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Numerical study and optimization of liquid-liquid flow in cyclone pipe
Journal Pre-proof Numerical study and optimization of liquid-liquid flow in cyclone pipe Jie Kou, Yi Chen, Junqiang Wu
PII:
S0255-2701(19)31120-1
DOI:
https://doi.org/10.1016/j.cep.2019.107725
Reference:
CEP 107725
To appear in:
Chemical Engineering and Processing - Process Intensification
Received Date:
6 September 2019
Revised Date:
31 October 2019
Accepted Date:
4 November 2019
Please cite this article as: Kou J, Chen Y, Wu J, Numerical study and optimization of liquid-liquid flow in cyclone pipe, Chemical Engineering and Processing - Process Intensification (2019), doi: https://doi.org/10.1016/j.cep.2019.107725
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Numerical study and optimization of liquid-liquid flow in cyclone pipe
Jie Kou, Yi Chen*, Junqiang Wu
Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, College of Pipeline and Civil
*Corresponding
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Engineering, China University of Petroleum (East China), Qingdao, China
author (Yi Chen). E-mail address: [email protected]
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Graphical abstract
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Highlights
•The effect of the cone angle on performance of liquid-liquid cyclone is obtained.
•The relation between length of reversed flow and separation efficiency is studied.
•Two suitable underflow tubes are designed.
•The novel liquid-liquid cyclone has a significant separating effect.
Abstract The performance of cyclone can be improved by changing operating conditions or geometric parameters. In the present study, the liquid-liquid flow in cyclone with guiding vanes was investigated by computational fluid dynamics (CFD). The two-phase swirling is numerically simulated by combining the Reynolds stress model with the Mixture model, and the results agree well with the experimental data in the literature. After that, further studies on
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the effects of velocity field, pressure field and separation performance under different cone angles are studied, which indicates the swirling intensity and residence time have important impact on performance of hydrocyclone. Subsequently, the results showed that the reverse
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flow unable to reach the overflow orifice, which lead to stagnant separation efficiency,
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especially for smaller droplets. To solve this problem, two suitable underflow tubes were
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designed, which greatly improved the performance of the cyclone.
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Keywords: hydrocyclone; CFD; cone angle; underflow tube; separation efficiency.
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1. Introduction Compared
with
the
traditional
gravity
sedimentation,
gas
flotation
and
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electro-coagulation, the cyclone has the characteristics of simple structure, small volume, light weight, no moving parts and short processing time, so it has been widely used [1]. In recent years, there is an urgent need for an efficient and compact oil-water separator on a space-limited platforms [2,3]. Due to the different density of oil and water, the centrifugal force received in the cyclone is different, the oil phase is less affected by the centrifugal force
and accumulates in the central region of the separator, while the water phase is greatly affected by the centrifugal force and is distributed on the inter-wall of the separator, finally achieving the separation of the mixed medium [4]. Due to the small difference in density, the separation of oil and water is difficult, and the application in liquid-liquid cyclones is far behind the solid-liquid cyclone [5,6]. According to the difference of the inlet geometry, it can be divided into two types: tangential inlet and axial inlet.
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Earlier researchers focused on experimental study. In 1967, Torrey Canyon oil spill accident in North Sea oil field in the United Kingdom prompted Martin Thew and Colman to study the use of static cyclones for oil-water separation [7]. Then, Trygve Husveg [8] studied
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the variation of separation performance of liquid-liquid cyclone under flow fluctuation
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conditions. Young et al. [9] proposed new cyclone geometry on the base of the 35 mm hydrocyclone designed by Colman and Thew [7]. In their experiments, the effects of
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operating parameters and geometric parameters such as inlet size, cylindrical diameter, cone
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angle, cylindrical section length, flow rate, and droplet diameter on separation efficiency were investigated. Recently, Most researchers have gradually focused on operating parameters
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[10,11], velocity fields [12], and oil droplet distribution [13] in deoiling cyclones. These above are studies of tangential inlet cyclone, but this structure is easy to cause the flow field
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to be unstable [14], and its radial distance is large [15]. The gas-liquid axial separator designed by Swanborn [16] avoided this drawback, then the axial liquid-liquid cyclone with guiding vanes was introduced by Maarten Dirkzwager [17] in 1996 . The internal flow field distribution was studied by laser Doppler velocimetry, and the influence of velocity profile on swirling field was discussed. Following Maarten Dirkzwager, Changes in oil droplet size
through the cyclone online was measured by Stephen Murphy and René Delfo [18] who used a Malvern laser particle size analyzer. Shi [19] et al. used particle image velocimetry (PIV) to experimentally study a new type of vane tube separator. The results showed that the more number of vanes, the smaller time and size of oil droplets entering central zone radially at low inlet flowrate. With the development of computational fluid dynamics (CFD), some commercial software has begun to be applied to the study of cyclone. N. Kharoua et al. [20]
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used the Mixture model to obtain oil phase volume concentration distribution in oil-water cyclone. The existing studies [21] showed that RSM and LES models has higher calculation accuracy, and can reasonably predict flow field distribution in a liquid-liquid cyclone by
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comparing the turbulence models such as standard k-ε, RNG k-ε, RSM, and LES. Dispersed
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phase model (DPM) and stochastic tracking method (STM) were usually used to describe the trajectory of oil droplets in cyclone qualitatively [22-24]. The oil phase was considered as a
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dispersed phase by DPM model. However, it is more suitable when the volume fraction of
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discrete phase less than 10% [25,26]. Huang [27] simulated the three-dimensional turbulence in deoiling cyclone using the Euler-Eulerian method and Reynolds stress model. The results
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showed that there is a large amount of crude oil accumulation near the central region. The separation efficiency was estimated based on phase concentration, and the separation curve of
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the Colman hydrocyclone was in good agreement with the measured values. Noroozi and Hashembadi [28,29] studied the effects of different types of inlet section on separation efficiency. The separation efficiency was increased by 10% and 8% with inlet of a spiral and an exponential body profile, respectively. In addition, some researches have been reported the deeper researches of internal mechanism, such as dynamic characteristics [22,24], droplet
breakage and coalescence [30-32], these above literatures showed that numerical simulation provides another effective tool for the study of cyclones. And only the geometry of conical section was considered by previous studies, the effect of underflow tube structure was rarely considered, and small particle size was not analyzed in depth, which had a great influence on the performance of cyclone. In this paper, the performance of cyclone with different cone angle is investigated by
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analyzing the internal flow field, and the working mechanism has been discussed. The underflow tube of original axial-flow cyclone with guiding vanes is modified for the droplets of smaller size on the basis of the above.
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2. Model descriptions
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2.1 Numerical model 2.1.1 Turbulence model
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The Reynold number of oil-water flow can be expressed as: ReDH dvm m / m
(1)
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Here d is the hydraulic diameter, ρm and μm are the density and viscosity of mixture, and vm is the average velocity.
(2)
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m (1 w )o w w
Where, μo and μw are the viscosity of oil and water, respectively. φw is the water volume
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fraction.
The average velocity is expressed as: vm Q / Ad
(3)
Where, Q is the total volume flowrate, and Ad is the cross-section area.
1
m
wo
o
1 wo
w
(4)
Where, ρo and ρw are the density of oil and water, respectively, wo is the oil mass fraction.
ReDH >2000 can be obtained from the data of section 3.2, so the flow regime is turbulent.
It is well known that the anisotropic for turbulence is assumed by RSM, which is recommended for the simulation of complex swirling flow. Therefore, this model was selected in the paper. The transport equations of the RSM turbulent model are defined as follows:
( uk rho ) Dij pij ij ij xk
(5)
Where rho u 'i u ' j is the Reynolds stress tensor, Dij，pij，Φij，and εij are stress diffusion,
t [ rho ] xk k xk
pi j [rik
u j xk
p
ui ] xk
1 pij 2
2 2 (rho ij ) C2 ( pij p ij ) 3 3
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i j C1
rjk
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Dij
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production, pressure strain, and dissipation, respectively. (6)
(7) (8) (9)
2 (10) 3 Where, p stands for the fluctuating kinetic energy production. μt is the turbulent viscosity, and σk = 1, C1 = 1.8 as well as C2 = 0.6 are empirical constants.
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2.1.2 Multiphase flow model
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ij ij
Mixture model assumes that the local equilibrium over short spatial length scales where the phases move at different velocities. It uses a single-fluid approach, just like the
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volume of fluid model but allows for the phases to be interpenetrating. And lower computational cost is needed as opposed to Eulerian–Eulerian approach. So this model is
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applied in the following works. The continuity equation for the mixture is ( mvm ) 0
(11)
Where ρm is the mixture density, vm is the mass-averaged velocity.
vm
n
k k v k m
k 1
(12)
m k 1 k k n
(13)
Where v k and αk are the velocity and volume fraction of the kth phase, respectively. The momentum equation is expressed as follows: ( m v m v m ) P [ m (v m v m )] m g ( k 1 k k v dr ,k v dr ,k ) R T
n
(14)
Where n is the number of phases, μm is the mixture viscosity, and v dr ,k is the drift velocity of the kth phase, R is the Reynolds stress.
m k 1 k k n
2.2 Computational geometry
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v dr ,k v k v m
(15) (16)
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Simulations were carried out on four hydrocyclones with different cone angles. The dimensions of these cyclones are shown in Figure. 1 and Table. 1. All the dimensions of inlet,
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vane structure and heights are the same, so the effect of different conical section on flow field
3. Numerical simulation
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can be studied specially.
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3.1 Grid-independent analysis
ICEM software is a built-in tool in CFD software, hybrid grid was carried out by it to
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reduce the quantity of grid cells and promote convergence, the main part of computational
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domain adopted the structured grid, only the region of vanes used the unstructured grid. The grid division of computational domain is displayed in Figure. 2. In CFD simulation, the size of grids has an important influence on the convergence and
the accuracy of simulation calculation results [33,34]. To avoid this influence, the separator models with 518507, 793271, , 1159025 and 6330164 grid elements are simulated in this paper. Table. 2 shows the calculation results of separation efficiency and pressure drop under
different grid sizes. It can be seen that when the size of grids is greater than 793271, the difference between the calculation results is small enough, so the numerical calculation of the axial-flow cyclone is followed by the grid size of 793271. 3.2 Solution method Fluent 14.5 can realistically simulate flow fields under complex conditions, heat distribution in various combustion thermal fields, phase transitions in chemical reflection
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processes and so on. The computational domain was occupied by the two-phase flow, in which water and oil represented the continuous phase and the dispersed phase respectively, in the all simulated cases μo = 0.03 Pa∙s, ρo= 850 kg/m3, μw= 0.001 Pa∙s and ρw = 998.2 kg/m3.
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Here, the velocity inlet boundary condition was applied at the inlet, where the axial inlet
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velocity was 0.5m/s. The actual turbulence intensity is calculated by I 0.16( ReDH )1/8 , The boundary condition normal to the outlet was prescribed as outflow where the overflow split
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was 20%. Besides, it was considered that all walls were defined to satisfy the non-slipping boundary condition（and the standard wall function is applied for turbulent flow near the
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wall.） （oil , content at the inlet is 15%.）, Schiller-Naumann model is used for the drag force,
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Manninen-at-al model is applied for the slip velocity. Pressure spatial discretization was set to PRESTO, while the spatial discretization other
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equations were defined in the Second-order upwind form. The solution of the equation was performed using SIMPLE, and the Residual scales in all simulations were adopted for 10-5. 3.3 Validation The separation efficiency in the simulation can be calculated by the following formula [35]:
s
M oo Qoo o Qoo M io Qio o Qio
(17)
Where Moo and Mio are the oil phase mass flowrate of overflow orifice and inlet respectively, Qoo and Qio are the oil phase volume flowrate of overflow orifice and inlet respectively. The mechanism of the Thew model is consistent with the model in this paper, oil and
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water is separated by centrifugal force, the difference is that the guiding vanes were not installed in Thew model, Thew model obtains the swirling field through the tangential inlet. This structure increases the radial dimension of the model and has a large impact force, the
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specific geometric parameters can be obtained from the literatures [10][29]. For the Thew model, the constant mass flow rate (20 l/min) at the inlet boundary as a plug flow is employed.
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The imposed mass flow rate boundary condition with respect to overflow split ratio (17%) as
leave the underflow).
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a percentage of inlet mass flow rate are used for outlets (17% exit from overflow and the rest
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To validate the reliability about the simulations, it is essential to compare the simulating results with the existing data. The comparison between experimental, analytical Thew model
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[10,29] and the present numerical results for separation efficiency and tangemtial velocity
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profile were shown in Figure. 3. As can be seen from Figure. 3(a), centrifugal device promotes the resistance and causes
the droplet to break down because of the fishhook effect [29], which can be founded in the experimental work. However, this phenomenon was ignored in the simulation process, which leads to a large error at this point. The turbulence models of RSM, RNG k-ε, and k-εwere used for simulation. The average separation error( 25～120 microns) of RSM, RNG k-ε, and
k-ε turbulence models and experiments was 8.67%, 13.71%, and 16.73%, respectively. It can be seen from that the RSM turbulence model used in this paper are reliable, Here simulations were also performed for the cyclone of Thew, and the corresponding computed tangential velocity profile was shown in Fig. 3(b). It can be concluded that the deviation is small and the numerical simulation can be credible. 4. Results and discussion
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4.1 Influence of cone angle 4.1.1Tangential velocity
The tangential velocity profile of different cone angles at z= -300 mm is shown in Figure.
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4. The peak of tangential velocity enhances significantly as the cone angle increases. This is
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because the cross-sectional area of the conical section downstream decreases under the condition of higher cone angle, which contributes to the dispersed oil droplets migrate to axial
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center with a shorter radial path. Moreover, the centrifugal acceleration is proportional to the
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square of tangential velocity, so the centrifugal force will increase sharply in the flow. However, the flow residence time of droplets reduces greatly owing to the shorter axial length
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of conical section and higher tangential velocity, which decreases the overall migration of the dispersed droplets.
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4.1.2 Axial velocity
The axial velocity profile at z = -300 mm is shown in Figure. 5 for different angles. The
positive and negative values of velocity represent the reverse (moving to the overflow orifice) and forward (moving to the underflow orifice) flow, respectively. Near the wall (0.02 mm < r < 0.025 mm), the forward velocity gradually increases as the cone angle decreases,
contributing the fast moving flow can deliver most of the dispersed droplets to the underflow orifice As can be seen from Figure. 5, an interesting tendency of the axial velocity profile emerges at the intermediate region (0.005 mm < r < 0.02 mm). The forward flow velocity decreases as the cone angle decreases; when the cone angle is 2 degree, the fluid even flows towards the overflow orifice. Therefore, droplets dispersed in the fluid at the intermediate region (0.005 mm < r < 0.02 mm) have a longer residence time for the lower cone angle due
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to slower axial velocity or reverse flow. 4.1.3 Static pressure
Figure. 6 shows the radial pressure distribution with different cone angles. It can be seen
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that the pressure near the wall is significantly higher than that in the central area of the
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cyclone. It is the result of a combination of swirling motion and centrifugal force. In addition, the pressure at the central point increases gradually with the increase of the cone angle, thus
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making the droplets near the wall move towards the center at a greater speed, and the radial
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pressure gradient also increased in this case. The effect of the cone angle on the pressure distribution along the central axis is shown in Figure. 7. The vertical coordinate represents the
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static pressure value and the horizontal coordinate represents the position on the central axis. The core pressure first increases and becomes maximum value and then decreases. A positive
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axial pressure gradient is created from the maximum pressure location to the overflow orifice, which is why the reverse flow occurs. As can be seen from Figure. 8, the positive axial pressure gradient generated by a smaller cone angle maintains a longer distance. 4.1.4 Separation efficiency The conical section is the key area for oil-water separation. Figure. 9 shows the
separation efficiency at different cone angles and particle sizes. It is found that separation efficiency gradually decreases with the cone angle increases. This is the combination of a smaller angular momentum change and a longer residence time. However, for all cone angles, the separation efficiency is low for droplet sizes less than 40μm. This is because small droplets are less sensitive to swirling motion, resulting particularly inefficient. And in the practical applications of liquid-liquid cyclones, it is crucial to separate small particle droplets.
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The trade-off between swirl intensity, length of the reverse flow, and residence time of droplets is necessary to optimize separation efficiency. Figure. 10 shows the relationship between the separation efficiency and the length of the reverse flow. As the cone angle
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increases, the separation efficiency decreases sharply. For the length of the reverse flow (Lc),
4.2 Optimization of the underflow tube
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the trend is entirely consistent. Therefore, the separation efficiency is proportional to Lc.
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The above simulation results reflected that there was still a swirling motion in the
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underflow tube, so the dispersed oil droplets would gather toward the center to form the underflow core, but this part of the oil droplet could not reach the overflow orifice due to the
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absence of reverse flow. Some droplets moved forward, and others moved in the reverse direction as shown in Figure. 7. This flowing feature inspired us that if we design a
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mechanism to collect the oil core flowing out of the underflow outlet, the separation efficiency of small droplets may greatly be improved. In this way, the adjusting range of operating parameters of the cyclone would be increased, and the separation efficiency could be maintained at a higher flowrate fluctuation. In this paper, two mechanisms for capturing droplets from the underflow outlet are studied.
4.2.1 Structure of the underflow tube The underflow tube was directly connected to the conical section with 6 degree. Two types of underflow structures were designed to evaluate overall performance. Structure-1 had a vortex finder with the same diameter as the original overflow tube, and its underflow outlet is tangentially connected to the underflow tube. Structure-2 had two slots as the underflow outlets, the vortex finder was the same as structure-1, and the total area of two slots was equal
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to the area of underflow outlet of the original 6 degree cyclone. These two structures of suitable size are shown in Figure. 11. The diameters of two overflow outlet tubes were Do and Do’ respectively, the split ratio of both overflow outlet tubes was 10%.
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4.2.2 Effect of underflow tube on static pressure along the center axis
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Figure. 12 shows the effect of different underflow structures on the center static pressure. It can be seen that the static pressure curves of the two structures are almost coincide until the
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tail of underflow tube, However, near the end of the underflow tube (z= - 950mm), the center
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pressure curves are obviously different. For structure-2, the core pressure decreases sharply at the end of the underflow tube, this is due to the slotted geometry of structure-2. In addition, its
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pressure gradient is small compared to the structure-1. 4.2.3 Effect of underflow tube on separation performance
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The effect of different structures on performance of hydrocyclone was evaluated as
shown in Figure. 13. η and η’ are the fractional separation efficiency of Do and Do’, respectively, the values of both were defined according to the efficiency formula in Section 3.3. ηT = (η + η’) is the total fractionation efficiency. The η between structure-1 and structure-2 is not much different. As the droplet size increases, the fractional efficiency of the
Do’ (η’) first increases and then decreases. This is because larger droplets increase the rate of migration, thereby increasing η’. At the same time, η is gradually increasing either, which reduces the number of possible droplets flowing to the Do’. Moreover, structure-2 provides a smaller η’ than structure-1 for larger droplets, the reason is that the migrated droplets are remixed through the slots in structure-2, thereby reducing η’. Figure 13 also shows that when we compare the separation efficiency with an original 6deg cyclone, the overall grade size
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efficiency (ηT) is greatly improved due to the addition of the underflow tool. η’ is an additional fractional separation efficiency. And for smaller oil droplets such as 40μm, the separation efficiency is greatly improved; the phase distribution contours of 6deg cyclone and
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6deg cyclone with structure-1 at 40 micron are shown in Figure. 14.
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5. Conclusions
To understand the influence of different cone angle on separation efficiency, the detailed
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flow field information of the cyclone is obtained by CFD simulation. It is found that the trend
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of tangential velocity and axial velocity distribution is absolutely consistent in all hydrocyclones, but the change of cone angle has a significant effect on the value, indicating
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that centrifugal acceleration will change dramatically. Moreover, the length of the reverse flow in the hydrocyclone of different cone angles is completely different. And the reverse
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flow at all cone angles cannot reach the underflow orifice. By adding an underflow tool, it has been found that the separation efficiency is greatly improved, especially for smaller oil droplets. This is because a portion of the oil droplets always flows out of the underflow orifice in the form of an oil core. Therefore, it is desirable to add an underflow tool to collect oil droplets flowing at the underflow orifice.
Appendix A. Nomenclature cross-section area (m2)
a
width of the slot (m)
b
height of the slot (m)
C1, C2
empirical constants
Ci, Cu
oil concentration of the overflow and underflow, respectively
Du
underflow tube diameter (m)
Dc
body diameter (m)
Du
overflow tube diameter (m)
Di
inlet diameter (m)
Dij
stress diffusion
Do
overflow tube diameter (m)
Do’
overflow tube’ diameter (m)
d
hydraulic diameter(m)
H
cyclone height (m)
Hc
cyclone cylinder height (m)
Hv
length of the vortex finder (m)
I
turbulence intensity
Lc
length of the reverse flow (m)
Mo, Mi
oil phase mass of overflow and inlet, respectively
n
number of phases
-p re
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fluctuating kinetic energy production shear production
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pij
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p
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Ad
Q
total volume flow (m3/s)
Qoo, Qio
oil phase overflow port and inlet flow rate, respectively
ReDH
Reynolds number of the mixture
R
Reynolds stress
r
radial position (m)
rho
Reynolds stress tensor
vm
average velocity (m/s)
vm
mass weighted average velocity (kg/s)
vk
velocity of the kth phase (m/s)
v dr ,k
drift velocity of the kth phase (m/s) letters
αk
volume fraction of the kth phase
θ
cyclone angle (deg)
ρk
the density of the kth phase (kg/m3)
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Greek
density of the mixture(kg/m3)
ρo, ρw
oil and water density (kg/m3)
µm
viscosity of mixture (Pa∙s)
μk
viscosity of the kth phase (Pa∙s)
μt
eddy viscosity (Pa∙s)
µo, µw
oil and water dynamic viscosity (Pa∙s)
η
separation efficiency of overflow tube (%)
ηs
separation efficiency in the simulation (%)
η’
separation efficiency of overflow tube’ (%)
ηT
total separation efficiency (%)
φw
the water volume fraction
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kronecker delta
εij
source term
pressure-strain
oil mass fraction
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wo
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δij
Φij
σk
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ρm
empirical constants
Acknowledgements
This study was supported by the Opening fund of Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, and the Fundamental Research Funds for the Central Universities.
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[25] W D Griffiths, F Boysan. Computational fluid dynamics (CFD) and empirical modelling
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of the performance of a number of cyclone samplers, J. Aerosol. Sci. 27(1996) 281-304. [26] O Husson, P H Verburg, M T Phung, et al. Numerical Modeling of the Fluid and Particle Penetration through Small Sampling Cyclones, J. Aerosol. Sci. 31 (2000) 1097-1119. [27] S Huang Numerical simulation of oil–water hydrocyclone using Reynolds-stress model for Eulerian multiphase flows, Can. J. Chem. Eng. 83 (2005) 829-834.
[28] S Noroozi, S H Hashemabadi. CFD Simulation of Inlet Design Effect on Deoiling Hydrocyclone Separation Efficiency, Chem. Eng. Technol. 32 (2009) 1885-1893. [29] S Noroozi, S H Hashemabadi CFD analysis of inlet chamber body profile effects on de-oiling hydrocyclone efficiency, Chem. Eng. Res. Des. 89 (2011) 968-977. [30] S Amini, D Mowla, M Golkar. Developing a new approach for evaluating a de-oiling hydrocyclone efficiency, Desalination, 285 (2012) 131-137.
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[31] S. Schutz, G. Gorbach, M. Piesche. Modeling fluid behavior and droplet interactions during liquid-liquid separation in hydrocyclones, Chem. Eng. Sci. 64 (2009) 3935-3952.
[32] Z B WANG, Y MA, Y H JIN. Droplet coalescence and breakup and its influence factors
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in vane-guided hydrocyclone, CIESC J. 62 (2011) 399-406.
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[33]W Siddique, L El-Gabry, I V Shevchuk, et al. Flow Structure, Heat Transfer and Pressure Drop in Varying Aspect Ratio Two-Pass Rectangular Smooth Channels, Heat Mass Transf. 48
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(2012):735-748.
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[34]W Siddique, I V Shevchuk, L El-Gabry, et al. On flow structure, heat transfer and pressure drop in varying aspect ratio two-pass rectangular channel with ribs at 45°, Heat Mass
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Transf. 49 (2013):679-694.
[35] Y MA, Z B WANG, Y H JIN. Simulation of oil-phase concentration field in vane-guided
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hydrocyclone, CIESC Journal. 62 (2011):420-426.
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Figures
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Figure. 1. The geometry of hydrocyclone and corresponding coordinate
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Figure. 2. A sample of grid generation for numerical simulation
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Figure. 3(a). Comparison of experimental and numerical simulation results for
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effect of oil droplet size on separation efficiency.
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Figure. 3(b). Comparison of numerical simulation results for tangential velocity plot
Figure. 3. Analysis of the numerical and experimental results
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Figure. 4. Tangential velocity profile with different cone angles at z = -300mm, particle
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sizes =70μm
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Figure. 5. Axial velocity profile with different cone angles at z = -300mm, particle sizes =70μm
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Figure. 6. Static pressure profile with different cone angles at z = -300mm, particle sizes
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=70μm
Figure. 7. Static pressure along the axial direction of the hydrocyclone with different
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cone angles, particle sizes =70μm
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Figure. 8. Reversed flow contours with different cone angles, particle sizes =70μm
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Figure. 9. Grade efficiency with different cone angles
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Figure. 10. Connection between separation efficiency and the length of reversed flow under
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different cone angles
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structure-1
structure-2
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Figure. 11. Shape and dimensions of structures (×10-3m)
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Figure. 12. Center static pressure profile with two structures
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Figure. 13. Grade efficiency with two structures
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Figure. 14. Comparison of oil distribution in the 6deg cyclone (left) and 6deg cyclone with
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structure-1 (right) at 40 micron
Tables cyclone height/H(×10-3m)
Common for all cyclones(×10-3m)
I-1
2
21.9
1105.3
Body diameter, Dc=50
I-2
4
18
1105.3
overerflow tube diameter, Do=8
I-3
6
18
1105.3
Inlet diameter, Di=50
I-4
10
18
1105.3
Cylinder height, Hc=200
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cyclone cyclone underflow tube no. angle/θ(deg) diameter/Du(×10-3m)
overflow pressure (MPa) 0.092 0.115 0.116 0.117
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518507 793271 1159025 6330164
separation efficiency (%) 59.44 61.28 62.27 62.31
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grid size
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Table. 1. Main dimensions of simulated hydrocyclones
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Table. 2. Validation of grid independence
underflow pressure (MPa) 0.083 0.084 0.084 0.084
PII:
S0255-2701(19)31120-1
DOI:
https://doi.org/10.1016/j.cep.2019.107725
Reference:
CEP 107725
To appear in:
Chemical Engineering and Processing - Process Intensification
Received Date:
6 September 2019
Revised Date:
31 October 2019
Accepted Date:
4 November 2019
Please cite this article as: Kou J, Chen Y, Wu J, Numerical study and optimization of liquid-liquid flow in cyclone pipe, Chemical Engineering and Processing - Process Intensification (2019), doi: https://doi.org/10.1016/j.cep.2019.107725
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Numerical study and optimization of liquid-liquid flow in cyclone pipe
Jie Kou, Yi Chen*, Junqiang Wu
Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, College of Pipeline and Civil
*Corresponding
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Engineering, China University of Petroleum (East China), Qingdao, China
author (Yi Chen). E-mail address: [email protected]
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Graphical abstract
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Highlights
•The effect of the cone angle on performance of liquid-liquid cyclone is obtained.
•The relation between length of reversed flow and separation efficiency is studied.
•Two suitable underflow tubes are designed.
•The novel liquid-liquid cyclone has a significant separating effect.
Abstract The performance of cyclone can be improved by changing operating conditions or geometric parameters. In the present study, the liquid-liquid flow in cyclone with guiding vanes was investigated by computational fluid dynamics (CFD). The two-phase swirling is numerically simulated by combining the Reynolds stress model with the Mixture model, and the results agree well with the experimental data in the literature. After that, further studies on
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the effects of velocity field, pressure field and separation performance under different cone angles are studied, which indicates the swirling intensity and residence time have important impact on performance of hydrocyclone. Subsequently, the results showed that the reverse
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flow unable to reach the overflow orifice, which lead to stagnant separation efficiency,
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especially for smaller droplets. To solve this problem, two suitable underflow tubes were
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designed, which greatly improved the performance of the cyclone.
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Keywords: hydrocyclone; CFD; cone angle; underflow tube; separation efficiency.
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1. Introduction Compared
with
the
traditional
gravity
sedimentation,
gas
flotation
and
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electro-coagulation, the cyclone has the characteristics of simple structure, small volume, light weight, no moving parts and short processing time, so it has been widely used [1]. In recent years, there is an urgent need for an efficient and compact oil-water separator on a space-limited platforms [2,3]. Due to the different density of oil and water, the centrifugal force received in the cyclone is different, the oil phase is less affected by the centrifugal force
and accumulates in the central region of the separator, while the water phase is greatly affected by the centrifugal force and is distributed on the inter-wall of the separator, finally achieving the separation of the mixed medium [4]. Due to the small difference in density, the separation of oil and water is difficult, and the application in liquid-liquid cyclones is far behind the solid-liquid cyclone [5,6]. According to the difference of the inlet geometry, it can be divided into two types: tangential inlet and axial inlet.
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Earlier researchers focused on experimental study. In 1967, Torrey Canyon oil spill accident in North Sea oil field in the United Kingdom prompted Martin Thew and Colman to study the use of static cyclones for oil-water separation [7]. Then, Trygve Husveg [8] studied
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the variation of separation performance of liquid-liquid cyclone under flow fluctuation
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conditions. Young et al. [9] proposed new cyclone geometry on the base of the 35 mm hydrocyclone designed by Colman and Thew [7]. In their experiments, the effects of
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operating parameters and geometric parameters such as inlet size, cylindrical diameter, cone
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angle, cylindrical section length, flow rate, and droplet diameter on separation efficiency were investigated. Recently, Most researchers have gradually focused on operating parameters
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[10,11], velocity fields [12], and oil droplet distribution [13] in deoiling cyclones. These above are studies of tangential inlet cyclone, but this structure is easy to cause the flow field
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to be unstable [14], and its radial distance is large [15]. The gas-liquid axial separator designed by Swanborn [16] avoided this drawback, then the axial liquid-liquid cyclone with guiding vanes was introduced by Maarten Dirkzwager [17] in 1996 . The internal flow field distribution was studied by laser Doppler velocimetry, and the influence of velocity profile on swirling field was discussed. Following Maarten Dirkzwager, Changes in oil droplet size
through the cyclone online was measured by Stephen Murphy and René Delfo [18] who used a Malvern laser particle size analyzer. Shi [19] et al. used particle image velocimetry (PIV) to experimentally study a new type of vane tube separator. The results showed that the more number of vanes, the smaller time and size of oil droplets entering central zone radially at low inlet flowrate. With the development of computational fluid dynamics (CFD), some commercial software has begun to be applied to the study of cyclone. N. Kharoua et al. [20]
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used the Mixture model to obtain oil phase volume concentration distribution in oil-water cyclone. The existing studies [21] showed that RSM and LES models has higher calculation accuracy, and can reasonably predict flow field distribution in a liquid-liquid cyclone by
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comparing the turbulence models such as standard k-ε, RNG k-ε, RSM, and LES. Dispersed
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phase model (DPM) and stochastic tracking method (STM) were usually used to describe the trajectory of oil droplets in cyclone qualitatively [22-24]. The oil phase was considered as a
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dispersed phase by DPM model. However, it is more suitable when the volume fraction of
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discrete phase less than 10% [25,26]. Huang [27] simulated the three-dimensional turbulence in deoiling cyclone using the Euler-Eulerian method and Reynolds stress model. The results
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showed that there is a large amount of crude oil accumulation near the central region. The separation efficiency was estimated based on phase concentration, and the separation curve of
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the Colman hydrocyclone was in good agreement with the measured values. Noroozi and Hashembadi [28,29] studied the effects of different types of inlet section on separation efficiency. The separation efficiency was increased by 10% and 8% with inlet of a spiral and an exponential body profile, respectively. In addition, some researches have been reported the deeper researches of internal mechanism, such as dynamic characteristics [22,24], droplet
breakage and coalescence [30-32], these above literatures showed that numerical simulation provides another effective tool for the study of cyclones. And only the geometry of conical section was considered by previous studies, the effect of underflow tube structure was rarely considered, and small particle size was not analyzed in depth, which had a great influence on the performance of cyclone. In this paper, the performance of cyclone with different cone angle is investigated by
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analyzing the internal flow field, and the working mechanism has been discussed. The underflow tube of original axial-flow cyclone with guiding vanes is modified for the droplets of smaller size on the basis of the above.
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2. Model descriptions
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2.1 Numerical model 2.1.1 Turbulence model
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The Reynold number of oil-water flow can be expressed as: ReDH dvm m / m
(1)
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Here d is the hydraulic diameter, ρm and μm are the density and viscosity of mixture, and vm is the average velocity.
(2)
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m (1 w )o w w
Where, μo and μw are the viscosity of oil and water, respectively. φw is the water volume
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fraction.
The average velocity is expressed as: vm Q / Ad
(3)
Where, Q is the total volume flowrate, and Ad is the cross-section area.
1
m
wo
o
1 wo
w
(4)
Where, ρo and ρw are the density of oil and water, respectively, wo is the oil mass fraction.
ReDH >2000 can be obtained from the data of section 3.2, so the flow regime is turbulent.
It is well known that the anisotropic for turbulence is assumed by RSM, which is recommended for the simulation of complex swirling flow. Therefore, this model was selected in the paper. The transport equations of the RSM turbulent model are defined as follows:
( uk rho ) Dij pij ij ij xk
(5)
Where rho u 'i u ' j is the Reynolds stress tensor, Dij，pij，Φij，and εij are stress diffusion,
t [ rho ] xk k xk
pi j [rik
u j xk
p
ui ] xk
1 pij 2
2 2 (rho ij ) C2 ( pij p ij ) 3 3
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i j C1
rjk
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Dij
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production, pressure strain, and dissipation, respectively. (6)
(7) (8) (9)
2 (10) 3 Where, p stands for the fluctuating kinetic energy production. μt is the turbulent viscosity, and σk = 1, C1 = 1.8 as well as C2 = 0.6 are empirical constants.
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2.1.2 Multiphase flow model
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ij ij
Mixture model assumes that the local equilibrium over short spatial length scales where the phases move at different velocities. It uses a single-fluid approach, just like the
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volume of fluid model but allows for the phases to be interpenetrating. And lower computational cost is needed as opposed to Eulerian–Eulerian approach. So this model is
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applied in the following works. The continuity equation for the mixture is ( mvm ) 0
(11)
Where ρm is the mixture density, vm is the mass-averaged velocity.
vm
n
k k v k m
k 1
(12)
m k 1 k k n
(13)
Where v k and αk are the velocity and volume fraction of the kth phase, respectively. The momentum equation is expressed as follows: ( m v m v m ) P [ m (v m v m )] m g ( k 1 k k v dr ,k v dr ,k ) R T
n
(14)
Where n is the number of phases, μm is the mixture viscosity, and v dr ,k is the drift velocity of the kth phase, R is the Reynolds stress.
m k 1 k k n
2.2 Computational geometry
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v dr ,k v k v m
(15) (16)
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Simulations were carried out on four hydrocyclones with different cone angles. The dimensions of these cyclones are shown in Figure. 1 and Table. 1. All the dimensions of inlet,
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vane structure and heights are the same, so the effect of different conical section on flow field
3. Numerical simulation
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can be studied specially.
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3.1 Grid-independent analysis
ICEM software is a built-in tool in CFD software, hybrid grid was carried out by it to
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reduce the quantity of grid cells and promote convergence, the main part of computational
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domain adopted the structured grid, only the region of vanes used the unstructured grid. The grid division of computational domain is displayed in Figure. 2. In CFD simulation, the size of grids has an important influence on the convergence and
the accuracy of simulation calculation results [33,34]. To avoid this influence, the separator models with 518507, 793271, , 1159025 and 6330164 grid elements are simulated in this paper. Table. 2 shows the calculation results of separation efficiency and pressure drop under
different grid sizes. It can be seen that when the size of grids is greater than 793271, the difference between the calculation results is small enough, so the numerical calculation of the axial-flow cyclone is followed by the grid size of 793271. 3.2 Solution method Fluent 14.5 can realistically simulate flow fields under complex conditions, heat distribution in various combustion thermal fields, phase transitions in chemical reflection
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processes and so on. The computational domain was occupied by the two-phase flow, in which water and oil represented the continuous phase and the dispersed phase respectively, in the all simulated cases μo = 0.03 Pa∙s, ρo= 850 kg/m3, μw= 0.001 Pa∙s and ρw = 998.2 kg/m3.
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Here, the velocity inlet boundary condition was applied at the inlet, where the axial inlet
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velocity was 0.5m/s. The actual turbulence intensity is calculated by I 0.16( ReDH )1/8 , The boundary condition normal to the outlet was prescribed as outflow where the overflow split
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was 20%. Besides, it was considered that all walls were defined to satisfy the non-slipping boundary condition（and the standard wall function is applied for turbulent flow near the
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wall.） （oil , content at the inlet is 15%.）, Schiller-Naumann model is used for the drag force,
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Manninen-at-al model is applied for the slip velocity. Pressure spatial discretization was set to PRESTO, while the spatial discretization other
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equations were defined in the Second-order upwind form. The solution of the equation was performed using SIMPLE, and the Residual scales in all simulations were adopted for 10-5. 3.3 Validation The separation efficiency in the simulation can be calculated by the following formula [35]:
s
M oo Qoo o Qoo M io Qio o Qio
(17)
Where Moo and Mio are the oil phase mass flowrate of overflow orifice and inlet respectively, Qoo and Qio are the oil phase volume flowrate of overflow orifice and inlet respectively. The mechanism of the Thew model is consistent with the model in this paper, oil and
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water is separated by centrifugal force, the difference is that the guiding vanes were not installed in Thew model, Thew model obtains the swirling field through the tangential inlet. This structure increases the radial dimension of the model and has a large impact force, the
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specific geometric parameters can be obtained from the literatures [10][29]. For the Thew model, the constant mass flow rate (20 l/min) at the inlet boundary as a plug flow is employed.
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The imposed mass flow rate boundary condition with respect to overflow split ratio (17%) as
leave the underflow).
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a percentage of inlet mass flow rate are used for outlets (17% exit from overflow and the rest
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To validate the reliability about the simulations, it is essential to compare the simulating results with the existing data. The comparison between experimental, analytical Thew model
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[10,29] and the present numerical results for separation efficiency and tangemtial velocity
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profile were shown in Figure. 3. As can be seen from Figure. 3(a), centrifugal device promotes the resistance and causes
the droplet to break down because of the fishhook effect [29], which can be founded in the experimental work. However, this phenomenon was ignored in the simulation process, which leads to a large error at this point. The turbulence models of RSM, RNG k-ε, and k-εwere used for simulation. The average separation error( 25～120 microns) of RSM, RNG k-ε, and
k-ε turbulence models and experiments was 8.67%, 13.71%, and 16.73%, respectively. It can be seen from that the RSM turbulence model used in this paper are reliable, Here simulations were also performed for the cyclone of Thew, and the corresponding computed tangential velocity profile was shown in Fig. 3(b). It can be concluded that the deviation is small and the numerical simulation can be credible. 4. Results and discussion
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4.1 Influence of cone angle 4.1.1Tangential velocity
The tangential velocity profile of different cone angles at z= -300 mm is shown in Figure.
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4. The peak of tangential velocity enhances significantly as the cone angle increases. This is
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because the cross-sectional area of the conical section downstream decreases under the condition of higher cone angle, which contributes to the dispersed oil droplets migrate to axial
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center with a shorter radial path. Moreover, the centrifugal acceleration is proportional to the
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square of tangential velocity, so the centrifugal force will increase sharply in the flow. However, the flow residence time of droplets reduces greatly owing to the shorter axial length
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of conical section and higher tangential velocity, which decreases the overall migration of the dispersed droplets.
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4.1.2 Axial velocity
The axial velocity profile at z = -300 mm is shown in Figure. 5 for different angles. The
positive and negative values of velocity represent the reverse (moving to the overflow orifice) and forward (moving to the underflow orifice) flow, respectively. Near the wall (0.02 mm < r < 0.025 mm), the forward velocity gradually increases as the cone angle decreases,
contributing the fast moving flow can deliver most of the dispersed droplets to the underflow orifice As can be seen from Figure. 5, an interesting tendency of the axial velocity profile emerges at the intermediate region (0.005 mm < r < 0.02 mm). The forward flow velocity decreases as the cone angle decreases; when the cone angle is 2 degree, the fluid even flows towards the overflow orifice. Therefore, droplets dispersed in the fluid at the intermediate region (0.005 mm < r < 0.02 mm) have a longer residence time for the lower cone angle due
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to slower axial velocity or reverse flow. 4.1.3 Static pressure
Figure. 6 shows the radial pressure distribution with different cone angles. It can be seen
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that the pressure near the wall is significantly higher than that in the central area of the
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cyclone. It is the result of a combination of swirling motion and centrifugal force. In addition, the pressure at the central point increases gradually with the increase of the cone angle, thus
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making the droplets near the wall move towards the center at a greater speed, and the radial
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pressure gradient also increased in this case. The effect of the cone angle on the pressure distribution along the central axis is shown in Figure. 7. The vertical coordinate represents the
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static pressure value and the horizontal coordinate represents the position on the central axis. The core pressure first increases and becomes maximum value and then decreases. A positive
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axial pressure gradient is created from the maximum pressure location to the overflow orifice, which is why the reverse flow occurs. As can be seen from Figure. 8, the positive axial pressure gradient generated by a smaller cone angle maintains a longer distance. 4.1.4 Separation efficiency The conical section is the key area for oil-water separation. Figure. 9 shows the
separation efficiency at different cone angles and particle sizes. It is found that separation efficiency gradually decreases with the cone angle increases. This is the combination of a smaller angular momentum change and a longer residence time. However, for all cone angles, the separation efficiency is low for droplet sizes less than 40μm. This is because small droplets are less sensitive to swirling motion, resulting particularly inefficient. And in the practical applications of liquid-liquid cyclones, it is crucial to separate small particle droplets.
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The trade-off between swirl intensity, length of the reverse flow, and residence time of droplets is necessary to optimize separation efficiency. Figure. 10 shows the relationship between the separation efficiency and the length of the reverse flow. As the cone angle
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increases, the separation efficiency decreases sharply. For the length of the reverse flow (Lc),
4.2 Optimization of the underflow tube
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the trend is entirely consistent. Therefore, the separation efficiency is proportional to Lc.
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The above simulation results reflected that there was still a swirling motion in the
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underflow tube, so the dispersed oil droplets would gather toward the center to form the underflow core, but this part of the oil droplet could not reach the overflow orifice due to the
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absence of reverse flow. Some droplets moved forward, and others moved in the reverse direction as shown in Figure. 7. This flowing feature inspired us that if we design a
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mechanism to collect the oil core flowing out of the underflow outlet, the separation efficiency of small droplets may greatly be improved. In this way, the adjusting range of operating parameters of the cyclone would be increased, and the separation efficiency could be maintained at a higher flowrate fluctuation. In this paper, two mechanisms for capturing droplets from the underflow outlet are studied.
4.2.1 Structure of the underflow tube The underflow tube was directly connected to the conical section with 6 degree. Two types of underflow structures were designed to evaluate overall performance. Structure-1 had a vortex finder with the same diameter as the original overflow tube, and its underflow outlet is tangentially connected to the underflow tube. Structure-2 had two slots as the underflow outlets, the vortex finder was the same as structure-1, and the total area of two slots was equal
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to the area of underflow outlet of the original 6 degree cyclone. These two structures of suitable size are shown in Figure. 11. The diameters of two overflow outlet tubes were Do and Do’ respectively, the split ratio of both overflow outlet tubes was 10%.
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4.2.2 Effect of underflow tube on static pressure along the center axis
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Figure. 12 shows the effect of different underflow structures on the center static pressure. It can be seen that the static pressure curves of the two structures are almost coincide until the
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tail of underflow tube, However, near the end of the underflow tube (z= - 950mm), the center
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pressure curves are obviously different. For structure-2, the core pressure decreases sharply at the end of the underflow tube, this is due to the slotted geometry of structure-2. In addition, its
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pressure gradient is small compared to the structure-1. 4.2.3 Effect of underflow tube on separation performance
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The effect of different structures on performance of hydrocyclone was evaluated as
shown in Figure. 13. η and η’ are the fractional separation efficiency of Do and Do’, respectively, the values of both were defined according to the efficiency formula in Section 3.3. ηT = (η + η’) is the total fractionation efficiency. The η between structure-1 and structure-2 is not much different. As the droplet size increases, the fractional efficiency of the
Do’ (η’) first increases and then decreases. This is because larger droplets increase the rate of migration, thereby increasing η’. At the same time, η is gradually increasing either, which reduces the number of possible droplets flowing to the Do’. Moreover, structure-2 provides a smaller η’ than structure-1 for larger droplets, the reason is that the migrated droplets are remixed through the slots in structure-2, thereby reducing η’. Figure 13 also shows that when we compare the separation efficiency with an original 6deg cyclone, the overall grade size
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efficiency (ηT) is greatly improved due to the addition of the underflow tool. η’ is an additional fractional separation efficiency. And for smaller oil droplets such as 40μm, the separation efficiency is greatly improved; the phase distribution contours of 6deg cyclone and
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6deg cyclone with structure-1 at 40 micron are shown in Figure. 14.
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5. Conclusions
To understand the influence of different cone angle on separation efficiency, the detailed
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flow field information of the cyclone is obtained by CFD simulation. It is found that the trend
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of tangential velocity and axial velocity distribution is absolutely consistent in all hydrocyclones, but the change of cone angle has a significant effect on the value, indicating
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that centrifugal acceleration will change dramatically. Moreover, the length of the reverse flow in the hydrocyclone of different cone angles is completely different. And the reverse
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flow at all cone angles cannot reach the underflow orifice. By adding an underflow tool, it has been found that the separation efficiency is greatly improved, especially for smaller oil droplets. This is because a portion of the oil droplets always flows out of the underflow orifice in the form of an oil core. Therefore, it is desirable to add an underflow tool to collect oil droplets flowing at the underflow orifice.
Appendix A. Nomenclature cross-section area (m2)
a
width of the slot (m)
b
height of the slot (m)
C1, C2
empirical constants
Ci, Cu
oil concentration of the overflow and underflow, respectively
Du
underflow tube diameter (m)
Dc
body diameter (m)
Du
overflow tube diameter (m)
Di
inlet diameter (m)
Dij
stress diffusion
Do
overflow tube diameter (m)
Do’
overflow tube’ diameter (m)
d
hydraulic diameter(m)
H
cyclone height (m)
Hc
cyclone cylinder height (m)
Hv
length of the vortex finder (m)
I
turbulence intensity
Lc
length of the reverse flow (m)
Mo, Mi
oil phase mass of overflow and inlet, respectively
n
number of phases
-p re
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fluctuating kinetic energy production shear production
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pij
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p
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Ad
Q
total volume flow (m3/s)
Qoo, Qio
oil phase overflow port and inlet flow rate, respectively
ReDH
Reynolds number of the mixture
R
Reynolds stress
r
radial position (m)
rho
Reynolds stress tensor
vm
average velocity (m/s)
vm
mass weighted average velocity (kg/s)
vk
velocity of the kth phase (m/s)
v dr ,k
drift velocity of the kth phase (m/s) letters
αk
volume fraction of the kth phase
θ
cyclone angle (deg)
ρk
the density of the kth phase (kg/m3)
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Greek
density of the mixture(kg/m3)
ρo, ρw
oil and water density (kg/m3)
µm
viscosity of mixture (Pa∙s)
μk
viscosity of the kth phase (Pa∙s)
μt
eddy viscosity (Pa∙s)
µo, µw
oil and water dynamic viscosity (Pa∙s)
η
separation efficiency of overflow tube (%)
ηs
separation efficiency in the simulation (%)
η’
separation efficiency of overflow tube’ (%)
ηT
total separation efficiency (%)
φw
the water volume fraction
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kronecker delta
εij
source term
pressure-strain
oil mass fraction
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wo
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δij
Φij
σk
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ρm
empirical constants
Acknowledgements
This study was supported by the Opening fund of Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, and the Fundamental Research Funds for the Central Universities.
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References
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Figures
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Figure. 1. The geometry of hydrocyclone and corresponding coordinate
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Figure. 2. A sample of grid generation for numerical simulation
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Figure. 3(a). Comparison of experimental and numerical simulation results for
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effect of oil droplet size on separation efficiency.
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Figure. 3(b). Comparison of numerical simulation results for tangential velocity plot
Figure. 3. Analysis of the numerical and experimental results
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Figure. 4. Tangential velocity profile with different cone angles at z = -300mm, particle
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sizes =70μm
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Figure. 5. Axial velocity profile with different cone angles at z = -300mm, particle sizes =70μm
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Figure. 6. Static pressure profile with different cone angles at z = -300mm, particle sizes
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=70μm
Figure. 7. Static pressure along the axial direction of the hydrocyclone with different
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cone angles, particle sizes =70μm
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Figure. 8. Reversed flow contours with different cone angles, particle sizes =70μm
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Figure. 9. Grade efficiency with different cone angles
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Figure. 10. Connection between separation efficiency and the length of reversed flow under
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different cone angles
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structure-1
structure-2
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Figure. 11. Shape and dimensions of structures (×10-3m)
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Figure. 12. Center static pressure profile with two structures
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Figure. 13. Grade efficiency with two structures
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Figure. 14. Comparison of oil distribution in the 6deg cyclone (left) and 6deg cyclone with
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structure-1 (right) at 40 micron
Tables cyclone height/H(×10-3m)
Common for all cyclones(×10-3m)
I-1
2
21.9
1105.3
Body diameter, Dc=50
I-2
4
18
1105.3
overerflow tube diameter, Do=8
I-3
6
18
1105.3
Inlet diameter, Di=50
I-4
10
18
1105.3
Cylinder height, Hc=200
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cyclone cyclone underflow tube no. angle/θ(deg) diameter/Du(×10-3m)
overflow pressure (MPa) 0.092 0.115 0.116 0.117
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518507 793271 1159025 6330164
separation efficiency (%) 59.44 61.28 62.27 62.31
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grid size
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Table. 1. Main dimensions of simulated hydrocyclones
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Table. 2. Validation of grid independence
underflow pressure (MPa) 0.083 0.084 0.084 0.084