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The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder
The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder Lu Duan, Xiaolin Wu, Zhongli Ji, Zhiyi Xiong, Jingxian Zhuang PII: DOI: Reference:
S0032-5910(16)30585-X doi: 10.1016/j.powtec.2016.09.019 PTEC 11929
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 February 2016 14 August 2016 9 September 2016
Please cite this article as: Lu Duan, Xiaolin Wu, Zhongli Ji, Zhiyi Xiong, Jingxian Zhuang, The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder, Powder Technology (2016), doi: 10.1016/j.powtec.2016.09.019
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ACCEPTED MANUSCRIPT Title: The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder Authors: Lu Duan a, c, Xiaolin Wu a, c, *, Zhongli Ji b, c, Zhiyi Xiong a, c, Jingxian Zhuang a, c
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Author’s Institution:
Department of Chemical Engineering, China University of Petroleum, Beijing, 102200, P. R.
b
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China;
Department of Mechanical and Transportation Engineering, China University of Petroleum,
c
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Beijing, 102200, P. R. China
Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of
First author: Lu Duan Corresponding
author:
Xiaolin
Wu
Tel:
86-010-89734336
E-mail:
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[email protected]
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Petroleum, Beijing 102249, P. R. China
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Corresponding author’s address: Department of Chemical Engineering, China University
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of Petroleum, Beijing, 18th Fuxue Rd., Beijing, 102200, China
Abstract: This paper aimed at studying the contribution of the reflux cone and the gaps in the
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vortex finder to the reduction of energy consumption in the cyclones. The flow field was calculated using Reynolds Stress Model (RSM). Based on the numerical investigations, the entropy generation analysis method was used to explain the mechanism of energy consumption inside cyclone separators. The regional entropy generation in four parts viz. the outlet pipe, the inlet part, the region around vortex finder and the region below vortex finder was calculated and analyzed to identify the zones where the energy is largely consumed. The results show that the reflux cone and the gaps help reduce the entropy generation in the gas-outlet pipe, in the regions around and under the vortex finder, whereas increase the entropy generation in the inlet part. In addition, the reflux cone restrains the reflux flow and mainly reduces the entropy generation in the region around the vortex finder. The gaps reduce the flow rate under the vortex finder and mainly reduce the entropy generation in that region. 1
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Keywords: cyclone separator; vortex finder; RSM; entropy generation analysis
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ACCEPTED MANUSCRIPT The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder
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Abstract: This paper aimed at studying the contribution of the reflux cone and the gaps in the
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vortex finder to the reduction of energy consumption in the cyclones. The flow field was
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calculated using Reynolds Stress Model (RSM). Based on the numerical investigations, the entropy generation analysis method was used to explain the mechanism of energy consumption inside cyclone separators. The regional entropy generation in four parts viz. the
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outlet pipe, the inlet part, the region around vortex finder and the region below vortex finder was calculated and analyzed to identify the zones where the energy is largely consumed. The
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results show that the reflux cone and the gaps help reduce the entropy generation in the gas-outlet pipe, in the regions around and under the vortex finder, whereas increase the
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entropy generation in the inlet part. In addition, the reflux cone restrains the reflux flow and
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mainly reduces the entropy generation in the region around the vortex finder. The gaps reduce
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the flow rate under the vortex finder and mainly reduce the entropy generation in that region.
1. Introduction
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Cyclone separators are widely used in the industrial process to remove particles larger than 10 μm from fluid flows. They are simply constructed, contain no moving parts, and have low manufacturing and maintenance costs. As a result, the cyclone separators, manufactured from materials including alumina, alumina-silica, zirconia, magnesia, beryllia, and silicon carbide [1], and the unique constructions such as the convex downward top or the vault top [1, 2], can be used under extreme conditions. For example, the cyclones can protect downstream equipment from contaminants in a high-pressure gas network [3]. Since high operating pressure provides a dense gas atmosphere and then leads to a high pressure drop, the structure of the cyclone separator must be optimized to reduce its pressure drop. Many theoretical and experimental studies have been carried out to determine the effect of the eight geometrical dimensions of the cyclones on performance [4, 5]. The results 3
ACCEPTED MANUSCRIPT indicated that the shape and size of the vortex finder play a vital role in the pressure drop and separation efficiency. Hoekstra [6] studied the tangential and axial mean velocities in the
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cyclones by Laser-Doppler Anemometry (LDA) and Computational Fluid Dynamics (CFD)
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and tested the effect of the non-dimensional diameter of the vortex finder in a range of 0.3 to 0.5. As the diameter of the vortex finder decreased, the tangential and axial mean velocities
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increased significantly, causing an increase in pressure drop, which was also observed using Large Eddy Simulation (LES) by Elsayed and Lacor [7]. El-Batsh et al. [8] found that the
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length of the vortex finder is less important than its diameter in affecting pressure drop. A performance map was developed to allow selection of the diameter and length of the vortex
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finder. Lim et al. [9] compared the performance of ten self-designed cyclones and found that cyclones with a cone-shaped vortex finder exhibit lower pressure drop and moderate separation efficiency compared with the cylinder-shaped vortex finders. Raoufi et al. [10] also
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evaluated the effect of the shape and diameter of vortex finder on cyclone performance using
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CFD method. The results showed that the low-pressure zone in the middle of the cyclones
pressure drop.
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expands with the small vortex finder divergence angle, decreasing separation efficiency and
Usually, separation efficiency improves simultaneously with an increase in the pressure
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drop [7]. Jin et al. [11, 12] developed a high-efficiency guide-vaned cyclone, called the PSC type cyclone, and found that gaps in the vortex finder improve flow field and performance. Xiong et al. [13] ameliorated the vortex finder configuration by adding a reflux cone and spiral gaps to reduce the pressure drop. They designed cyclones with six types of cone-shaped vortex finders and tested performance at different flow rates and particle concentrations. They found that the cyclone separator with a vortex finder that has a reflux cone and spiral gaps with dextrorotation of 15° was optimal, and reduced the pressure drop by 73 % compared with the one without the reflux cone and spiral gaps. However, this study did not describe the flow field patterns or the mechanism of energy consumption reduction. The CFD method is a high effective, reliable, labor-saving, and time-saving approach to predict the flow behavior and performance of cyclones [14, 15, 16, 17, 18]. The entropy 4
ACCEPTED MANUSCRIPT generation analysis method, based on the numerical results, is a favorable approach to evaluate energy consumption because the exergy loss is proportional to the entropy generation
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[19]. This approach has been widely used to study and improve the flow and heat transfer
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equipment including the centrifugal fan [20] and heat exchangers [21, 22, 23, 24, 25]. Therefore, the entropy generation analysis method can analyze the mechanism of energy
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consumption and help identify the high energy consumption regions inside the cyclone separator.
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In this study, the flow field of cyclone separators with four different vortex finders was simulated using Reynolds stress Model (RSM). The numerical results were compared with the
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experimental data to assess the reliability of the simulation results. Entropy generation was calculated based on the simulated results. The effects of the configuration of vortex finder on
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2. Material and methods
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energy consumption were studied using the entropy generation analysis method.
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2.1 Construction of the cyclones
Fig. 1 presents the basic geometrical dimensions of the cyclone separator and its flow pattern. In the inlet part, eight vanes were arranged symmetrically, as shown in the
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cross-section A-A, to allow swirling flow in the clockwise direction.
Fig.1 Geometry and inside flow of the cyclone separator
Four vortex finders are considered in this study, as presented in Fig.2. Type A was a basic cone-shaped vortex finder. This was modified by adding a reflux cone to give Type B. Type B was modified by slotting18 straight gaps to give Type C, and 18 spiral gaps with 15° dextrorotation for Type D. The gaps are slanted in the opposite direction of gas flow, as shown in cross-section B-B in Fig. 2. Two different vortex finders with spiral gaps with either a 5
ACCEPTED MANUSCRIPT dextrorotation of 30° or a levorotation of 15° were also studied in Xiong’s work [13]. The performance of these two vortex finders was not as good as the Type D cyclone, so were not
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included in this study.
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Fig.2 Geometries of the vortex finders
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2.2 CFD method 2.2.1 Turbulent model
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The flow field in the cyclone separator is three-dimensional, high swirling and intense anisotropic turbulence. RSM and LES were verified to be the favorable turbulent models to
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simulate the flow field in cyclones [26, 27, 28]. However, the RSM model has lower
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computer capacity requirements and shorter running time compared with LES [27]. RSM also provides a better prediction in the boundary layer with the relative coarse grids [29]. In
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addition, LES does not provide the turbulent dissipation rate directly, which required to determine the entropy generation [30]. Therefore, RSM was selected to predict the flow field in the cyclones. The details of RSM model are provided in reference [31].
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2.2.2 Gas-solid two-phase flow model The inlet particle concentration ranged from 100 to 500 mg/m3, for a volume fraction far less than 10%. Thus, the particle interaction is negligible and the Eulerian-Lagrangian approach, called discrete phase model (DPM), can be used to track individual particles [31]. Only the drag force and the gravity are taken into consideration here due to the small fluid-to-particle density ratio [15]. According to Newton’s laws of motion, the equation of motion for a particle can be written as [31]:
g p dup 18 CD Re u up 2 dt pd p 24 p
(1)
where the u is the fluid phase velocity, u p is the particle velocity, 6
is the molecular
ACCEPTED MANUSCRIPT viscosity of fluid, p is the particle density, d p is the particle diameter, Re
d p u p u
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the correlations developed by Morsi and Alexander[32].
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is the relative Reynolds number, and CD is the drag coefficient, which can be calculated by
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Discrete random walk (DRW) is used to evaluate the effect of turbulent dispersion on particle motion. The separation efficiency was determined by counting the particle numbers at the inlet and outlet of the cyclone separator.
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2.2.3 Computational methodology
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The following methods were used in the simulation: the SIMPLEC (semi-implicit method pressure-linked equations consistent) algorithm was used for pressure-velocity coupling, the PRESTO! (Pressure Staggering Option) pressure interpolation scheme was
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applied for pressure discretization because of the high rotating flows, the QUICK
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discretization scheme was used to calculate momentum, and the second-order upwind discretization scheme was used to obtain the turbulent kinetic energy and turbulent dissipation
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rate. The simulation was performed via the commercial software Fluent 6.3.26 on a workstation with an Intel Xeon 2.9 GHz CPU and 64 GB RAM.
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2.2.4 Boundary condition
The velocity inlet boundary condition was set at the inlet. The flow rate ranged from 214 to 482 m3/h. The parameters of the inlet boundary condition were set according to reference [31]. The outflow boundary condition was utilized at the outlet. Air enters the inlet with different velocities at 300 K. The flow is assumed to be fully developed flow at the inlet and outlet. The no-slip condition and the adiabatic condition are assumed at the walls. The standard wall function is applied to solve turbulent flow problems in the wall regions. 2.3 Entropy generation analysis method 2.3.1 Entropy generation In a non-reacting flow system, the energy consumption in cyclones results from direct dissipation, turbulent dissipation, and wall friction [ 33-35]. There are several models to 7
ACCEPTED MANUSCRIPT predict entropy generation including the model of Bejan [36] that relied on direct dissipation, Kork and Herwig [33-35] who utilized turbulent dissipation, and Duan et al [37, 38] who
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focused on wall friction. The entropy generation caused by direct dissipation can be neglected
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because its accounts for less than 1.5 % of the total entropy generation in a cyclone separator [37, 38]. Thus, in this study, entropy generation due to turbulent dissipation and wall friction
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is taken into consideration, which are listed as follows:
In turbulent flow, the turbulence kinetic energy, defined as k, is dissipated into heat
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by viscous force in the Kolmogorov microscales [39], resulting in energy dissipation. The
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volumetric entropy generation rate due to turbulent dissipation is associated with the turbulent kinetic energy dissipation, which can be written as [33-35]
(2)
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Sgen,t
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where ρ is the gas density, ε is the turbulent energy dissipation rate, and T is the gas temperature.
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In the RSM turbulent model, two transport equations for k and ε are solved to calculate the turbulence kinetic energy and turbulent dissipation rate [31].
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The entropy generation due to turbulent dissipation can be determined by integrating Eq. (2) over the flow in the cyclone:
dV Sgen,t Sgen,t
(3)
in which Ω denotes the entire volume of the cyclone.
The isotropic assumption for ε in RSM deviates considerably because ε is strongly anisotropic in the low-Reynolds-number near-wall regions [40-42], resulting in an under estimate of entropy generation [33-35]. Therefore, a model to calculate wall entropy generation was developed by Duan et al. [37, 38], and is written as
Sgen,w
wvp T
dA
(4)
where vp is the fluid velocity at each node in a grid cell and w is the wall-shear stress. 8
ACCEPTED MANUSCRIPT 2.3.2 Exergy loss Since turbulent dissipation and wall friction are the main factors determining energy
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consumption [37, 38], the resulting entropy generation determines the exergy loss, which can
(5)
where T0 is the inlet gas temperature.
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I T0 Sgen,t Sgen,w
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be expressed as
The exergy loss can also be determined by the exergy analysis method, written as
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1 Iex H1 H2 T0 s1 s2 qm qm V12 V22 2
(6)
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where qm is the mass flow rate. s1 and s2 represent the thermodynamic entropy at the inlet and outlet, respectively. V1 and V2 represent the gas velocity at the inlet and outlet,
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2.4 Grid division and grid test
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respectively.
The three complex vortex finders with reflux cone and gaps were created using ProE.4.0
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and were imported into the Gambit code. The four cyclone separators were established using Gambit 2.4.6. They were meshed mainly using the structured grid and partially applying the
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unstructured grid. Since the grid has a crucial impact on calculating the flow field and the entropy generation [38], five levels of grids for each cyclone were tested to evaluate the entropy generation analysis method and the grid independency. As the grid level increased, the thickness of the wall-adjacent grids decreased and the grid number increased. The turbulent wall coordinates (y+) can be obtained in the post-process, and generally decrease with the decrease of the thickness of the wall-adjacent grids. The grid number and the turbulent wall coordinate for each level of grids are shown in Table 1. According to section 2.3.2, the exergy loss can be determined by two methods viz., entropy generation analysis and exergy analysis, with little deviation at a reasonable y+[39]. This deviation, can be written as Eq. (7), and is proposed to evaluate the effect of the thickness of the wall adjacent grid on the entropy generation. 9
ACCEPTED MANUSCRIPT =
Iex I 100% Iex
(7)
Table 1 shows the relative deviations of exergy loss for each level of grid when the flow
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rate was set to 375m3/h. As presented in Table 1, the relative deviations of exergy loss at the
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level 3 grids are generally less than those in the other four levels of grids.
Table 1
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Exergy loss in the cyclone meshed with different wall-adjacent grid thicknesses
In addition, the grid independency was tested by comparing the pressure drop between the grids of level
i and i 1 for each cyclone (i ranged from 2 to 5). As is shown in Table 2,
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the relative deviations of pressure drop between the grids of level 3 and level 4 were less than
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3.6 %. With the further increase of grid number, there was no significant improvement in the
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relative deviation of pressure drop, suggesting that the grids of level 3 produce grid independent results.
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Table 2
The grid independency test for the four types of cyclones.
Combining the grid independency and exergy loss results, the flow field and the entropy generation for Type A, Type B, Type C, and Type D were reasonably predicted with grid numbers of 454848, 471088, 589589, and 629408, respectively.
3. Results and discussion 3.1 Reduction rates in energy consumption Table 3 compares the numerical results and experimental data for the relative reductions 10
ACCEPTED MANUSCRIPT of pressure drop of the modified cyclone separators at different inlet flow rates. The relative reduction of pressure drop of Type A versus Type B cyclones is used to estimate the effect of
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reflux cone on saving energy. The pressure drops of the Type C and Type D cyclones are
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compared with that of the Type B cyclone to illustrate the effect of different types of gaps on saving energy. As is shown in Table 3, the numerical results are generally in good agreement
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with the experimental data, except for the testing results for the Type D cyclone. The CFD method underestimates the reduction of pressure drop of the Type D cyclone separator.
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Overall, the simulation results indicate the trend of the pressure drop reduction for the three
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modified types of cyclone separators.
Table 3
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The reduction of pressure drop between the experimental data and numerical results
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Table 4 shows the reduction of exergy loss of the modified cyclones. The exergy loss for each cyclone separator is in direct proportion to the pressure drop [38] and can be determined using Eqs. (2)- (6). As is shown in Table 4, the relative reduction of exergy loss agrees well
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with the relative reduction of pressure drop, indicating that the entropy generation analysis method can effectively evaluate the reduction of energy consumption for modified cyclone separators.
Table 4 Reduction of exergy loss for modified cyclone separators
3.2 Flow pattern 3.2.1 Velocity vector In this section, the velocity vector was observed for a flow rate of 375 m3/h. As is shown 11
ACCEPTED MANUSCRIPT in Fig. 3, three planes were studied in the gas-outlet pipe (z = 200 mm) and near the vortex finder (z = -100 mm and y = 0 mm). In Type A and Type B cyclones, both the outer downward
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flow and the inner upward flow occur in the clockwise direction. However, due to the gaps in
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the vortex finder, part of the flow in the Type C and Type D cyclones are in the counter-clockwise direction especially in the near wall regions, as shown by the planes of z =
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200 mm and z= -100 mm. The flow field is even totally in the opposite direction in the gas-outlet pipe of the Type C cyclone. In the gas-outlet pipe of the Type D cyclone, the inner
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flow is in the clockwise direction, but the outer flow is in the counter-clockwise direction. Through the gaps, a small portion of airflow enters the vortex finder and destroys the
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boundary layer of the swirling flow in the near-wall region [13]. Thus, the upward flow rate in the near-wall region of the vortex finder decreases dramatically in Type C and Type D cyclones relative to that in Type A and Type B cyclones, as shown in Fig. 3 (c). As a result,
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the energy dissipation is significantly reduced. The velocity vector in the vortex finders of
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Type A and Type B cyclones indicates that the reflux flow is restrained effectively by adding a
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reflux cone. In addition, the spiral gaps expand the flow areas and increase the airflow
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through the vortex finder, resulting in the reflux flow. (a) z = 200 mm (b) z = -100 mm
(c)
y = 0 mm
Fig. 3. Velocity vector at various positions in the different types of cyclone separators
3.2.2 Velocity contours For the four types of cyclones, the contours of the tangential and axial velocities on the plane of y = 0 mm are depicted in Fig. 4. The maximum tangential and axial velocities of the modified cyclones all decrease, compared to those of the original cyclone separator. Owing to the gaps, the maximum tangential velocity shifts from the space under the vortex finder to the 12
ACCEPTED MANUSCRIPT annular space outside the vortex finder, and the maximum axial velocity moves from the under part to the upper part of the vortex finder. The non-symmetry flow field is also found to
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be ameliorated by adding gaps. In the gas-outlet pipe of the Type C and Type D cyclones, the
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partial swirling flow turns to the inverse direction compared with those in Type A and Type B
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cyclones.
Fig. 4.
(b) Axial velocity
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(a) Tangential velocity
Velocity contours on the plane of y = 0 mm
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3.2.3 Velocity profile
Fig. 5 shows the tangential and axial components of gas velocity at various axial
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positions on the plane of y = 0 mm. There are four positions located in the gas-outlet pipe at z
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= 200 mm, among the vortex finder at z = -100 mm, in the cylindrical part at z = -300 mm and in the conical part at z = -500 mm, respectively. The magnitude of the tangential velocity in
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Type C and Type D cyclones is generally less than that in Type A and Type B cyclones, indicating that the swirling intensity in Type C and Type D cyclones is weaker than that in
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Type A and Type B cyclones. In the gas-outlet pipe of Type C cyclone, the tangential velocity is below zero, indicating that the airflow direction is opposite to that in Type A and Type B cyclones. The tangential velocity pattern mainly shows the same behavior of the Rankine vortex. In the space under the vortex finder, the magnitude of axial velocities in the near wall regions of Type C and Type D cyclones is larger than that in Type A and Type B cyclones, allowing better separation efficiency, as shown by Xiong [13]. In the space under the vortex finder of Type A and Type B cyclones, the axial velocity pattern shows an inverted V profile, which would increase stress on the vortex finder and increase vibration and noise [43]. And in the vortex finder of Type A and Type B cyclones, it shows a V profile. In the Type C and Type D cyclones, the axial velocity patterns exhibit a small W profile in the vortex finder and an 13
ACCEPTED MANUSCRIPT inverted W profile in the space under the vortex finder. In addition, the symmetry of the flow
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field is improved by the gaps in the vortex finder.
Fig. 5. Tangential and axial velocities at various axial positions on the plane through the
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Z-axis: P1—z= 200 mm; P2—z= -100 mm; P3—z= -300 mm; P4—z= -500 mm
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3.3 Distribution of entropy generation due to turbulent dissipation
As is presented in Fig. 6, the distribution of volumetric entropy generation rate due to
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turbulent dissipation was analyzed for a flow rate of 375 m3/h. In the space under the vortex finder, the value for the Type C and Type D cyclones is about two orders smaller than that in Type A and Type B cyclones due to the weak swirling intensity, resulting from the escape of
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flow through the gaps. The value in the Type B cyclone is generally less than that in the Type
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A cyclone, indicating that the vortex finder with a reflux cone leads to a decrease of energy
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consumption, which was also reported by Lim et al. [9], Raoufi et al. [10], and Xiong [13].
,t is generally obtained inside the vortex For these four types of cyclones, the maximum Sgen finders. It moves up from the entrance to the upper part of the vortex finder by the addition of
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gaps. In addition, the large value in Type A and Type C cyclones is located at the center of the vortex finer, whereas it is achieved in the near-wall regions in the Type B and Type D cyclones.
Fig. 6. Contours of the entropy generation rate on the plane of y = 0 mm and on the Z-axis
Fig. 7 also presents the volumetric entropy generation rate due to turbulent dissipation at the same positions as Fig. 5. It is also observed that the value in the space under the vortex finder of Type C and Type D cyclones is less than that of Type A and Type B cyclones. However, in the center of the gas-outlet pipe of Type C and Type D cyclone, the value is 14
ACCEPTED MANUSCRIPT slightly larger than that of the other two cyclones due to the interaction of the flows in the inverse direction. Whereas, in the near-wall regions of the gas-outlet pipe, the value in Type A
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and Type B cyclone is enormously less than it in Type C and Type D cyclone. The tangential
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and axial velocities in the annular part outside the vortex finders of Type C and Type D cyclones are larger than those of Type A and Type B cyclones. As a result, the entropy
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generation rate for Type C and Type D cyclones is larger than that for Type A and Type B
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cyclones.
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Fig 7. Sgen ,t at various axial positions on the plan through the Z-coordinate: P1—z= 200 mm;
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3.4 Regional entropy generation
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P2—z= -100 mm; P3—z= -300 mm; P4—z= -500 mm
,t varies in different regions for the four As described above, the distribution of Sgen
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types of cyclones. Thus, each cyclone is divided into four regions, including: the gas-outlet pipe, the inlet part, and the regions around and under the vortex finder, as presented in Fig. 8. The regional entropy generation due to turbulent dissipation and wall friction was calculated
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by Eqs. (1) - (4) for each cyclone at flow rate of 375 m3/h.
Fig. 8. Regions inside the cyclone
Fig. 9 shows the regional entropy generation for each cyclone separator. It shows that the reflux cone and the gaps in the vortex finder reduce entropy generation in the regions around the vortex finder, under the vortex finder, and in the gas-outlet pipe. The reflux cone restrains reflux flow in the vortex finder. As a result, the entropy generation of Type B cyclone decreases by 36.5 % compared with that of the Type A cyclone, including 29.4 % around the 15
ACCEPTED MANUSCRIPT vortex finder, 7.3 % under the vortex finder, and 0.7 % in the gas-outlet pipe. The non-symmetry of the flow field was improved and the magnitude of the tangential and axial
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velocities decreased due to the gaps. Thus, for Type C cyclone, the entropy generation
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decreases by 33.4 % compared with that of Type B cyclone, including 27.1 % under the vortex finder, 5.2 % in the gas-outlet pipe, and 4.0 % around the vortex finder. In addition, for
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the Type D cyclone), the entropy generation reduces by 47.8 % compared with that of the Type B cyclone, with 30.2 % under the vortex finder, 7.7 % in the gas-outlet pipe, and 12.9 %
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around the vortex finder. These results indicate that spiral gaps are superior to the straight gaps for the reduction of energy consumption. However, the entropy generation in the inlet
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part of the three modified cyclones increases by 0.9 %, 3.0 % and 3.0 %, respectively, likely
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due to the increase of the swirling intensity in the annular space outside the vortex finder.
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Fig. 9. Entropy generation for different regions in the four types of cyclones.
3.5 Grade separation efficiency
Fig. 10 shows the grade separation efficiency for the four cyclone separators, as
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calculated by the Eulerian-Lagrangian multiphase model at an inlet flow rate of 375 m3/h. The particle density is 2700kg/m3 and the inlet particle concentration is 200 mg/m3. It is found that the grade efficiency of Type B cyclone is generally less than that of the Type A cyclone, which differs from the findings of Xiong’s work [13]. However, compared with the grade efficiency of the Type A cyclone, an improvement is observed for the Type C and Type D cyclones, in agreement with the experimental data from Xiong’s work [13]. The Type D cyclone shows better separation performance than the Type C cyclone.
Fig.10. Separation efficiency for the four types of cyclones
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ACCEPTED MANUSCRIPT 4. Conclusions The entropy generation analysis method combined with CFD method was successfully
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applied to investigate the flow field and the mechanism of the energy consumption in four types of cyclones. The cyclones were considered in four parts: the gas-outlet pipe, the inlet
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part, the region around the vortex finder, and the region under the vortex finder. The entropy generation of each part was then calculated and analyzed at flow rate of 375 m3/h. The results
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showed that the reflux cone ameliorated the reflux flow in the vortex finder to effectively reduce the overall energy consumption in the cyclone separator, as the entropy generation of
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the Type B cyclone was decreased by 36.5 % compared to that of the Type A cyclone. The region around the vortex finder is the key region for decreasing entropy generation for the Type B cyclone. The gaps reduce the flow rate under the vortex finder and can effectively
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reduce energy consumption. The overall entropy generation of the Type C and Type D
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cyclones decreased by 33.4 % and 47.8%, respectively, compared to the Type B cyclone. The
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region under the vortex finder is the key region that contributed to decrease entropy generation for Type C and Type D cyclones. In addition, the grade separation efficiency of Type C and Type D cyclones was slightly higher than that of the Type A cyclone, suggesting
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that Type C and Type D vortex finders can improve cyclone performance. The Type D cyclone separator is the optimum one, exhibiting the lowest entropy generation and the highest separation efficiency.
Notation H
enthalpy, J/s
I
exergy loss by the entropy generation analysis, J/s
Iex
exergy loss by the exergy analysis, J/s
p
pressure, Pa
qm
mass flow rate, kg/s 17
ACCEPTED MANUSCRIPT Reynold’s number
T
gas temperature, K
T0
fluid temperature at inlet, K
V
fluid velocity, m/s
vp
fluid velocity at the node in the first grid cell near the wall, m·s-1
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T
Re
Greek symbols cyclone pressure drop, Pa
Sgen,t
entropy generation due to turbulent dissipation, W/K
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Sgen,w wall entropy generation, W/K
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∆p
density, kg·m-3
μ
dynamic viscosity，Pa·s
ε
turbulent dissipation rate，W/kg
w
wall-shear stress, Pa
Ω
entire cyclone
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D
ρ
Superscripts and subscripts volumetric rate
1
variable at inlet
2
variable at outlet
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'''
Acknowledgements This work was supported by the general project “The cyclone separator performance investigation based on entropy generation theory” sponsored by the National Natural Science Foundation of China (No. 51474229), and the Special and Significant Projects of National Science and Technology “Safe operation technology optimization of ten billion level natural gas purification plant” (No. 2011ZX05017-005) sponsored by the Ministry of National 18
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ACCEPTED MANUSCRIPT References [1]
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G.G. Sun, S.Q. Li, S.X. Yang, et al, Performance and application of a cyclone at high
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A.J. Hoekstra, Gas Flow Field and Collection Efficiency of Cyclone Separators, Ph.D.
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thesis, Technical University Delft, 2000 K. Elsayed, C. Lacor, The effect of cyclone vortex finder dimensions on the flow pattern
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and performance using LES, Comput Fluids, 71(2013) 224-239 H.M. El-Batsh, Improving cyclone performance by proper selection of the exit pipe, Appl Math Model, 37(7) (2013) 5286-5303 K.S. Lim, H.S. Kim, K.W. Lee, characteristics of the collection efficiency for a cyclone
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with different vortex finder shape, J Aerosol Sci. 35(6) (2004) 743-754 [10] A. Raoufi, M. Shams, M. Farzaneh, et al., numerical simulation and optimization of fluid flow in cyclone vortex finder, Chem Eng Process. 47(1) (2008) 128-137 [11] Y.H. Jin, C. Fan, M.X. Shi, Research and development of PSC-300 high efficiency cyclone tube with large gas capacity, Petroleum Refinery Engineering. 32 (2) (2002) 24-27 [12] Y.H. Jin, J.J. Wang, H.W. Wang, et al., Experimental and numerical study of gas flow in PSC type cyclone tube, Journal of China University of Petroleum. 30 (6) (2006) 71-82 [13] Z.Y. Xiong, Z.L. Ji, X.L. Wu, Development of a cyclone separator with high efficiency and low pressure drop in axial inlet cyclones, Powder Technol. 253 (2014) 644-649 [14] A.C. Hoffmann, L.E. Stein, Gas Cyclones and Swirl Tubes: Principles, Design and Operation, 2nd Ed. New York: Springer, 2002, pp. 41-55 20
ACCEPTED MANUSCRIPT [15] T.G. Chuah, J. Gimbun, T.S.Y. Choong, A CFD study of the effect of cone dimensions on sampling aerocyclones performance and hydrodynamics, Powder Technol. 162 (2-1) (2006) 126-132
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[16] H. Shalaby, K. Pachdler, K. Wozniak, et al., Comparative study of the continuous phase
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flow in a cyclone separator using different turbulence models, Int J Numer Meth Fl. 48 (11) (2005) 1175-1197
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[17] K.W. Chu, S.B. Kuang, A.B. Yu, et al., Particle scale modeling of the multiphase flow in a dense medium cyclone: effect of fluctuation of solids flowrate, Miner Eng. 33 (2012a) 34-45
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[18] K.W. Chu, B. Wang, A.B. Yu, A. Vince, Particle scale modeling of the multiphase flow in a dense medium cyclone: effect of vortex finder outlet pressure, Miner Eng. 31
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[19] H.F. Oztopa, K. AL-Salem, A review on entropy generation in natural and mixed convection heat transfer for energy systems, Renewable and Sustainable Energy
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Reviews. 16 (2012) 911-920
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[20] A. Behzadmehr, Y. Mercadier, Numerical study of flow parameters and entropy generation on a centrifugal fan, Int J Exergy. 6 (1) (2009) 80-92
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[21] T.A. Jankowski, Minimizing entropy generation in internal flows by adjusting the shape of the cross-section, Int J Heat Mass Tran. 52 (15-16) (2009) 3439-3445 [22] R. Ben-Mansour, A.Z. Sahin, Entropy generation in developing laminar fluid flow through a circular pipe with variable properties, Heat Mass Transfer. 42 (1) (2005) 1-11
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[23] E. Amani, M.R.H. Nobari, A numerical investigation of entropy generation in the entrance region of curved pipes at constant wall temperature, Energy. 36 (8) (2011) 4909-4918
[24] A. Biyikoglu, Entropy generation due to flow across the abrupt contraction of pipe joints, Appl Therm Eng. 29 (5-6) (2009) 841-847 [25] I. Kurbas, A. Durmus, H. Eren, et al., Effect of propeller type swirl generators on the entropy generation and efficiency of heat exchangers, Int J Therm Sci. 46 (3) (2007) 300-307 [26] A.J. Hoekstra, J.J. Derksen, H.E.A. VanDenAkker, An experimental and numerical study of turbulent swirling flow in gas cyclones, Chem Eng Sci. 54 (13-14) (1999) 2055-2065 [27] M.D. Slack, R.O. Prasad, A. Bakker, et al., Advances in cyclone modeling using 21
ACCEPTED MANUSCRIPT unstructured grids, Chem Eng Res Des. 78 (8) (2000) 1098-1104 [28] C. Fredriksson, Exploratory experimental and theoretical studies of cyclone gasification of wood powder, Ph.D. thesis, Lulea University of Technology, Sweden, 2003.
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[29] B. Wegner, A. Maltsev, C. Schneider, et al., Assessment of unsteady RANS in predicting
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swirl flow instability based on LES and experiments, Int J Heat Fluid Fl. 25 (3) (2004) 528-536
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[30] M. Soos, R. Kaufmann, R. Winteler, et al., Determination of maximum turbulent energy dissipation rate generated by a Rushto impeller through Large Eddy Simulation, AIChE J. 59 (10) (2013) 3642-3658
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[31] Fluent.Inc, Fluent6.3 User’s Guide., 2006, 12.37-12.47
[32] Morsi S A, Alexander A J. An investigation of particle trajectories in two phase flow
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systems. J. Fluid Mech., 1972, 55 (2): 193-208.
[33] F. Kock, H. Herwig, Local entropy production in turbulent shear flows: a high-Reynolds number model with wall functions, Int J Heat Mass Tran. 47 (10-11) (2004) 2205-2215
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[34] F. Kock, H. Herwig, Entropy production calculation for turbulent shear flows and their
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implementation in CFD codes, Int J Heat Mass Tran. 26 (4) (2005) 672-680 [35] F. Kock, H. Herwig, Direct and indirect methods of calculating entropy generation rates
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in turbulent convective heat transfer problems, Int J Heat Mass Tran. 43 (3) (2007) 207-
[36] Bejan A, Entropy Generation through Heat and Fluid Flow. Wiley, New York, 1982, 48-105
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[37] L. Duan, X.L. Wu, Z.L. Ji, Application of entropy generation method for analyzing energy consumption of cyclone separator, Journal of CIESC. 65 (2) (2014) 583-592 [38] L. Duan, X.L. Wu, Z.L. Ji, et al., Entropy generation analysis on cyclone separators with different exit pipe diameters and inlet dimensions, Chem Eng Sci. 138 (2015) 622-633 [39] M. T. Landahl; E. Mollo-Christensen (1992). Turbulence and Random Processes in Fluid Mechanics (2nd ed.). Cambridge University Press. p. 10. ISBN 978-0521422130. [40] B.E. Launder, W.C. Reynolds, Asymptotic near-wall stress dissipation rates in a turbulent flow, Phys. Fluids. 26 (1983) 1157-1158 [41] S. Jakirlic, K. Hanjalic, A new approach to modeling near-wall turbulence energy and stress dissipation, J. Fluid Mech. 459 (2002) 139-166 [42] M. Hallback, J. Groth, A.V. Johansson, An algebraic model for nonisotropic turbulent 22
ACCEPTED MANUSCRIPT dissipation rate in Reynolds stress closures, Phys Fluids. 2 (10) (1990) 1859-1866 [43] K. Elsayed, C. Lacor, The effect of cyclone inlet dimensions on the flow pattern and
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performance, Appl Math Model. 35(4) (2011) 1952-1968
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ACCEPTED MANUSCRIPT Table 1 Exergy loss in the cyclone meshed with different wall-adjacent grid thicknesses Type C
Type D
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Type B
n
y+
δ
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Type A
Grid levels
n
y+
δ
n
y+
δ
n
y+
δ
1
90360
875
27.6
132920
564
7.7
159589
452
175221
657
6.3
2
228412
529
14.2
275356
430
5.3
331874
324
10.3
313089
420
4.9
3
454848
423
1.1
471088
379
3.1
589589
306
1.3
629408
370
2.9
4
1090294
385
4.5
924716
319
0.6
968076
287
6.3
1071277
274
11.0
5
1846419
320
6.0
1728576
264
8.8
197
10.1
1786738
230
7.1
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9.2
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1460842
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Table 2
P1 P2 100 /% P1
6.4
10.4
P2 P3 100 /% P2
4.6
7.0
P3 P4 100 /% P3
3.5
1.61
P4 P5 100 /% P4
2.5
Type C
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Type B
7.8
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Type A
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Grid level
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The grid independency test for the four types of cyclones.
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0.9
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Type D 6.2
7.0
3.4
3.6
2.9
0.8
1.8
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214
268
321
375
428
482
average
pAexp pBexp 100% pAexp
36.6
38.0
39.6
40.3
41.1
38.7
39.1
pBexp pCexp 100% pBexp
23.1
33.2
44.3
33.8
22.8
26.1
30.5
pBexp pDexp 100% pBexp
62.5
63.0
63.5
59.4
55.0
56.0
59.9
pCFD pBCFD A 100% pCFD A
36.6
34.6
38.8
43.5
40.0
39.7
38.8
pBCFD pCCFD 100% pBCFD
32.9
33.8
31.2
28.6
29.6
31.9
31.3
pBCFD pDCFD 100% pBCFD
46.1
47.3
43.2
45.0
46.2
45.5
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44.9
26
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qV m3/h
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The reduction of pressure drop between the experimental data and numerical results
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214
268
321
375
428
482
average
I ACFD IBCFD 100% I ACFD
33.1
30.8
36.0
40.8
36.5
37.4
35.8
IBCFD ICCFD 100% IBCFD
35.7
34.6
33.1
30.4
31.8
32.1
33.0
IBCFD IDCFD 100% IBCFD
48.6
49.8
46.6
46.7
46.1
47.1
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qV m3/h
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Reduction of exergy loss for modified cyclone separators
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ACCEPTED MANUSCRIPT Highlights: The gaps ameliorate the non-symmetry flow field in the cyclones.
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The reflux cone mainly reduce the energy consumption around the vortex finder.
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The gaps mainly reduce the energy consumption under the vortex finder.
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The spiral gaps is superior to the straight gaps in reducing the energy consumption.
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S0032-5910(16)30585-X doi: 10.1016/j.powtec.2016.09.019 PTEC 11929
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 February 2016 14 August 2016 9 September 2016
Please cite this article as: Lu Duan, Xiaolin Wu, Zhongli Ji, Zhiyi Xiong, Jingxian Zhuang, The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder, Powder Technology (2016), doi: 10.1016/j.powtec.2016.09.019
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ACCEPTED MANUSCRIPT Title: The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder Authors: Lu Duan a, c, Xiaolin Wu a, c, *, Zhongli Ji b, c, Zhiyi Xiong a, c, Jingxian Zhuang a, c
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a
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Author’s Institution:
Department of Chemical Engineering, China University of Petroleum, Beijing, 102200, P. R.
b
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China;
Department of Mechanical and Transportation Engineering, China University of Petroleum,
c
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Beijing, 102200, P. R. China
Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of
First author: Lu Duan Corresponding
author:
Xiaolin
Wu
Tel:
86-010-89734336
E-mail:
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[email protected]
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Petroleum, Beijing 102249, P. R. China
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Corresponding author’s address: Department of Chemical Engineering, China University
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of Petroleum, Beijing, 18th Fuxue Rd., Beijing, 102200, China
Abstract: This paper aimed at studying the contribution of the reflux cone and the gaps in the
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vortex finder to the reduction of energy consumption in the cyclones. The flow field was calculated using Reynolds Stress Model (RSM). Based on the numerical investigations, the entropy generation analysis method was used to explain the mechanism of energy consumption inside cyclone separators. The regional entropy generation in four parts viz. the outlet pipe, the inlet part, the region around vortex finder and the region below vortex finder was calculated and analyzed to identify the zones where the energy is largely consumed. The results show that the reflux cone and the gaps help reduce the entropy generation in the gas-outlet pipe, in the regions around and under the vortex finder, whereas increase the entropy generation in the inlet part. In addition, the reflux cone restrains the reflux flow and mainly reduces the entropy generation in the region around the vortex finder. The gaps reduce the flow rate under the vortex finder and mainly reduce the entropy generation in that region. 1
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Keywords: cyclone separator; vortex finder; RSM; entropy generation analysis
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ACCEPTED MANUSCRIPT The flow pattern and entropy generation in an axial inlet cyclone with reflux cone and gaps in the vortex finder
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Abstract: This paper aimed at studying the contribution of the reflux cone and the gaps in the
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vortex finder to the reduction of energy consumption in the cyclones. The flow field was
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calculated using Reynolds Stress Model (RSM). Based on the numerical investigations, the entropy generation analysis method was used to explain the mechanism of energy consumption inside cyclone separators. The regional entropy generation in four parts viz. the
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outlet pipe, the inlet part, the region around vortex finder and the region below vortex finder was calculated and analyzed to identify the zones where the energy is largely consumed. The
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results show that the reflux cone and the gaps help reduce the entropy generation in the gas-outlet pipe, in the regions around and under the vortex finder, whereas increase the
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entropy generation in the inlet part. In addition, the reflux cone restrains the reflux flow and
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mainly reduces the entropy generation in the region around the vortex finder. The gaps reduce
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the flow rate under the vortex finder and mainly reduce the entropy generation in that region.
1. Introduction
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Cyclone separators are widely used in the industrial process to remove particles larger than 10 μm from fluid flows. They are simply constructed, contain no moving parts, and have low manufacturing and maintenance costs. As a result, the cyclone separators, manufactured from materials including alumina, alumina-silica, zirconia, magnesia, beryllia, and silicon carbide [1], and the unique constructions such as the convex downward top or the vault top [1, 2], can be used under extreme conditions. For example, the cyclones can protect downstream equipment from contaminants in a high-pressure gas network [3]. Since high operating pressure provides a dense gas atmosphere and then leads to a high pressure drop, the structure of the cyclone separator must be optimized to reduce its pressure drop. Many theoretical and experimental studies have been carried out to determine the effect of the eight geometrical dimensions of the cyclones on performance [4, 5]. The results 3
ACCEPTED MANUSCRIPT indicated that the shape and size of the vortex finder play a vital role in the pressure drop and separation efficiency. Hoekstra [6] studied the tangential and axial mean velocities in the
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cyclones by Laser-Doppler Anemometry (LDA) and Computational Fluid Dynamics (CFD)
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and tested the effect of the non-dimensional diameter of the vortex finder in a range of 0.3 to 0.5. As the diameter of the vortex finder decreased, the tangential and axial mean velocities
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increased significantly, causing an increase in pressure drop, which was also observed using Large Eddy Simulation (LES) by Elsayed and Lacor [7]. El-Batsh et al. [8] found that the
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length of the vortex finder is less important than its diameter in affecting pressure drop. A performance map was developed to allow selection of the diameter and length of the vortex
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finder. Lim et al. [9] compared the performance of ten self-designed cyclones and found that cyclones with a cone-shaped vortex finder exhibit lower pressure drop and moderate separation efficiency compared with the cylinder-shaped vortex finders. Raoufi et al. [10] also
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evaluated the effect of the shape and diameter of vortex finder on cyclone performance using
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CFD method. The results showed that the low-pressure zone in the middle of the cyclones
pressure drop.
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expands with the small vortex finder divergence angle, decreasing separation efficiency and
Usually, separation efficiency improves simultaneously with an increase in the pressure
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drop [7]. Jin et al. [11, 12] developed a high-efficiency guide-vaned cyclone, called the PSC type cyclone, and found that gaps in the vortex finder improve flow field and performance. Xiong et al. [13] ameliorated the vortex finder configuration by adding a reflux cone and spiral gaps to reduce the pressure drop. They designed cyclones with six types of cone-shaped vortex finders and tested performance at different flow rates and particle concentrations. They found that the cyclone separator with a vortex finder that has a reflux cone and spiral gaps with dextrorotation of 15° was optimal, and reduced the pressure drop by 73 % compared with the one without the reflux cone and spiral gaps. However, this study did not describe the flow field patterns or the mechanism of energy consumption reduction. The CFD method is a high effective, reliable, labor-saving, and time-saving approach to predict the flow behavior and performance of cyclones [14, 15, 16, 17, 18]. The entropy 4
ACCEPTED MANUSCRIPT generation analysis method, based on the numerical results, is a favorable approach to evaluate energy consumption because the exergy loss is proportional to the entropy generation
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[19]. This approach has been widely used to study and improve the flow and heat transfer
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equipment including the centrifugal fan [20] and heat exchangers [21, 22, 23, 24, 25]. Therefore, the entropy generation analysis method can analyze the mechanism of energy
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consumption and help identify the high energy consumption regions inside the cyclone separator.
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In this study, the flow field of cyclone separators with four different vortex finders was simulated using Reynolds stress Model (RSM). The numerical results were compared with the
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experimental data to assess the reliability of the simulation results. Entropy generation was calculated based on the simulated results. The effects of the configuration of vortex finder on
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2. Material and methods
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energy consumption were studied using the entropy generation analysis method.
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2.1 Construction of the cyclones
Fig. 1 presents the basic geometrical dimensions of the cyclone separator and its flow pattern. In the inlet part, eight vanes were arranged symmetrically, as shown in the
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cross-section A-A, to allow swirling flow in the clockwise direction.
Fig.1 Geometry and inside flow of the cyclone separator
Four vortex finders are considered in this study, as presented in Fig.2. Type A was a basic cone-shaped vortex finder. This was modified by adding a reflux cone to give Type B. Type B was modified by slotting18 straight gaps to give Type C, and 18 spiral gaps with 15° dextrorotation for Type D. The gaps are slanted in the opposite direction of gas flow, as shown in cross-section B-B in Fig. 2. Two different vortex finders with spiral gaps with either a 5
ACCEPTED MANUSCRIPT dextrorotation of 30° or a levorotation of 15° were also studied in Xiong’s work [13]. The performance of these two vortex finders was not as good as the Type D cyclone, so were not
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Fig.2 Geometries of the vortex finders
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2.2 CFD method 2.2.1 Turbulent model
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The flow field in the cyclone separator is three-dimensional, high swirling and intense anisotropic turbulence. RSM and LES were verified to be the favorable turbulent models to
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simulate the flow field in cyclones [26, 27, 28]. However, the RSM model has lower
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computer capacity requirements and shorter running time compared with LES [27]. RSM also provides a better prediction in the boundary layer with the relative coarse grids [29]. In
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addition, LES does not provide the turbulent dissipation rate directly, which required to determine the entropy generation [30]. Therefore, RSM was selected to predict the flow field in the cyclones. The details of RSM model are provided in reference [31].
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2.2.2 Gas-solid two-phase flow model The inlet particle concentration ranged from 100 to 500 mg/m3, for a volume fraction far less than 10%. Thus, the particle interaction is negligible and the Eulerian-Lagrangian approach, called discrete phase model (DPM), can be used to track individual particles [31]. Only the drag force and the gravity are taken into consideration here due to the small fluid-to-particle density ratio [15]. According to Newton’s laws of motion, the equation of motion for a particle can be written as [31]:
g p dup 18 CD Re u up 2 dt pd p 24 p
(1)
where the u is the fluid phase velocity, u p is the particle velocity, 6
is the molecular
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d p u p u
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the correlations developed by Morsi and Alexander[32].
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is the relative Reynolds number, and CD is the drag coefficient, which can be calculated by
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Discrete random walk (DRW) is used to evaluate the effect of turbulent dispersion on particle motion. The separation efficiency was determined by counting the particle numbers at the inlet and outlet of the cyclone separator.
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2.2.3 Computational methodology
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The following methods were used in the simulation: the SIMPLEC (semi-implicit method pressure-linked equations consistent) algorithm was used for pressure-velocity coupling, the PRESTO! (Pressure Staggering Option) pressure interpolation scheme was
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applied for pressure discretization because of the high rotating flows, the QUICK
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discretization scheme was used to calculate momentum, and the second-order upwind discretization scheme was used to obtain the turbulent kinetic energy and turbulent dissipation
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rate. The simulation was performed via the commercial software Fluent 6.3.26 on a workstation with an Intel Xeon 2.9 GHz CPU and 64 GB RAM.
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2.2.4 Boundary condition
The velocity inlet boundary condition was set at the inlet. The flow rate ranged from 214 to 482 m3/h. The parameters of the inlet boundary condition were set according to reference [31]. The outflow boundary condition was utilized at the outlet. Air enters the inlet with different velocities at 300 K. The flow is assumed to be fully developed flow at the inlet and outlet. The no-slip condition and the adiabatic condition are assumed at the walls. The standard wall function is applied to solve turbulent flow problems in the wall regions. 2.3 Entropy generation analysis method 2.3.1 Entropy generation In a non-reacting flow system, the energy consumption in cyclones results from direct dissipation, turbulent dissipation, and wall friction [ 33-35]. There are several models to 7
ACCEPTED MANUSCRIPT predict entropy generation including the model of Bejan [36] that relied on direct dissipation, Kork and Herwig [33-35] who utilized turbulent dissipation, and Duan et al [37, 38] who
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focused on wall friction. The entropy generation caused by direct dissipation can be neglected
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because its accounts for less than 1.5 % of the total entropy generation in a cyclone separator [37, 38]. Thus, in this study, entropy generation due to turbulent dissipation and wall friction
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is taken into consideration, which are listed as follows:
In turbulent flow, the turbulence kinetic energy, defined as k, is dissipated into heat
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by viscous force in the Kolmogorov microscales [39], resulting in energy dissipation. The
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volumetric entropy generation rate due to turbulent dissipation is associated with the turbulent kinetic energy dissipation, which can be written as [33-35]
(2)
T
D
Sgen,t
TE
where ρ is the gas density, ε is the turbulent energy dissipation rate, and T is the gas temperature.
CE P
In the RSM turbulent model, two transport equations for k and ε are solved to calculate the turbulence kinetic energy and turbulent dissipation rate [31].
AC
The entropy generation due to turbulent dissipation can be determined by integrating Eq. (2) over the flow in the cyclone:
dV Sgen,t Sgen,t
(3)
in which Ω denotes the entire volume of the cyclone.
The isotropic assumption for ε in RSM deviates considerably because ε is strongly anisotropic in the low-Reynolds-number near-wall regions [40-42], resulting in an under estimate of entropy generation [33-35]. Therefore, a model to calculate wall entropy generation was developed by Duan et al. [37, 38], and is written as
Sgen,w
wvp T
dA
(4)
where vp is the fluid velocity at each node in a grid cell and w is the wall-shear stress. 8
ACCEPTED MANUSCRIPT 2.3.2 Exergy loss Since turbulent dissipation and wall friction are the main factors determining energy
T
consumption [37, 38], the resulting entropy generation determines the exergy loss, which can
(5)
where T0 is the inlet gas temperature.
SC R
I T0 Sgen,t Sgen,w
IP
be expressed as
The exergy loss can also be determined by the exergy analysis method, written as
NU
1 Iex H1 H2 T0 s1 s2 qm qm V12 V22 2
(6)
MA
where qm is the mass flow rate. s1 and s2 represent the thermodynamic entropy at the inlet and outlet, respectively. V1 and V2 represent the gas velocity at the inlet and outlet,
TE
2.4 Grid division and grid test
D
respectively.
The three complex vortex finders with reflux cone and gaps were created using ProE.4.0
CE P
and were imported into the Gambit code. The four cyclone separators were established using Gambit 2.4.6. They were meshed mainly using the structured grid and partially applying the
AC
unstructured grid. Since the grid has a crucial impact on calculating the flow field and the entropy generation [38], five levels of grids for each cyclone were tested to evaluate the entropy generation analysis method and the grid independency. As the grid level increased, the thickness of the wall-adjacent grids decreased and the grid number increased. The turbulent wall coordinates (y+) can be obtained in the post-process, and generally decrease with the decrease of the thickness of the wall-adjacent grids. The grid number and the turbulent wall coordinate for each level of grids are shown in Table 1. According to section 2.3.2, the exergy loss can be determined by two methods viz., entropy generation analysis and exergy analysis, with little deviation at a reasonable y+[39]. This deviation, can be written as Eq. (7), and is proposed to evaluate the effect of the thickness of the wall adjacent grid on the entropy generation. 9
ACCEPTED MANUSCRIPT =
Iex I 100% Iex
(7)
Table 1 shows the relative deviations of exergy loss for each level of grid when the flow
IP
T
rate was set to 375m3/h. As presented in Table 1, the relative deviations of exergy loss at the
SC R
level 3 grids are generally less than those in the other four levels of grids.
Table 1
MA
NU
Exergy loss in the cyclone meshed with different wall-adjacent grid thicknesses
In addition, the grid independency was tested by comparing the pressure drop between the grids of level
i and i 1 for each cyclone (i ranged from 2 to 5). As is shown in Table 2,
D
the relative deviations of pressure drop between the grids of level 3 and level 4 were less than
TE
3.6 %. With the further increase of grid number, there was no significant improvement in the
CE P
relative deviation of pressure drop, suggesting that the grids of level 3 produce grid independent results.
AC
Table 2
The grid independency test for the four types of cyclones.
Combining the grid independency and exergy loss results, the flow field and the entropy generation for Type A, Type B, Type C, and Type D were reasonably predicted with grid numbers of 454848, 471088, 589589, and 629408, respectively.
3. Results and discussion 3.1 Reduction rates in energy consumption Table 3 compares the numerical results and experimental data for the relative reductions 10
ACCEPTED MANUSCRIPT of pressure drop of the modified cyclone separators at different inlet flow rates. The relative reduction of pressure drop of Type A versus Type B cyclones is used to estimate the effect of
T
reflux cone on saving energy. The pressure drops of the Type C and Type D cyclones are
IP
compared with that of the Type B cyclone to illustrate the effect of different types of gaps on saving energy. As is shown in Table 3, the numerical results are generally in good agreement
SC R
with the experimental data, except for the testing results for the Type D cyclone. The CFD method underestimates the reduction of pressure drop of the Type D cyclone separator.
NU
Overall, the simulation results indicate the trend of the pressure drop reduction for the three
MA
modified types of cyclone separators.
Table 3
TE
D
The reduction of pressure drop between the experimental data and numerical results
CE P
Table 4 shows the reduction of exergy loss of the modified cyclones. The exergy loss for each cyclone separator is in direct proportion to the pressure drop [38] and can be determined using Eqs. (2)- (6). As is shown in Table 4, the relative reduction of exergy loss agrees well
AC
with the relative reduction of pressure drop, indicating that the entropy generation analysis method can effectively evaluate the reduction of energy consumption for modified cyclone separators.
Table 4 Reduction of exergy loss for modified cyclone separators
3.2 Flow pattern 3.2.1 Velocity vector In this section, the velocity vector was observed for a flow rate of 375 m3/h. As is shown 11
ACCEPTED MANUSCRIPT in Fig. 3, three planes were studied in the gas-outlet pipe (z = 200 mm) and near the vortex finder (z = -100 mm and y = 0 mm). In Type A and Type B cyclones, both the outer downward
T
flow and the inner upward flow occur in the clockwise direction. However, due to the gaps in
IP
the vortex finder, part of the flow in the Type C and Type D cyclones are in the counter-clockwise direction especially in the near wall regions, as shown by the planes of z =
SC R
200 mm and z= -100 mm. The flow field is even totally in the opposite direction in the gas-outlet pipe of the Type C cyclone. In the gas-outlet pipe of the Type D cyclone, the inner
NU
flow is in the clockwise direction, but the outer flow is in the counter-clockwise direction. Through the gaps, a small portion of airflow enters the vortex finder and destroys the
MA
boundary layer of the swirling flow in the near-wall region [13]. Thus, the upward flow rate in the near-wall region of the vortex finder decreases dramatically in Type C and Type D cyclones relative to that in Type A and Type B cyclones, as shown in Fig. 3 (c). As a result,
D
the energy dissipation is significantly reduced. The velocity vector in the vortex finders of
TE
Type A and Type B cyclones indicates that the reflux flow is restrained effectively by adding a
CE P
reflux cone. In addition, the spiral gaps expand the flow areas and increase the airflow
AC
through the vortex finder, resulting in the reflux flow. (a) z = 200 mm (b) z = -100 mm
(c)
y = 0 mm
Fig. 3. Velocity vector at various positions in the different types of cyclone separators
3.2.2 Velocity contours For the four types of cyclones, the contours of the tangential and axial velocities on the plane of y = 0 mm are depicted in Fig. 4. The maximum tangential and axial velocities of the modified cyclones all decrease, compared to those of the original cyclone separator. Owing to the gaps, the maximum tangential velocity shifts from the space under the vortex finder to the 12
ACCEPTED MANUSCRIPT annular space outside the vortex finder, and the maximum axial velocity moves from the under part to the upper part of the vortex finder. The non-symmetry flow field is also found to
T
be ameliorated by adding gaps. In the gas-outlet pipe of the Type C and Type D cyclones, the
IP
partial swirling flow turns to the inverse direction compared with those in Type A and Type B
SC R
cyclones.
Fig. 4.
(b) Axial velocity
NU
(a) Tangential velocity
Velocity contours on the plane of y = 0 mm
MA
3.2.3 Velocity profile
Fig. 5 shows the tangential and axial components of gas velocity at various axial
D
positions on the plane of y = 0 mm. There are four positions located in the gas-outlet pipe at z
TE
= 200 mm, among the vortex finder at z = -100 mm, in the cylindrical part at z = -300 mm and in the conical part at z = -500 mm, respectively. The magnitude of the tangential velocity in
CE P
Type C and Type D cyclones is generally less than that in Type A and Type B cyclones, indicating that the swirling intensity in Type C and Type D cyclones is weaker than that in
AC
Type A and Type B cyclones. In the gas-outlet pipe of Type C cyclone, the tangential velocity is below zero, indicating that the airflow direction is opposite to that in Type A and Type B cyclones. The tangential velocity pattern mainly shows the same behavior of the Rankine vortex. In the space under the vortex finder, the magnitude of axial velocities in the near wall regions of Type C and Type D cyclones is larger than that in Type A and Type B cyclones, allowing better separation efficiency, as shown by Xiong [13]. In the space under the vortex finder of Type A and Type B cyclones, the axial velocity pattern shows an inverted V profile, which would increase stress on the vortex finder and increase vibration and noise [43]. And in the vortex finder of Type A and Type B cyclones, it shows a V profile. In the Type C and Type D cyclones, the axial velocity patterns exhibit a small W profile in the vortex finder and an 13
ACCEPTED MANUSCRIPT inverted W profile in the space under the vortex finder. In addition, the symmetry of the flow
IP
T
field is improved by the gaps in the vortex finder.
Fig. 5. Tangential and axial velocities at various axial positions on the plane through the
SC R
Z-axis: P1—z= 200 mm; P2—z= -100 mm; P3—z= -300 mm; P4—z= -500 mm
NU
3.3 Distribution of entropy generation due to turbulent dissipation
As is presented in Fig. 6, the distribution of volumetric entropy generation rate due to
MA
turbulent dissipation was analyzed for a flow rate of 375 m3/h. In the space under the vortex finder, the value for the Type C and Type D cyclones is about two orders smaller than that in Type A and Type B cyclones due to the weak swirling intensity, resulting from the escape of
D
flow through the gaps. The value in the Type B cyclone is generally less than that in the Type
TE
A cyclone, indicating that the vortex finder with a reflux cone leads to a decrease of energy
CE P
consumption, which was also reported by Lim et al. [9], Raoufi et al. [10], and Xiong [13].
,t is generally obtained inside the vortex For these four types of cyclones, the maximum Sgen finders. It moves up from the entrance to the upper part of the vortex finder by the addition of
AC
gaps. In addition, the large value in Type A and Type C cyclones is located at the center of the vortex finer, whereas it is achieved in the near-wall regions in the Type B and Type D cyclones.
Fig. 6. Contours of the entropy generation rate on the plane of y = 0 mm and on the Z-axis
Fig. 7 also presents the volumetric entropy generation rate due to turbulent dissipation at the same positions as Fig. 5. It is also observed that the value in the space under the vortex finder of Type C and Type D cyclones is less than that of Type A and Type B cyclones. However, in the center of the gas-outlet pipe of Type C and Type D cyclone, the value is 14
ACCEPTED MANUSCRIPT slightly larger than that of the other two cyclones due to the interaction of the flows in the inverse direction. Whereas, in the near-wall regions of the gas-outlet pipe, the value in Type A
T
and Type B cyclone is enormously less than it in Type C and Type D cyclone. The tangential
IP
and axial velocities in the annular part outside the vortex finders of Type C and Type D cyclones are larger than those of Type A and Type B cyclones. As a result, the entropy
SC R
generation rate for Type C and Type D cyclones is larger than that for Type A and Type B
NU
cyclones.
MA
Fig 7. Sgen ,t at various axial positions on the plan through the Z-coordinate: P1—z= 200 mm;
TE
3.4 Regional entropy generation
D
P2—z= -100 mm; P3—z= -300 mm; P4—z= -500 mm
,t varies in different regions for the four As described above, the distribution of Sgen
CE P
types of cyclones. Thus, each cyclone is divided into four regions, including: the gas-outlet pipe, the inlet part, and the regions around and under the vortex finder, as presented in Fig. 8. The regional entropy generation due to turbulent dissipation and wall friction was calculated
AC
by Eqs. (1) - (4) for each cyclone at flow rate of 375 m3/h.
Fig. 8. Regions inside the cyclone
Fig. 9 shows the regional entropy generation for each cyclone separator. It shows that the reflux cone and the gaps in the vortex finder reduce entropy generation in the regions around the vortex finder, under the vortex finder, and in the gas-outlet pipe. The reflux cone restrains reflux flow in the vortex finder. As a result, the entropy generation of Type B cyclone decreases by 36.5 % compared with that of the Type A cyclone, including 29.4 % around the 15
ACCEPTED MANUSCRIPT vortex finder, 7.3 % under the vortex finder, and 0.7 % in the gas-outlet pipe. The non-symmetry of the flow field was improved and the magnitude of the tangential and axial
T
velocities decreased due to the gaps. Thus, for Type C cyclone, the entropy generation
IP
decreases by 33.4 % compared with that of Type B cyclone, including 27.1 % under the vortex finder, 5.2 % in the gas-outlet pipe, and 4.0 % around the vortex finder. In addition, for
SC R
the Type D cyclone), the entropy generation reduces by 47.8 % compared with that of the Type B cyclone, with 30.2 % under the vortex finder, 7.7 % in the gas-outlet pipe, and 12.9 %
NU
around the vortex finder. These results indicate that spiral gaps are superior to the straight gaps for the reduction of energy consumption. However, the entropy generation in the inlet
MA
part of the three modified cyclones increases by 0.9 %, 3.0 % and 3.0 %, respectively, likely
D
due to the increase of the swirling intensity in the annular space outside the vortex finder.
CE P
TE
Fig. 9. Entropy generation for different regions in the four types of cyclones.
3.5 Grade separation efficiency
Fig. 10 shows the grade separation efficiency for the four cyclone separators, as
AC
calculated by the Eulerian-Lagrangian multiphase model at an inlet flow rate of 375 m3/h. The particle density is 2700kg/m3 and the inlet particle concentration is 200 mg/m3. It is found that the grade efficiency of Type B cyclone is generally less than that of the Type A cyclone, which differs from the findings of Xiong’s work [13]. However, compared with the grade efficiency of the Type A cyclone, an improvement is observed for the Type C and Type D cyclones, in agreement with the experimental data from Xiong’s work [13]. The Type D cyclone shows better separation performance than the Type C cyclone.
Fig.10. Separation efficiency for the four types of cyclones
16
ACCEPTED MANUSCRIPT 4. Conclusions The entropy generation analysis method combined with CFD method was successfully
IP
T
applied to investigate the flow field and the mechanism of the energy consumption in four types of cyclones. The cyclones were considered in four parts: the gas-outlet pipe, the inlet
SC R
part, the region around the vortex finder, and the region under the vortex finder. The entropy generation of each part was then calculated and analyzed at flow rate of 375 m3/h. The results
NU
showed that the reflux cone ameliorated the reflux flow in the vortex finder to effectively reduce the overall energy consumption in the cyclone separator, as the entropy generation of
MA
the Type B cyclone was decreased by 36.5 % compared to that of the Type A cyclone. The region around the vortex finder is the key region for decreasing entropy generation for the Type B cyclone. The gaps reduce the flow rate under the vortex finder and can effectively
D
reduce energy consumption. The overall entropy generation of the Type C and Type D
TE
cyclones decreased by 33.4 % and 47.8%, respectively, compared to the Type B cyclone. The
CE P
region under the vortex finder is the key region that contributed to decrease entropy generation for Type C and Type D cyclones. In addition, the grade separation efficiency of Type C and Type D cyclones was slightly higher than that of the Type A cyclone, suggesting
AC
that Type C and Type D vortex finders can improve cyclone performance. The Type D cyclone separator is the optimum one, exhibiting the lowest entropy generation and the highest separation efficiency.
Notation H
enthalpy, J/s
I
exergy loss by the entropy generation analysis, J/s
Iex
exergy loss by the exergy analysis, J/s
p
pressure, Pa
qm
mass flow rate, kg/s 17
ACCEPTED MANUSCRIPT Reynold’s number
T
gas temperature, K
T0
fluid temperature at inlet, K
V
fluid velocity, m/s
vp
fluid velocity at the node in the first grid cell near the wall, m·s-1
SC R
IP
T
Re
Greek symbols cyclone pressure drop, Pa
Sgen,t
entropy generation due to turbulent dissipation, W/K
MA
Sgen,w wall entropy generation, W/K
NU
∆p
density, kg·m-3
μ
dynamic viscosity，Pa·s
ε
turbulent dissipation rate，W/kg
w
wall-shear stress, Pa
Ω
entire cyclone
CE P
TE
D
ρ
Superscripts and subscripts volumetric rate
1
variable at inlet
2
variable at outlet
AC
'''
Acknowledgements This work was supported by the general project “The cyclone separator performance investigation based on entropy generation theory” sponsored by the National Natural Science Foundation of China (No. 51474229), and the Special and Significant Projects of National Science and Technology “Safe operation technology optimization of ten billion level natural gas purification plant” (No. 2011ZX05017-005) sponsored by the Ministry of National 18
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
MA
NU
SC R
IP
T
Science and Technique.
19
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SC R
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[16] H. Shalaby, K. Pachdler, K. Wozniak, et al., Comparative study of the continuous phase
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[17] K.W. Chu, S.B. Kuang, A.B. Yu, et al., Particle scale modeling of the multiphase flow in a dense medium cyclone: effect of fluctuation of solids flowrate, Miner Eng. 33 (2012a) 34-45
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[20] A. Behzadmehr, Y. Mercadier, Numerical study of flow parameters and entropy generation on a centrifugal fan, Int J Exergy. 6 (1) (2009) 80-92
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implementation in CFD codes, Int J Heat Mass Tran. 26 (4) (2005) 672-680 [35] F. Kock, H. Herwig, Direct and indirect methods of calculating entropy generation rates
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[36] Bejan A, Entropy Generation through Heat and Fluid Flow. Wiley, New York, 1982, 48-105
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[37] L. Duan, X.L. Wu, Z.L. Ji, Application of entropy generation method for analyzing energy consumption of cyclone separator, Journal of CIESC. 65 (2) (2014) 583-592 [38] L. Duan, X.L. Wu, Z.L. Ji, et al., Entropy generation analysis on cyclone separators with different exit pipe diameters and inlet dimensions, Chem Eng Sci. 138 (2015) 622-633 [39] M. T. Landahl; E. Mollo-Christensen (1992). Turbulence and Random Processes in Fluid Mechanics (2nd ed.). Cambridge University Press. p. 10. ISBN 978-0521422130. [40] B.E. Launder, W.C. Reynolds, Asymptotic near-wall stress dissipation rates in a turbulent flow, Phys. Fluids. 26 (1983) 1157-1158 [41] S. Jakirlic, K. Hanjalic, A new approach to modeling near-wall turbulence energy and stress dissipation, J. Fluid Mech. 459 (2002) 139-166 [42] M. Hallback, J. Groth, A.V. Johansson, An algebraic model for nonisotropic turbulent 22
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AC
CE P
TE
D
MA
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IP
T
performance, Appl Math Model. 35(4) (2011) 1952-1968
23
ACCEPTED MANUSCRIPT Table 1 Exergy loss in the cyclone meshed with different wall-adjacent grid thicknesses Type C
Type D
T
Type B
n
y+
δ
IP
Type A
Grid levels
n
y+
δ
n
y+
δ
n
y+
δ
1
90360
875
27.6
132920
564
7.7
159589
452
175221
657
6.3
2
228412
529
14.2
275356
430
5.3
331874
324
10.3
313089
420
4.9
3
454848
423
1.1
471088
379
3.1
589589
306
1.3
629408
370
2.9
4
1090294
385
4.5
924716
319
0.6
968076
287
6.3
1071277
274
11.0
5
1846419
320
6.0
1728576
264
8.8
197
10.1
1786738
230
7.1
NU
SC R
9.2
AC
CE P
TE
D
MA
1460842
24
ACCEPTED MANUSCRIPT
Table 2
P1 P2 100 /% P1
6.4
10.4
P2 P3 100 /% P2
4.6
7.0
P3 P4 100 /% P3
3.5
1.61
P4 P5 100 /% P4
2.5
Type C
IP
Type B
7.8
SC R
Type A
NU
Grid level
T
The grid independency test for the four types of cyclones.
AC
CE P
TE
D
MA
0.9
25
Type D 6.2
7.0
3.4
3.6
2.9
0.8
1.8
ACCEPTED MANUSCRIPT Table 3
214
268
321
375
428
482
average
pAexp pBexp 100% pAexp
36.6
38.0
39.6
40.3
41.1
38.7
39.1
pBexp pCexp 100% pBexp
23.1
33.2
44.3
33.8
22.8
26.1
30.5
pBexp pDexp 100% pBexp
62.5
63.0
63.5
59.4
55.0
56.0
59.9
pCFD pBCFD A 100% pCFD A
36.6
34.6
38.8
43.5
40.0
39.7
38.8
pBCFD pCCFD 100% pBCFD
32.9
33.8
31.2
28.6
29.6
31.9
31.3
pBCFD pDCFD 100% pBCFD
46.1
47.3
43.2
45.0
46.2
45.5
SC R
NU
MA
AC
CE P
TE
D
44.9
26
IP
qV m3/h
T
The reduction of pressure drop between the experimental data and numerical results
ACCEPTED MANUSCRIPT Table 4
214
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average
I ACFD IBCFD 100% I ACFD
33.1
30.8
36.0
40.8
36.5
37.4
35.8
IBCFD ICCFD 100% IBCFD
35.7
34.6
33.1
30.4
31.8
32.1
33.0
IBCFD IDCFD 100% IBCFD
48.6
49.8
46.6
46.7
46.1
47.1
SC R 44.7
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qV m3/h
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Reduction of exergy loss for modified cyclone separators
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Graphical abstract
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ACCEPTED MANUSCRIPT Highlights: The gaps ameliorate the non-symmetry flow field in the cyclones.
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The reflux cone mainly reduce the energy consumption around the vortex finder.
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The gaps mainly reduce the energy consumption under the vortex finder.
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The spiral gaps is superior to the straight gaps in reducing the energy consumption.
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