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Numerical and experimental investigations of the effects of the breakup of oil droplets on the performance of oil–gas cyclone separators in oil-injected compressor systems
Accepted Manuscript Numerical and Experimental Investigations of the Effects of the Breakup of Oil Droplets on the Performance of Oil-gas Cyclone Separators in Oil-injected Compressor Systems Xiang Gao, Jinfeng Chen, Jianmei Feng, Xueyuan Peng PII:
S0140-7007(13)00151-5
DOI:
10.1016/j.ijrefrig.2013.06.004
Reference:
JIJR 2539
To appear in:
International Journal of Refrigeration
Received Date: 18 January 2013 Revised Date:
7 June 2013
Accepted Date: 10 June 2013
Please cite this article as: Gao, X., Chen, J., Feng, J., Peng, X., Numerical and Experimental Investigations of the Effects of the Breakup of Oil Droplets on the Performance of Oil-gas Cyclone Separators in Oil-injected Compressor Systems, International Journal of Refrigeration (2013), doi: 10.1016/j.ijrefrig.2013.06.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.
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Highlights The results showed that the breakup of oil droplets occurred in the separation process. The breakup of oil droplets influenced certainly the separation efficiency.
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The inlet velocity determined the possibility of the breakup of oil droplets.
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Numerical and Experimental Investigations of the Effects of the Breakup of Oil Droplets on the Performance of Oil-gas Cyclone Separators in Oil-injected
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Compressor Systems Xiang Gao, Jinfeng Chen, Jianmei Feng,* Xueyuan Peng School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China
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ABSTRACT
A numerical simulation was conducted of the dynamic trajectories and the separation performance of oil droplets,
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with a focus on the breakup of oil droplets in an oil-gas cyclone separator. The separation efficiency was also studied experimentally, and the oil droplets’ diameter distributions before and after the separator were measured with a Malvern particle size analyser to verify the simulation model. Both the experimental and simulation results showed that the breakup of oil droplets occurred in the separation process, clearly influencing the separation efficiency. In addition, the results indicated that inlet velocity played an important role in separation efficiency, as it not only
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significantly affected the tangential velocity inside the separator, but also determined the possibility and degree of the breakup of oil droplets.
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Key Words: Oil-gas Cyclone Separator, Numerical Simulation, Breakup of Oil Droplets, Separation Efficiency
*
Corresponding author: Jianmei Feng, School of Energy and Power Engineering, Xi’an Jiaotong University, 28 Xianning Road, Xi’an, Shaanxi, 710049, China, Tel & Fax: (+86)29-82663785 Email: [email protected]
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1. Introduction Two-stage separation processes are frequently adopted to effectively recycle the oil injected into a compressor and get high-quality compressed gas (Xing, 2000). The first-stage separator, also known as the preliminary separator,
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uses mechanical impact principles to capture most of the oil droplets mixed into the gas while the second-stage separator, often called the filter, uses the agglomeration method to absorb the residual oil mist. The separation efficiency of the first-stage separator significantly influences the residual oil content that enters the filter, thereby directly determining the filter’s life-span and the performance of the compressor system. Improving the separation
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efficiency of the first-stage separator is an important step in purifying the discharge gas and achieving the best performance in oil-injected compressor systems (Hammerl et al., 2000). At present, the oil-gas cyclone separator is
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widely accepted as a first-stage separator in oil-injected compressor systems because of its simple geometry and easy maintenance.
A considerable number of studies have used numerical simulations to examine the performance of the cyclone separator. Many of these studies have focused on the gas flow field in the cyclone chamber. The Reynolds stress turbulence model (RSM), based on the Reynolds Averaged Navier-Stokes equations (RANS), has been widely
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accepted. For example, Gronald and Derksen (2011) compared the finite volume RANS model with two LES approaches in their study. They pointed out that the unsteady RANS-based simulation that results from a relatively coarse grid can provide reasonable and industrially relevant results with limited computational effort. Using the RSM model, Slack et al. (2000) simulated the flow field in a conventional high-efficiency Stairmand cyclone. The
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simulated results showed consistent agreement with the Laser Droplet Anemometry measurements. Hoekstra et al. (1999) simulated the gas flow field with many different turbulence models and reported that the prediction made by
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the RSM model was in reasonable agreement with the measured profiles of all three swirl numbers. Many numerical studies have also tried to study the particle motion in the swirling flow in a cyclone separator by using the discrete phase model (DPM), based on the Euler-Lagrangian method. Matsuzaki et al. (2006) investigated the particle motions in the swirling flow in a cyclone using Large Eddy simulation (LES) and were able to predict the performance of particle separation from the particle tracing results. Elsayed and Lacor (2011) studied the effect of a cyclone’s inlet pipe size on its performance and simulated the particle motion using the DPM model. Several previous investigations studied the gas flow field and the particle motion in the cyclone experimentally. Hoekstra (2000) systematically investigated the gas flow field and the collection efficiency of cyclone separators. He
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tested the pressure drop, velocity distribution and collection efficiency of solid-gas cyclone separators with different structures. Using a high-speed motion analyser, Wang et al. (2008) determined the motion trajectory of solid particles’ inside the hydrocyclone. The results were useful in understanding the particle dynamics in the separation
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process. These studies were performed on either the flow field, or the solid particles motion in the cyclone. However, there is an essential difference in the particle morphology of the oil-gas cyclone separator. The properties of the liquid particles are different than those of the solid particles. To the authors’ knowledge, few previous studies of oil-gas
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cyclone separators have focused on this difference. Wiencke (2011) analysed the fundamental principles of the design of gravity liquid separators and applied the single-droplet model to the sizing of gravity liquid separators.
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Shan et al. (2007) reported that the breakup of the droplets played an important role in determining the final particle size and velocity distribution in precursor plasma spray. Similarly, for the oil-gas cyclone separator, the high speed swirling flow field led the oil droplets to breakup in the separation process, affecting the separation performance. Therefore, it is important to develop a better understanding of the dynamics of the oil droplets and their separation process in the flow field inside the oil-gas cyclone separator.
Using the RSM model together with the Taylor analogy breakup model (TAB), this study examined the effect of the
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breakup of oil droplets on separation performance in the oil-gas cyclone separator. The experimental investigation was undertaken to obtain the oil droplets’ diameter distributions before and after the separator process, and to compare these experimental results with the numerical prediction. The separation efficiencies at different inlet
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velocities were also measured. The purpose of this study was to discuss the existence of the breakup of oil droplets
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and analyse its effect on separation efficiency.
2. Physical Model
Fig. 1 provides a schematic view of the oil-gas cyclone separator used in this experiment, which is commonly used in oil-injected compressor systems. The structural parameters of the cyclone are shown in Table 1. The oil-gas mixture enters tangentially through the inlet pipe on top of the cyclone separator and then rotates downward between the cylinder and the central channel. Due to the centrifugal force, larger oil droplets moving to the separator wall are separated and the remaining smaller oil droplets follow the discharge gas to finally escape through the outlet.
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3. Numerical Simulation The RSM model, which has been widely accepted in many previous studies of cyclones, was used to describe the swirling flow field. For the tracking of oil droplets, the DPM model was applied using one-way coupling, with the
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assumption that the discrete phase had no effect on the continuous phase flow field because the oil volume concentration was quite low in this study, usually less than 1 per cent. The governing equations for the gas flow field were from Elsayed and Lacor (2011).
3.1 Oil-droplet model
dt
= FD (u − u p ) +
g (ρ p − ρ )
ρp
+ Fadd
(1)
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du p
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The governing equation of the oil droplets in the flow field was given as follows
where u and up were the velocities of the gas and oil droplet; ρ and ρP were the densities of the gas and oil droplet; g was the acceleration of gravity; FD was the coefficient; Fadd was the additional force. The first item on the right-hand side described the drag force per unit particle mass and the second item was the gravity force per unit particle mass. The coefficient FD was calculated by
18µ C D Re ⋅ ρ p d p 2 24
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FD =
(2)
where µ was the dynamic viscosity of the gas; dp was the radii of the oil droplet; Re was the relative Reynolds
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number and CD was the drag coefficient that were calculated as follows
Re =
ρd p u p − u
C D = a1 +
µ a a2 + 3 Re rp Re rp
(3)
(4)
where a1, a2 and a3 were constants among some special Reynolds number range indicated by Morsi and Alexander (1972).
The additional force Fadd included forces such as the thermophoretic force, the Brownian force, and Saffman’s lift force. Because the other forces were much lower than the Saffman’s lift force, Fadd was approximately equal to the Saffman’s lift force (Saffman, 1965) and can be expressed as
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Fadd =
2 Kv1/ 2 ρd ij
ρ p d p ( d lk d kl )1/ 4
(u − u p )
(5)
where K=2.594; dij, dlk and dkl was the deformation rate tensor; ν was the kinematic viscosity.
of the velocity yielded displacement and thereby the trajectory of the oil droplet
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The velocity of the oil droplet can be predicted by integrating equation over discrete time steps. Further integration
x p = ∫ u pX dt , y p = ∫ u pY dt ,
z p = ∫ u pZ dt . When the trajectory equations were solved by integration over discrete time steps, the gas velocity
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was the mean gas-phase velocity.
3.2 Droplets breakup model
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The TAB model was used to account for the breakup of droplets. The TAB model developed by O’Rourke and Amsden (1987) was chosen because it fits the cyclone’s low-Weber-number condition.
3.2.1 Droplet distortion
The following equation was used to describe the droplet breakup in the TAB model
dx d 2x = mp 2 dt dt
(6)
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F − kx − d p
where F was the external force of the droplet, x was the displacement of the droplet equator from its spherical (undisturbed) position and mp was the mass of the droplet. The coefficients of the equation (6) were taken from
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Taylor’s analogy (Taylor, 1963)
F ρ u02 = CF ρ p rp mp σ k = Ck ρ p rp3 mp d µ p = Cd p 2 ρ p rp m p
(7)
where rp was the radius of the droplet (undisturbed), σ was the surface tension of the droplet, µP was the dynamic viscosity of the droplet and the constants CF=1/3, Ck=8 and Cd=5 were chosen to match the relevant examples and theory (Larsen and Howell, 1986). The droplet was assumed to break when the distortion grew to a critical ratio of the droplet radius (O’Rourke and
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Amsden, 1987). This breakup requirement was given as x>Cbr (Cb=1/2).
3.2.2 Size of child droplets The size of the child droplets was determined by equating the energy of the parent droplet to the combined energy of
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the child droplets
E parent = Echild
(8)
The energy of the parent droplet included surface energy, vibration and torsion deformation energy
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E parent = Esurf + Eosc The surface energy was given as
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Esurf = 4π rp2σ
(9)
(10)
and the vibration and torsion deformation energy was calculated by
Eosc = K
π 5
dy 2 ) + ω 2 y2 dt
ρ p rp5 (
(11)
mode, which was equal to 10/3.
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where y = Cb ; K was the ratio of the total energy in distortion and oscillation to the energy in the fundamental rp
The child droplets were assumed to be non distorted and non oscillating. Thus, the energy of the child droplets can be shown to be
rp
rp 32
+
π 6
ρ p rp 5 (
dy 2 ) dt
(12)
rp 32 was the Sauter mean radius of the droplet size distribution that was given by equating the energy of the
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where
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Echild = 4π 2σ
parent and child droplets (equation 9 and equation 12), setting y = 1 and
ω 2 = 8σ / ρ p r 3 (O’Rourke and
Amsden, 1987)
rp 32 =
rp 3 2 8 Ky 2 ρ p rp (dy / dt ) dy 2 + 1+ ( ) 20 dt σ
(13)
For the Sauter droplet size distribution, rp 32 = 0.7 rp max , rp max was the maximum among the droplets radius distributions. 6
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Once the size of the child droplets was determined, the number of child droplets can easily be determined by mass conservation.
3.2.3 Velocity of child droplets
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The TAB model allowed for a velocity component normal to the parent droplet velocity to be imposed upon the child droplets. When breakup occurred, the equator of the parent droplet was traveling at a velocity of
dx = Cb r (dy / dt ) . Therefore, the child droplets would have a velocity normal to the parent droplet velocity given dt
where
Cv , as a constant, was equal to 1.
3.3 Boundary conditions
dy dt
(14)
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unormal = Cν Cb rp
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by
A velocity inlet boundary condition was used at the inlet of the cyclone separator; specifically, a velocity normal to the inlet surface was specified. The pressure outlet boundary condition was set at the cyclone outlet according to the
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back pressure of the compressor system. In current study, both by the theoretical calculation and test observation, the two-phase flow was indicated to be the misty flow in the tube before entering the separator. Therefore, the homogeneous flow model was employed and then the oil droplets velocity was assumed to be the same as the gas inlet velocity at the inlet (Faghri and Zhang, 2006). Meanwhile, the droplets size distribution at the inlet was given
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as the experimental results. A no-slip boundary condition was adopted for the gas flow on all of the walls. For the oil droplets phase, the reflect boundary condition was applied to the cylindrical wall and the trap boundary condition
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was applied to the underside wall. The reflect boundary condition meant that the droplets encountered a rebound force and might break or return to the gas flow field if they made contact at a high tangential velocity. When droplets arrived at the underside wall, the trap boundary condition meant that they were separated and the trajectory calculation was terminated. If the droplets crossed the inlet and the outlet, the escape boundary condition applied, i.e. the droplets escaped and the trajectories calculation was also terminated.
3.4 Solver settings The solver settings for the gas flow field in this study were drawn from Kaya and Karagoz (2008). They investigated the performance of different discretisation schemes and the suitability of various numerical schemes in highly 7
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complex swirling flows in the simulation of cyclone separators; the best settings are summarised in Table 2. The PRESTO pressure interpolation scheme was one of the more successful schemes and the SIMPLEC algorithm for pressure velocity coupling gave predictions closer to the experimental data. The QUICK scheme for momentum
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equations was highly recommended. The choices were the second-order upwind scheme for the turbulent kinetic energy and turbulent dissipation rate and the first-order upwind scheme for the Reynolds stress.
The time step used for the unsteady simulation should be a tiny fraction of the average residence time (Chuah et al., 2006), and is determined from the cyclone volume and the gas flow rate. The minimum residence time in this study
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was about 0.06 s, so a time step of 1e-04 s was chosen as sufficient to properly reveal the transient phenomena.
3.5 The grid and the grid independency study
and meshed separately, as shown in Fig. 2.
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The geometry of the entire separator was divided into a number of blocks, and unstructured grids were generated
The gird independence study was performed by comparing the simulation results obtained under different grid numbers, as shown in Table 3 and Fig. 3. The maximum difference between the results of the coarser and finer grids was less than 10%, suggesting that grid independency results could be achieved in the coarser mesh of 95261 cells.
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However, to eliminate any uncertainty, simulations were performed using a mesh with 218876 cells.
4. Experiment 4.1 Test rig
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To obtain the separation efficiency and droplet size distribution at the inlet and outlet of the cyclone separator, the experimental system shown in Fig. 4 was built. Air was used as the work fluid. The oil-gas mixture discharged from
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the compressor first flowed into the horizontal oil-gas separator, and then entered the cyclone separator. After being separated by the cyclone separator, the mixture flowed through the oil filter and the AO/AA superfine oil filter. The gas flow rate through the measuring section was varied by adjusting valves 2 and 3. The Malvern particle size analysers were set before and after the cyclone separator. To ensure the accuracy of the Malvern particle size analyser, the horizontal oil-gas separator was added before the oil-gas mixture entered the cyclone separator. Pure nitrogen was added to the measuring section, as in the previous study by Feng et al. (2008).
4.2 Test conditions The separation efficiencies of the cyclone separator under different test conditions were measured. The gas flow rate 8
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ranged from 0.5 m3.min-1 to 1.2 m3.min-1, and the oil-gas mixture inlet velocity ranged from 14 m.s-1 to 18 m.s-1. The oil injection flow rate ranged from 1930 L.h-1 to 1950 L.h-1. All of the parameters were measured at the constant compressor discharge pressure of 0.8 MPa and a temperature of 90°C.
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4.3 Uncertainty analysis The accuracies of the instruments used in the experiment are shown in Table 4. Following the Kline method, an uncertainty analysis was carried out on the experiment results (Kline and McClintock, 1953). The square of errors was calculated as follows
(15)
WU was the total uncertainty associated with the dependent variable U , yi was the independent variable
that affected the dependent variable U
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where
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1/ 2
2 N ∂U WU = ∑ ( Wyi ) i =1 ∂yi
and Wyi was the uncertainty of the variable yi . The maximum
uncertainties were established to be 0.35% for the inlet velocity, 1.732% for the separation efficiency and 1% for the
5. Results and Discussion
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droplet size distribution.
5.1 Validation of numerical simulation results
The cyclone separator in this study was a cylinder-based oil-gas cyclone separator, which is different in structure
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from the solid-gas cone cyclone separators used in previous studies. Furthermore, due to the limited experimental conditions, it was very difficult to measure the gas flow velocity distributions of the studied separator. To validate
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the simulation model, indirect verifications of two aspects were conducted as stated below. First, the subsequent method was used to simulate the high efficiency Stairmand cyclone, of which the tangential and axial velocity distributions have been measured in previous studies (Hoekstra, 2000). Fig. 5 illustrates the comparison of simulated and tested tangential and axial velocity distributions at an axial position located at Z=942.5mm from the cyclone bottom. Given the complexity of the turbulence swirling flow in the cyclones, the agreement between the simulation and the experimental data was considered to be acceptable. Second, as Fig. 6 reveals, the simulated static pressure drops were compared with the experimental data. The results showed that the relative errors of the static pressure drops were less than 10%, so the simulation method used in this 9
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study is suitable for analysing the gas flow field of the separator. It was also found that the static pressure drop increases as the inlet velocity increases due to increasing friction between the gas and the wall.
5.2 Simulated gas flow field and trajectory of oil droplets
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5.2.1 Gas flow field The static pressures and tangential velocity distributions at six different sections along the Z axis with an inlet velocity of 17.3 m.s-1 are shown in Fig. 7. As expected, the profiled tangential velocity exhibited a so-called Rankine-type vortex, which consists of a free vortex in the outer region and an inner forced vortex at the centre. The
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variation relationship is similar to other reports, particularly for gas-solid cyclone separators (Elsayed and Lacor, 2011).
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The tangential velocities with different inlet velocities at the section Y=0, Z=75 mm and Z=15 mm are shown in Fig. 8. Obviously, the tangential velocity increased as the inlet velocity was enhanced. The higher tangential velocity improved the probability of the oil droplet reaching the wall. In other words, if the breakup of oil droplets is ignored, the separation efficiency may increase continuously as the inlet velocity grows.
5.2.2 Trajectory of oil droplets
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The trajectories of the oil droplets at different times with an inlet velocity of 18.1 m.s-1 are shown in Fig. 9. Clearly, once the oil-gas mixture entered tangentially into the cyclone cylinder through the inlet pipe, oil droplets with relatively smaller diameters moved faster due to their smaller inertial forces on smaller radii, compared to the larger droplets, as shown at 0.01 s in Fig. 9.
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The results also showed that the larger oil droplets were more easily separated by arriving at the cylinder wall. In addition, the oil droplets were separated near the end of the separation process, at about 0.15 s for the specified
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operation condition; however, there were a few oil droplets floating on the topside wall. These oil droplets were considered to be separated as they did not escape from the outlet in current short time simulations. But for a long time, the phenomenon may decrease the separation efficiency similar to the "dust rings" in solid-gas cyclone separator (Wang et al., 2006). In this paper, the effects of the phenomenon on the separation efficiency were ignored.
5.3 Droplet size distribution The droplet size distribution at the inlet fitted with the experimental data from the Rosin-Rammler function is shown in Fig 10; this was used as the oil droplets’ inlet distribution setting in the simulations above. The volume fraction of the vertical ordinate was defined as the fraction of droplets of diameter greater than d which was given 10
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by Yd = e − ( d / d ) , where d was the size constant and n was the size distribution parameter. The percentage of n
droplets at inlet, by volume, with a diameter less than 10 µm was about 5%, whereas for the diameter between 10 µm and 45 µm it was 35% and for the diameter larger than 45 µm, it was 60%.
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Fig. 11 illustrates the comparison of the droplet size distributions between the inlet and outlet of the cyclone separator. The volume percentage of droplets at the outlet was quite different than the percentage of the oil volume at the inlet. Compared the droplets distribution between the inlet and outlet, Fig.11 shows that the droplets with diameter greater than 45 um reduced significantly. The increase in the percentage of oil droplets smaller than 20um
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at the outlet implied that droplet breakup happened during the separation process. It was also evident that the percentage of smaller diameter oil droplets increased at the outlet as the inlet velocity increased. This meant that a
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higher velocity inside the separator led to easier droplet breakup. The percentage of 10 µm-droplets increased in volume from 3% at the inlet to 7.5% at the outlet when the inlet velocity was 15.2 m.s-1. If the inlet velocity reached 18.1 m.s-1, the percentage of 10 µm-diameter droplets would increase to 10%.
5.4 Separation efficiency and the effects of breakup The separation efficiency was defined as η, as follows
m out ) × 100(% ) m total
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η = (1 −
(16)
where m out was the mass of the oil that flowed out of the separator with the discharge gas and m total was the mass of the oil that entered the separator with the inlet oil-gas mixture.
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Fig. 12 shows the comparison of separation efficiencies between the simulated results and the experimental data with different inlet velocities. The effects of oil droplet breakup on separation efficiency can be determined by
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combining Figs. 11 and 12. The separation efficiencies measured at different conditions were about 70%-80%. However, the simulated separation efficiencies under the same conditions were almost 100% when the simulation model did not consider the breakup of droplets. When the breakup of oil droplets was taken into account using the TAB breakup model, the simulated separator efficiencies decreased. The maximum relative error between the simulated results and the experiment data was about 20%. The tested separation efficiency did not increase constantly with increasing inlet velocity and an optimal inlet velocity existed for the best performance. This inconsistency indicated that, when the inlet velocity is low, the separation efficiency increases with inlet velocity because the centrifugal force of the droplets increases to help the separation, but does not cause droplet breakup. 11
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However, if the inlet velocity increases further, the effects of droplet breakup are the main factor in the decrease of separation efficiency. Fig 11 shows that increasing inlet velocity increases the possibility of oil droplets breakup. In addition, as can be seen, the measured separation efficiency was lower than the simulated results, even for the
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model including the droplets breakup behaviour. This can be explained by the fact that in numerical simulation, the oil level on the bottom was treated as the wall boundary and the trap boundary condition was applied, so that the oil droplets were assumed to be separated if they reached this surface. In the experiment, however, due to the effect of the high speed swirling flow, the oil separated on the baffle might be blown back into the flow field and finally
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escape through the outlet (Hoffmann and Stein, 2004). This phenomenon would definitely decrease the separation
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efficiency, but it was neglected in the simulation model.
6. Conclusions
The effects of oil droplet breakup and inlet velocity on oil gas cyclone separator performance were investigated numerically and experimentally. Based on the results, the following conclusions can be drawn. •
The breakup of oil droplets occurred in the oil gas cyclone separator and influenced the separation
•
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performance.
The simulated results proved that the RSM numerical model that included the TAB model was a promising tool for understanding the behaviour of oil droplets in the gas flow field during the separation process.
•
Inlet velocity played an important role in separator efficiency, as it determined the tangential velocity inside
•
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the separator, and increasing inlet velocity caused an increase in the possibility of oil droplet breakup. Further investigation of different structures of cyclone separators and of the mechanisms of oil droplet
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breakup are required to design more efficient separators.
ACKNOWLEDGMENT
The research was supported by the National Natural Science Foundation of China (Research Project 50906068/E060502).
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inlet height (mm)
b
inlet width (mm)
CD
drag coefficient
D
cyclone diameter (mm)
DPM
discrete phase model
d
central channel diameter (mm), radius (m)
d
size constant (m)
dij,dlk,dkl
deformation rate tensor (s-1)
E
energy (J)
F
force (N)
Fadd
additional force (N)
FD
coefficient
g
gravity acceleration (m•s-2)
H
cyclone height (mm)
h
central channel height (mm)
L
inlet length (mm)
LES
Large Eddy simulation
m
mass (kg)
n
size distribution parameter
R
cyclone radius (m)
Re RSM
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RANS
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a
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NOMENCLATURE
Reynolds Averaged Navier-Stokes
Reynolds number Reynolds stress turbulence model
r
radius (m)
rp 32
Sauter mean radius of the droplet size distribution (m)
TAB
Taylor analogy breakup model
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velocity (m•s-1)
W
uncertainty
X, Y, Z
coordinates (mm);
x
displacement of the droplet equator from its spherical (undisturbed) position, position (m)
Yd
volume fraction
y
independent variable, position (m)
z
position (m)
η
efficiency
µ
dynamic viscosity (Pa•s)
ν
kinematic viscosity (m2•s-1)
ρ
density (kg.m-3)
σ
surface tension (N•m-1)
ω
angular frequency (Hz)
additional
child
child oil droplet
max
maximum
p
oil droplet
p32
Sauter droplet size distribution
parent
parent oil droplet
Out
out of the separator
surf Total X, Y, Z
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osc
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add
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Subscripts
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u
vibration and torsion deformation
surface total
direction
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O’Rourke, P.J., Amsden, A.A., 1987. The Tab method for numerical calculation of spray droplet breakup. SAE Technical Paper 872089. Saffman, P. G., 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22(2), 385–400.
precursor plasma spraying. J. Therm. Spray Technol. 16(5-6), 698-704.
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Shan, Y., Coyle, T.W., Mostaghimi, J., 2007. Numerical simulation of droplet breakup and collision in the solution
Slack, M.D., Prasad, R.O., Bakker, A., Boysan, F., 2000. Advances in cyclone modeling using unstructured grids. Trans. IChemE. 78(A), 1098-1104.
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Taylor, G.I., 1963. The Shape and acceleration of a drop in a high speed air stream. Technical report. In the Scientific Papers of G. I. Taylor, ed., G. K. Batchelor.
Math. Modell. 30(11), 1326–1342.
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Wang, B., Xu, D.L., Chu, K.W., Yu, A.B., 2006. Numerical study of gas-solid flow in a cyclone separator. Appl.
Wang, Z.B., Chu, L.Y., Chen, W.M., Wang, S.G., 2008. Experimental investigation of the motion trajectory of solid particles inside the hydrocyclone by a Lagrange method. Che. Eng. J. 138(1-3), 1-9. Wiencke, B., 2011. Fundamental principles for sizing and design of gravity separators for industrial refrigeration. Int. J. Refrigeration. 34(8),2092-2018.
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Xing, Z.W., 2000. Screw compressor theory and designing and applications. Mechanical Industry Press, Beijing.
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Figures
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Fig. 1 Schematic view of the cyclone separator
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Fig. 2 Computational grid for the cyclone separator
Fig. 3 Computational tangential velocities of three grid levels (Inlet velocity 14.4 m.s-1, section Y=0, Z=55 mm)
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Valve 2
Oil filter Differential manometer
Malvern Particle Size Analyser Compressor
Horizontal Oil-gas separator
Malvern Particle Size Analyser
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Thermometer
Oil-gas cyclone separator
Pressure gauge Valve 1
Flow meter
Valve 3
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Nozzle flow meter
Q1
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Oil cooler Thermometer
AA
AO
Q3
Q2
Gas container
Differential manometer
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(a)
(b) Fig. 4 The flow diagram and pictures of the test rig
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Fig. 5 Comparisons of the simulated and experimental results for the tangential and axial velocity distributions (Y=0,
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Z=942.5mm)
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Fig. 6 Comparison of the simulated and measured pressure drops
Fig. 7 Static pressure and tangential velocity at different sections (Y=0, inlet velocity 17.33 m.s-1) 19
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Fig. 8 Tangential velocity with different inlet velocities (Y=0, Z=75 mm and Z=15 mm)
Fig. 9 Trajectories of oil droplets at different times (inlet velocity 18.1 m.s-1, particle traces coloured by particle diameter)
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Fig. 10 Droplet size distribution at inlet as a Rosin-Rammler function
Fig. 11 Droplet size distributions at the inlet and the outlet of the separator with different inlet velocities
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Fig. 12 Comparison of the simulated and experimental separation efficiencies with different inlet velocities
Figure Captions
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Fig. 1 Schematic view of the cyclone separator Fig. 2 Computational grid for the cyclone separator
Fig. 3 Computational tangential velocities of three grid levels (Inlet velocity 14.4 m.s-1, section Y=0, Z=55 mm) Fig. 4(a) The flow diagram of the test rig
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Fig. 4(b) The pictures of the test rig
Fig. 5 Comparisons of the simulated and experimental results for the tangential and axial velocity distributions
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Fig. 6 Comparison of the simulated and measured pressure drops Fig. 7 Static pressure and tangential velocity at different sections (Y=0, inlet velocity 17.33 m.s-1) Fig. 8 Tangential velocity with different inlet velocities (Y=0, Z=75 mm and Z=15 mm) Fig. 9 Trajectories of oil droplets at different times (inlet velocity 18.1 m.s-1, particle traces coloured by particle diameter) Fig. 10 Droplet size distribution at inlet as a Rosin-Rammler function Fig. 11 Droplet size distributions at the inlet and the outlet of the separator with different inlet velocities Fig. 12 Comparison of the simulated and experimental separation efficiencies with different inlet velocities 22
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Tables
Table 1 Dimensionless parameters of the cylinder diameter of the cyclone separator (D=65 mm) Central channel
Central channel
Inlet pipe
Inlet pipe
diameter D
height H
diameter d
height h
height a
width b
1.0
3.0
0.5
1.0
0.5
0.15
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Cyclone
Table 2 Numerical settings for the current simulations
Scheme
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Numerical setting
PRESTO
Pressure velocity coupling
SIMPLEC
Momentum discretisation
QUICK
Turbulent kinetic energy
Second-order upwind
Turbulent dissipation rate
Second-order upwind
Reynolds stress
First-order upwind
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Pressure discretisation
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Dimension/D
Cyclone
Table 3 Computational pressure drop of three grid levels (inlet velocity 14.4 m.s-1)
Static pressure drop/N.m-2
Total pressure drop/N.m-2
95261
1222
1338
218876
1321
1438
399603
1174
1309
% Difference a
3.9
2.2
Total number of cells
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Dimension
a.The percentage difference between the coarsest and finest grids
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Table 4 Accuracies of instruments in the experiment Instrument
Pressure
Thermometer
gauge 0.5
0.1
Measuring
Differential
Malvern particle
meter
cylinder
manometer
size analyser
0.35
1
1
1
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Accuracy (%)
Nozzle flow
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Table.1 Dimensionless parameters to the cylinder diameter of the cyclone separator studied (D=65mm) Cyclone
Central channel
Central channel
Inlet pipe
Inlet pipe
diameter D
height H
diameter d
height h
height a
width b
1.0
3.0
0.5
1.0
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Dimension/D
Cyclone
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Dimension
0.5
0.15
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Table.2 Numerical settings for the current simulations Scheme
Pressure discretization
PRESTO
Pressure velocity coupling
SIMPLEC
Momentum discretization
QUICK
Turbulent kinetic energy
Second order upwind
Turbulent dissipation rate
Second order upwind
Reynolds stress
First order upwind
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Numerical setting
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Table.3 Computational pressure drop of three levels of grid (Inlet velocity 14.4 m.s-1)
Static pressure drop/N.m-2
Total pressure drop /N.m-2
95261
1222
1338
218876
1321
1438
399603
1174
1309
%Difference a
3.9
2.2
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Total number of cells
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a.The percentage difference between the coarsest and finest grid
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Table.4 Accuracies of instruments in the experiment Pressure
Thermometer
gauge 0.5
0.1
Measuring
Differential
Malvern particle
meter
cylinder
manometer
size analyzer
0.35
1
1
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Accuracy(%)
Nozzle flow
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Instrument
1
S0140-7007(13)00151-5
DOI:
10.1016/j.ijrefrig.2013.06.004
Reference:
JIJR 2539
To appear in:
International Journal of Refrigeration
Received Date: 18 January 2013 Revised Date:
7 June 2013
Accepted Date: 10 June 2013
Please cite this article as: Gao, X., Chen, J., Feng, J., Peng, X., Numerical and Experimental Investigations of the Effects of the Breakup of Oil Droplets on the Performance of Oil-gas Cyclone Separators in Oil-injected Compressor Systems, International Journal of Refrigeration (2013), doi: 10.1016/j.ijrefrig.2013.06.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.
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Highlights The results showed that the breakup of oil droplets occurred in the separation process. The breakup of oil droplets influenced certainly the separation efficiency.
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The inlet velocity determined the possibility of the breakup of oil droplets.
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Numerical and Experimental Investigations of the Effects of the Breakup of Oil Droplets on the Performance of Oil-gas Cyclone Separators in Oil-injected
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Compressor Systems Xiang Gao, Jinfeng Chen, Jianmei Feng,* Xueyuan Peng School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China
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ABSTRACT
A numerical simulation was conducted of the dynamic trajectories and the separation performance of oil droplets,
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with a focus on the breakup of oil droplets in an oil-gas cyclone separator. The separation efficiency was also studied experimentally, and the oil droplets’ diameter distributions before and after the separator were measured with a Malvern particle size analyser to verify the simulation model. Both the experimental and simulation results showed that the breakup of oil droplets occurred in the separation process, clearly influencing the separation efficiency. In addition, the results indicated that inlet velocity played an important role in separation efficiency, as it not only
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significantly affected the tangential velocity inside the separator, but also determined the possibility and degree of the breakup of oil droplets.
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Key Words: Oil-gas Cyclone Separator, Numerical Simulation, Breakup of Oil Droplets, Separation Efficiency
*
Corresponding author: Jianmei Feng, School of Energy and Power Engineering, Xi’an Jiaotong University, 28 Xianning Road, Xi’an, Shaanxi, 710049, China, Tel & Fax: (+86)29-82663785 Email: [email protected]
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1. Introduction Two-stage separation processes are frequently adopted to effectively recycle the oil injected into a compressor and get high-quality compressed gas (Xing, 2000). The first-stage separator, also known as the preliminary separator,
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uses mechanical impact principles to capture most of the oil droplets mixed into the gas while the second-stage separator, often called the filter, uses the agglomeration method to absorb the residual oil mist. The separation efficiency of the first-stage separator significantly influences the residual oil content that enters the filter, thereby directly determining the filter’s life-span and the performance of the compressor system. Improving the separation
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efficiency of the first-stage separator is an important step in purifying the discharge gas and achieving the best performance in oil-injected compressor systems (Hammerl et al., 2000). At present, the oil-gas cyclone separator is
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widely accepted as a first-stage separator in oil-injected compressor systems because of its simple geometry and easy maintenance.
A considerable number of studies have used numerical simulations to examine the performance of the cyclone separator. Many of these studies have focused on the gas flow field in the cyclone chamber. The Reynolds stress turbulence model (RSM), based on the Reynolds Averaged Navier-Stokes equations (RANS), has been widely
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accepted. For example, Gronald and Derksen (2011) compared the finite volume RANS model with two LES approaches in their study. They pointed out that the unsteady RANS-based simulation that results from a relatively coarse grid can provide reasonable and industrially relevant results with limited computational effort. Using the RSM model, Slack et al. (2000) simulated the flow field in a conventional high-efficiency Stairmand cyclone. The
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simulated results showed consistent agreement with the Laser Droplet Anemometry measurements. Hoekstra et al. (1999) simulated the gas flow field with many different turbulence models and reported that the prediction made by
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the RSM model was in reasonable agreement with the measured profiles of all three swirl numbers. Many numerical studies have also tried to study the particle motion in the swirling flow in a cyclone separator by using the discrete phase model (DPM), based on the Euler-Lagrangian method. Matsuzaki et al. (2006) investigated the particle motions in the swirling flow in a cyclone using Large Eddy simulation (LES) and were able to predict the performance of particle separation from the particle tracing results. Elsayed and Lacor (2011) studied the effect of a cyclone’s inlet pipe size on its performance and simulated the particle motion using the DPM model. Several previous investigations studied the gas flow field and the particle motion in the cyclone experimentally. Hoekstra (2000) systematically investigated the gas flow field and the collection efficiency of cyclone separators. He
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tested the pressure drop, velocity distribution and collection efficiency of solid-gas cyclone separators with different structures. Using a high-speed motion analyser, Wang et al. (2008) determined the motion trajectory of solid particles’ inside the hydrocyclone. The results were useful in understanding the particle dynamics in the separation
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process. These studies were performed on either the flow field, or the solid particles motion in the cyclone. However, there is an essential difference in the particle morphology of the oil-gas cyclone separator. The properties of the liquid particles are different than those of the solid particles. To the authors’ knowledge, few previous studies of oil-gas
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cyclone separators have focused on this difference. Wiencke (2011) analysed the fundamental principles of the design of gravity liquid separators and applied the single-droplet model to the sizing of gravity liquid separators.
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Shan et al. (2007) reported that the breakup of the droplets played an important role in determining the final particle size and velocity distribution in precursor plasma spray. Similarly, for the oil-gas cyclone separator, the high speed swirling flow field led the oil droplets to breakup in the separation process, affecting the separation performance. Therefore, it is important to develop a better understanding of the dynamics of the oil droplets and their separation process in the flow field inside the oil-gas cyclone separator.
Using the RSM model together with the Taylor analogy breakup model (TAB), this study examined the effect of the
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breakup of oil droplets on separation performance in the oil-gas cyclone separator. The experimental investigation was undertaken to obtain the oil droplets’ diameter distributions before and after the separator process, and to compare these experimental results with the numerical prediction. The separation efficiencies at different inlet
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velocities were also measured. The purpose of this study was to discuss the existence of the breakup of oil droplets
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and analyse its effect on separation efficiency.
2. Physical Model
Fig. 1 provides a schematic view of the oil-gas cyclone separator used in this experiment, which is commonly used in oil-injected compressor systems. The structural parameters of the cyclone are shown in Table 1. The oil-gas mixture enters tangentially through the inlet pipe on top of the cyclone separator and then rotates downward between the cylinder and the central channel. Due to the centrifugal force, larger oil droplets moving to the separator wall are separated and the remaining smaller oil droplets follow the discharge gas to finally escape through the outlet.
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3. Numerical Simulation The RSM model, which has been widely accepted in many previous studies of cyclones, was used to describe the swirling flow field. For the tracking of oil droplets, the DPM model was applied using one-way coupling, with the
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assumption that the discrete phase had no effect on the continuous phase flow field because the oil volume concentration was quite low in this study, usually less than 1 per cent. The governing equations for the gas flow field were from Elsayed and Lacor (2011).
3.1 Oil-droplet model
dt
= FD (u − u p ) +
g (ρ p − ρ )
ρp
+ Fadd
(1)
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du p
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The governing equation of the oil droplets in the flow field was given as follows
where u and up were the velocities of the gas and oil droplet; ρ and ρP were the densities of the gas and oil droplet; g was the acceleration of gravity; FD was the coefficient; Fadd was the additional force. The first item on the right-hand side described the drag force per unit particle mass and the second item was the gravity force per unit particle mass. The coefficient FD was calculated by
18µ C D Re ⋅ ρ p d p 2 24
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FD =
(2)
where µ was the dynamic viscosity of the gas; dp was the radii of the oil droplet; Re was the relative Reynolds
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number and CD was the drag coefficient that were calculated as follows
Re =
ρd p u p − u
C D = a1 +
µ a a2 + 3 Re rp Re rp
(3)
(4)
where a1, a2 and a3 were constants among some special Reynolds number range indicated by Morsi and Alexander (1972).
The additional force Fadd included forces such as the thermophoretic force, the Brownian force, and Saffman’s lift force. Because the other forces were much lower than the Saffman’s lift force, Fadd was approximately equal to the Saffman’s lift force (Saffman, 1965) and can be expressed as
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Fadd =
2 Kv1/ 2 ρd ij
ρ p d p ( d lk d kl )1/ 4
(u − u p )
(5)
where K=2.594; dij, dlk and dkl was the deformation rate tensor; ν was the kinematic viscosity.
of the velocity yielded displacement and thereby the trajectory of the oil droplet
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The velocity of the oil droplet can be predicted by integrating equation over discrete time steps. Further integration
x p = ∫ u pX dt , y p = ∫ u pY dt ,
z p = ∫ u pZ dt . When the trajectory equations were solved by integration over discrete time steps, the gas velocity
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was the mean gas-phase velocity.
3.2 Droplets breakup model
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The TAB model was used to account for the breakup of droplets. The TAB model developed by O’Rourke and Amsden (1987) was chosen because it fits the cyclone’s low-Weber-number condition.
3.2.1 Droplet distortion
The following equation was used to describe the droplet breakup in the TAB model
dx d 2x = mp 2 dt dt
(6)
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F − kx − d p
where F was the external force of the droplet, x was the displacement of the droplet equator from its spherical (undisturbed) position and mp was the mass of the droplet. The coefficients of the equation (6) were taken from
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Taylor’s analogy (Taylor, 1963)
F ρ u02 = CF ρ p rp mp σ k = Ck ρ p rp3 mp d µ p = Cd p 2 ρ p rp m p
(7)
where rp was the radius of the droplet (undisturbed), σ was the surface tension of the droplet, µP was the dynamic viscosity of the droplet and the constants CF=1/3, Ck=8 and Cd=5 were chosen to match the relevant examples and theory (Larsen and Howell, 1986). The droplet was assumed to break when the distortion grew to a critical ratio of the droplet radius (O’Rourke and
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Amsden, 1987). This breakup requirement was given as x>Cbr (Cb=1/2).
3.2.2 Size of child droplets The size of the child droplets was determined by equating the energy of the parent droplet to the combined energy of
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the child droplets
E parent = Echild
(8)
The energy of the parent droplet included surface energy, vibration and torsion deformation energy
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E parent = Esurf + Eosc The surface energy was given as
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Esurf = 4π rp2σ
(9)
(10)
and the vibration and torsion deformation energy was calculated by
Eosc = K
π 5
dy 2 ) + ω 2 y2 dt
ρ p rp5 (
(11)
mode, which was equal to 10/3.
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where y = Cb ; K was the ratio of the total energy in distortion and oscillation to the energy in the fundamental rp
The child droplets were assumed to be non distorted and non oscillating. Thus, the energy of the child droplets can be shown to be
rp
rp 32
+
π 6
ρ p rp 5 (
dy 2 ) dt
(12)
rp 32 was the Sauter mean radius of the droplet size distribution that was given by equating the energy of the
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where
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Echild = 4π 2σ
parent and child droplets (equation 9 and equation 12), setting y = 1 and
ω 2 = 8σ / ρ p r 3 (O’Rourke and
Amsden, 1987)
rp 32 =
rp 3 2 8 Ky 2 ρ p rp (dy / dt ) dy 2 + 1+ ( ) 20 dt σ
(13)
For the Sauter droplet size distribution, rp 32 = 0.7 rp max , rp max was the maximum among the droplets radius distributions. 6
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Once the size of the child droplets was determined, the number of child droplets can easily be determined by mass conservation.
3.2.3 Velocity of child droplets
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The TAB model allowed for a velocity component normal to the parent droplet velocity to be imposed upon the child droplets. When breakup occurred, the equator of the parent droplet was traveling at a velocity of
dx = Cb r (dy / dt ) . Therefore, the child droplets would have a velocity normal to the parent droplet velocity given dt
where
Cv , as a constant, was equal to 1.
3.3 Boundary conditions
dy dt
(14)
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unormal = Cν Cb rp
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by
A velocity inlet boundary condition was used at the inlet of the cyclone separator; specifically, a velocity normal to the inlet surface was specified. The pressure outlet boundary condition was set at the cyclone outlet according to the
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back pressure of the compressor system. In current study, both by the theoretical calculation and test observation, the two-phase flow was indicated to be the misty flow in the tube before entering the separator. Therefore, the homogeneous flow model was employed and then the oil droplets velocity was assumed to be the same as the gas inlet velocity at the inlet (Faghri and Zhang, 2006). Meanwhile, the droplets size distribution at the inlet was given
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as the experimental results. A no-slip boundary condition was adopted for the gas flow on all of the walls. For the oil droplets phase, the reflect boundary condition was applied to the cylindrical wall and the trap boundary condition
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was applied to the underside wall. The reflect boundary condition meant that the droplets encountered a rebound force and might break or return to the gas flow field if they made contact at a high tangential velocity. When droplets arrived at the underside wall, the trap boundary condition meant that they were separated and the trajectory calculation was terminated. If the droplets crossed the inlet and the outlet, the escape boundary condition applied, i.e. the droplets escaped and the trajectories calculation was also terminated.
3.4 Solver settings The solver settings for the gas flow field in this study were drawn from Kaya and Karagoz (2008). They investigated the performance of different discretisation schemes and the suitability of various numerical schemes in highly 7
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complex swirling flows in the simulation of cyclone separators; the best settings are summarised in Table 2. The PRESTO pressure interpolation scheme was one of the more successful schemes and the SIMPLEC algorithm for pressure velocity coupling gave predictions closer to the experimental data. The QUICK scheme for momentum
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equations was highly recommended. The choices were the second-order upwind scheme for the turbulent kinetic energy and turbulent dissipation rate and the first-order upwind scheme for the Reynolds stress.
The time step used for the unsteady simulation should be a tiny fraction of the average residence time (Chuah et al., 2006), and is determined from the cyclone volume and the gas flow rate. The minimum residence time in this study
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was about 0.06 s, so a time step of 1e-04 s was chosen as sufficient to properly reveal the transient phenomena.
3.5 The grid and the grid independency study
and meshed separately, as shown in Fig. 2.
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The geometry of the entire separator was divided into a number of blocks, and unstructured grids were generated
The gird independence study was performed by comparing the simulation results obtained under different grid numbers, as shown in Table 3 and Fig. 3. The maximum difference between the results of the coarser and finer grids was less than 10%, suggesting that grid independency results could be achieved in the coarser mesh of 95261 cells.
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However, to eliminate any uncertainty, simulations were performed using a mesh with 218876 cells.
4. Experiment 4.1 Test rig
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To obtain the separation efficiency and droplet size distribution at the inlet and outlet of the cyclone separator, the experimental system shown in Fig. 4 was built. Air was used as the work fluid. The oil-gas mixture discharged from
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the compressor first flowed into the horizontal oil-gas separator, and then entered the cyclone separator. After being separated by the cyclone separator, the mixture flowed through the oil filter and the AO/AA superfine oil filter. The gas flow rate through the measuring section was varied by adjusting valves 2 and 3. The Malvern particle size analysers were set before and after the cyclone separator. To ensure the accuracy of the Malvern particle size analyser, the horizontal oil-gas separator was added before the oil-gas mixture entered the cyclone separator. Pure nitrogen was added to the measuring section, as in the previous study by Feng et al. (2008).
4.2 Test conditions The separation efficiencies of the cyclone separator under different test conditions were measured. The gas flow rate 8
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ranged from 0.5 m3.min-1 to 1.2 m3.min-1, and the oil-gas mixture inlet velocity ranged from 14 m.s-1 to 18 m.s-1. The oil injection flow rate ranged from 1930 L.h-1 to 1950 L.h-1. All of the parameters were measured at the constant compressor discharge pressure of 0.8 MPa and a temperature of 90°C.
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4.3 Uncertainty analysis The accuracies of the instruments used in the experiment are shown in Table 4. Following the Kline method, an uncertainty analysis was carried out on the experiment results (Kline and McClintock, 1953). The square of errors was calculated as follows
(15)
WU was the total uncertainty associated with the dependent variable U , yi was the independent variable
that affected the dependent variable U
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where
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1/ 2
2 N ∂U WU = ∑ ( Wyi ) i =1 ∂yi
and Wyi was the uncertainty of the variable yi . The maximum
uncertainties were established to be 0.35% for the inlet velocity, 1.732% for the separation efficiency and 1% for the
5. Results and Discussion
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droplet size distribution.
5.1 Validation of numerical simulation results
The cyclone separator in this study was a cylinder-based oil-gas cyclone separator, which is different in structure
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from the solid-gas cone cyclone separators used in previous studies. Furthermore, due to the limited experimental conditions, it was very difficult to measure the gas flow velocity distributions of the studied separator. To validate
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the simulation model, indirect verifications of two aspects were conducted as stated below. First, the subsequent method was used to simulate the high efficiency Stairmand cyclone, of which the tangential and axial velocity distributions have been measured in previous studies (Hoekstra, 2000). Fig. 5 illustrates the comparison of simulated and tested tangential and axial velocity distributions at an axial position located at Z=942.5mm from the cyclone bottom. Given the complexity of the turbulence swirling flow in the cyclones, the agreement between the simulation and the experimental data was considered to be acceptable. Second, as Fig. 6 reveals, the simulated static pressure drops were compared with the experimental data. The results showed that the relative errors of the static pressure drops were less than 10%, so the simulation method used in this 9
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study is suitable for analysing the gas flow field of the separator. It was also found that the static pressure drop increases as the inlet velocity increases due to increasing friction between the gas and the wall.
5.2 Simulated gas flow field and trajectory of oil droplets
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5.2.1 Gas flow field The static pressures and tangential velocity distributions at six different sections along the Z axis with an inlet velocity of 17.3 m.s-1 are shown in Fig. 7. As expected, the profiled tangential velocity exhibited a so-called Rankine-type vortex, which consists of a free vortex in the outer region and an inner forced vortex at the centre. The
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variation relationship is similar to other reports, particularly for gas-solid cyclone separators (Elsayed and Lacor, 2011).
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The tangential velocities with different inlet velocities at the section Y=0, Z=75 mm and Z=15 mm are shown in Fig. 8. Obviously, the tangential velocity increased as the inlet velocity was enhanced. The higher tangential velocity improved the probability of the oil droplet reaching the wall. In other words, if the breakup of oil droplets is ignored, the separation efficiency may increase continuously as the inlet velocity grows.
5.2.2 Trajectory of oil droplets
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The trajectories of the oil droplets at different times with an inlet velocity of 18.1 m.s-1 are shown in Fig. 9. Clearly, once the oil-gas mixture entered tangentially into the cyclone cylinder through the inlet pipe, oil droplets with relatively smaller diameters moved faster due to their smaller inertial forces on smaller radii, compared to the larger droplets, as shown at 0.01 s in Fig. 9.
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The results also showed that the larger oil droplets were more easily separated by arriving at the cylinder wall. In addition, the oil droplets were separated near the end of the separation process, at about 0.15 s for the specified
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operation condition; however, there were a few oil droplets floating on the topside wall. These oil droplets were considered to be separated as they did not escape from the outlet in current short time simulations. But for a long time, the phenomenon may decrease the separation efficiency similar to the "dust rings" in solid-gas cyclone separator (Wang et al., 2006). In this paper, the effects of the phenomenon on the separation efficiency were ignored.
5.3 Droplet size distribution The droplet size distribution at the inlet fitted with the experimental data from the Rosin-Rammler function is shown in Fig 10; this was used as the oil droplets’ inlet distribution setting in the simulations above. The volume fraction of the vertical ordinate was defined as the fraction of droplets of diameter greater than d which was given 10
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by Yd = e − ( d / d ) , where d was the size constant and n was the size distribution parameter. The percentage of n
droplets at inlet, by volume, with a diameter less than 10 µm was about 5%, whereas for the diameter between 10 µm and 45 µm it was 35% and for the diameter larger than 45 µm, it was 60%.
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Fig. 11 illustrates the comparison of the droplet size distributions between the inlet and outlet of the cyclone separator. The volume percentage of droplets at the outlet was quite different than the percentage of the oil volume at the inlet. Compared the droplets distribution between the inlet and outlet, Fig.11 shows that the droplets with diameter greater than 45 um reduced significantly. The increase in the percentage of oil droplets smaller than 20um
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at the outlet implied that droplet breakup happened during the separation process. It was also evident that the percentage of smaller diameter oil droplets increased at the outlet as the inlet velocity increased. This meant that a
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higher velocity inside the separator led to easier droplet breakup. The percentage of 10 µm-droplets increased in volume from 3% at the inlet to 7.5% at the outlet when the inlet velocity was 15.2 m.s-1. If the inlet velocity reached 18.1 m.s-1, the percentage of 10 µm-diameter droplets would increase to 10%.
5.4 Separation efficiency and the effects of breakup The separation efficiency was defined as η, as follows
m out ) × 100(% ) m total
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η = (1 −
(16)
where m out was the mass of the oil that flowed out of the separator with the discharge gas and m total was the mass of the oil that entered the separator with the inlet oil-gas mixture.
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Fig. 12 shows the comparison of separation efficiencies between the simulated results and the experimental data with different inlet velocities. The effects of oil droplet breakup on separation efficiency can be determined by
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combining Figs. 11 and 12. The separation efficiencies measured at different conditions were about 70%-80%. However, the simulated separation efficiencies under the same conditions were almost 100% when the simulation model did not consider the breakup of droplets. When the breakup of oil droplets was taken into account using the TAB breakup model, the simulated separator efficiencies decreased. The maximum relative error between the simulated results and the experiment data was about 20%. The tested separation efficiency did not increase constantly with increasing inlet velocity and an optimal inlet velocity existed for the best performance. This inconsistency indicated that, when the inlet velocity is low, the separation efficiency increases with inlet velocity because the centrifugal force of the droplets increases to help the separation, but does not cause droplet breakup. 11
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However, if the inlet velocity increases further, the effects of droplet breakup are the main factor in the decrease of separation efficiency. Fig 11 shows that increasing inlet velocity increases the possibility of oil droplets breakup. In addition, as can be seen, the measured separation efficiency was lower than the simulated results, even for the
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model including the droplets breakup behaviour. This can be explained by the fact that in numerical simulation, the oil level on the bottom was treated as the wall boundary and the trap boundary condition was applied, so that the oil droplets were assumed to be separated if they reached this surface. In the experiment, however, due to the effect of the high speed swirling flow, the oil separated on the baffle might be blown back into the flow field and finally
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escape through the outlet (Hoffmann and Stein, 2004). This phenomenon would definitely decrease the separation
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efficiency, but it was neglected in the simulation model.
6. Conclusions
The effects of oil droplet breakup and inlet velocity on oil gas cyclone separator performance were investigated numerically and experimentally. Based on the results, the following conclusions can be drawn. •
The breakup of oil droplets occurred in the oil gas cyclone separator and influenced the separation
•
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performance.
The simulated results proved that the RSM numerical model that included the TAB model was a promising tool for understanding the behaviour of oil droplets in the gas flow field during the separation process.
•
Inlet velocity played an important role in separator efficiency, as it determined the tangential velocity inside
•
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the separator, and increasing inlet velocity caused an increase in the possibility of oil droplet breakup. Further investigation of different structures of cyclone separators and of the mechanisms of oil droplet
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breakup are required to design more efficient separators.
ACKNOWLEDGMENT
The research was supported by the National Natural Science Foundation of China (Research Project 50906068/E060502).
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inlet height (mm)
b
inlet width (mm)
CD
drag coefficient
D
cyclone diameter (mm)
DPM
discrete phase model
d
central channel diameter (mm), radius (m)
d
size constant (m)
dij,dlk,dkl
deformation rate tensor (s-1)
E
energy (J)
F
force (N)
Fadd
additional force (N)
FD
coefficient
g
gravity acceleration (m•s-2)
H
cyclone height (mm)
h
central channel height (mm)
L
inlet length (mm)
LES
Large Eddy simulation
m
mass (kg)
n
size distribution parameter
R
cyclone radius (m)
Re RSM
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RANS
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a
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NOMENCLATURE
Reynolds Averaged Navier-Stokes
Reynolds number Reynolds stress turbulence model
r
radius (m)
rp 32
Sauter mean radius of the droplet size distribution (m)
TAB
Taylor analogy breakup model
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velocity (m•s-1)
W
uncertainty
X, Y, Z
coordinates (mm);
x
displacement of the droplet equator from its spherical (undisturbed) position, position (m)
Yd
volume fraction
y
independent variable, position (m)
z
position (m)
η
efficiency
µ
dynamic viscosity (Pa•s)
ν
kinematic viscosity (m2•s-1)
ρ
density (kg.m-3)
σ
surface tension (N•m-1)
ω
angular frequency (Hz)
additional
child
child oil droplet
max
maximum
p
oil droplet
p32
Sauter droplet size distribution
parent
parent oil droplet
Out
out of the separator
surf Total X, Y, Z
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osc
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add
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Subscripts
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u
vibration and torsion deformation
surface total
direction
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REFERENCES Chuah, H., Gimbun, J., Choong, T.S., 2006. A CFD study of the effect of cone dimensions on sampling aerocyclones performance and hydrodynamics. Powder Technol. 162(2), 126-132.
Math. Modell. 35(4), 1952-1968.
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Elsayed, K., Lacor, C., 2011. The effect of cyclone inlet dimensions on the flow pattern and performance. Appl.
Faghri, A., Zhang, Y., 2006. Transport Phenomena in Multiphase Systems. Elsevier, Burlington, MA.
Feng, J., Chang, Y., Peng, X., Qu, Z., 2008. Investigation of the oil-gas separation in a horizontal separator for
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oil-injected compressor units. IMechE:J. Power Energy. 222(A4), 403-412.
Gronald, G., Derksen, J.J., 2011. Simulating turbulent swirling flow in a gas cyclone: A comparison of Various
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modeling approaches. Powder Technol. 205(1), 160-171.
Guo, L.J., 2002. Two-phase and multiphase flow mechanics. Xi’an Jiaotong University Press, Xi’an, China. Hammerl, K., Tinder, L., Frank, M., 2000. Modification in the design of the oil injection system for screw compressor. In: International Compressor Engineering Conference at Purdue, West Lafayette, USA. Hoekstra, A.J., Derksen, J.J., Van Der Akker., 1999. An experimental and numerical study of turbulent swirling flow
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in gas cyclones. Chem. Eng. Sci. 54(13-14), 602-608.
Hoekstra, A.J., 2000. Gas flow field and collection efficiency of cyclone separators. Ph.D. Thesis, Technical University Delft, Stevinweg, Netherlands.
Hoffmann, A.J., Stein LE, 2004. Gas cyclones and swirl channels: principles, design and operation. Chemical
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Industry Press, Beijing, China.
Kaya, F., Karagoz, I., 2008. Performance analysis of numerical schemes in highly swirling turbulence flow in
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cyclones. Curr. Sci. 94(10), 1273-1278. Kline, S.J., McClintock, F.A., 1953. Describing uncertainties in single-sample experiments. Mech. Eng. 75(1), 3-8. Larsen, M.E., Howell, J.R., 1986. Least squares smoothing of direct exchange areas in zonal analysis. J. Heat Transfer. 108(1), 239-242.
Matsuzaki, K., Ushijima, H., Munekata, M., 2006. Numerical study on particle motions in swirling flows in a cyclone separator. J. Therm Sci. 15(2), 181-185. Morsi, S.A., Alexander, A.J., 1972. An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55(02), 193-208.
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O’Rourke, P.J., Amsden, A.A., 1987. The Tab method for numerical calculation of spray droplet breakup. SAE Technical Paper 872089. Saffman, P. G., 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22(2), 385–400.
precursor plasma spraying. J. Therm. Spray Technol. 16(5-6), 698-704.
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Shan, Y., Coyle, T.W., Mostaghimi, J., 2007. Numerical simulation of droplet breakup and collision in the solution
Slack, M.D., Prasad, R.O., Bakker, A., Boysan, F., 2000. Advances in cyclone modeling using unstructured grids. Trans. IChemE. 78(A), 1098-1104.
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Taylor, G.I., 1963. The Shape and acceleration of a drop in a high speed air stream. Technical report. In the Scientific Papers of G. I. Taylor, ed., G. K. Batchelor.
Math. Modell. 30(11), 1326–1342.
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Wang, B., Xu, D.L., Chu, K.W., Yu, A.B., 2006. Numerical study of gas-solid flow in a cyclone separator. Appl.
Wang, Z.B., Chu, L.Y., Chen, W.M., Wang, S.G., 2008. Experimental investigation of the motion trajectory of solid particles inside the hydrocyclone by a Lagrange method. Che. Eng. J. 138(1-3), 1-9. Wiencke, B., 2011. Fundamental principles for sizing and design of gravity separators for industrial refrigeration. Int. J. Refrigeration. 34(8),2092-2018.
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Xing, Z.W., 2000. Screw compressor theory and designing and applications. Mechanical Industry Press, Beijing.
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Figures
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Fig. 1 Schematic view of the cyclone separator
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Fig. 2 Computational grid for the cyclone separator
Fig. 3 Computational tangential velocities of three grid levels (Inlet velocity 14.4 m.s-1, section Y=0, Z=55 mm)
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Valve 2
Oil filter Differential manometer
Malvern Particle Size Analyser Compressor
Horizontal Oil-gas separator
Malvern Particle Size Analyser
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Thermometer
Oil-gas cyclone separator
Pressure gauge Valve 1
Flow meter
Valve 3
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Nozzle flow meter
Q1
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Oil cooler Thermometer
AA
AO
Q3
Q2
Gas container
Differential manometer
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(a)
(b) Fig. 4 The flow diagram and pictures of the test rig
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Fig. 5 Comparisons of the simulated and experimental results for the tangential and axial velocity distributions (Y=0,
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Z=942.5mm)
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Fig. 6 Comparison of the simulated and measured pressure drops
Fig. 7 Static pressure and tangential velocity at different sections (Y=0, inlet velocity 17.33 m.s-1) 19
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Fig. 8 Tangential velocity with different inlet velocities (Y=0, Z=75 mm and Z=15 mm)
Fig. 9 Trajectories of oil droplets at different times (inlet velocity 18.1 m.s-1, particle traces coloured by particle diameter)
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Fig. 10 Droplet size distribution at inlet as a Rosin-Rammler function
Fig. 11 Droplet size distributions at the inlet and the outlet of the separator with different inlet velocities
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Fig. 12 Comparison of the simulated and experimental separation efficiencies with different inlet velocities
Figure Captions
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Fig. 1 Schematic view of the cyclone separator Fig. 2 Computational grid for the cyclone separator
Fig. 3 Computational tangential velocities of three grid levels (Inlet velocity 14.4 m.s-1, section Y=0, Z=55 mm) Fig. 4(a) The flow diagram of the test rig
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Fig. 4(b) The pictures of the test rig
Fig. 5 Comparisons of the simulated and experimental results for the tangential and axial velocity distributions
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Fig. 6 Comparison of the simulated and measured pressure drops Fig. 7 Static pressure and tangential velocity at different sections (Y=0, inlet velocity 17.33 m.s-1) Fig. 8 Tangential velocity with different inlet velocities (Y=0, Z=75 mm and Z=15 mm) Fig. 9 Trajectories of oil droplets at different times (inlet velocity 18.1 m.s-1, particle traces coloured by particle diameter) Fig. 10 Droplet size distribution at inlet as a Rosin-Rammler function Fig. 11 Droplet size distributions at the inlet and the outlet of the separator with different inlet velocities Fig. 12 Comparison of the simulated and experimental separation efficiencies with different inlet velocities 22
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Tables
Table 1 Dimensionless parameters of the cylinder diameter of the cyclone separator (D=65 mm) Central channel
Central channel
Inlet pipe
Inlet pipe
diameter D
height H
diameter d
height h
height a
width b
1.0
3.0
0.5
1.0
0.5
0.15
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Cyclone
Table 2 Numerical settings for the current simulations
Scheme
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Numerical setting
PRESTO
Pressure velocity coupling
SIMPLEC
Momentum discretisation
QUICK
Turbulent kinetic energy
Second-order upwind
Turbulent dissipation rate
Second-order upwind
Reynolds stress
First-order upwind
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Pressure discretisation
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Dimension/D
Cyclone
Table 3 Computational pressure drop of three grid levels (inlet velocity 14.4 m.s-1)
Static pressure drop/N.m-2
Total pressure drop/N.m-2
95261
1222
1338
218876
1321
1438
399603
1174
1309
% Difference a
3.9
2.2
Total number of cells
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Dimension
a.The percentage difference between the coarsest and finest grids
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Table 4 Accuracies of instruments in the experiment Instrument
Pressure
Thermometer
gauge 0.5
0.1
Measuring
Differential
Malvern particle
meter
cylinder
manometer
size analyser
0.35
1
1
1
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Accuracy (%)
Nozzle flow
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Table.1 Dimensionless parameters to the cylinder diameter of the cyclone separator studied (D=65mm) Cyclone
Central channel
Central channel
Inlet pipe
Inlet pipe
diameter D
height H
diameter d
height h
height a
width b
1.0
3.0
0.5
1.0
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Dimension/D
Cyclone
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Dimension
0.5
0.15
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Table.2 Numerical settings for the current simulations Scheme
Pressure discretization
PRESTO
Pressure velocity coupling
SIMPLEC
Momentum discretization
QUICK
Turbulent kinetic energy
Second order upwind
Turbulent dissipation rate
Second order upwind
Reynolds stress
First order upwind
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Numerical setting
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Table.3 Computational pressure drop of three levels of grid (Inlet velocity 14.4 m.s-1)
Static pressure drop/N.m-2
Total pressure drop /N.m-2
95261
1222
1338
218876
1321
1438
399603
1174
1309
%Difference a
3.9
2.2
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Total number of cells
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a.The percentage difference between the coarsest and finest grid
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Table.4 Accuracies of instruments in the experiment Pressure
Thermometer
gauge 0.5
0.1
Measuring
Differential
Malvern particle
meter
cylinder
manometer
size analyzer
0.35
1
1
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Accuracy(%)
Nozzle flow
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Instrument
1