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Experimental and CFD study on the effects of surface roughness on cyclone performance
Accepted Manuscript Experimental and CFD Study on the Effects of Surface Roughness on Cyclone Performance Faqi Zhou, Guogang Sun, Yuming Zhang, Hui Ci, Qing Wei PII: DOI: Reference:
S1383-5866(17)33206-9 https://doi.org/10.1016/j.seppur.2017.11.017 SEPPUR 14171
To appear in:
Separation and Purification Technology
Received Date: Revised Date: Accepted Date:
30 September 2017 7 November 2017 7 November 2017
Please cite this article as: F. Zhou, G. Sun, Y. Zhang, H. Ci, Q. Wei, Experimental and CFD Study on the Effects of Surface Roughness on Cyclone Performance, Separation and Purification Technology (2017), doi: https://doi.org/ 10.1016/j.seppur.2017.11.017
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Experimental and CFD Study on the Effects of Surface Roughness on Cyclone Performance Faqi Zhoua,b, Guogang Suna,b*, Yuming Zhanga,b, Hui Cia,b, Qing Weia,b a
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China
b
Beijing Key Laboratory of Process Fluid Filtration and Separation, Beijing 102249, PR China
* Corresponding author. Tel: +86-010-89734820 * Corresponding author. E-mail addresses: [email protected]
ABSTRACT Surface roughness is a highly practical parameter during the manufacture and operation of cyclone separators, but is not often researched. This study was carried out to investigate the effects of surface roughness on flow field and cyclone performance numerically and experimentally. The simulated pressure drops were in good agreement with the experimental data. The results also showed that surface roughness considerably influences the velocity distribution, boundary layer thickness, natural vortex length, separation efficiency, and pressure drop in the separator. The maximum separation efficiency related to surface roughness was revealed, as well. These results may provide a workable reference for the effects of surface roughness on the flow field and corresponding separation performance in cyclone separators.
Keywords: Cyclone separator; Surface roughness; Separation efficiency; Pressure drop; Flow field
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1. Introduction Gas cyclone separators are commonly used in a variety of industries to separate dust from gas or for product recovery. They are popular due to their geometrical simplicity, relative power economy, and flexibility [1]. Cyclone performance, which is typically characterized by pressure drop and particle separation efficiency, is the main criterion for evaluating a cyclone separator design. Most of the extant research on cyclone performance is based on the assumption of a smooth surface [2-13]. In actuality, however, the cyclone separator material has a certain surface roughness due to the manufacturing process. Cyclones installed with lining and bricks have especially rough surfaces. Furthermore, the roughness of any given cyclone changes throughout operation due to the erosion or deposition of particles from the surface. Despite its importance as a practical parameter, surface roughness has been largely ignored in the extant research on cyclone separators. There are some useful mathematical models for the surface roughness of cyclone separators [14-18]. It is generally taken as a part of the friction factor for deriving or modifying the tangential velocity formula to predict the pressure drop and separation efficiency. There has been no experimental data provided to verify these mathematical models. Recently, Ji et al. [19] investigated surface roughness in a cyclone preheater; their results showed that pressure drop and separation efficiency decrease as surface roughness increases. The structure used in this study, however, differed slightly from the conventional cyclone separator. In addition, the particle size distribution and properties of the experimental powder were unknown. Skorve [20] investigated the effects of surface roughness on vortex length in a cyclone separator; they found that vortex length decreases along with surface roughness, but did not explore the effects on pressure drop or separation efficiency. Kaya et al. [21] reported that the tangential velocity, pressure drop, and separation efficiency all decrease as surface roughness increase as-evidenced by CFD method. However, the cyclone separator they used was very small-scale and the results were not validated by experimental data. Ci et al. [22] similarly found that tangential velocity greatly decreases with surface roughness in a volute
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cyclone separator as well, but the effects on pressure drop and separation efficiency were not fully researched. Table 1 provides a quick review of these important studies on the effects of surface roughness on cyclone performance. Table 1 Earlier publications on the effects of surface roughness on cyclone performance Author Skorve [20]
Method
Cone
Roughness/mm Comment Vortex length decreased with surface
Experiment
No
0.1, 0.2
roughness. No results on pressure drop or efficiency.
Tangential velocity, radial velocity, and Liu et al. [23]
static pressure in the outer swirl region CFD
Yes
0.2, 0.4
decreased with surface roughness. No results on separation efficiency; no experimental data. Tangential velocity, pressure drop, and
Kaya et al. [21]
CFD
Yes
0.341, 0.527,
separation efficiency decreased as surface
0.682, 0.868
roughness increased. No experimental data for validation.
Ci et al. [22]
Tangential velocity markedly decreased with CFD
Yes
1.0, 2.0, 3.0
surface roughness. No separation efficiency results; no experimental data.
In summary, previous studies have provided relatively little experimental data or simulation results with respect to the effects of surface roughness on cyclone performance. Few researchers have explored the effects of surface roughness on the flow field or separation performance in the cyclone. There is not sufficient data supporting the industrial design of cyclone separators, to this effect. In the present study, we attempted to fill this research gap by conducting experimental and CFD tests on a Stairmand cyclone to investigate the effects of surface roughness on flow field and separation performance. We hope that our results provide a workable reference regarding the detailed separation process and precise effects of surface roughness on the flow field and separation performance of cyclone separators.
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2. Experiment 2.1. Experimental system The experimental system, mainly consisting of air draft system, measurement system, and a cyclone model, is shown in Fig. 1. A Stairmand cyclone separator with barrel diameter of 190 mm was manufactured from standard organic glass with initial inner surface roughness of 0.01 mm. The detailed geometry and dimensions of our separator are shown in Fig. 2 and Table 2, respectively. The surface roughness was changed by pasting sand paper with varying roughness (0.061, 0.08, 0.12, 0.18, 0.25, 0.43, 1, and 2 mm) on the inner wall surface of the cylinder and cone (see in Fig.1 ).
Fig. 1. Schematic diagram of experimental system: (1) particle bin, (2) particle feeder, (3) differential pressure sensor, (4) cyclone separator, (5) particle discharge bin, (6) sand paper, (7) Pitot tube, (8) knife switch, (9) filter, (10) fan.
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Fig. 2. Schematic diagram of cyclone separator. Table 2 Geometrical dimensions of experimental cyclone Structure
a/mm
b/mm
De/mm
S/mm
h/mm
H/mm
B/mm
D/mm
Ld/mm
Value
95
38
80
95
280
745
80
190
1100
2.2. Particles used We used talcum powder with a physical density of 2700 kg/m3 as experimental particles. The particle size distribution as-measured by a Mastersizer 2000 laser particle size analyzer is shown in Fig. 3. The volume mean particle diameter was approximately 17.56 μm.
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Fig. 3. Particle size distribution of talcum powder. 2.3. Experimental procedure and methods We conducted all experiments at atmospheric pressure and ambient temperature. Particle-laden gas was forced into the cyclone inlet with a centrifugal fan. The air flow rate was controlled by a knife switch in the outlet pipe and measured with a Pitot-tube in the outlet pipe. Particles were fed into the inlet by a star-type feeder. The inlet velocity ranged from 10 to 25 m/s and the feeding particle concentration was 20 g/m3 throughout the experiment. In the cyclone, most particles were separated from the gas and ultimately collected in the discharge bin underneath. After passing through the cyclone, the gas was passed through a filter to remove any remaining particles. Pressure drops were measured with dynamic differential pressure sensor fixed between the inlet and outlet. The measurement range was 0-10 kPa with 0.25% precision. The sampling frequency and sampling time were set to 500 Hz and 60 s, respectively. Each experiment was repeated at least three times to ensure relative error below 5%. The averages were used for subsequent calculations.
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3. Numerical study 3.1. CFD model The key to the success of CFD simulation lies in an accurate description of the turbulent behavior of the inner flow. The k-epsilon turbulence model and its variants do not effectively simulate the highly swirling turbulent flow in cyclones due to the assumption of isotropic turbulence structure [24]. The Reynolds stress model (RSM), conversely, has proven an accurate simulation of cyclones as it accounts for the effects of stream curvature, rotation, swirl, and rapid changes in strain [25-27]. Over recent years, large eddy simulation (LES) has grown popular for this purpose as well. Previous researchers [28, 29] have found that LES is more accurate than RSM in the simulation of cyclones; Shukla et al. [29] found that the mean velocities predicted by LES and RSM are very close. Given the accuracy of results and low computational cost, we used RSM in this study to predict the flow field in the cyclone separator. Basic information regarding this model can be found in our reference [30]. We simulated the dispersed phase by tracking a large number of spherical dispersed particles through the converged flow field of continuous flow in the Lagrangian reference frame by using a two-way coupling method via Discrete phase model (DPM). The finite volume method was used to discretize the partial differential equations of the model using the SIMPLE (semi-implicit method for pressure linked equations) method for pressure velocity coupling and QUICK (quadratic upwind interpolation of convective kinematics) scheme to interpolate the variables on the surface of the control volume. The implicit coupled solution algorithm was selected. In this simulation, the 10 -4 convergence criterion accuracy for the calculations was applied, and 0.0002 s was selected as the time step size. The simulation was performed via the commercial software Fluent 6.3.26 on a work station with a CPU of Intel Xeon 2.9 GHz and RAM of 64 GB. 3.2. Surface roughness modeling Surface roughness increases the resistance to flow and momentum transfer. This leads to a 7
shift in the velocity profile in the boundary layer. Therefore, surface roughness can be taken into account in the law of the wall [21]. The mean velocity (u) at a given distance from the wall (y) is determined by the friction velocity (u*), kinematic viscosity (ν), and surface roughness height (ks) in the turbulent boundary layer per the law of the wall, where surface roughness causes a downward shift. The law of the wall can be written for rough-wall boundary layers as follows: u u* (1 k )ln( yu* v) B B(ks )
(1)
where the von Karman constant κ ≈ 0.41 and B is an empirical constant for smooth walls. The friction velocity definition is: u* ( w )0.5
(2)
where τw is the wall shear stress and ρ is the fluid density. The roughness function, ∆B, depends on dimensionless surface roughness, ks+, which is defined as follows: ks ks u* v
(3)
In the case of hydrodynamically smooth flows (ks+< 2.25), the roughness function ∆B = 0. The roughness function is calculated by: B (1 k )ln(1 Cs ks )
(4)
If the flow is in a fully rough regime, (ks+> 90) and B (1 k )ln((ks 2.25) 87.75 Cs ks ) sin[0.4258ln(ks 0.811)]
(5)
Otherwise, the values of 5.56 and 0.5 apply as the roughness constants B and Cs, respectively. 3.3. Grid division and independence Figure 4 shows our computational cyclone model containing 682968 CFD cells. The whole computational domain was divided by the structured hexahedron grids. The grids were densified near the walls to allow us to accurately solve the complex turbulent flow in the boundary layer. The first grids were 0.05 mm away from the wall. The growth factor of the grid spacing from the walls to the center region was 1.2 in the wall-normal direction. We conducted mesh-independent analysis with 385750, 682968, and 895350 hexahedral
8
cells generated by Gambit 2.3.6, respectively. The differences in cyclone pressure drop between 385750 and 895350 hexahedral cells are about 8.3%, and the differences in cyclone pressure drops between 682968 and 895350 hexahedral cells are less than 4.7%. In addition, the relative error in tangential velocity at the position Z=-150 mm between 385750 and 895350 hexahedral cells is about 5.6%, and the relative error in tangential velocity between 682968 and 895350 hexahedral cells is less than 1.2%. As the differences of pressure drop and tangential velocity between 682968 and 895350 hexahedral cells are so small, the grids with 682968 hexahedral cells produce grid independent results.
Fig. 4. Grid representation of simulated cyclone.
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Fig. 5. The distributions of tangential velocity at the position Z=-150 in cyclone. 3.4. Boundary conditions A presumed uniform inlet velocity Vi = 20 m/s was specified at the normal-to-inlet surface of the cyclone. The surface roughness heights of the cylinder and cone were set to 0.01, 0.08, 0.18, 0.43, 1, and 2 mm, respectively. Other parts of the rough surface were set to 0.01 mm. The hydraulic diameter equaled 54.29 mm with turbulent intensity of 3.7%. The outflow boundary condition was imposed at the outlet. Air was forced into the inlet at various velocities and temperature of 300 K. The flow was assumed to be fully developed at the outlet. Near-wall treatment was achieved by using standard wall functions. We used the constant viscosity and ideal gas law for density to calculate the fluid properties. The non-dimensional wall unit (y+) values were checked to ensure that they were within the log-law region. 4. Results and discussion 4.1. Pressure drop of cyclone separator Pressure drops are defined here as the mean values of differential pressure signals measured between the inlet and outlet of the cyclone separator with a dynamic differential pressure sensor (Fig. 2). Variations in pressure drop with surface roughness for a variety of inlet
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velocities are shown in Fig. 6. The simulation results agreed reasonably well with the experimental data. Overall, pressure drop decreased as surface roughness increased. When the inlet velocity was smaller (Vi=10m/s), the effects of surface roughness were negligible. The decrease in pressure drop with the increase in surface roughness was more pronounced at higher inlet velocities. The curves changed sharply along with surface roughness as inlet velocity increased, as well.
Fig. 6. Cyclone separator pressure drop as a function of surface roughness. There are two particularly likely factors in the decreasing pressure drops we observed. Pressure drop is generally caused by friction loss between the fluid and wall as well as internal vortex flow. The latter accounted for a major part of the pressure drop in our observations. Wall friction increased with surface roughness while tangential velocity decreased as surface roughness increased, as shown in Fig. 9. The rotation intensity in the cyclone body and vortex finder was weakened as surface roughness increased. This led to higher static pressure in the vortex finder. As particles were loaded, the pressure drop was also affected by the interaction between them and the wall. The mean free path for particles between wall collisions grew shorter than that in the case of a smooth wall (or with smaller surface roughness) [31]. This
11
resulted in more energy loss and thus a significant reduction in pressure drop, as shown in Fig. 6. 4.2. Separation efficiency Figure 7 shows our separation efficiency results with four different inlet velocities as a function of surface roughness. There was a consistent critical value of separation efficiency along with surface roughness for all four velocities. Surface roughness above or below this critical value led to a decrease in separation efficiency, which marks a notable departure from the numerical simulation results reported by Kaya et al. [21]. We observed an increase in separation efficiency by about 3%. At inlet velocity of 10, 15, and 20 m/s, the critical value was a surface roughness of approximately 0.08 mm. However, at inlet velocity of 25 m/s, the maximum separation efficiency was located at surface roughness of about 0.12 mm.
Fig. 7. Cyclone separator collection efficiency as a function of surface roughness. The curves of efficiency versus inlet velocity with surface roughness of ks=0.01, 0.08, or 0.43 mm are shown in Fig. 8. The separation efficiency markedly decreased as surface roughness increased. A critical value of separation efficiency again appeared with increasing inlet velocity due to the effects of the radial distance of the rebounded particles from the inner wall [32]. We define this critical velocity as the “maximum-efficiency inlet velocity” [32, 33]. The rebounded particles obtained more kinetic energy at higher inlet velocities, to the point 12
where the radial distance traveled by a rebounded particle was longer than the width of the downward gas flow. Finally, the particles were rebounded back into the upward gas flow. Within the rapid, upward gas flow, the particles moved towards the vortex finder quickly with little separation. Therefore, the particles rebounded out of the downward gas flow would escape from the cyclone separator without being captured. At lower inlet velocities, the rebounded particles possessed less kinetic energy, so the radial distance traveled by a given rebounded particle was shorter than the width of the downward gas flow. The particles in this case moved towards the wall again via centrifugal force. The loss of energy due to collision decreased the velocity of the particles, and in the next rebounding process, the radial distance of the particle was truncated. Particles not escaping the cyclone after the first collision were unlikely to rebound into the upward gas flow in the following motion and thus unlikely to be captured. The decrease in separation efficiency at high inlet velocities was primarily caused by the escape of rebounded particles after the first collision. In this study, the maximum-efficiency inlet velocity was 21 m/s with a surface roughness of approximately ks=0.01 or 0.08 mm. The maximum-efficiency inlet velocity was 20 m/s with a surface roughness of ks=0.43 mm. In other words, small surface roughness seemed to have little effect on the maximum-efficiency inlet velocity. As surface roughness increased, the collision between the particles and wall increased; as more particles entered the upward gas flow, they moved towards the vortex finder quicker and with less separation. As a result, the separation efficiency and maximum-efficiency inlet velocity decreased.
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Fig. 8. Collection efficiency with varying inlet velocity. 4.3. Tangential velocity Tangential velocity is an important component of the gas flow in a cyclone due to its effect on the particle separation process and pressure drop. Figure 9 compares the tangential (Vt) velocity profiles at the axial positions of Z=-120, -260, -450, and -700 mm, respectively. We found that surface roughness significantly influenced the tangential velocity distributions. Tangential velocity profiles in the outer vortex were reduced by increasing surface roughness, as were the maximum tangential velocity values. However, the tangential velocity profiles remained effectually unchanged in the core region. The positions of the maximum tangential velocities at these sections gradually moved toward the center as surface roughness increased. The maximum tangential velocities slightly decreased along the cyclone, but this decrease seemed to be unaffected by surface roughness.
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Fig. 9. Tangential velocity profiles with surface roughness at different sections. 4.4. Axial velocity Figure 10 compares the axial (Vz) velocity profiles at the positions Z=-120, -260, -450, and -700 mm, respectively. Two distinct regions are visible in the axial velocity profiles: an outer vortex region where the velocity profiles move downward and an inner region where they move upward. The effects of surface roughness were negligible in the outer vortex near the wall, but were significant on the axial velocity profiles in the inner region. The inner axial velocity profiles became larger and changed from an M-shape distribution into an inverted V-shape as surface roughness increased. This is attributable to the weakening retention phenomenon in the vortex core area.
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Fig. 10. Axial velocity profiles with surface roughness at different sections. 4.5. Radial velocity Figure 11 shows the radial velocity (Vr) profiles varying with surface roughness at the axial positions of Z=-120, -260, -450, and -700 mm, respectively. The radial velocity pointed towards the center of the cyclone separator in most areas of the flow field and was oriented towards the wall in some fractions. The influence of roughness on radial velocity differed in these different areas. In most areas, radial velocity decreased with roughness; this caused a decrease in resistance for the particles moving towards the wall. These particles were more likely to be separated, dragged towards the inner wall, and captured.
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Fig. 11. Radial velocity profiles with surface roughness at different sections. 4.6. Natural vortex length According to Yang et al. [32], the natural vortex length is the distance from the entrance of the vortex finder to the vortex end. Adequately defining the vortex end is the key to measuring the natural vortex length. At the end of vortex, the fluid pressure gradient significantly decreases and the static pressure in the center and surrounding area becomes consistent. Thus, changes in the fluid pressure gradient reveal the position of the vortex end. We analyzed the static pressure distribution in the cyclone separator with different surface roughness values, as shown in Fig. 12, to investigate the influence of surface roughness on the natural vortex length. The circles in Fig. 12 indicate the vortex end positions which we used to determine the natural vortex length via the changes in static pressure. The vortex end steadily moved upwards as surface roughness increased. When ks=0.01-0.43 mm, the vortex end was in the dipleg position (with the tail end in the legs); the natural vortex length decreased slowly as surface roughness increased. When ks was 1 mm, the vortex end was situated nearer to the dust
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outlet. When ks = 2 mm, the vortex end was nearer to the cone. To this effect, the natural vortex length grew shorter as the surface roughness of the inner wall in the cylinder and cone increased.
Fig. 12. Static pressure distribution of cyclone separator with surface roughness. (Circles indicate vortex end position.) 4.7. Boundary layer thickness Based on the boundary layer separation theory reported by Kim et al. [34, 35], we divided the cyclone into two regions: the turbulent-core region and the near-wall region (or “boundary layer region”). Li et al. [36] reported several effects of boundary layer thickness on the separation efficiency in a cyclone separator per an elementary numerical analysis of the interaction between particles and the gas phase. They found that separation efficiency increases as boundary layer thickness decreases. We calculated boundary layer thickness, δ, as follows: N
(1 ui Vi ) ( yi1 yi )
(6)
i 1
where ui is the fluid velocity magnitude at point i in the boundary layer region; Vi is the inlet gas velocity; i= 1, 2, .., N, represents all points from the wall to the point where fluid velocity is 18
equal to inlet gas velocity; and yi is the radial position of point i. Figure 13 shows the curve of boundary layer thickness with surface roughness near the wall at the Z=-260 mm section (270 angle direction). Thickness generally increased with surface roughness. When surface roughness was less than 0.18 mm, boundary layer thickness was nearly constant. Though surface roughness affected the tangential velocity, radial velocity, and axial velocity components to some extent, the velocity magnitude and fluid velocity gradient near boundary layer region barely changed, thus the relative lack of changes in the boundary layer. When surface roughness exceeded 0.18 mm, there was an increase in wall friction loss which caused a rapid decrease in the velocity magnitude and fluid velocity gradient near the boundary layer region – this caused a gradual increase in boundary layer thickness.
Fig. 13. Boundary layer thickness with surface roughness. 4.8. Discussion According to the turbulent boundary layer theory explained by Qian et al. [37], particles in the near-wall region (i.e., boundary layer) were not only affected by centrifugal force, FC, and drag force, FD, but also determined by Saffman force, FS, generated in the relatively high gradient of fluid velocity near said boundary layer (Fig. 14). The Saffman lift acting on the particles in our system was indeed significant [37].
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Fig. 14. Schematic drawing of forces on a near-wall particle. We explored the critical value of separation efficiency corresponding to surface roughness based on the collision between the particles and inner wall, velocity distribution, and forces acting on the particles near the boundary layer. When surface roughness was less than 0.1 mm, the tangential velocity and boundary layer thickness remained almost unchanged as surface roughness increased. That is to say, the centrifugal force, FC, and Saffman force, FS, remained almost constant. The radial velocity decreased to a relatively larger extent and thus decreased the drag force acting on the particles. This caused more particles to be dragged into the near-wall region for separation. The smaller surface roughness also meant weaker collisions between particles and the inner wall [31, 38]. Particles entering the near-wall region did not move into the fast upward gas flow after bouncing against the inner wall, so there was less particle separation efficiency under these conditions. When the roughness was greater than 0.1 mm, the tangential velocity decreased considerably as surface roughness increased. The centrifugal force decreased and fewer particles entered the near-wall region for separation. There was stronger collision between the particles and inner wall due to the shorter mean free path, as well [31, 38]. More particles were sucked into the internal swirl after bouncing against the wall and then forced out of the cyclone separator without being captured. This reduced the separation efficiency of the system. Increased surface roughness also increased the boundary layer thickness [36] and further
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decreased the separation efficiency. 5. Conclusions In this study, we investigated the effects of surface roughness ranging from 0.01 to 2 mm on the performance and flow field of a Stairmand cyclone separator with a particle concentration of 20 g/m3 and inlet velocities of 10-25 m/s. Our conclusions can be summarized as follows. 1) The effects of surface roughness on cyclone pressure drop are negligible at lower velocities. At higher velocities, pressure drop decreases with surface roughness. 2) Surface roughness considerably influences the separation efficiency. There is a critical value of surface roughness below or above which there is a marked decrease in separation efficiency. Separation efficiency can be increased by a maximum of about 3% at the critical value. The value may be controlled by collision between the particles and inner wall, as well as the velocity distribution and forces acting on the particles, near the boundary layer region. 3) There is a maximum-efficiency inlet velocity which exists regardless of surface roughness, as inlet velocity affects the radial distance traveled by the rebounded particles from the inner wall. We found that maximum-efficiency inlet velocity decreases as surface roughness increases. 4) The tangential velocity in the cyclone decreases as surface roughness increases due to the increase in flow resistance and weakening swirl. Any excessive increase in surface roughness decreases the radial velocity and increases the upward axial velocity in the core region, which improves particle retention in the vortex core area. The natural vortex length gradually decreases as surface roughness increases. 5) Some particles may significantly increase surface roughness as they cause surface abrasion or are retained on the cyclone wall during the collection process. The appropriate cyclone surfaces roughness should be controlled to ensure optimal separation performance (high separation efficiency, low pressure drop) for an optimized cyclone separator.
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Acknowledgments The authors gratefully acknowledge the support from the National Basic Research Program [grant number 2014CB744304] and National Natural Science Foundation [grant number 21276274].
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-stics for cyclones, AIChE J. 43 (2004) 2446-2455. [36] X.D. Li, J.H. Yan, Y.C. Cao, M.J. Ni, K.F. Cen, Numerical simulation of the effect -s of turbulence intensity and boundary layer on separation efficiency in a cyclone s -eparator, Chem. Eng. J. 95 (2003) 235-240. [37] F.P. Qian, M.Y. Zhang, An extended model for determining the separation efficiency of a cyclone with boundary layer theory, Proceedings of the Csee. 27 (2007) 71-7 5. [38] M. Sommerfeld, Analysis of collision effects for turbulent gas–particle flow in a ho -rizontal channel: Part I. Particle transport. Int. J. Multiphas. Flow. 29 (2003) 675-69 9.
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Graphical abstract
27
Highlights Effects of roughness on pressure drop are different at low and high inlet
velocity. Cyclone separation efficiency has a critical value along with roughness. Natural vortex length is gradually shortened with roughness increasing. Roughness changes axial velocity distribution from M-shape into inverted
V-shape. Appropriate roughness is proposed to retain optimal separation performance.
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S1383-5866(17)33206-9 https://doi.org/10.1016/j.seppur.2017.11.017 SEPPUR 14171
To appear in:
Separation and Purification Technology
Received Date: Revised Date: Accepted Date:
30 September 2017 7 November 2017 7 November 2017
Please cite this article as: F. Zhou, G. Sun, Y. Zhang, H. Ci, Q. Wei, Experimental and CFD Study on the Effects of Surface Roughness on Cyclone Performance, Separation and Purification Technology (2017), doi: https://doi.org/ 10.1016/j.seppur.2017.11.017
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Experimental and CFD Study on the Effects of Surface Roughness on Cyclone Performance Faqi Zhoua,b, Guogang Suna,b*, Yuming Zhanga,b, Hui Cia,b, Qing Weia,b a
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China
b
Beijing Key Laboratory of Process Fluid Filtration and Separation, Beijing 102249, PR China
* Corresponding author. Tel: +86-010-89734820 * Corresponding author. E-mail addresses: [email protected]
ABSTRACT Surface roughness is a highly practical parameter during the manufacture and operation of cyclone separators, but is not often researched. This study was carried out to investigate the effects of surface roughness on flow field and cyclone performance numerically and experimentally. The simulated pressure drops were in good agreement with the experimental data. The results also showed that surface roughness considerably influences the velocity distribution, boundary layer thickness, natural vortex length, separation efficiency, and pressure drop in the separator. The maximum separation efficiency related to surface roughness was revealed, as well. These results may provide a workable reference for the effects of surface roughness on the flow field and corresponding separation performance in cyclone separators.
Keywords: Cyclone separator; Surface roughness; Separation efficiency; Pressure drop; Flow field
1
1. Introduction Gas cyclone separators are commonly used in a variety of industries to separate dust from gas or for product recovery. They are popular due to their geometrical simplicity, relative power economy, and flexibility [1]. Cyclone performance, which is typically characterized by pressure drop and particle separation efficiency, is the main criterion for evaluating a cyclone separator design. Most of the extant research on cyclone performance is based on the assumption of a smooth surface [2-13]. In actuality, however, the cyclone separator material has a certain surface roughness due to the manufacturing process. Cyclones installed with lining and bricks have especially rough surfaces. Furthermore, the roughness of any given cyclone changes throughout operation due to the erosion or deposition of particles from the surface. Despite its importance as a practical parameter, surface roughness has been largely ignored in the extant research on cyclone separators. There are some useful mathematical models for the surface roughness of cyclone separators [14-18]. It is generally taken as a part of the friction factor for deriving or modifying the tangential velocity formula to predict the pressure drop and separation efficiency. There has been no experimental data provided to verify these mathematical models. Recently, Ji et al. [19] investigated surface roughness in a cyclone preheater; their results showed that pressure drop and separation efficiency decrease as surface roughness increases. The structure used in this study, however, differed slightly from the conventional cyclone separator. In addition, the particle size distribution and properties of the experimental powder were unknown. Skorve [20] investigated the effects of surface roughness on vortex length in a cyclone separator; they found that vortex length decreases along with surface roughness, but did not explore the effects on pressure drop or separation efficiency. Kaya et al. [21] reported that the tangential velocity, pressure drop, and separation efficiency all decrease as surface roughness increase as-evidenced by CFD method. However, the cyclone separator they used was very small-scale and the results were not validated by experimental data. Ci et al. [22] similarly found that tangential velocity greatly decreases with surface roughness in a volute
2
cyclone separator as well, but the effects on pressure drop and separation efficiency were not fully researched. Table 1 provides a quick review of these important studies on the effects of surface roughness on cyclone performance. Table 1 Earlier publications on the effects of surface roughness on cyclone performance Author Skorve [20]
Method
Cone
Roughness/mm Comment Vortex length decreased with surface
Experiment
No
0.1, 0.2
roughness. No results on pressure drop or efficiency.
Tangential velocity, radial velocity, and Liu et al. [23]
static pressure in the outer swirl region CFD
Yes
0.2, 0.4
decreased with surface roughness. No results on separation efficiency; no experimental data. Tangential velocity, pressure drop, and
Kaya et al. [21]
CFD
Yes
0.341, 0.527,
separation efficiency decreased as surface
0.682, 0.868
roughness increased. No experimental data for validation.
Ci et al. [22]
Tangential velocity markedly decreased with CFD
Yes
1.0, 2.0, 3.0
surface roughness. No separation efficiency results; no experimental data.
In summary, previous studies have provided relatively little experimental data or simulation results with respect to the effects of surface roughness on cyclone performance. Few researchers have explored the effects of surface roughness on the flow field or separation performance in the cyclone. There is not sufficient data supporting the industrial design of cyclone separators, to this effect. In the present study, we attempted to fill this research gap by conducting experimental and CFD tests on a Stairmand cyclone to investigate the effects of surface roughness on flow field and separation performance. We hope that our results provide a workable reference regarding the detailed separation process and precise effects of surface roughness on the flow field and separation performance of cyclone separators.
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2. Experiment 2.1. Experimental system The experimental system, mainly consisting of air draft system, measurement system, and a cyclone model, is shown in Fig. 1. A Stairmand cyclone separator with barrel diameter of 190 mm was manufactured from standard organic glass with initial inner surface roughness of 0.01 mm. The detailed geometry and dimensions of our separator are shown in Fig. 2 and Table 2, respectively. The surface roughness was changed by pasting sand paper with varying roughness (0.061, 0.08, 0.12, 0.18, 0.25, 0.43, 1, and 2 mm) on the inner wall surface of the cylinder and cone (see in Fig.1 ).
Fig. 1. Schematic diagram of experimental system: (1) particle bin, (2) particle feeder, (3) differential pressure sensor, (4) cyclone separator, (5) particle discharge bin, (6) sand paper, (7) Pitot tube, (8) knife switch, (9) filter, (10) fan.
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Fig. 2. Schematic diagram of cyclone separator. Table 2 Geometrical dimensions of experimental cyclone Structure
a/mm
b/mm
De/mm
S/mm
h/mm
H/mm
B/mm
D/mm
Ld/mm
Value
95
38
80
95
280
745
80
190
1100
2.2. Particles used We used talcum powder with a physical density of 2700 kg/m3 as experimental particles. The particle size distribution as-measured by a Mastersizer 2000 laser particle size analyzer is shown in Fig. 3. The volume mean particle diameter was approximately 17.56 μm.
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Fig. 3. Particle size distribution of talcum powder. 2.3. Experimental procedure and methods We conducted all experiments at atmospheric pressure and ambient temperature. Particle-laden gas was forced into the cyclone inlet with a centrifugal fan. The air flow rate was controlled by a knife switch in the outlet pipe and measured with a Pitot-tube in the outlet pipe. Particles were fed into the inlet by a star-type feeder. The inlet velocity ranged from 10 to 25 m/s and the feeding particle concentration was 20 g/m3 throughout the experiment. In the cyclone, most particles were separated from the gas and ultimately collected in the discharge bin underneath. After passing through the cyclone, the gas was passed through a filter to remove any remaining particles. Pressure drops were measured with dynamic differential pressure sensor fixed between the inlet and outlet. The measurement range was 0-10 kPa with 0.25% precision. The sampling frequency and sampling time were set to 500 Hz and 60 s, respectively. Each experiment was repeated at least three times to ensure relative error below 5%. The averages were used for subsequent calculations.
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3. Numerical study 3.1. CFD model The key to the success of CFD simulation lies in an accurate description of the turbulent behavior of the inner flow. The k-epsilon turbulence model and its variants do not effectively simulate the highly swirling turbulent flow in cyclones due to the assumption of isotropic turbulence structure [24]. The Reynolds stress model (RSM), conversely, has proven an accurate simulation of cyclones as it accounts for the effects of stream curvature, rotation, swirl, and rapid changes in strain [25-27]. Over recent years, large eddy simulation (LES) has grown popular for this purpose as well. Previous researchers [28, 29] have found that LES is more accurate than RSM in the simulation of cyclones; Shukla et al. [29] found that the mean velocities predicted by LES and RSM are very close. Given the accuracy of results and low computational cost, we used RSM in this study to predict the flow field in the cyclone separator. Basic information regarding this model can be found in our reference [30]. We simulated the dispersed phase by tracking a large number of spherical dispersed particles through the converged flow field of continuous flow in the Lagrangian reference frame by using a two-way coupling method via Discrete phase model (DPM). The finite volume method was used to discretize the partial differential equations of the model using the SIMPLE (semi-implicit method for pressure linked equations) method for pressure velocity coupling and QUICK (quadratic upwind interpolation of convective kinematics) scheme to interpolate the variables on the surface of the control volume. The implicit coupled solution algorithm was selected. In this simulation, the 10 -4 convergence criterion accuracy for the calculations was applied, and 0.0002 s was selected as the time step size. The simulation was performed via the commercial software Fluent 6.3.26 on a work station with a CPU of Intel Xeon 2.9 GHz and RAM of 64 GB. 3.2. Surface roughness modeling Surface roughness increases the resistance to flow and momentum transfer. This leads to a 7
shift in the velocity profile in the boundary layer. Therefore, surface roughness can be taken into account in the law of the wall [21]. The mean velocity (u) at a given distance from the wall (y) is determined by the friction velocity (u*), kinematic viscosity (ν), and surface roughness height (ks) in the turbulent boundary layer per the law of the wall, where surface roughness causes a downward shift. The law of the wall can be written for rough-wall boundary layers as follows: u u* (1 k )ln( yu* v) B B(ks )
(1)
where the von Karman constant κ ≈ 0.41 and B is an empirical constant for smooth walls. The friction velocity definition is: u* ( w )0.5
(2)
where τw is the wall shear stress and ρ is the fluid density. The roughness function, ∆B, depends on dimensionless surface roughness, ks+, which is defined as follows: ks ks u* v
(3)
In the case of hydrodynamically smooth flows (ks+< 2.25), the roughness function ∆B = 0. The roughness function is calculated by: B (1 k )ln(1 Cs ks )
(4)
If the flow is in a fully rough regime, (ks+> 90) and B (1 k )ln((ks 2.25) 87.75 Cs ks ) sin[0.4258ln(ks 0.811)]
(5)
Otherwise, the values of 5.56 and 0.5 apply as the roughness constants B and Cs, respectively. 3.3. Grid division and independence Figure 4 shows our computational cyclone model containing 682968 CFD cells. The whole computational domain was divided by the structured hexahedron grids. The grids were densified near the walls to allow us to accurately solve the complex turbulent flow in the boundary layer. The first grids were 0.05 mm away from the wall. The growth factor of the grid spacing from the walls to the center region was 1.2 in the wall-normal direction. We conducted mesh-independent analysis with 385750, 682968, and 895350 hexahedral
8
cells generated by Gambit 2.3.6, respectively. The differences in cyclone pressure drop between 385750 and 895350 hexahedral cells are about 8.3%, and the differences in cyclone pressure drops between 682968 and 895350 hexahedral cells are less than 4.7%. In addition, the relative error in tangential velocity at the position Z=-150 mm between 385750 and 895350 hexahedral cells is about 5.6%, and the relative error in tangential velocity between 682968 and 895350 hexahedral cells is less than 1.2%. As the differences of pressure drop and tangential velocity between 682968 and 895350 hexahedral cells are so small, the grids with 682968 hexahedral cells produce grid independent results.
Fig. 4. Grid representation of simulated cyclone.
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Fig. 5. The distributions of tangential velocity at the position Z=-150 in cyclone. 3.4. Boundary conditions A presumed uniform inlet velocity Vi = 20 m/s was specified at the normal-to-inlet surface of the cyclone. The surface roughness heights of the cylinder and cone were set to 0.01, 0.08, 0.18, 0.43, 1, and 2 mm, respectively. Other parts of the rough surface were set to 0.01 mm. The hydraulic diameter equaled 54.29 mm with turbulent intensity of 3.7%. The outflow boundary condition was imposed at the outlet. Air was forced into the inlet at various velocities and temperature of 300 K. The flow was assumed to be fully developed at the outlet. Near-wall treatment was achieved by using standard wall functions. We used the constant viscosity and ideal gas law for density to calculate the fluid properties. The non-dimensional wall unit (y+) values were checked to ensure that they were within the log-law region. 4. Results and discussion 4.1. Pressure drop of cyclone separator Pressure drops are defined here as the mean values of differential pressure signals measured between the inlet and outlet of the cyclone separator with a dynamic differential pressure sensor (Fig. 2). Variations in pressure drop with surface roughness for a variety of inlet
10
velocities are shown in Fig. 6. The simulation results agreed reasonably well with the experimental data. Overall, pressure drop decreased as surface roughness increased. When the inlet velocity was smaller (Vi=10m/s), the effects of surface roughness were negligible. The decrease in pressure drop with the increase in surface roughness was more pronounced at higher inlet velocities. The curves changed sharply along with surface roughness as inlet velocity increased, as well.
Fig. 6. Cyclone separator pressure drop as a function of surface roughness. There are two particularly likely factors in the decreasing pressure drops we observed. Pressure drop is generally caused by friction loss between the fluid and wall as well as internal vortex flow. The latter accounted for a major part of the pressure drop in our observations. Wall friction increased with surface roughness while tangential velocity decreased as surface roughness increased, as shown in Fig. 9. The rotation intensity in the cyclone body and vortex finder was weakened as surface roughness increased. This led to higher static pressure in the vortex finder. As particles were loaded, the pressure drop was also affected by the interaction between them and the wall. The mean free path for particles between wall collisions grew shorter than that in the case of a smooth wall (or with smaller surface roughness) [31]. This
11
resulted in more energy loss and thus a significant reduction in pressure drop, as shown in Fig. 6. 4.2. Separation efficiency Figure 7 shows our separation efficiency results with four different inlet velocities as a function of surface roughness. There was a consistent critical value of separation efficiency along with surface roughness for all four velocities. Surface roughness above or below this critical value led to a decrease in separation efficiency, which marks a notable departure from the numerical simulation results reported by Kaya et al. [21]. We observed an increase in separation efficiency by about 3%. At inlet velocity of 10, 15, and 20 m/s, the critical value was a surface roughness of approximately 0.08 mm. However, at inlet velocity of 25 m/s, the maximum separation efficiency was located at surface roughness of about 0.12 mm.
Fig. 7. Cyclone separator collection efficiency as a function of surface roughness. The curves of efficiency versus inlet velocity with surface roughness of ks=0.01, 0.08, or 0.43 mm are shown in Fig. 8. The separation efficiency markedly decreased as surface roughness increased. A critical value of separation efficiency again appeared with increasing inlet velocity due to the effects of the radial distance of the rebounded particles from the inner wall [32]. We define this critical velocity as the “maximum-efficiency inlet velocity” [32, 33]. The rebounded particles obtained more kinetic energy at higher inlet velocities, to the point 12
where the radial distance traveled by a rebounded particle was longer than the width of the downward gas flow. Finally, the particles were rebounded back into the upward gas flow. Within the rapid, upward gas flow, the particles moved towards the vortex finder quickly with little separation. Therefore, the particles rebounded out of the downward gas flow would escape from the cyclone separator without being captured. At lower inlet velocities, the rebounded particles possessed less kinetic energy, so the radial distance traveled by a given rebounded particle was shorter than the width of the downward gas flow. The particles in this case moved towards the wall again via centrifugal force. The loss of energy due to collision decreased the velocity of the particles, and in the next rebounding process, the radial distance of the particle was truncated. Particles not escaping the cyclone after the first collision were unlikely to rebound into the upward gas flow in the following motion and thus unlikely to be captured. The decrease in separation efficiency at high inlet velocities was primarily caused by the escape of rebounded particles after the first collision. In this study, the maximum-efficiency inlet velocity was 21 m/s with a surface roughness of approximately ks=0.01 or 0.08 mm. The maximum-efficiency inlet velocity was 20 m/s with a surface roughness of ks=0.43 mm. In other words, small surface roughness seemed to have little effect on the maximum-efficiency inlet velocity. As surface roughness increased, the collision between the particles and wall increased; as more particles entered the upward gas flow, they moved towards the vortex finder quicker and with less separation. As a result, the separation efficiency and maximum-efficiency inlet velocity decreased.
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Fig. 8. Collection efficiency with varying inlet velocity. 4.3. Tangential velocity Tangential velocity is an important component of the gas flow in a cyclone due to its effect on the particle separation process and pressure drop. Figure 9 compares the tangential (Vt) velocity profiles at the axial positions of Z=-120, -260, -450, and -700 mm, respectively. We found that surface roughness significantly influenced the tangential velocity distributions. Tangential velocity profiles in the outer vortex were reduced by increasing surface roughness, as were the maximum tangential velocity values. However, the tangential velocity profiles remained effectually unchanged in the core region. The positions of the maximum tangential velocities at these sections gradually moved toward the center as surface roughness increased. The maximum tangential velocities slightly decreased along the cyclone, but this decrease seemed to be unaffected by surface roughness.
14
Fig. 9. Tangential velocity profiles with surface roughness at different sections. 4.4. Axial velocity Figure 10 compares the axial (Vz) velocity profiles at the positions Z=-120, -260, -450, and -700 mm, respectively. Two distinct regions are visible in the axial velocity profiles: an outer vortex region where the velocity profiles move downward and an inner region where they move upward. The effects of surface roughness were negligible in the outer vortex near the wall, but were significant on the axial velocity profiles in the inner region. The inner axial velocity profiles became larger and changed from an M-shape distribution into an inverted V-shape as surface roughness increased. This is attributable to the weakening retention phenomenon in the vortex core area.
15
Fig. 10. Axial velocity profiles with surface roughness at different sections. 4.5. Radial velocity Figure 11 shows the radial velocity (Vr) profiles varying with surface roughness at the axial positions of Z=-120, -260, -450, and -700 mm, respectively. The radial velocity pointed towards the center of the cyclone separator in most areas of the flow field and was oriented towards the wall in some fractions. The influence of roughness on radial velocity differed in these different areas. In most areas, radial velocity decreased with roughness; this caused a decrease in resistance for the particles moving towards the wall. These particles were more likely to be separated, dragged towards the inner wall, and captured.
16
Fig. 11. Radial velocity profiles with surface roughness at different sections. 4.6. Natural vortex length According to Yang et al. [32], the natural vortex length is the distance from the entrance of the vortex finder to the vortex end. Adequately defining the vortex end is the key to measuring the natural vortex length. At the end of vortex, the fluid pressure gradient significantly decreases and the static pressure in the center and surrounding area becomes consistent. Thus, changes in the fluid pressure gradient reveal the position of the vortex end. We analyzed the static pressure distribution in the cyclone separator with different surface roughness values, as shown in Fig. 12, to investigate the influence of surface roughness on the natural vortex length. The circles in Fig. 12 indicate the vortex end positions which we used to determine the natural vortex length via the changes in static pressure. The vortex end steadily moved upwards as surface roughness increased. When ks=0.01-0.43 mm, the vortex end was in the dipleg position (with the tail end in the legs); the natural vortex length decreased slowly as surface roughness increased. When ks was 1 mm, the vortex end was situated nearer to the dust
17
outlet. When ks = 2 mm, the vortex end was nearer to the cone. To this effect, the natural vortex length grew shorter as the surface roughness of the inner wall in the cylinder and cone increased.
Fig. 12. Static pressure distribution of cyclone separator with surface roughness. (Circles indicate vortex end position.) 4.7. Boundary layer thickness Based on the boundary layer separation theory reported by Kim et al. [34, 35], we divided the cyclone into two regions: the turbulent-core region and the near-wall region (or “boundary layer region”). Li et al. [36] reported several effects of boundary layer thickness on the separation efficiency in a cyclone separator per an elementary numerical analysis of the interaction between particles and the gas phase. They found that separation efficiency increases as boundary layer thickness decreases. We calculated boundary layer thickness, δ, as follows: N
(1 ui Vi ) ( yi1 yi )
(6)
i 1
where ui is the fluid velocity magnitude at point i in the boundary layer region; Vi is the inlet gas velocity; i= 1, 2, .., N, represents all points from the wall to the point where fluid velocity is 18
equal to inlet gas velocity; and yi is the radial position of point i. Figure 13 shows the curve of boundary layer thickness with surface roughness near the wall at the Z=-260 mm section (270 angle direction). Thickness generally increased with surface roughness. When surface roughness was less than 0.18 mm, boundary layer thickness was nearly constant. Though surface roughness affected the tangential velocity, radial velocity, and axial velocity components to some extent, the velocity magnitude and fluid velocity gradient near boundary layer region barely changed, thus the relative lack of changes in the boundary layer. When surface roughness exceeded 0.18 mm, there was an increase in wall friction loss which caused a rapid decrease in the velocity magnitude and fluid velocity gradient near the boundary layer region – this caused a gradual increase in boundary layer thickness.
Fig. 13. Boundary layer thickness with surface roughness. 4.8. Discussion According to the turbulent boundary layer theory explained by Qian et al. [37], particles in the near-wall region (i.e., boundary layer) were not only affected by centrifugal force, FC, and drag force, FD, but also determined by Saffman force, FS, generated in the relatively high gradient of fluid velocity near said boundary layer (Fig. 14). The Saffman lift acting on the particles in our system was indeed significant [37].
19
Fig. 14. Schematic drawing of forces on a near-wall particle. We explored the critical value of separation efficiency corresponding to surface roughness based on the collision between the particles and inner wall, velocity distribution, and forces acting on the particles near the boundary layer. When surface roughness was less than 0.1 mm, the tangential velocity and boundary layer thickness remained almost unchanged as surface roughness increased. That is to say, the centrifugal force, FC, and Saffman force, FS, remained almost constant. The radial velocity decreased to a relatively larger extent and thus decreased the drag force acting on the particles. This caused more particles to be dragged into the near-wall region for separation. The smaller surface roughness also meant weaker collisions between particles and the inner wall [31, 38]. Particles entering the near-wall region did not move into the fast upward gas flow after bouncing against the inner wall, so there was less particle separation efficiency under these conditions. When the roughness was greater than 0.1 mm, the tangential velocity decreased considerably as surface roughness increased. The centrifugal force decreased and fewer particles entered the near-wall region for separation. There was stronger collision between the particles and inner wall due to the shorter mean free path, as well [31, 38]. More particles were sucked into the internal swirl after bouncing against the wall and then forced out of the cyclone separator without being captured. This reduced the separation efficiency of the system. Increased surface roughness also increased the boundary layer thickness [36] and further
20
decreased the separation efficiency. 5. Conclusions In this study, we investigated the effects of surface roughness ranging from 0.01 to 2 mm on the performance and flow field of a Stairmand cyclone separator with a particle concentration of 20 g/m3 and inlet velocities of 10-25 m/s. Our conclusions can be summarized as follows. 1) The effects of surface roughness on cyclone pressure drop are negligible at lower velocities. At higher velocities, pressure drop decreases with surface roughness. 2) Surface roughness considerably influences the separation efficiency. There is a critical value of surface roughness below or above which there is a marked decrease in separation efficiency. Separation efficiency can be increased by a maximum of about 3% at the critical value. The value may be controlled by collision between the particles and inner wall, as well as the velocity distribution and forces acting on the particles, near the boundary layer region. 3) There is a maximum-efficiency inlet velocity which exists regardless of surface roughness, as inlet velocity affects the radial distance traveled by the rebounded particles from the inner wall. We found that maximum-efficiency inlet velocity decreases as surface roughness increases. 4) The tangential velocity in the cyclone decreases as surface roughness increases due to the increase in flow resistance and weakening swirl. Any excessive increase in surface roughness decreases the radial velocity and increases the upward axial velocity in the core region, which improves particle retention in the vortex core area. The natural vortex length gradually decreases as surface roughness increases. 5) Some particles may significantly increase surface roughness as they cause surface abrasion or are retained on the cyclone wall during the collection process. The appropriate cyclone surfaces roughness should be controlled to ensure optimal separation performance (high separation efficiency, low pressure drop) for an optimized cyclone separator.
21
Acknowledgments The authors gratefully acknowledge the support from the National Basic Research Program [grant number 2014CB744304] and National Natural Science Foundation [grant number 21276274].
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Graphical abstract
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Highlights Effects of roughness on pressure drop are different at low and high inlet
velocity. Cyclone separation efficiency has a critical value along with roughness. Natural vortex length is gradually shortened with roughness increasing. Roughness changes axial velocity distribution from M-shape into inverted
V-shape. Appropriate roughness is proposed to retain optimal separation performance.
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