ARTICLE pubs.acs.org/IECR
Simulation Analysis of Multiphase Flow and Performance of Hydrocyclones at Different Atmospheric Pressures Yanxia Xu, Xingfu Song,* Ze Sun, Guimin Lu, Ping Li, and Jianguo Yu* National Engineering Research Center for Integrated Utilization of Salt Lake Resources, East China University of Science and Technology, Shanghai 200237, China ABSTRACT: A hydrocyclone, as a common liquid/solid grading instrument, was chosen to separate calcium sulfate particles from crude carnallite during the KCl production process on the Tibetan Plateau in China, because CaSO4 particles are independent of KCl particles and have a smaller particle size distribution. The local altitude on the Tibetan Plateau in China is over 3000 m, so the effects of low atmospheric pressure on the separation performance of the hydrocyclone should be considered. In this article, the computational fluid dynamics (CFD) simulation technique was used to investigate the hydrodynamics and particles separation performance of an industrial hydrocyclone with a 428-mm diameter at both plain and plateau atmospheric pressures. In this CFD approach, the Reynolds stress model (RSM) was used to describe the turbulent fluid flow, the volume of fluid (VOF) multiphase model was used to simulate the interface between the liquid phase and the air core, and the stochastic Lagrangian model was used to track the particle flow. The mathematical models deveoped for the industrial hydrocyclone were tested by comparing the predicted results with the flow fields measured by Hsieh (Ph.D. Thesis, The University of Utah, Salt Lake City, UT, 1988). According to the simulation results, the environmental atmospheric pressures on the plain and plateau had effects mainly on the flow field inside the air core and near the interface between the air core and the liquid phase. It was found the direction of the axial velocity on the cylinder part and the values of the tangential velocity changed under the different environmental atmospheric pressures. When the industrial hydrocyclone was operated in the plateau environment, the separation efficiency for small particles decreased about 10% at the overflow, which was not good for CaSO4 removal, but there was no effect on the particles size larger than 350 μm, and more energy was consumed, although the difference in the split ratio was small.
1. INTRODUCTION Potassium chloride (KCl) is an indispensable potash fertilizer and chemical raw material. In China, Qinghai Salt Lake, which is the largest national salt lake located in the northwest of China, is an important potassium production base. During the KCl production14 process, the content of calcium sulfate (CaSO4), with a small crystal size, lower density, and range of 1.32.6%, has serious effects on the grade of KCl, resulting in only agricultural KCl being produced. Thus, an effective technique for separating CaSO4 particles from crude carnallites is needed. The cyclone is an important centrifugal separation and classification apparatus. In the past, various cyclones58 have been developed for different industrial needs. In this work, a hydrocyclone,911 as a solid/liquid classification method, was selected to remove the CaSO4 impurity from carnallite in a 100000 ton/year KCl production process by reverse flotation and cold crystallization, because of its compact dimensions, operational simplicity, high separation efficiency, and capacity. To detect its complex internal flow behavior, computational fluid dynamics (CFD)1216 was applied. In the past several years, significant progress had been made in the mathematical modeling of hydrocyclone processes based on computational fluid dynamics (CFD). Boysan et al.17 developed one of the first CFD models and showed that the standard kε turbulence model is inadequate to simulate swirling flow. Delgadillo et al.18 compared three turbulenceclosure models, namely, the renormalization group kε model, the Reynolds stress model (RSM), and the large-eddy simulation model. Thus, recent studies1922 have indicated r 2011 American Chemical Society
that the RSM can improve the accuracy of numerical solutions. Furthermore, large-eddy simulation has also been taken into consideration.2325 On this basis, specific applications were investigated, namely, particle separation efficiency, hydrocyclone dimension design, air core, and so on. For instance, through CFD, Schuetz et al.26 and Cullivan et al.27 investigated the complex internal flow and separation efficiency, Brennan et al.28 predicted the cut size of a hydrocyclone, Bhaskar et al.29 studied fly-ash particle classification in hydrocyclones, and Gupta et al.30 studied the mechanism of air-core and vortex formation in a hydrocyclone. Wang et al.3133 presented a numerical study of gasliquidsolid multiphase flow in hydrocyclones with different dimensions of body construction and also study the “fish-hook” phenomenon in hydrocyclones. Delgadillo et al.34 designed a hydrocyclone using CFD, Chu et al.35 put forward a new hydrocyclone designed with a solid core fixed along the central axis and presented its separation performance, Olson et al.36 optimized a hydrocyclone design using a CFD model, and Hwang et al.37 also studied the effects of hydrocyclone structure on separation efficiency. Moreover, Narasimha et al.23 predicted the air-core diameter and shape on the basis of the CFD simulations, Evan et al.38 studied the flow in a hydrocyclone operating with an air core and an inserted metal rod, and Sripriya et al.39 also studied the performance Received: May 29, 2011 Accepted: November 22, 2011 Revised: November 3, 2011 Published: November 22, 2011 443
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Figure 2. Crystal size distribution of the crude potassium chloride product.
2. MATHEMATICAL MODEL Figure 1 shows a schematic of the industrial hydrocyclone with liquid/solid classification used to remove CaSO4 particles from carnallite, and Table 1 lists its geometrical parameters. During the KCl production process, the hydrocyclone device is placed on the low-sodium carnallite construction section, and the slurry after flotation, consisting of brine and crude potassium chloride product, is input into the hydrocyclone. The mass flow is about 500 m3/h, and the crystal size distribution of the crude potassium chloride product is shown in Figure 2. As shown in this figure, the particles smaller than 74 μm are calcium sulfate particles, whereas the larger particles are the potassium chloride product. Through the hydrocyclone effect, the particles with different diameters are separated. The slurry in the underflow with a small amount of CaSO4 is directed to the next step, and the concentration of CaSO4 particles in the overflow is removed from the crude potassium chloride product. However, the two outlets, namely, the vortex finder and the spigot, are connected with the atmosphere. Thus, it is necessary to study whether the low atmospheric pressure on the plateau has effects on the multiphase flow and the performance of the hydrocyclone. 2.1. Model Description. The governing equations for the velocity field in an incompressible fluid can be written as
Figure 1. (a) Schematic and (b) grid representations of the original hydrocyclone.
Table 1. Geometry of the Hydrocyclone parameter
symbol
value (mm)
Dc Di
428 138
vortex-finder diameter
Do
180
spigot diameter
Du
152
vortex-finder length
Lv
271
cylindrical-part length
Lc
552
included angle
α
20°
body diameter inlet diameter
and flow characteristics in the presence and absence of an air core. As a whole, through CFD simulations, the multiphase flow and separation performance of a hydrocyclone can be obtained distinctly, and a number of variations and modifications of the geometrical variables in the basic design and operating parameters of hydrocyclones have been examined by various investigators for different industrial applications. To date, however, little research has been done on the hydrodynamics and separation performance of hydrocyclones when operating at different environmental atmospheric pressures. In this article, a hydrocyclone, as a common liquid/solid grading instrument, was chosen to separate calcium sulfate particles from crude carnallite during the KCl production process on the Tibetan Plateau in China, because CaSO4 particles are independent of KCl particles and have a smaller particle size distribution. The local altitude on the Tibetan Plateau in China is over 3000 m, so the effects of low atmospheric pressure on the hydrodynamics and separation performance of the hydrocyclone should be considered. Here, the effects of the environmental atmospheric pressure on the multiphase flow field and separation efficiency of the hydrocyclone were analyzed by the CFD simulation technique. According to the simulation results, the feasibility of removal CaSO4 particles from carnallite by an industrial hydrocyclone on the Tibetan Plateau was evaluated.
∂F ∂p þ ðFui Þ ¼ 0 ∂t ∂xi ∂ðFui Þ ∂ þ ðFui uj Þ ∂t ∂xj " !# ∂uj ∂p ∂ ∂ui ∂ þ μ þ ð Fuj ui Þ ¼ þ ∂xi ∂xj ∂xj ∂xj ∂xi
ð1Þ
ð2Þ
The velocity can be decomposed into its mean and fluctuating components 0
ui ¼ ui þ ui
ð3Þ
where ui is the mean velocity and u0i is the fluctuating velocity (i = 1, 2, 3) and the Reynolds stress term Fu0i u0j includes the turbulence closure, which must be modeled in order to close eq 2. Although the large eddy simulation (LES) shows 444
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considerable potential, it is enormously computationally expensive, and a subgrid-scale model accounting for the effects of particles has not yet been used in LES simulations. Meanwhile, the Reynolds stress model (RSM) has been shown to predict anisotropic turbulence well. Thus, in this work, the RSM was selected instead of an LES. According to the RSM, Fu0i u0j is modeled by the equation ∂ ∂ ðFuk u0i u0j Þ ¼ DT, ij þ Pij þ ϕij þ εij ðFu0i u0j Þ þ ∂t ∂xk
which is defined as Rep ¼
ð4Þ
where ζ is a normally distributed random number and the remainder of the right-hand side is the local root-mean-square value of the velocity fluctuations. Because the kinetic energy of turbulence is known at each point in the flow, these values of the root-mean-square fluctuating components can be defined (assuming isotropy) as qffiffiffiffiffiffi qffiffiffiffiffiffi qffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 2 2 0 0 u ¼ v ¼ w0 2 ¼ 2k=3 ð12Þ
ð5Þ
where αk is the volume fraction of the kth phase, which varies between 0 and 1, and uj is the velocity component in direction j. A single momentum equation is solved throughout the domain, and the resulting velocity field is shared between the two phases. This momentum equation is dependent on the volume fraction of fluid phase with the properties F and μ, given by
The particle is assumed to interact with the fluid-phase eddy over the smaller of the eddy lifetime and the eddy crossing time. More details about the mathematics model can be found in ref 19. Figure 1b shows the computational domain of the model. The whole computational domain is divided into 327174 unstructured hexahedron grids. The grids are refined near the walls and vortex finder. The “velocity inlet” boundary condition is used at the hydrocyclone inlets, and both outlets used the “pressure outlet” condition. The simulations were conducted using Fluent 6.3 software. Second-order upwinding and the SIMPLE pressure velocity coupling algorithm were used. The convergence strategy used the unsteady solver, and the time step was chosen in the range of 10 4103 s. Trial tests showed that there was no sensitivity of the results to the time step in this range. In this work, the time step was chosen as 103 s. 2.2. Simulation Conditions. Table 2 lists all of the simulation conditions investigated. The key different condition between the plateau and the plain is the atmosphere. The pressures at the two outlets (the vortex finder and the spigot) were set to 1 and 0.7 atm, which are equal to the plain and plateau atmospheric pressures, respectively. The inlet brine velocity and particle velocity were both 7.29 m/s. Particles with a density of 2960 kg/m3 were injected at the inlet, and the volume percentage of particles in the feed was 5%. Therefore, particleparticle interactions and the effects of the particle volume fraction on the liquid phase were negligible. The crystal size distribution of the crude potassium chloride product shown in Figure 2 is well described by the RosinRammler model in Figure 3.
" !# ∂uj ∂ ∂ ∂p ∂ ∂ui ðFui uj Þ ¼ þ μ þ ðFuj Þ þ þ Fgi ∂xj ∂xi ∂t ∂xi ∂xi ∂xj
ð6Þ In general, for a k-phase system, the volume fraction averaged density F takes on the form F¼
∑ αk Fk
ð7Þ
All other properties (e.g., viscosity) are computed in the same way. The implicit interface tracking algorithm in the VOF is used to obtain numerical solution. The additional model used in the hydrocyclone problem is the particle trajectory prediction. The motion of a particle is described by the stochastic Lagrangian multiphase flow model. The buoyancy force and liquid drag force on particles are calculated in a Lagrangian reference frame as dB up
¼ FD ð B u B u pÞ þ dt
gBðFp FÞ Fp
ð8Þ
where the first term on the right-hand side is the drag force per unit particle mass and FD ¼
Rep 18μ CD 2 24 d p Fp
ð10Þ
The turbulent dispersion of particles in the stochastic tracking is predicted by integrating the trajectory equations for individual particles, using the instantaneous fluid velocity, u + u0 , along the particle path during the integration. A stochastic method (random-walk model) is used to determine the instantaneous gas velocity. In the discrete-random-walk (DRW) model, the fluctuating velocity components are discrete piecewise-constant functions of time. Their random value is kept constant over an interval of time given by the characteristic lifetime of the eddies. In the DRW model, the interaction of a particle with a succession of discrete stylized fluid-phase turbulent eddies is simulated. Each eddy is characterized by a Gaussian distribution qffiffiffiffiffiffi ð11Þ u0 ¼ ζ u0 2
where F, ui, u0i , and xi are the liquid density, velocity, velocity fluctuation, and positional length, respectively. The two terms on the left are the local time derivative of the stress and the convective transport term, respectively. The tangential acceleration applied to the flow creates a high centrifugal force that pushes the fluid to the wall, creating a low pressure in the central axis. The low pressure in the core of the hydrocyclone gives the right conditions to suck air into the system. The interface is modeled with the volume of fluid (VOF) multiphase model, whose model equations are ∂αk ∂αk þ uj ¼0 ∂t ∂xi
Fdp ðup uÞ μ
ð9Þ
3. RESULTS AND DISCUSSION
Here, uBp is the particle velocity, uB is the fluid-phase velocity, Fp is the density of particles, and dp is the diameter of the particles. CD is the drag coefficient and Rep is the relative Reynolds number,
3.1. Model Validation. It was necessary to validate the accuracy of the mathematical models developed in this article, 445
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Table 2. Parameters of the Hydrocyclone Simulation Conditions properties of the liquid phase (brine)
Table 3. Geometry of Hsieh’s Hydrocyclone parameter
F = 1280 kg/m3, μ = 0.0071 mPa 3 s
properties of the particle phase
F = 2960 kg/m
volume percentage of particles in the feed
5 vol %
crystal size distribution
described with the
3
RosinRammler model pressure at the two outlets
0.7 atm, 1.0 atm
(vortex finder and spigot) velocity of the inlet brine and particles
7.29 m/s
symbol
value (mm)
body diameter
Dc
75
inlet diameter
Di
25
vortex-finder diameter
Do
25
spigot diameter
Du
12.5
vortex-finder length
Lv
50
cylindrical-part length
Lc
75
included angle
α
20°
Figure 3. Comparison of RosinRammler model and experiment.
before using them for numerical experiments. This was done by comparing the predicted and experimentally measured flow fields including the tangential and axial velocity distributions at different axial locations. Many experimental studies on the flow fields inside hydrocyclones have been performed,40,41 and the model selected was taken from the work of Hsieh42 in a 75-mm hydrocyclone. The geometric parameters of the hydrocyclone are listed in Table 3. The overall computational domain was divided into 74871 unstructured hexahedron grids as shown in Figure 4, and the measurement data were obtained from ref 42. Figure 5ac shows the experimental and predicted tangential and axial velocity components at different locations from the top wall (i.e., 60, 120, and 170 mm). According to Figure 5, the simulation results exhibited the same trend as the experimental results, but still there were some errors in the precision, especially for the axial velocity. The results were closer to those in refs 43 and 19. 3.2. Flow Fields in a Hydrocyclone at Two Environmental Atmospheric Pressures. The distribution of the flow field directly determines the classification performance of a hydrocyclone. In a hydrocyclone, the tangential and radial velocities mainly determine the positions of particles, whereas the value of the radial velocity is so small that it is not discussed in this article. There exists the locus of zero vertical velocity (LZVV). The particles inside the LZVV flow from the overflow, whereas those outside it flow from the underflow. The properties of the air core in the middle of the hydrocyclone affect the performance of the hydrocyclone. Even though there are no particles in the air
Figure 4. (a) Schematic and (b) grid representations of Hsieh’s hydrocyclone.
core, the space between the air core and the locus of zero vertical velocity (LZVV) directly determines the small-particle separation efficiency. The effects of different atmospheric pressures on the flow field and air core in an industrial hydrocyclone were analyzed by CFD simulations. 3.2.1. Air Core Development. The air core is a unique phenomenon inside hydrocyclones. The three-dimensional motion of the fluid flow in the hydrocyclone accelerates as the radius decreases, which converts the static pressure of the flow into a dynamic pressure, except for friction losses. When the flow velocity increases to a maximum value along the radius direction, as the radius decreases, the surplus hydrostatic pressure has no sufficient energy to compensate the energy loss and continues to maintain the growth of the flow velocity simultaneously. Therefore, the flow begins to decrease as the radius decreases. When the radius continues to decrease to a certain position, the fluid static pressure reduces to zero. Within this radius, a negativepressure zone is formed. Based on the same pressure between the hydrocyclone underflow and the atmosphere generally, the negative-pressure zone is able to absorb outside air, thus forming an air core. From the flow field development view in hydrocyclone, only when the liquid fills in the hydrocyclone does the 446
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Figure 5. Comparison between the measured and predicted tangential (right) and axial (left) velocities at different locations from the top wall: (a) 60, (b) 120, and (c) 170 mm.
air core appear. Figure 6 shows the simulation results of the flow field development in a hydrocyclone on the plateau and on the plain, clearly demonstrating this behavior. The results show that the air core will remain steady after some seconds of the flow filling in. The plane is located on the surface of x = 0 mm. The air core is only in the middle of the hydrocyclone, whereas the liquid exits near the wall, as shown in Figure 6, where air is represented by blue and liquid by red. The reason is that centrifugal force
develops liquid under the swirling flow. When the liquid fills in the hydrocyclone, the air-phase volume is close to 1 in the center of the hydrocyclone, and it runs from the spigot through the vortex finder. It is worth noticing that atmospheric pressure affects the development process of the flow field in the hydrocyclone, as shown in Figure 6a,b. The development processes in the hydrocyclone at the atmospheric pressures of the plateau and the plain are different before 1.0 s. 447
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Figure 6. Development of the hydrocyclone flow field on the (a) plateau and (b) plain from 0 to 12.0 s.
The air core is the main complex part in the hydrocyclone; near the air core there are two or three phases. The atmospheric pressure influences the shape of the air core, as shown in
Figure 7a. Regarding the whole hydrocyclone in Figure 7a, the shape and average diameter of the air core in the hydrocyclone are more changeable on the plain than on the plateau. Figure 7b 448
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Figure 7. Air core in the hydrocyclone on the plateau and plain.
Figure 8. Tangential velocity distribution on the surface of z = 250 mm. Figure 9. Tangential velocity distribution on the surface of z = 0 mm.
shows an enlargement of the cube part of the hydrocyclone in Figure 7a. From the enlargement in Figure 7b, it can be seen that the air-core diameters on the plain are not all smaller than those on the plateau throughout the hydrocyclone. Rather, in the part of the hydrocyclone of the height from z = 0 mm to z = 100 mm, the air-core diameters on the plain are larger than those on the plateau, and the opposite is true in the part of the hydrocyclone from z = 100 mm to z = 0 mm. 3.2.2. Velocity Distribution. The flow fields on the two surfaces z = 0 mm and z = 250 mm were selected for further study. Figure 8 shows the tangential velocity distribution on the surface of z = 250 mm in the hydrocyclone under atmospheric pressure on the plateau and on the plain. The shapes of the two velocity distributions are nearly the same. Figure 8 indicates that the tangential velocity remains the same near the wall.
As the radius decreases, the tangential velocity on the plain becomes higher than that on the plateau. The position of the maximum velocity on the surface of z = 250 mm in the hydrocyclone on the plain is closer to the center, opposite to the case on the plateau. The situation on the surface of z = 0 mm in Figure 9 is similar to that in Figure 8. For a better explanation, the sections of the hydrocyclone at heights from z = 100 mm to z = 100 mm were selected, and the tangential velocity and air core are compared in Figure 10. From Figure 10, it can be clearly seen that the greatest effects of the environmental atmospheric pressure on the tangential velocity are inside the air core and near the interface of the air and brine. In the part of the hydrocyclone from z = 20 mm to 449
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Figure 10. Tangential velocity and air core of the hydrocyclone at heights from z = 100 mm to z = 100 mm.
Figure 11. Axial velocity distribution on the surface of z = 250 mm. Figure 12. Axial velocity distribution on the surface of z = 0 mm.
z = 100 mm, the tangential velocities on the plain are higher than those on the plateau. Near the height of z = 20 mm, the tangential velocities on the plateau and plain basically remain the same, whereas at heights lower than 20 mm, the tangential velocities on the plateau become higher than those on the plain. However, the two tangential velocities far from the air core are almost the same. The axial velocity in the whole hydrocyclone results in the flow rate on the overflow and underflow, which increases as the radius increases gradually from the wall to the center. From Figures 11 and 12, it can be seen that they also remain the same near the wall both on the plateau and on the plain. In Figure 11, as the radius decreases, the axial velocity on the plateau first is lower than that on the plain, and then in the center of the
hydrocyclone, it becomes higher. However, in Figure 12, an evident difference is found in the center of the hydrocyclone. The velocity value on the plateau is negative, suggesting that the flow moves downward and rapidly as the radius decreases, opposite the situation on the plain. This means that it will change the flow rate on the overflow and underflow. In other words, it will change the production capacity of the hydrocyclone. To further investigate the effects of the environmental atmospheric pressure on the axial velocity, the axial velocities at the different atmospheric pressures of the plateau and the plain in the hydrocyclone are shown in Figure 13. Figure 13a shows the axial velocities at different heights in the whole hydrocyclone. Regarding the overall hydrocyclone, the 450
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Figure 13. Axial velocity, air core, and LZVV of the hydrocyclone.
axial velocities in the center on the plain are mostly higher than those on the plateau. For clearer visualization, an enlargement of the part from z = 0 mm to z = 100 mm is shown in Figure 13b, where the different types of air core and LZVV are also marked. As shown in Figure 13b, in the part of hydrocyclone from z = 0 mm to z = 100 mm, the influence on the movement of the air core is clear, directly affecting the motion direction of the air core. The velocities on the plateau are downward, opposite to those on the plain, and near the part of hydrocyclone from z = 20 mm to z = 0 mm, the velocities gradually become zero. However, at heights lower than z = 20 mm, the velocities on the plateau become upward, whereas those on the plateau are in the same direction, but with a smaller value. In general, the axial velocities upward in the center on the plain are higher than those on the plateau. 3.3. Effect on Separation Performance of the Hydrocyclone. As shown in Figure 2, the particles smaller than 74 μm are calcium sulfate particles that need to be separated by the hydrocyclone, whereas the larger particles are potassium chloride and need to be kept in the actual industrial production process.
Through calculation, the classification efficiency was determined. The classification efficiency (E) is given by E¼
Mu 100% Mi
ð13Þ
where Mi and Mu are the different particle mass flows of the inlet and underflow, respectively. Figure 14 shows the different partition curves calculated for the atmospheric pressures on the plateau and plain, which are similar to the classic curve.44 The environmental atmospheric pressure was found to have little effect on the separation efficiency of particles larger than 100 μm, whereas the separation efficiency of particles larger than 350 μm can reach 100% on both the plateau and plain. However, the fine-particle separation efficiency to the underflow on the plateau is about 10% higher than the results obtained on the plain. For the industrial production process, this means that less calcium sulfate particles with a small size can be removed from the crude potassium chloride products from the vortex finder on the plateau, resulting in a lower calcium sulfate removal efficiency. We speculate that, 451
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5. CONCLUSIONS To investigate the effects of operating environment and provide reference to practical industrial applications, CFD has been used to quantify the flow and particle fields in a hydrocyclone under the environmental atmospheric pressures of the plateau and plain. The following conclusions can be made: (1) The flow fields in a hydrocyclone operating at different atmospheric pressures are different. Changes in atmospheric pressure mainly affect the flow field inside the air core and near the interface between the air core and the liquid. The atmospheric pressure has little impact on the tangential velocity of the liquid, whereas a great impact of the atmospheric pressure on the tangential velocity distribution mainly occurs inside the air core. There is great influence of the atmospheric pressure on the movement of the air core, directly affecting the direction of motion of the air core on the cylinder part of the hydrocyclone. (2) The atmospheric pressure has little effect on particles larger than 350 μm. However, compared to the plain, small-particle separation efficiency to the overflow on the plateau decreases by about 10%, and more energy is consumed, whereas the difference in the split ratio is small. (3) A hydrocyclone, as a common liquid/solid grading instrument, can be used to separate calcium sulfate particles from crude carnallite during the KCl production process on the Tibetan Plateau in China, because CaSO4 particles are independent of KCl particles and have a smaller particle size distribution. The local altitude on the Tibetan Plateau in China is over 3000 m, so the effects of low atmospheric pressure on the hydrodynamics and separation performance of hydrocyclones should be considered. (4) The geometry of a hydrocyclone applied on the plateau should differ from that of one used on the plain. Further studies will focus on the design of the hydrocyclone structure operating on the plateau. A more efficient hydrocyclone suitable for the plateau environment is anticipated.
Figure 14. Particle separation efficiencies on the plateau and plain.
Table 4. Split Ratio and Pressure Drop on the Plateau and Plain at Atmospheric Pressure split ratio (%)
pressure drop (MPa)
plateau (0.7 atm)
69.36
0.28
plain (1.0 atm)
71.11
0.27
because of the atmospheric pressure, the axial velocities in the center (mainly inside the air core and near the interface between the liquid phase and the air core) on the plain are higher than those on the plateau, as shown in Figure 13. Thus, higher axial velocities drive more small particles upward, resulting in a higher separation efficiency to the overflow of the small particles on the plain. However, further experimental and industrial testing should be done to validate this conclusion. To evaluate the hydrocyclone performance, the split ratio and pressure drop were also considered. The split ratio is defined as Qu 100% S¼ Qo
ð14Þ
where Qu and Qo are the brine mass flows of the inlet and underflow, respectively. The pressure drop between the inlet and the vortex finder is given by Δpo ¼ pi po
ð15Þ
where pi and po are the pressures of the inlet and the vortex finder, respectively. The simulation results for the split ratio and pressure drop on the plateau and plain are reported in Table 4. The split ratios of the hyrocyclone on the plateau and plain are 69.36% and 71.11%, respectively. The percent difference between them, defined as Splateau Splain 100% Splain
’ AUTHOR INFORMATION
ð16Þ
is about 2.45%, which is not significant. However, the pressure drops of the hydrocyclone on the plateau and the plain were 0.28 MPa and 0.27 MPa, which means that more energy is consumed on the plateau.
Corresponding Author
*Tel.: 86-21-64252170. E-mail:
[email protected] (X.S.), jgyu@ ecust.edu.cn (J.Y.).
’ ACKNOWLEDGMENT This work was supported by MOST Project of Personnel Service Corporate Actions (2009GJG20011), Program for New Century Excellent Talents in University (NCET-08-0776), Shanghai Leading Academic Discipline Project (No. B506), and Fundamental Research Funds for the Central Universities. ’ NOMENCLATURE E = classification efficiency (%) Mi = solid mass flow of the inlet (kg/s) Mu = different solid mass flow of the underflow (kg/s) pi = pressure of the inlet (MPa) po = pressure of the vortex finder (MPa) Δpo = pressure drop (MPa) Qu = brine mass flow of the inlet (kg/s) Qo = brine mass flow of the underflow (kg/s) S = split ratio between the underflow and the overflow (%) 452
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dx.doi.org/10.1021/ie201147e |Ind. Eng. Chem. Res. 2012, 51, 443–453
