex finder, and the radial and axial turbulence components were all reduced by eliminating the air core, i.e. the flow field characteristics inside the hydrocyclone with solid core became more suitable for the separation process. By replacing the air core with solid core, the hydrocyclone separation performance was improved effectively. Comparing the hydrocyclones with air core and solid core, it was proved to be featured with higher total separation efficiency, larger reduced separation efficiency, smaller corrected cut size and higher separation sharpness, although the hydrocyclone cone shape changed from common type, to parabola type, and to hyperbola type. By increasing the inner space of the hydrocyclone cone, the improvement of separation performance became more remarkable. © 2004 Elsevier B.V. All rights reserved. Keywords: Hydrocyclone; Separation; Turbulence; Powder technology; Hydrodynamics
1. Introduction Hydrocyclones are getting more and more interest from various industries, because of their obvious advantages such as simple structure, low cost, large capacity and small volume. Besides a large amount of applications in mineral processing, hydrocyclone separation technique has been used in an increasing number of applications recently in environmental engineering, petrochemical engineering, food engineering, electrochemical engineering, bioengineering, pulping process and so on. It is well known that the hydrocyclone separation performance is determined by the fluid flow characteristics inside the hydrocyclone. Because of the inherent fluid flow characteristics inside the common hydrocyclone, the separation ∗ Corresponding author. Tel.: +86-28-8546-0682; fax: +86-28-8540-4976. E-mail address: [email protected] (L.-Y. Chu).
0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.01.002
process in the common hydrocyclone is always accompanied by some inherent disadvantages, such as unsatisfactory separation efficiency and sharpness [1]. Although the geometry and operation of hydrocyclones is simple in nature, explaining the detailed mechanisms by which they work has proved to be extremely complicated [2–4]. In the conventional hydrocyclone, there generally exist outer and inner helical flows, a circulation flow, a short-circuit flow and an air core. The air core has a large effect on the hydrocyclone flow field and the separation performance; consequently a lot of researches have been made on it previously [5–15]. Among the previous investigations, most of them were just concerned with the prediction and measurement of the air-core diameter and shape [5–11]. Only a few studies have been made on the influence of the air core on hydrocyclone separation performance. Xu et al. [12] reported that the hydrocyclone efficiency could be improved by eliminating the forced vortex (the forced vortex inside the hydrocyclone including air core and liquid forced vortex) with a
1442
L.-Y. Chu et al. / Chemical Engineering and Processing 43 (2004) 1441–1448
solid rod inserted from the vortex finder into the hydrocyclone; however, Lee and Williams [13] reported an opposite result that the solid rod degraded the hydrocyclone efficiency. Recently, the authors have investigated the effects of various central inserts on hydrocyclone separation efficiency [14,15]. The results also showed that the insertion of a cylindrical rod could improve the separation efficiency [14]. Why two opposite results came out about the effect of replacing the air core with a solid rod on the hydrocyclone efficiency? To answer the question, a further systematical investigation should be carried out on both the flow field and the separation performance of the hydrocyclone. However, a comprehensive understanding of the influence of the air core on both the flow field characteristics inside the hydrocyclone and the hydrocyclone separation performance is still lacking. The objective of this study is to understand the comprehensive effect of the air core on both the flow field and the separation performance of hydrocyclones by replacing the air core with a solid core. The structure design of the solid core will be different from those reported previously. Hydrocyclones with different cone shapes will be also introduced in this study to ascertain the influence behavior of the air core on the performance. A Laser Doppler Anemometer (LDA) will be used to investigate the turbulent flow field inside hydrocyclones with and without air cores, in order to probe into the influence mechanism of the existence of air core on the performance. The hydrocyclone performance indices will include total separation efficiency, reduced separation efficiency, cut size, separation sharpness, flow ratio and capacity, so that useful guidance could be obtained for designing efficient hydrocyclones.
2. Experimental 2.1. Apparatus A conventional type hydrocyclone was designed according to Rietema’s optimum geometry for separation [16]. The hydrocyclone geometry is shown in Fig. 1. With the same geometric parameters, a new hydrocyclone was designed with a solid core as shown in Fig. 2(b). The fixation of the solid core here was designed different from those reported in previous investigations. Previously two main fixation methods were reported as follows. (1) The solid core was just inserting into the hydrocyclone from the vortex finder and then fixing the solid core outside the vortex finder, that is, the solid core was fixed in the manner of a cantilever [12]; and (2) the solid core was positioned along the central axis aided by vortex finder and body supports inside the hydrocyclone, in which the body supports were used to hold the solid rod centrally and reduce excessive vibration of the rod at lower parts of the hydrocyclone [13]. Using the first method, it might be difficult to ensure the solid core acting as a stationary core rod because of the serious vibration; however, the
Fig. 1. Geometry of the common type hydrocyclone.
body supports in the second method might certainly destroy the regular flow field inside the hydrocyclone. Therefore, a new fixation method was developed in this study. The solid core was inserted through the hydrocyclone via the vortex finder and the underflow pipe, and then fixed outside the overflow and underflow chambers as illustrated in Fig. 2(b), so that the rod could be fixed stably and the main flow field inside the hydrocyclone will not be disturbed. The diameter of the solid rod was selected as 6 mm to ensure no air core existed any more. To investigate the influence behavior of the air core on the hydrocyclone performance in more details, hydrocyclones with common type cone, parabola type cone and hyperbola type cone were designed as illustrated in Fig. 2. Except the shape of the cone, other geometric parameters of these hydrocyclones were all the same. The lengths of the cone sections were all 177.2 mm. For the parabola type cone, the generatrix equation was designed as follows: Z = 0.003272r 3 − 0.823
(1)
where, the coordinate center was chosen at the center of the smaller end of cone part; Z stands for the axial position (mm); and r for the radial position (mm). For the hyperbola type cone, the equation of the generatrix was designed as Z = 1259.58r −0.1 − 876.67
(2)
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Fig. 2. Schematic diagram of hydrocyclones. (a) Common type hydrocyclone (No. C10); (b) new type hydrocyclone designed with a solid core (No. C11); (c) hydrocyclone with a parabola type cone (No. C20); (d) hydrocyclone with a parabola type cone and a solid core (No. C21); (e) hydrocyclone with a hyperbola type cone (No. C30); and (f) hydrocyclone with a hyperbola type cone and a solid core (No. C31).
where, the coordinate center was at the center of the larger end of cone part, and Z and r are the same as those in Eq. (1). To observe the air core condition inside the hydrocyclones, the hydrocyclones were all made of transparent Perspex. The solid rods were made of stainless steel, and the diameters were all 6 mm. 2.2. Measurement of the flow field inside hydrocyclones A laser Doppler anemometer (2D-LDA-10, Dantec Elektronik, Denmark) was used to measure the flow fields inside hydrocyclones with and without air core, in order to provide some fundamental data for investigating the influence of the air core on hydrocyclone performance. The velocity was measured from the frequency of the Doppler burst. In the measurements, an optical compensating box was fixed around the hydrocyclone. The optical compensating boxing was of rectangular cross section and was filled with water. The hydrocyclone and the compensating box were both made of transparent Perspex and polished. The optical error was rectified during the measuring. The radial and axial components of time-averaged velocity and turbulence at certain positions inside hydrocyclones with and without air core were measured. Liquid used in the experiments was water, in which some special tracing particles were added. The measured points inside the hydrocyclone were a series of netted points. The axial position of the measured points or the axial distance from top was 10, 35, 60, 85, 110, 145, 170, 195, and 220 mm. The radial step of the measured points in the hydrocyclone
was 3 mm. Constant inlet pressure of 80 kPa was maintained in the whole experiments. 2.3. Separation experiments Solid particles were made of quartz with density of 2650 kg/m3 . The liquid phase was water. Particle size distribution was measured by a particle size analyzer (MARVERN 2000, UK), and that of the feed is shown in Fig. 3. The solid weight concentration of the feed slurry was 0.8 wt.% in all the separation experiments. Before the separation process, feed slurry with 0.8 wt.% solid concentration was prepared by adding 1.6 kg of solid particles of quartz into 200 kg of water. To maintain the solid concentration constantly in the separation process, samples were taken from both underflow and overflow with the same time
Fig. 3. Particle size distribution of the feed slurry.
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interval. A centrifugal pump was used in the experiments. The inlet pressure was also kept at 80 kPa constantly. The mass flow rates and volume flow rates of the feed slurry, overflow and underflow of hydrocyclone were measured simultaneously. To minimize the experimental errors, the measurements carried out 3–5 times and the arithmetically averaged values were taken as the results. To check the reliability of the mass balance, samples were simultaneously taken from all the feed, underflow and overflow, and then the solid weight concentrations and the particle size distributions of the samples were measured.
2.4. Definition of hydrocyclone performance indices 2.4.1. Separation efficiency Total separation efficiency is defined by the following equation: Et =
Gu Cu G e Ce
(3)
where Gu and Ge are the mass flows of underflow and feed, respectively, and Cu and Ce are the solid weight concentrations of underflow and feed.
Fig. 4. Comparison of flow field characteristics inside hydrocyclones with and without air core. (䊊) With air core; (䊉) with solid core.
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Reduced separation efficiency is defined as Et =
Et − Rf 1 − Rf
(4)
where, Et is the reduced separation efficiency, Rf is called the flow ratio that is the ratio of volume flow of underflow to that of feed, and Et is the total separation efficiency. 2.4.2. Corrected cut size Grade efficiency is featured with probability characteristics, and the grade efficiency curve is also called as probability distribution curve because the curve stands for the probability that the particles with a certain size grade could be separated into underflow from the feed of hydrocyclone. Therefore, according to the grade efficiency curve, the particle size grade related to the grade efficiency of 50% is a size grade of the particles with 50% separation probability, which is called cut size d50 [2]. The corresponding particle size related to the reduced grade efficiency is called corrected cut size d50C . 2.4.3. Separation sharpness Separation sharpness or so-called classification sharpness depends on the steepness of the grade efficiency curve. A quite common way to measure the separation sharpness is to take a ratio of two sizes corresponding to two different percentages (symmetrical around 50%) on the grade efficiency curve. In this study, the separation sharpness is defined as follows: d30C H(30/70) = (5) d70C stands for the separation sharpness, and d30C where H(30/70) and d70C for the two sizes corresponding to 30 and 70% on the reduced grade efficiency curve, respectively. The larger the separation sharpness, the better the separation or classification process.
2.4.4. Capacity Capacity or so-called throughput is the feed flow rate of the hydrocyclone.
3. Results and discussion 3.1. Flow field characteristics inside hydrocyclones with and without air core The comparison of the time-averaged velocity and turbulence profiles inside the hydrocyclones with air core and with solid core is shown in Fig. 4. With eliminating the air core by solid core, the axial velocity components in the central area nearby the entrance of the vortex finder become smaller, while those in other areas almost remains at the same magnitude level. Fig. 5 shows the schematic illustration of flow patterns inside hydrocyclones with air core and
Fig. 5. Schematic illustration of flow patterns inside hydrocyclones with and without air core. (a) With air core; (b) with solid core.
with solid core. The air in the air core always moved upwards, therefore, an upward drag force was acted on the liquid at the liquid/air interface by the air; on the other hand, when the air core was replaced by a solid core, not only was the above-mentioned upward drag force disappeared, but also a downward friction force was acted on the liquid at the liquid/solid interface by the solid core. As a result, the upward axial velocity of liquid in the central area decreased when the air core was replaced with a solid core. The decrease of the axial velocity of fluid nearby the entrance of vortex finder is beneficial to reducing the mixing of coarse particles in overflow products. Compared with that in the conventional hydrocyclone with air core, the magnitude of the radial velocity components in the hydrocyclone with solid core is obviously smaller, although the distribution profiles are similar. Because the overflow discharge velocity of liquid was heavily dependent on the upward axial velocity of liquid at the entrance of the vortex finder, the solid core reduced the overflow discharge rate because of the decrease of the upward axial velocity of liquid at the entrance of the vortex finder. As a result, the radial velocity of liquid near the entrance of vortex finder decreased. The reduction in radial velocity components is advantageous for separating fine particles, because the drag forces, which act towards the center, are reduced. Compared with those in the hydrocyclone with air core, both the radial and axial turbulence components in the hydrocyclone with solid core reduced generally. Especially in the cone section of hydrocyclone, the radial turbulence components reduced remarkably. Because of the shaking and rocking of the air core inside the conventional hydrocyclone, the symmetry and the equilibrium of the flow field for separation is negatively affected. By replacing the air core with solid core, the flow field characteristics inside
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Fig. 6. Reduced grade efficiency curves of different hydrocyclones.
the hydrocyclone was stabilized, and then the turbulence reduced. In a more stable flow field, the separation process would be sharper. That is to say, the separation performance could be enhanced by eliminating the air core. 3.2. Effect of the air core on hydrocyclone separation performance The reduced grade efficiency curves of different hydrocyclones with and without air core are illustrated in Fig. 6, and the effects of air core on hydrocyclone performance indices are shown in Fig. 7. Compared with those hydrocyclones with air core, the hydrocyclones with solid core were all featured with higher total separation efficiency, higher reduced separation efficiency, smaller corrected cut size, and higher separation sharpness, no matter what kind of cone shape was introduced. That is the experimental results showed that the replacement of the air core by the solid core improved the hydrocyclone separation performance. Compared with that of the hydrocyclone with common type cone, the performance improvement degree of the hydrocyclone with parabola type cone was more remarkable; on the other hand, that of the hydrocyclone with hyperbola cone was lower. This verified that the improvement of the hydrocyclone separation performance indices was resulted from replacing the air core by the solid core. In the hydrocyclone with parabola cone, the inner space of the lower part was larger, therefore, the fluctuation of the size and position of the air core was more serious, i.e. the rocking and shape changing of the air core were more remarkable. With the inner space of the hydrocyclone cone section decreasing, the shape and size fluctuation and the rocking of the air core weakened. The rocking and shaking of the air core might cause the instability and degrade the asymmetry and equilibrium of the liquid flow field inside the hydrocyclone. After eliminating the air
core by inserting solid core, the flow field inside the hydrocyclone could be stabilized. That is to say, the negative effect of the air core on the separation performance of the hydrocyclone with parabola cone should be the largest, that of the hydrocyclone with hyperbola cone should be the smallest, and that of the hydrocyclone with common cone should lay in the middle. Consequently, the improvement degree of the separation performance indices of the hydrocyclone with parabola cone should be the largest by removing the air core, and that with common cone should take the second place, and that with hyperbola cone should be the lowest. Why did an opposite result come out in the previous experimental investigations reported by Lee and Williams [13]? A most probable explanation could be made as follows. The negative effect on the separation efficiency might be mainly due to their “body supports” designed for fixing the solid rod. The main flow field inside the hydrocyclone might be disturbed by the body supports, and the negative effect of this on the separation efficiency might be more remarkable than the positive effect of eliminating the air core. As a result, the hydrocyclone separation efficiency was not improved, but deteriorated. This indicates that, in order to improve the separation efficiency by replacing the air core with solid insert, the main nature of the liquid flow field should not be disturbed. The experimental results showed that, the replacement of the air core by solid core always led to larger flow ratio and lower capacity in this study. In the central area, both the radial and axial velocity components of liquid flowing towards the vortex finder were reduced by replacing the air core with solid core. As a result, the overflow flowrate decreased. Correspondingly, the relative volume flowrate ratio of underflow to feed increased. The increase in the flow ratio verified again that the flow field inside the hydrocyclone was stabilized by eliminating the air core but not by reducing the cross section of the underflow, because more underflow discharged when the air core was replaced by the solid core. In fact, the solid core did not decrease the cross section area for the overflow and underflow discharges remarkably, because the solid core just occupied the space where the air core existed (as illustrated in Fig. 5). The reasons for the lower capacity might be explained as follows. The overflow rate, which occupied the main part of the total liquid flow, decreased due to the above-mentioned cause, i.e. the overflow discharge velocity was decreased by the solid core. Therefore, a lower capacity was resulted from the decrease of the overflow rate. As to the influence degree of replacing the air core by a solid core on the flow rates, it was the most remarkable in the hydrocyclone with a common type cone, and the smallest in that with a parabola type cone. In summary, by replacing the air core with solid core, the flow field characteristics inside the hydrocyclone became more suitable for separation, which resulted in higher separation efficiency and sharpness.
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Fig. 7. Performance comparison between hydrocyclones with and without air core. (a) Total separation efficiency; (b) reduced separation efficiency; (c) corrected cut size; (d) separation sharpness; (e) flow ratio; and (f) capacity.
4. Conclusions By introducing a solid core, the air core inside the hydrocyclone was eliminated effectively. By eliminating the air core, the radial and axial velocity components in the area that just under the vortex finder, and the radial and axial
turbulence components were all reduced, i.e. the flow field characteristics inside the hydrocyclone became more beneficial for the separation process. The separation performance of the hydrocyclone was improved effectively by eliminating the air core with a solid core. Compared with the common type hydrocyclone with air core, the hydrocyclone
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with solid core was proven to be featured with higher total separation efficiency, larger reduced separation efficiency, smaller corrected cut size, and higher separation sharpness. With increasing the inner space of the hydrocyclone cone, the separation performance improvement became more remarkable.
Acknowledgements The research was supported by the Scientific Foundation of State Key Laboratory of Hydraulics on High-Speed Flows (Grant No. 0104).
Appendix A. Nomenclature Ce Cu d d30C d50 d50C d70C Et Et Ge Gu G (d) H(30/70) r Rf Z
solid weight concentration of feed (%) solid weight concentration of underflow (%) particle size (m) particle size corresponding to 30% on the reduced grade efficiency curve (m) cut size (m) corrected cut size (m) particle size corresponding to 70% on the reduced grade efficiency curve (m) total separation efficiency (%) reduced separation efficiency (%) mass flow of feed (kg/s) mass flow of underflow (kg/s) reduced grade efficiency (%) separation sharpness (–) radial position (mm) flow ratio (%) axial position (mm)
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