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Impacts of the vortex finder eccentricity on the flow pattern and performance of a gas cyclone
Accepted Manuscript Impacts of the Vortex Finder Eccentricity on the Flow Pattern and Performance of a Gas Cyclone Farzad Parvaz, Seyyed Hossein Hosseini, Goodarz Ahmadi, Khairy Elsayed PII: DOI: Reference:
S1383-5866(17)31369-2 http://dx.doi.org/10.1016/j.seppur.2017.06.046 SEPPUR 13824
To appear in:
Separation and Purification Technology
Received Date: Revised Date: Accepted Date:
30 April 2017 13 June 2017 16 June 2017
Please cite this article as: F. Parvaz, S. Hossein Hosseini, G. Ahmadi, K. Elsayed, Impacts of the Vortex Finder Eccentricity on the Flow Pattern and Performance of a Gas Cyclone, Separation and Purification Technology (2017), doi: http://dx.doi.org/10.1016/j.seppur.2017.06.046
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Impacts of the Vortex Finder Eccentricity on the Flow Pattern and Performance of a Gas Cyclone Farzad Parvaz a, Seyyed Hossein Hosseini b, Goodarz Ahmadi c, Khairy Elsayed d a
Department of Mechanical Engineering, Semnan University, P.O. Box 35131-191, Semnan, Iran b
c d
Department of Chemical Engineering, Ilam University, Ilam 69315–516, Iran
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
Mechanical Power Engineering Department, Faculty of Engineering at El-Mattaria, Helwan Uinversity, Masaken El-Helmia P.O. Cairo 11718, Egypt
Abstract The impact of eccentricity of the vortex finder with deviations in the range of 4–10% on the flow pattern and performance of gas cyclone was studied. The Eulerian-Lagrangian approach in conjunction with the Reynolds stress turbulence model (RSM) of the ANSYS-FLUENT 15 code was used in these simulations. It was found that with increasing deviation of vortex finder up to 10%, the tangential velocity was increased. The maximum tangential velocity obtained for the radial profiles was 1.8 times that of the inlet velocity and the lowest tangential velocity was 1.58 times that of the inlet velocity. The maximum periodic variation in axial and tangential velocities was in the free vortex (central portion of the cyclone). It was shown that increasing the eccentricity of the vortex finder led to an increase in the intensity of oscillation of the axial velocity. For 6% eccentricity, the axial velocity was reduced due to a decrease in the oscillation rate downstream of the cyclone, which is a major factor affecting the cyclone performance. The pressure drop was also increased with increasing eccentricity of the vortex finder. It was found that the gas cyclone with an eccentricity of 8% was more efficient for droplets larger than 1 µm. In this case, also the liquid film flow does not occur on the cyclone wall. Key words: Eccentricity of vortex finder, Eulerian-Lagrangian, RSM, Wall-film, Rebound
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1. Introduction The gas cyclone is one of the most effective gas-cleaning equipment that is widely used in various industries. The device uses the centrifugal force to separate particles from the gas flow. The gas cyclones are also used for air filtration and purification. With increasing computational power, recent progresses in numerical algorithms, and better understanding of multiphase flows, the computational fluid dynamics (CFD) has established its application among other numerical methods and experimental procedures to study gas cyclones in different aspects. Hoekstra et al [1] in CFD simulation of a gas cyclone, evaluated three turbulence closure models, namely, RSM, k-ε, and RNG k-ε for three swirl numbers. They found that the predictions made by RSM model were in a close agreement with the measured data of mean tangential and axial velocities, whilst the other turbulence models predictions showed a great deviation from the experimental data. The same results by RSM were found for a high-efficiency cyclone, in which the measured data were extracted by Laser Doppler Velocimetry [2]. Shukla et al. [3] also compared the RSM and LES approaches for the cyclone separators. Their results showed that LES is a better choice. Using the LES methodology Souza et al. [4] simulated the mean flow field in the cyclones. They used hexahedral elements for all simulations and compared the LES results to the RSM predictions. It was shown that in addition to independence of ad hoc parameters, LES is a robust, reliable modeling option for simulation of small cyclone separators. In simulation of a cyclone, Alahmadi et al. [5] by applying the rotation and curvature impacts in the Shear Stress Transport with Curvature Correction (SSTCC) turbulence model found the more accurate predictions compared to RSM, while the computational time for their model was superior to the RSM. Wang et al. [6] performed computational and experimental studies of the behavior of oil droplets and their separation in gas-oil cyclones. In particular, they simulated the
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trajectories of droplets in the cyclone swirling flows and included the breaking up of droplets, droplets collisions also droplets impacting the cyclone walls. Zhu et al. [7] studied the flow inside a 5 mm mini hydro-cyclone using the direct numerical simulation (DNS) approach. They found that the flow through the mini-cyclone became unsteady at Reynolds number of about 300. They also found Görtler vortices at the vortex finder inner and concave walls for the air velocity of 0.2 m/s. They also showed that the cyclone efficiency increases by increasing the inlet velocity. Several CFD works on the effects of other cyclone geometrical parameters, such as inlet parameters have been reported in the literature. Chuah et al [8] studied the impact of cone tip diameter of a cyclone and found that a decrease in cone tip diameter, the maximum tangential and axial velocities increase, and also leads to increasing the cyclone pressure drop. Elsayed and Lacor [9] studied the impact of cone tip diameter on the flow field and performance of three gas cyclones using large eddy simulation (LES). It was found that the cone tip-diameter has a minor influence on the collection efficiency as well as the pressure drop. Elsayed and Lacor [10] studied the inlet dimensions of five cyclones and found that with increasing the inlet dimensions, the maximum tangential velocity and pressure drop are reduced. In addition, the cut off size is reduced by increasing the inlet dimensions that causes in increase in the cyclone efficiency. It was also shown that varying the inlet width is more significant compared to the inlet height. Using an Eulerian-Lagrangian method, Oh et al. [11] examined the performance of a uniflow cyclone. The investigated the flow patterns and particle trajectories in a class of gas-dust cyclones. They showed that the Eulerian-Lagrangian approach is an appropriate method for characterizing the particle behavior. It was shown that the particle diameter, the gas velocity, and
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the gas temperature significantly affect the cyclone performance. Safikhani and Mehrabian [12] numerically examined a new cyclone design. They used the RSM model for simulating the turbulent flow inside the cyclone and the Lagrangian trajectory analysis method for particles tracking. Their results showed the presence a low-pressure region is in the central part of the cyclone. The turbulent kinetic energy was found to be high at the entrance of the vortex finder. They reported that the cyclone efficiency decreased by increasing the diameter of vortex limiter. Lakhbir et al. [13] studied the effects of cylinder length and cone size on the pressure drop and the cyclone performance. They found that increasing the cylinder length to 5.5 times that of the cyclone diameter reduces the pressure drop by about 34% and increases efficiency by 9.5%. On the other hand, increasing the length of the cone up to 6.5 times that of the diameter of the cyclone causes 29% drop in pressure losses and an increase in efficiency by 11%. Qian and Wu [14] studied the effects of the inlet angle on the flow pattern and the performance of cyclone for separation of particles using the computational fluid dynamics (CFD) approach. They compared the influence of the inlet angle on the flow pattern in cyclones and showed that the inlet angle significantly affects the flow pattern and the cyclone performance. They found that when the input angle is 45 degree the separation efficiency greatly increases and the pressure drop decreases by 15%. Xiang and Lee [15] studied effects of cyclone length on its performance using CFD simulations. They concluded that the tangential velocity decreases with increasing the cyclone length. Karagoz et al. [16] evaluated the effects of cyclone parameters on particle cut off size. They reported good agreements between their model predictions and the experimental data. Surmen et al. [17] also predicted the particle cut-off-size using a theoretical model and discussed the effects of cyclone geometry including the inlet and outlet cross section areas and code diameter, fluid properties including Reynolds number, and wall roughness. There are many
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additional studies on the effect of the design parameters such as the cyclone length, the geometry of inlet and outlet on the cyclone performance. These studies suggest that a slight change in the cyclone parameters significantly affects the flow patterns in the cyclone and its particle removal efficiency [18–21]. Regarding the vortex finder influences, several numerical works have been reported. Gao et al. [22] studied the central channel diameter and height effects on the flow field in the separator chamber by CFD model including RSM. They observed that with decreasing the diameter of central channel, tangential velocity and cyclone pressure drop increase and showed that the central channel size is an important parameter affecting the flow pattern in the gas cyclones. They also found that the maximum tangential velocity in the cyclone is 1.8-2 times the gas velocity in the inlet channel. Using a numerical simulation approach, Gao et al. [23] investigated the oil droplet trajectories and their break-up in the oil-gas cyclone. They compared their simulation results for the size distribution of oil droplets with their measured data. It was shown that increasing the cyclone flow velocity not only affects the droplets separation efficiency but also significantly influences the breaking up of droplets. They showed that inclusion of the droplet break up improves the accuracy of the simulation results and their agreement with the measured experimental data [23]. Ghordat et al. [24] studied the effect of size and shape of the vortex finder using an EulerianEulerian two-fluid model (TFM). Several cyclone shapes including normal, reverse cone, cylindrical and conical were studied and a range of inlet particle concentrations and sizes was simulated for each model. They evaluated the effect of geometry of the vortex finder on the predicted tangential and axial velocities as well as the efficiency of particle removal.
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El-Batsh [25] optimized the dimensions of the vortex finder for improving the cyclone performance by CFD model including RSM. The model revealed that by increasing the vortex finder diameter the pressure drop through the cyclone decreases and also this increase greatly affects the collection efficiency. Whilst the vortex finder length impact on the cyclone performance was insignificant. Elsayed and Lacor [26] studied the influence of the vortex finder dimensions on the flow pattern and cyclone performance by evaluating nine different vortex finder dimensions using LES approach. They found that the vortex finder diameter and length greatly affect the dimensionless pressure drop (Euler number) and Stokes number and also cause the change in the axial and tangential velocity profiles. Elsayed [27] introduces a new vortex finder shape to minimize the pressure drop in gas cyclone using the discrete adjoint approach. In addition, Elsayed [27] showed that the computational time for the grid independence studied can be significantly reduced by using the adjoint method. Raoufi et al. [28] studied the impacts of vortex finder shape and diameter on the flow pattern and performance of gas cyclones by CFD model containing RSM. It should be mentioned that the four vortex finders in different cylinder-shaped and six vortex finders in various cone-shaped were used and it was found that the vortex finder shape has major impact on the flow pattern and separation efficiency of the cyclone. It was also observed that the gas volume flow rate affects the gas flow pattern for different vortex finder’ shapes. de Souza et al. [29] compared two different approaches, namely, a Post Cyclone (PoC) and the use of a double overflow duct to increase the gas cyclone performance using LES methodology. Both cases give advantage in terms of the remaining swirl in the overflow duct. It was shown that
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PoC increases the cyclone performance even for particle diameter lower than two micron in small scale of gas cyclone separator. de Souza et al. [30] evaluated the length and shape of the outlet duct on the grade efficiency and pressure drop inside a small cyclone by the numerical method of LES. They proved the outlet duct length and shape has small influence on the cyclone flow filed. Their results revealed a complex relationship between the cut off diameter and the gas outlet duct length and shape. In the light of above review, the present work is concerned with the effect of deviation of the vortex finder from the cyclone center on the gas flow pattern and the droplet removal efficiency. The specific objectives are (a) Evaluation of the effect of eccentric on the pattern of gas flow in the cyclone; (b) Assessment of the influence of eccentricity on the performance of gas cyclone in the droplet removal.
In addition, considering the formation of a liquid film on the wall due to
the deposition of droplet was also studied. 2. Numerical model description A brief description of governing equations on the current issue, the used computational grids, used initial and boundary conditions, and also the used numerical schemes is performed as follows: 2.1. Continuous Phase Equations For a cyclone, the nature of the flow is turbulent due to the highly swirling behavior of the flow, and its structure is three dimensional. Therefore, a suitable turbulence model should be chosen for CFD modeling of gas cyclones [10,8,21,31]. In the current study, the gas flow in the cyclone is assumed as unsteady and incompressible flow with constant temperature. For an isothermal flows, the continuity and Reynolds average Navier-Stokes equations are given as, =0
(1)
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(2) In Equation (2), system,
is the average velocity and P is the average pressure,
is the coordinate
is the kinematic viscosity and ρ is the gas density. The Reynolds stress tensor, need to be modeled. Here,
is the ith fluctuating velocity component.
=
2.2. Turbulence Modeling In this study the RSM turbulence model, which has been widely used for simulation of gas cyclones, is applied in additional to the transport equation for the rate of dissipation. The RSM equation is given by
(3) In the above equation, turbulence production is given by (4) where, P stands for the fluctuating kinetic energy production. kinetic viscosity and
=1,
= 1.8 as well as
shown in Eq. (3) is turbulence
= 0.6 that are empirical constant are used in
the simulation. In addition, the transport equation of the turbulence dissipation rate can be written as:
(5) It should be noted that, in Eq. (5) K= values of
,
, and
is the fluctuating kinetic energy. The constants’
are 1.3, 1.44 and 1.92, respectively.
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2.3. Dispersed phase In the present work, it is assumed that the volume fraction of droplets is less than 10% and the Eulerian-Lagrangian method under the one-way coupling assumption is used for tracking droplets. The droplets force equilibrium relationship according to Newton's second law in x, y, and z directions, respectively, are: (6) (7) (8) where (9) In the above equation, the particle Reynolds number is defined as
(10) Here
is the gas velocity and
density of droplet and
is the droplet velocity, ρ is the density of the gas,
is the
is the diameter of droplet.
The drag coefficient is given as, (11) In the above equation,
and
are constant coefficients for spherical droplets that are
functions of Reynolds number [32]. In this study, the discrete random walk (DRW) method is used for evaluating the fluctuation velocity of the gas [33].
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Values of the fluctuation velocity during the eddy lifetime
is calculated using
(12)
In the above equation, ζ is a zero mean and unit variance Gaussian random number.
is the
root-mean- square fluctuation velocity in the i-direction. In the present study, the eddy life time is estimated using [34], (13) Here r is a uniform random number between zero and one, and TL is the integral time scale given as (14) where
is constant. Here a value of
0.3 is used [34, 22].
2.4. CFD grids The numerical grids for different geometries were provided in Cartesian coordinate using structured meshes. The computational domain was meshed using the Gambit software. The schematic of the cyclone and the computational domain consisting of the hexahedral nonuniform elements are shown in Figure 1. In addition, Figure 2 shows the vortex finder with different eccentricities that can be defined as Eccentricity % =100×( distance of central of deviated vortex finder to the center of vortex finder without any eccentricity)/ radius of vortex finder The information regarding dimensions of the cyclone under study is tabulated in Table 1. To assure that the CFD results are grid independent, three different grids are examined. Figure 3 shows a comparison of the simulation results for the tangential velocity at level z = 0.75D for 10
different grid sizes. This figure shows that the grid independence was reached with the medium size grid with the total number of cells of 455900, which is also consistent with the earlier CFD simulation of gas cyclones reported in [10]. 2.5. Boundary conditions For boundary conditions, it is assumed that air enters the inlet channel with a uniform velocity of 19.5 m/s. The corresponding turbulence intensity and length scale are, respectively, 5% and 0.07 of the channel width. At the outlet pipe, the outflow boundary conditions are imposed. Solid walls are treated as non-slip surfaces. In the near wall region, the fluid flow is modeled using the standard wall function (SWF) that the researchers have shown the very encouraging results by SWF model [13,25,33]. The SWF provide near-wall boundary conditions for conservation equations so that the viscous sublayer does not have to be resolved and the need for a very fine mesh is circumvented. In order to study the contacting droplets to the walls, reflect and wall-film boundary conditions are chosen for the discrete phase. The density of water is 999 kg/m3 and its dynamic viscosity is 0.001 Pa.s. 2.6. Time step The resident time depends on the cyclone volume and the gas volume flow rate and is calculated as tres.=Vcyclone /Qin
(15)
In this study, the resident time is 0.237 s and a time step of 0.0001s is used for the droplet trajectory analysis. 2.5. Numerical schemes
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The detailed information used in the present CFD modeling such as discretization scheme of pressure, momentum, turbulent kinetic energy, turbulent dissipation rate, and Reynolds stress as well as pressure/velocity coupling are depicted in Table 2. 3. Results and discussion 3.1. Model validation For validation of the model, the simulation results are compared with the experimental data of Hoekstra [31]. Here simulations are performed for the exact geometry of the experimental cyclone.
In addition to the comparison of the axial and tangential velocities at z = 0.75D, the
pressure drop for different velocities is also compared. Figures 4 and 5 compare the numerical results against the experimental data, respectively, for the tangential and axial velocities and the cyclone pressure drop. It is seen that the RSM turbulence model predicts the tangential and axial velocity, as well as, the cyclone pressure drop, reasonably, which they are in general agreement with the experimental data of Hoekstra [31]. It is also seen that both numerical results and measured data show a nonlinear increase of cyclone pressure drop with increasing gas inlet velocity. To validate the simulation results for the discrete phase comparison of the model prediction for the droplet removal with the experimental data of Ehteram et al. [35] was performed and the results for the flow rate of 48 L/min are presented in Figure 6. It is seen that the experimental data and computational results have the same trend of variations for the droplets smaller than 13 micron. For larger droplets, the CFD results saturate to 100% and are independent the droplet size. This figure also shows that the CFD model over-predicts the cyclone efficiency compared with the experimental data. It is worth mentioning that demising-cyclone operated by Ehteram et
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al. [23] is the very small dimensions to evaluate the discrete phase i.e. droplet, that causes the difference between the model results and experiments to be not unexpected. In the Souza et al. (2012) work, it is evident that the CFD model is sensitive to geometric changes. Nevertheless, an acceptable agreement of the model simulation with the use of Lagrangian droplet trajectory analysis and the trend of the measured data is achieved. Therefore, it may be concluded that the model is able to predict the hydrodynamics of the gas cyclones with the reasonable approximation. 3.2. Study of the characteristics of the gas cyclone flow field In this section, the effects of vortex finder eccentricity on the gas cyclone flow pattern including the variations of the tangential and axial velocities are studied. For nine various levels shown in Table 3, the cyclone pressure drops are provided. 3.3. Tangential velocity The tangential and axial velocities of gas flow within gas cyclone are very important. The tangential velocity creates the centrifugal force, which significantly affects the separation of droplets. Previous studies demonstrated that the tangential velocity is similar to the Rankine vortex [3]. The Rankine vortex includes two regions, namely, the free (irrotational) vortex and the forced (viscous) vortex, which behaves as a solid body at the central part. The tangential velocity in the inner region (forced vortex) increases with radius until it reaches a peak value, and then decreases with radius in the outer region (free vortex). The tangential velocity profiles at the different levels of the cyclone, depicted in Table 3, for the various eccentricity of vortex finder are presented in Figure 7.
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In this section, the effect of changes in the vortex finder position on the pattern of tangential velocity is studied. The tangential velocity profiles in sections S1 to S9 depicted in Figure 7 show that the variations of tangential velocity for different sections are similar. This velocity profiles display the Rankine vortex consisting the two important regions: an outer free vortex and an inner solid rotation appeared in the central part. Clearly, the eccentricity of the vortex finder affects the flow pattern in the gas cyclone. In particular, the behavior of the tangential velocity profile near the outlet pipe is markedly affected. The main reason for the change in the behavior of the flow pattern of gas cyclone with the eccentricity of the vortex finder returns to deviation in the flow outlet. As can be seen, the maximum effect is in the area of the forced vortex. In the core area of the vortex, the non-uniformity in tangential velocity appears (see cases 4 and 8% eccentricity) that by increasing the distance from the outlet pipe, the intensity of this nonuniformity, decreases. However, in the free vortex area, these fluctuations are not observed. A comparison between the radial profiles of tangential velocity for various eccentricity percentages at the levels of S1, S4, S7 and S9 is shown in Figure 8. As can be seen in the figure, with increasing deviation vortex finder, vortex area is increased that is an important factor in separation. The maximum tangential velocity is 1.8 times that of input velocity and the minimum tangential velocity is 1.58 times the input velocity. However, by being close to the bottom of gas cyclone, radial profiles are almost out of the symmetry mode and its fluctuations are reduced. The flow in gas cyclone is very complex and the processing vortex core (PVC) in a cyclone separator plays a dominant role in such complexity. For the case of 4% eccentricity there are considerable changes in the flow pattern close to the vortex finder. This causes such the unfamiliar velocity profile at S1 (see Figs. 7 and 8). 3.4. Axial velocity
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The axial velocity of gas cyclone that causes droplets moving towards the top and bottom of the cyclone is another important parameter that effects the cyclone separation. Figure 9 shows the axial velocity for different sections. The axial velocity created in the gas cyclone includes two regions. One is upstream flow area and the second is downstream flow area, and each of the areas is created in radial position. It should be noted that the tangential velocity created between the two flows is in its minimum values approximately zero and the axial velocity also reaches to the lower than zero for the case in which vortex finder is in the center of cyclone. In the case of eccentricity of the vortex finder, most of the flow fluctuations occur in the flow core. As observed in section S1, the flow is reversed in the central part towards the outlet pipe. With being a way from the vortex finder, the reversed flow intensity is reduced in downward parts. In addition, with increasing vortex finder deviation, such event does not happen. With increasing eccentricity of vortex finder, axial velocity profiles at different levels are normal, as the fluctuations do not appear. Figure 10 shows a comparison between the axial velocities in level stations of S1, S4, S7, and S9 for the different amount of vortex finder eccentricity. The figure shows that the computed profiles are as inverted W and the maximum axial velocity appears in the radial range of 0.03 to 0.05. Axial velocity profiles are almost identical for all the changes considered in the vortex finder. It is observed that the axial velocity increases with an increase in the vortex finder eccentricity up to 8%. However, the axial velocity reduces by increasing the vortex finder eccentricity from 8% to 10%. It is because of the downwards flow rate that is an important factor affecting the separation efficiency. For instance, in the section S4, the axial velocity decreases for the case of vortex finder with deviation 4% from the center compared to 6% and 8%. Therefore, from the mentioned decrease in axial velocity for the case of 4% eccentricity and also
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the different behavior of axial velocity in various levels for the case of 6% eccentricity compared to the other cases, it can be found that the flow in the cyclone is quite complex and the further studies are necessary in this field. 3.5. Pressure drop and Performance of the gas cyclone The pressure drop in the cyclone is calculated as the difference in total pressure (rather that in static pressure) between the inlet and the outlet sections. With increasing pressure drop in the cyclone, the dissipated energy has a further drop in order to the separation of droplets. Therefore, reducing this critical parameter in the cyclone can be a significant factor for design and performance of the gas cyclone. In general, the dimensionless pressure drop form in gas cyclone is the ratio of the head of static pressure to dynamic pressure that is defined as: (16) where
is pressure loss, and
is inlet gas velocity. Cyclone pressure drop with respect to the
percentage of vortex finder eccentricity is plotted in Figure 11. This figure clearly shows that the pressure drop increases by enhancing the vortex finder eccentricity. This increase in the pressure drop in the eccentric vortex finder can be referred to the losses due to direction change of the inner and outer flow streams inside and outside the vortex finder with respect to the concentric vortex finder. The performance of the gas cyclone that is an important factor in gas cyclones is studied here. The effect of vortex finder eccentricity on the collection efficiency of the cyclone is shown in Figure 12. The figure clearly shows that cyclone efficiency significantly growths by increasing the droplet size for each case. It is well known that the dominant flow pattern in the cyclone directly affects the efficiency of droplets. In this section, the cyclone performance under different
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vortex finder eccentricity percentages for two boundary conditions of wall-film and rebound are presented in Figure 12. As can be seen in the figure, the eccentricity of the vortex finder causes the reduction of efficiency compared to the case in which the vortex finder is in the center of the cyclone. In addition, it can be observed that both mentioned boundary conditions regarding the splashing the droplets to the wall predict the same trend in terms of efficiency versus droplet size. However, by considering rebound condition on the wall, the efficiency improved about 7.7%. The efficiency of 8% vortex finder deviation increases with respect to both wall boundary conditions for the droplets’ size more than 1 µm. However, for droplets smaller than 1 µm, the efficiency of 4% vortex finder eccentricity is at its maximum value. Figure 13 shows the droplets trajectory and pathline through the cyclone, while, Figure 14 shows droplets pathline from the top view. As can be seen in these figures, the forced vortex length has its highest value for the case of 4% vortex finder eccentricity leading to migration of fine droplets from the center of the cyclone to the outlet pipe. Moreover, as observed in Figure 13 the main cause of reduction in efficiency of 8% deviation is deviation of forced vortex from the central axis. Totally, it can be found that the eccentricity of vortex finder has an adverse effect on the cyclone performance such as increasing the pressure drop and decreasing the cyclone efficiency.
4. Conclusions In the study, the effect of vortex finder eccentricity on the hydrodynamics parameters, namely, tangential and axial velocity of the gas phase, cyclone pressure drop and cyclone performance was evaluated using a computational fluid dynamics approach. In order to simulate the air flow,
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the path of droplets, an Eulerian-Lagrangian method was used. The main conclusions that can be drawn are as follows: 1. The tangential velocity increased with increasing eccentricity of the vortex finder. Comparing the radial profiles showed that the tangential velocity for 10% deviation is 1.8 time of the inlet velocity. With changing the vortex finder position, the tangential velocity pattern showed nonuniformity of flow core near the outlet pipe and by moving towards the bottom of the cyclone, the intensity of this non-uniformity was reduced. 2. It was found that the axial velocity has a complex pattern in the gas cyclones, which significantly affects the performance of the cyclone. However, the predicted axial velocity of downstream flow for 8% eccentricity of vortex finder is the largest one, by further increasing the eccentricity vortex finder i.e. 10%, the downstream flow velocity reduces. In the meantime, the downstream flow velocity is an important factor in moving droplets that significantly impacts on the performance of the cyclone. 3. With changes in outlet pipe of gas in the positive direction of x-axis, the pressure drop increased. 4. Including the eccentricity of the vortex finder in the cyclone design causes the instability of forced vortex as can be seen in the case of 6%. The cyclone containing droplets lower than 1 µm showed the maximum efficiency for the case of 4% compared to the other vortex finder deviations from the center. In overall, vortex finder eccentricity has undesirable results in terms of efficiency and energy consumption (pressure drop) 5. The efficiency of cyclone using two boundary conditions of wall-film and rebound boundary regarding the splashing the droplets to the wall against the droplet size was studied. It was found
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that by considering the contact of droplets with the walls (rebound condition), the efficiency is actually increased up to 7.7%.
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[20] K.S. Lim, H.S. Kim, K.W. Lee, Characteristics of the collection efficiency for a cyclone with different vortex finder shapes, J. Aerosol Sci. 35(2004) 743–754. [21] A. Raoufi, M. Shams, M. Farzaneh, R. Ebrahimi, Numerical simulation and optimization of fluid flow in cyclone vortex finder, Chem. Eng. Process. 47(2008) 128–137. [22] X. Gao, J. Chen, J. Feng, and X. Peng, Numerical investigation of the effects of the central channel on the flow field in an oil–gas cyclone separator, Comput. Fluids. 92 (2013 ) 45–55. [23] X. Gao, J. Chen, J. Feng, X. Peng, Numerical and experimental investigations of the effects of the breakup of oil droplets on the performance of oil–gas cyclone separators in oil-injected compressor systems, Int. J. Refrig. 36 (2013) 1894–1904. [24] M. Ghodrat, S.B. Kuang, A.B. Yu, A. Vince, G.D. Barnett, P.J. Barnett, Numerical analysis of hydrocyclones with different vortex finder configurations, Minerals Eginering. 63 (2014) 125–138. [25] H. M. El-Batsh, Improving cyclone performance by proper selection of the exit pipe, Appl. Math. Model. 37 (2013) 5286-5303. [26] K. Elsayed, C. Lacor, The effect of cyclone vortex finder dimensions on the flow pattern and performance using LES, Comput. Fluids.71 (2013) 224-239. [27] K. Elsayed, Design of a novel gas cyclone vortex finder using the adjoint method, sep.purif.Technol. 142 (2015) 274–286. [28] A. Raoufi, M. Shams, M. Farzaneh, and R. Ebrahimi, Numerical simulation and optimization of fluid flow in cyclone vortex finder, Chem. Eng. Process. Process Intensif. 47 (2008 ) 128-137. [29] F.J. Souza, R.D.V. Salvo, D.D.M. Martins, Simulation of the performance of small cyclone separators through the use of Post Cyclones (PoC) and annular overflow ducts,
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sep.purif.Technol. 142 (2015) 71-82. [30] F.J. Souza, R.D.V. Salvo, D.D.M. Martins, Effects of the gas outlet duct length and shape on the performance of cyclone separators, sep.purif.Technol. 142 (2015) 90-100. [31] A.J. Hoekstra, Gas flow field and collection efficiency of cyclone separators. PhD Thesis, Technical University Delft, Stevinweg; 2000. [32] S.A. Morsi, A.J. Alexander, An investigation of particle trajectories in two-phase flow systems, J. Fluid Mech. 55(1972) 193–208. [33] K. Elsayed, C. Lacor, The effect of the dust outlet geometry on the performance and hydrodynamics of gas cyclones, Comput. Fluids. 68 (2012) 134–147. [34] ANSYS Fluent User’s Guide, ANSYS Inc, Southpointe, Canonsburg, PA, USA, 2013. [35] M.A. Ehteram, H.B. Tabrizi, M. Mesbah, G. Ahmadi, M.A. Mirsalim, Experimental study on the effect of connecting ducts on demisting cyclone efficiency, Exp. Therm. Fluid Sci. 39 (2012) 26–36.
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Captions Table 1. The geometrical dimensions of the cyclone. Table 2. Numerical schemes for the current simulation. Table 3. Position of the plotting sections. Figure 1. Geometry and grid of the problem. Figure 2. Deviations of output pipe compared to the cyclone center. Figure 3. Computational tangential velocity for the three grid levels (Z=0.75D). Figure 4. Comparison of tangential and axial velocity distribution with experimental data in the section of z = 0.75D. Figure 5. Comparison of the pressure distribution with experimental data. Figure 6. Comparison of numerical efficiency with experimental data [23]. Figure 7. The radial profiles of tangential velocity in different parts of S1-S9. Figure 8. Deviation effects of vortex finder on the radial profiles of the tangential velocity in levels of S1, S4, S7 and S9. Figure 9. The radial profiles of axial velocity in different levels of S1–S9. Figure 10. Deviation effects of vortex finder on the radial profiles of the axial velocity in levels of S1, S4, S7 and S9. Figure 11. The eccentricity effects of the vortex finder on the pressure drop.
23
Figure 12. The cyclone efficiency by considering the wall-film and rebound boundary conditions. Figure 13. Predicted droplets trajectory and pathline for different eccentricity percentages (colored by ). Figure 14. The droplets pathline from the top view (colored by ).
24
Figure 1
25
Figure 2
26
Figure 3
27
Figure 4
28
Figure 5
29
Figure 6
30
Figure 7
31
Figure 8
32
Figure 9
33
Figure 10
34
Figure 11
35
Figure 12
36
Figure 13
37
Figure 14
38
Table 1. The geometrical dimensions of the cyclone Dimension
Length (m )
Dimension ratio ( Dimension/D)
Body diameter, D
0.205
1
Inlet height, a
0.105
0.5
Inlet width, b
0.041
0.2
Gas outlet diameter, Dx
0.105
0.5
Gas outlet duct length, S
0.105
0.5
0.076875
0.375
Cylinder height, h
0.3075
1.5
Cyclone height, Ht
0.82
4
Duct length, Li
0.15375
0.75
Outlet trube length, Le
0.1025
0.5
Cone-tip diameter, Bc
Table 2. Numerical schemes for the current simulation Numerical setting
Scheme
Pressure discretization
Body force weighted
Pressure velocity coupling SIMPLE Momentum discretization
QUICK
Turbulent kinetic energy
Second-order upwind
Turbulent dissipation rate
Second-order upwind
Reynolds stress
First-order upwind
41
Table 3. Position of the plotting sections. section
S1
S2
S3
S4
S5
S6
S7
S8
S9
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
a: measured from the top inlet section
42
Graphical abstract The vortex finder eccentricity impact on the flow pattern of an aero-cyclone was studied by CFD and the results were presented.
39
Highlights ○ Study of vortex finder eccentricity impact on some hydrodynamics parameters by CFD ○ Study of collection efficiency for cyclones with and without vortex finder eccentricity ○ Vortex finder eccentricity affect the pressure drop and instability of forced vortex ○ Impact of boundary conditions of wall-film and rebound on the collection efficiency
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S1383-5866(17)31369-2 http://dx.doi.org/10.1016/j.seppur.2017.06.046 SEPPUR 13824
To appear in:
Separation and Purification Technology
Received Date: Revised Date: Accepted Date:
30 April 2017 13 June 2017 16 June 2017
Please cite this article as: F. Parvaz, S. Hossein Hosseini, G. Ahmadi, K. Elsayed, Impacts of the Vortex Finder Eccentricity on the Flow Pattern and Performance of a Gas Cyclone, Separation and Purification Technology (2017), doi: http://dx.doi.org/10.1016/j.seppur.2017.06.046
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Impacts of the Vortex Finder Eccentricity on the Flow Pattern and Performance of a Gas Cyclone Farzad Parvaz a, Seyyed Hossein Hosseini b, Goodarz Ahmadi c, Khairy Elsayed d a
Department of Mechanical Engineering, Semnan University, P.O. Box 35131-191, Semnan, Iran b
c d
Department of Chemical Engineering, Ilam University, Ilam 69315–516, Iran
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
Mechanical Power Engineering Department, Faculty of Engineering at El-Mattaria, Helwan Uinversity, Masaken El-Helmia P.O. Cairo 11718, Egypt
Abstract The impact of eccentricity of the vortex finder with deviations in the range of 4–10% on the flow pattern and performance of gas cyclone was studied. The Eulerian-Lagrangian approach in conjunction with the Reynolds stress turbulence model (RSM) of the ANSYS-FLUENT 15 code was used in these simulations. It was found that with increasing deviation of vortex finder up to 10%, the tangential velocity was increased. The maximum tangential velocity obtained for the radial profiles was 1.8 times that of the inlet velocity and the lowest tangential velocity was 1.58 times that of the inlet velocity. The maximum periodic variation in axial and tangential velocities was in the free vortex (central portion of the cyclone). It was shown that increasing the eccentricity of the vortex finder led to an increase in the intensity of oscillation of the axial velocity. For 6% eccentricity, the axial velocity was reduced due to a decrease in the oscillation rate downstream of the cyclone, which is a major factor affecting the cyclone performance. The pressure drop was also increased with increasing eccentricity of the vortex finder. It was found that the gas cyclone with an eccentricity of 8% was more efficient for droplets larger than 1 µm. In this case, also the liquid film flow does not occur on the cyclone wall. Key words: Eccentricity of vortex finder, Eulerian-Lagrangian, RSM, Wall-film, Rebound
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1. Introduction The gas cyclone is one of the most effective gas-cleaning equipment that is widely used in various industries. The device uses the centrifugal force to separate particles from the gas flow. The gas cyclones are also used for air filtration and purification. With increasing computational power, recent progresses in numerical algorithms, and better understanding of multiphase flows, the computational fluid dynamics (CFD) has established its application among other numerical methods and experimental procedures to study gas cyclones in different aspects. Hoekstra et al [1] in CFD simulation of a gas cyclone, evaluated three turbulence closure models, namely, RSM, k-ε, and RNG k-ε for three swirl numbers. They found that the predictions made by RSM model were in a close agreement with the measured data of mean tangential and axial velocities, whilst the other turbulence models predictions showed a great deviation from the experimental data. The same results by RSM were found for a high-efficiency cyclone, in which the measured data were extracted by Laser Doppler Velocimetry [2]. Shukla et al. [3] also compared the RSM and LES approaches for the cyclone separators. Their results showed that LES is a better choice. Using the LES methodology Souza et al. [4] simulated the mean flow field in the cyclones. They used hexahedral elements for all simulations and compared the LES results to the RSM predictions. It was shown that in addition to independence of ad hoc parameters, LES is a robust, reliable modeling option for simulation of small cyclone separators. In simulation of a cyclone, Alahmadi et al. [5] by applying the rotation and curvature impacts in the Shear Stress Transport with Curvature Correction (SSTCC) turbulence model found the more accurate predictions compared to RSM, while the computational time for their model was superior to the RSM. Wang et al. [6] performed computational and experimental studies of the behavior of oil droplets and their separation in gas-oil cyclones. In particular, they simulated the
2
trajectories of droplets in the cyclone swirling flows and included the breaking up of droplets, droplets collisions also droplets impacting the cyclone walls. Zhu et al. [7] studied the flow inside a 5 mm mini hydro-cyclone using the direct numerical simulation (DNS) approach. They found that the flow through the mini-cyclone became unsteady at Reynolds number of about 300. They also found Görtler vortices at the vortex finder inner and concave walls for the air velocity of 0.2 m/s. They also showed that the cyclone efficiency increases by increasing the inlet velocity. Several CFD works on the effects of other cyclone geometrical parameters, such as inlet parameters have been reported in the literature. Chuah et al [8] studied the impact of cone tip diameter of a cyclone and found that a decrease in cone tip diameter, the maximum tangential and axial velocities increase, and also leads to increasing the cyclone pressure drop. Elsayed and Lacor [9] studied the impact of cone tip diameter on the flow field and performance of three gas cyclones using large eddy simulation (LES). It was found that the cone tip-diameter has a minor influence on the collection efficiency as well as the pressure drop. Elsayed and Lacor [10] studied the inlet dimensions of five cyclones and found that with increasing the inlet dimensions, the maximum tangential velocity and pressure drop are reduced. In addition, the cut off size is reduced by increasing the inlet dimensions that causes in increase in the cyclone efficiency. It was also shown that varying the inlet width is more significant compared to the inlet height. Using an Eulerian-Lagrangian method, Oh et al. [11] examined the performance of a uniflow cyclone. The investigated the flow patterns and particle trajectories in a class of gas-dust cyclones. They showed that the Eulerian-Lagrangian approach is an appropriate method for characterizing the particle behavior. It was shown that the particle diameter, the gas velocity, and
3
the gas temperature significantly affect the cyclone performance. Safikhani and Mehrabian [12] numerically examined a new cyclone design. They used the RSM model for simulating the turbulent flow inside the cyclone and the Lagrangian trajectory analysis method for particles tracking. Their results showed the presence a low-pressure region is in the central part of the cyclone. The turbulent kinetic energy was found to be high at the entrance of the vortex finder. They reported that the cyclone efficiency decreased by increasing the diameter of vortex limiter. Lakhbir et al. [13] studied the effects of cylinder length and cone size on the pressure drop and the cyclone performance. They found that increasing the cylinder length to 5.5 times that of the cyclone diameter reduces the pressure drop by about 34% and increases efficiency by 9.5%. On the other hand, increasing the length of the cone up to 6.5 times that of the diameter of the cyclone causes 29% drop in pressure losses and an increase in efficiency by 11%. Qian and Wu [14] studied the effects of the inlet angle on the flow pattern and the performance of cyclone for separation of particles using the computational fluid dynamics (CFD) approach. They compared the influence of the inlet angle on the flow pattern in cyclones and showed that the inlet angle significantly affects the flow pattern and the cyclone performance. They found that when the input angle is 45 degree the separation efficiency greatly increases and the pressure drop decreases by 15%. Xiang and Lee [15] studied effects of cyclone length on its performance using CFD simulations. They concluded that the tangential velocity decreases with increasing the cyclone length. Karagoz et al. [16] evaluated the effects of cyclone parameters on particle cut off size. They reported good agreements between their model predictions and the experimental data. Surmen et al. [17] also predicted the particle cut-off-size using a theoretical model and discussed the effects of cyclone geometry including the inlet and outlet cross section areas and code diameter, fluid properties including Reynolds number, and wall roughness. There are many
4
additional studies on the effect of the design parameters such as the cyclone length, the geometry of inlet and outlet on the cyclone performance. These studies suggest that a slight change in the cyclone parameters significantly affects the flow patterns in the cyclone and its particle removal efficiency [18–21]. Regarding the vortex finder influences, several numerical works have been reported. Gao et al. [22] studied the central channel diameter and height effects on the flow field in the separator chamber by CFD model including RSM. They observed that with decreasing the diameter of central channel, tangential velocity and cyclone pressure drop increase and showed that the central channel size is an important parameter affecting the flow pattern in the gas cyclones. They also found that the maximum tangential velocity in the cyclone is 1.8-2 times the gas velocity in the inlet channel. Using a numerical simulation approach, Gao et al. [23] investigated the oil droplet trajectories and their break-up in the oil-gas cyclone. They compared their simulation results for the size distribution of oil droplets with their measured data. It was shown that increasing the cyclone flow velocity not only affects the droplets separation efficiency but also significantly influences the breaking up of droplets. They showed that inclusion of the droplet break up improves the accuracy of the simulation results and their agreement with the measured experimental data [23]. Ghordat et al. [24] studied the effect of size and shape of the vortex finder using an EulerianEulerian two-fluid model (TFM). Several cyclone shapes including normal, reverse cone, cylindrical and conical were studied and a range of inlet particle concentrations and sizes was simulated for each model. They evaluated the effect of geometry of the vortex finder on the predicted tangential and axial velocities as well as the efficiency of particle removal.
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El-Batsh [25] optimized the dimensions of the vortex finder for improving the cyclone performance by CFD model including RSM. The model revealed that by increasing the vortex finder diameter the pressure drop through the cyclone decreases and also this increase greatly affects the collection efficiency. Whilst the vortex finder length impact on the cyclone performance was insignificant. Elsayed and Lacor [26] studied the influence of the vortex finder dimensions on the flow pattern and cyclone performance by evaluating nine different vortex finder dimensions using LES approach. They found that the vortex finder diameter and length greatly affect the dimensionless pressure drop (Euler number) and Stokes number and also cause the change in the axial and tangential velocity profiles. Elsayed [27] introduces a new vortex finder shape to minimize the pressure drop in gas cyclone using the discrete adjoint approach. In addition, Elsayed [27] showed that the computational time for the grid independence studied can be significantly reduced by using the adjoint method. Raoufi et al. [28] studied the impacts of vortex finder shape and diameter on the flow pattern and performance of gas cyclones by CFD model containing RSM. It should be mentioned that the four vortex finders in different cylinder-shaped and six vortex finders in various cone-shaped were used and it was found that the vortex finder shape has major impact on the flow pattern and separation efficiency of the cyclone. It was also observed that the gas volume flow rate affects the gas flow pattern for different vortex finder’ shapes. de Souza et al. [29] compared two different approaches, namely, a Post Cyclone (PoC) and the use of a double overflow duct to increase the gas cyclone performance using LES methodology. Both cases give advantage in terms of the remaining swirl in the overflow duct. It was shown that
6
PoC increases the cyclone performance even for particle diameter lower than two micron in small scale of gas cyclone separator. de Souza et al. [30] evaluated the length and shape of the outlet duct on the grade efficiency and pressure drop inside a small cyclone by the numerical method of LES. They proved the outlet duct length and shape has small influence on the cyclone flow filed. Their results revealed a complex relationship between the cut off diameter and the gas outlet duct length and shape. In the light of above review, the present work is concerned with the effect of deviation of the vortex finder from the cyclone center on the gas flow pattern and the droplet removal efficiency. The specific objectives are (a) Evaluation of the effect of eccentric on the pattern of gas flow in the cyclone; (b) Assessment of the influence of eccentricity on the performance of gas cyclone in the droplet removal.
In addition, considering the formation of a liquid film on the wall due to
the deposition of droplet was also studied. 2. Numerical model description A brief description of governing equations on the current issue, the used computational grids, used initial and boundary conditions, and also the used numerical schemes is performed as follows: 2.1. Continuous Phase Equations For a cyclone, the nature of the flow is turbulent due to the highly swirling behavior of the flow, and its structure is three dimensional. Therefore, a suitable turbulence model should be chosen for CFD modeling of gas cyclones [10,8,21,31]. In the current study, the gas flow in the cyclone is assumed as unsteady and incompressible flow with constant temperature. For an isothermal flows, the continuity and Reynolds average Navier-Stokes equations are given as, =0
(1)
7
(2) In Equation (2), system,
is the average velocity and P is the average pressure,
is the coordinate
is the kinematic viscosity and ρ is the gas density. The Reynolds stress tensor, need to be modeled. Here,
is the ith fluctuating velocity component.
=
2.2. Turbulence Modeling In this study the RSM turbulence model, which has been widely used for simulation of gas cyclones, is applied in additional to the transport equation for the rate of dissipation. The RSM equation is given by
(3) In the above equation, turbulence production is given by (4) where, P stands for the fluctuating kinetic energy production. kinetic viscosity and
=1,
= 1.8 as well as
shown in Eq. (3) is turbulence
= 0.6 that are empirical constant are used in
the simulation. In addition, the transport equation of the turbulence dissipation rate can be written as:
(5) It should be noted that, in Eq. (5) K= values of
,
, and
is the fluctuating kinetic energy. The constants’
are 1.3, 1.44 and 1.92, respectively.
8
2.3. Dispersed phase In the present work, it is assumed that the volume fraction of droplets is less than 10% and the Eulerian-Lagrangian method under the one-way coupling assumption is used for tracking droplets. The droplets force equilibrium relationship according to Newton's second law in x, y, and z directions, respectively, are: (6) (7) (8) where (9) In the above equation, the particle Reynolds number is defined as
(10) Here
is the gas velocity and
density of droplet and
is the droplet velocity, ρ is the density of the gas,
is the
is the diameter of droplet.
The drag coefficient is given as, (11) In the above equation,
and
are constant coefficients for spherical droplets that are
functions of Reynolds number [32]. In this study, the discrete random walk (DRW) method is used for evaluating the fluctuation velocity of the gas [33].
9
Values of the fluctuation velocity during the eddy lifetime
is calculated using
(12)
In the above equation, ζ is a zero mean and unit variance Gaussian random number.
is the
root-mean- square fluctuation velocity in the i-direction. In the present study, the eddy life time is estimated using [34], (13) Here r is a uniform random number between zero and one, and TL is the integral time scale given as (14) where
is constant. Here a value of
0.3 is used [34, 22].
2.4. CFD grids The numerical grids for different geometries were provided in Cartesian coordinate using structured meshes. The computational domain was meshed using the Gambit software. The schematic of the cyclone and the computational domain consisting of the hexahedral nonuniform elements are shown in Figure 1. In addition, Figure 2 shows the vortex finder with different eccentricities that can be defined as Eccentricity % =100×( distance of central of deviated vortex finder to the center of vortex finder without any eccentricity)/ radius of vortex finder The information regarding dimensions of the cyclone under study is tabulated in Table 1. To assure that the CFD results are grid independent, three different grids are examined. Figure 3 shows a comparison of the simulation results for the tangential velocity at level z = 0.75D for 10
different grid sizes. This figure shows that the grid independence was reached with the medium size grid with the total number of cells of 455900, which is also consistent with the earlier CFD simulation of gas cyclones reported in [10]. 2.5. Boundary conditions For boundary conditions, it is assumed that air enters the inlet channel with a uniform velocity of 19.5 m/s. The corresponding turbulence intensity and length scale are, respectively, 5% and 0.07 of the channel width. At the outlet pipe, the outflow boundary conditions are imposed. Solid walls are treated as non-slip surfaces. In the near wall region, the fluid flow is modeled using the standard wall function (SWF) that the researchers have shown the very encouraging results by SWF model [13,25,33]. The SWF provide near-wall boundary conditions for conservation equations so that the viscous sublayer does not have to be resolved and the need for a very fine mesh is circumvented. In order to study the contacting droplets to the walls, reflect and wall-film boundary conditions are chosen for the discrete phase. The density of water is 999 kg/m3 and its dynamic viscosity is 0.001 Pa.s. 2.6. Time step The resident time depends on the cyclone volume and the gas volume flow rate and is calculated as tres.=Vcyclone /Qin
(15)
In this study, the resident time is 0.237 s and a time step of 0.0001s is used for the droplet trajectory analysis. 2.5. Numerical schemes
11
The detailed information used in the present CFD modeling such as discretization scheme of pressure, momentum, turbulent kinetic energy, turbulent dissipation rate, and Reynolds stress as well as pressure/velocity coupling are depicted in Table 2. 3. Results and discussion 3.1. Model validation For validation of the model, the simulation results are compared with the experimental data of Hoekstra [31]. Here simulations are performed for the exact geometry of the experimental cyclone.
In addition to the comparison of the axial and tangential velocities at z = 0.75D, the
pressure drop for different velocities is also compared. Figures 4 and 5 compare the numerical results against the experimental data, respectively, for the tangential and axial velocities and the cyclone pressure drop. It is seen that the RSM turbulence model predicts the tangential and axial velocity, as well as, the cyclone pressure drop, reasonably, which they are in general agreement with the experimental data of Hoekstra [31]. It is also seen that both numerical results and measured data show a nonlinear increase of cyclone pressure drop with increasing gas inlet velocity. To validate the simulation results for the discrete phase comparison of the model prediction for the droplet removal with the experimental data of Ehteram et al. [35] was performed and the results for the flow rate of 48 L/min are presented in Figure 6. It is seen that the experimental data and computational results have the same trend of variations for the droplets smaller than 13 micron. For larger droplets, the CFD results saturate to 100% and are independent the droplet size. This figure also shows that the CFD model over-predicts the cyclone efficiency compared with the experimental data. It is worth mentioning that demising-cyclone operated by Ehteram et
12
al. [23] is the very small dimensions to evaluate the discrete phase i.e. droplet, that causes the difference between the model results and experiments to be not unexpected. In the Souza et al. (2012) work, it is evident that the CFD model is sensitive to geometric changes. Nevertheless, an acceptable agreement of the model simulation with the use of Lagrangian droplet trajectory analysis and the trend of the measured data is achieved. Therefore, it may be concluded that the model is able to predict the hydrodynamics of the gas cyclones with the reasonable approximation. 3.2. Study of the characteristics of the gas cyclone flow field In this section, the effects of vortex finder eccentricity on the gas cyclone flow pattern including the variations of the tangential and axial velocities are studied. For nine various levels shown in Table 3, the cyclone pressure drops are provided. 3.3. Tangential velocity The tangential and axial velocities of gas flow within gas cyclone are very important. The tangential velocity creates the centrifugal force, which significantly affects the separation of droplets. Previous studies demonstrated that the tangential velocity is similar to the Rankine vortex [3]. The Rankine vortex includes two regions, namely, the free (irrotational) vortex and the forced (viscous) vortex, which behaves as a solid body at the central part. The tangential velocity in the inner region (forced vortex) increases with radius until it reaches a peak value, and then decreases with radius in the outer region (free vortex). The tangential velocity profiles at the different levels of the cyclone, depicted in Table 3, for the various eccentricity of vortex finder are presented in Figure 7.
13
In this section, the effect of changes in the vortex finder position on the pattern of tangential velocity is studied. The tangential velocity profiles in sections S1 to S9 depicted in Figure 7 show that the variations of tangential velocity for different sections are similar. This velocity profiles display the Rankine vortex consisting the two important regions: an outer free vortex and an inner solid rotation appeared in the central part. Clearly, the eccentricity of the vortex finder affects the flow pattern in the gas cyclone. In particular, the behavior of the tangential velocity profile near the outlet pipe is markedly affected. The main reason for the change in the behavior of the flow pattern of gas cyclone with the eccentricity of the vortex finder returns to deviation in the flow outlet. As can be seen, the maximum effect is in the area of the forced vortex. In the core area of the vortex, the non-uniformity in tangential velocity appears (see cases 4 and 8% eccentricity) that by increasing the distance from the outlet pipe, the intensity of this nonuniformity, decreases. However, in the free vortex area, these fluctuations are not observed. A comparison between the radial profiles of tangential velocity for various eccentricity percentages at the levels of S1, S4, S7 and S9 is shown in Figure 8. As can be seen in the figure, with increasing deviation vortex finder, vortex area is increased that is an important factor in separation. The maximum tangential velocity is 1.8 times that of input velocity and the minimum tangential velocity is 1.58 times the input velocity. However, by being close to the bottom of gas cyclone, radial profiles are almost out of the symmetry mode and its fluctuations are reduced. The flow in gas cyclone is very complex and the processing vortex core (PVC) in a cyclone separator plays a dominant role in such complexity. For the case of 4% eccentricity there are considerable changes in the flow pattern close to the vortex finder. This causes such the unfamiliar velocity profile at S1 (see Figs. 7 and 8). 3.4. Axial velocity
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The axial velocity of gas cyclone that causes droplets moving towards the top and bottom of the cyclone is another important parameter that effects the cyclone separation. Figure 9 shows the axial velocity for different sections. The axial velocity created in the gas cyclone includes two regions. One is upstream flow area and the second is downstream flow area, and each of the areas is created in radial position. It should be noted that the tangential velocity created between the two flows is in its minimum values approximately zero and the axial velocity also reaches to the lower than zero for the case in which vortex finder is in the center of cyclone. In the case of eccentricity of the vortex finder, most of the flow fluctuations occur in the flow core. As observed in section S1, the flow is reversed in the central part towards the outlet pipe. With being a way from the vortex finder, the reversed flow intensity is reduced in downward parts. In addition, with increasing vortex finder deviation, such event does not happen. With increasing eccentricity of vortex finder, axial velocity profiles at different levels are normal, as the fluctuations do not appear. Figure 10 shows a comparison between the axial velocities in level stations of S1, S4, S7, and S9 for the different amount of vortex finder eccentricity. The figure shows that the computed profiles are as inverted W and the maximum axial velocity appears in the radial range of 0.03 to 0.05. Axial velocity profiles are almost identical for all the changes considered in the vortex finder. It is observed that the axial velocity increases with an increase in the vortex finder eccentricity up to 8%. However, the axial velocity reduces by increasing the vortex finder eccentricity from 8% to 10%. It is because of the downwards flow rate that is an important factor affecting the separation efficiency. For instance, in the section S4, the axial velocity decreases for the case of vortex finder with deviation 4% from the center compared to 6% and 8%. Therefore, from the mentioned decrease in axial velocity for the case of 4% eccentricity and also
15
the different behavior of axial velocity in various levels for the case of 6% eccentricity compared to the other cases, it can be found that the flow in the cyclone is quite complex and the further studies are necessary in this field. 3.5. Pressure drop and Performance of the gas cyclone The pressure drop in the cyclone is calculated as the difference in total pressure (rather that in static pressure) between the inlet and the outlet sections. With increasing pressure drop in the cyclone, the dissipated energy has a further drop in order to the separation of droplets. Therefore, reducing this critical parameter in the cyclone can be a significant factor for design and performance of the gas cyclone. In general, the dimensionless pressure drop form in gas cyclone is the ratio of the head of static pressure to dynamic pressure that is defined as: (16) where
is pressure loss, and
is inlet gas velocity. Cyclone pressure drop with respect to the
percentage of vortex finder eccentricity is plotted in Figure 11. This figure clearly shows that the pressure drop increases by enhancing the vortex finder eccentricity. This increase in the pressure drop in the eccentric vortex finder can be referred to the losses due to direction change of the inner and outer flow streams inside and outside the vortex finder with respect to the concentric vortex finder. The performance of the gas cyclone that is an important factor in gas cyclones is studied here. The effect of vortex finder eccentricity on the collection efficiency of the cyclone is shown in Figure 12. The figure clearly shows that cyclone efficiency significantly growths by increasing the droplet size for each case. It is well known that the dominant flow pattern in the cyclone directly affects the efficiency of droplets. In this section, the cyclone performance under different
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vortex finder eccentricity percentages for two boundary conditions of wall-film and rebound are presented in Figure 12. As can be seen in the figure, the eccentricity of the vortex finder causes the reduction of efficiency compared to the case in which the vortex finder is in the center of the cyclone. In addition, it can be observed that both mentioned boundary conditions regarding the splashing the droplets to the wall predict the same trend in terms of efficiency versus droplet size. However, by considering rebound condition on the wall, the efficiency improved about 7.7%. The efficiency of 8% vortex finder deviation increases with respect to both wall boundary conditions for the droplets’ size more than 1 µm. However, for droplets smaller than 1 µm, the efficiency of 4% vortex finder eccentricity is at its maximum value. Figure 13 shows the droplets trajectory and pathline through the cyclone, while, Figure 14 shows droplets pathline from the top view. As can be seen in these figures, the forced vortex length has its highest value for the case of 4% vortex finder eccentricity leading to migration of fine droplets from the center of the cyclone to the outlet pipe. Moreover, as observed in Figure 13 the main cause of reduction in efficiency of 8% deviation is deviation of forced vortex from the central axis. Totally, it can be found that the eccentricity of vortex finder has an adverse effect on the cyclone performance such as increasing the pressure drop and decreasing the cyclone efficiency.
4. Conclusions In the study, the effect of vortex finder eccentricity on the hydrodynamics parameters, namely, tangential and axial velocity of the gas phase, cyclone pressure drop and cyclone performance was evaluated using a computational fluid dynamics approach. In order to simulate the air flow,
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the path of droplets, an Eulerian-Lagrangian method was used. The main conclusions that can be drawn are as follows: 1. The tangential velocity increased with increasing eccentricity of the vortex finder. Comparing the radial profiles showed that the tangential velocity for 10% deviation is 1.8 time of the inlet velocity. With changing the vortex finder position, the tangential velocity pattern showed nonuniformity of flow core near the outlet pipe and by moving towards the bottom of the cyclone, the intensity of this non-uniformity was reduced. 2. It was found that the axial velocity has a complex pattern in the gas cyclones, which significantly affects the performance of the cyclone. However, the predicted axial velocity of downstream flow for 8% eccentricity of vortex finder is the largest one, by further increasing the eccentricity vortex finder i.e. 10%, the downstream flow velocity reduces. In the meantime, the downstream flow velocity is an important factor in moving droplets that significantly impacts on the performance of the cyclone. 3. With changes in outlet pipe of gas in the positive direction of x-axis, the pressure drop increased. 4. Including the eccentricity of the vortex finder in the cyclone design causes the instability of forced vortex as can be seen in the case of 6%. The cyclone containing droplets lower than 1 µm showed the maximum efficiency for the case of 4% compared to the other vortex finder deviations from the center. In overall, vortex finder eccentricity has undesirable results in terms of efficiency and energy consumption (pressure drop) 5. The efficiency of cyclone using two boundary conditions of wall-film and rebound boundary regarding the splashing the droplets to the wall against the droplet size was studied. It was found
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that by considering the contact of droplets with the walls (rebound condition), the efficiency is actually increased up to 7.7%.
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[9] K. Elsayed, C. Lacor, Numerical modeling of the flow field and performance in cyclones of different cone-tip diameters, Comput. Fluids. 51 (2011) 48-59. [10] K. Elsayed, C. Lacor, The effect of cyclone inlet dimensions on the flow pattern and performance, Appl. Math. Model. 35 (2011) 1952-1968. [11] J. Oh, S. Choi, J. Kim, Numerical simulation of an internal flow field in a uniflow cyclone separator, Powder Technol. 274 (2015) 135–145. [12] H. Safikhani, P. Mehrabian, Numerical study of flow field in new cyclone separators, Adv Powder Technol. 27 (2016) 379–387. [13] L.S. Brar, R.P. Sharma, K. Elsayed, The effect of the cyclone length on the performance of Stairmand high-efficiency cyclone, Powder Technol. 286 (2015) 668–677. [14] F. Qian, Y. Wu, Effects of the inlet section angle on the separation performance of a cyclone, Chem. Eng. Res. Des. 87 (2009) 1567–1572 . [15] R.B. Xiang, K.W. Lee, Numerical study of flow field in cyclones of different height, Chem. Eng. Process. 44 (2005) 877–883. [16] I. Karagoz, A. Avci, A. Surmen, O.Sendogan, Design and performance evaluation of a new cyclone separator, J. Aerosol Sci. 59 (2013) 57–64. [17] A. Surmen, A. Avci, M.I. Karamangil, Prediction of the maximum-efficiency cyclone length for a cyclone with a tangential entry, Powder Technol. 207 (2011) 1–8. [18] D. Misiulia, K. Elsayed, A. G. Andersson, Geometry optimization of a deswirler for cyclone separator in terms of pressure drop using CFD and artificial neural network, Sep. Purif. Technol. 185 (2017) 10-23. [19] R. Xiang, S.H. Park, K.W. Lee ,Effects of cone dimension on cyclone performance, J. Aerosol Sci. 32 (2001) 549–561.
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[20] K.S. Lim, H.S. Kim, K.W. Lee, Characteristics of the collection efficiency for a cyclone with different vortex finder shapes, J. Aerosol Sci. 35(2004) 743–754. [21] A. Raoufi, M. Shams, M. Farzaneh, R. Ebrahimi, Numerical simulation and optimization of fluid flow in cyclone vortex finder, Chem. Eng. Process. 47(2008) 128–137. [22] X. Gao, J. Chen, J. Feng, and X. Peng, Numerical investigation of the effects of the central channel on the flow field in an oil–gas cyclone separator, Comput. Fluids. 92 (2013 ) 45–55. [23] X. Gao, J. Chen, J. Feng, X. Peng, Numerical and experimental investigations of the effects of the breakup of oil droplets on the performance of oil–gas cyclone separators in oil-injected compressor systems, Int. J. Refrig. 36 (2013) 1894–1904. [24] M. Ghodrat, S.B. Kuang, A.B. Yu, A. Vince, G.D. Barnett, P.J. Barnett, Numerical analysis of hydrocyclones with different vortex finder configurations, Minerals Eginering. 63 (2014) 125–138. [25] H. M. El-Batsh, Improving cyclone performance by proper selection of the exit pipe, Appl. Math. Model. 37 (2013) 5286-5303. [26] K. Elsayed, C. Lacor, The effect of cyclone vortex finder dimensions on the flow pattern and performance using LES, Comput. Fluids.71 (2013) 224-239. [27] K. Elsayed, Design of a novel gas cyclone vortex finder using the adjoint method, sep.purif.Technol. 142 (2015) 274–286. [28] A. Raoufi, M. Shams, M. Farzaneh, and R. Ebrahimi, Numerical simulation and optimization of fluid flow in cyclone vortex finder, Chem. Eng. Process. Process Intensif. 47 (2008 ) 128-137. [29] F.J. Souza, R.D.V. Salvo, D.D.M. Martins, Simulation of the performance of small cyclone separators through the use of Post Cyclones (PoC) and annular overflow ducts,
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Captions Table 1. The geometrical dimensions of the cyclone. Table 2. Numerical schemes for the current simulation. Table 3. Position of the plotting sections. Figure 1. Geometry and grid of the problem. Figure 2. Deviations of output pipe compared to the cyclone center. Figure 3. Computational tangential velocity for the three grid levels (Z=0.75D). Figure 4. Comparison of tangential and axial velocity distribution with experimental data in the section of z = 0.75D. Figure 5. Comparison of the pressure distribution with experimental data. Figure 6. Comparison of numerical efficiency with experimental data [23]. Figure 7. The radial profiles of tangential velocity in different parts of S1-S9. Figure 8. Deviation effects of vortex finder on the radial profiles of the tangential velocity in levels of S1, S4, S7 and S9. Figure 9. The radial profiles of axial velocity in different levels of S1–S9. Figure 10. Deviation effects of vortex finder on the radial profiles of the axial velocity in levels of S1, S4, S7 and S9. Figure 11. The eccentricity effects of the vortex finder on the pressure drop.
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Figure 12. The cyclone efficiency by considering the wall-film and rebound boundary conditions. Figure 13. Predicted droplets trajectory and pathline for different eccentricity percentages (colored by ). Figure 14. The droplets pathline from the top view (colored by ).
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Figure 1
25
Figure 2
26
Figure 3
27
Figure 4
28
Figure 5
29
Figure 6
30
Figure 7
31
Figure 8
32
Figure 9
33
Figure 10
34
Figure 11
35
Figure 12
36
Figure 13
37
Figure 14
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Table 1. The geometrical dimensions of the cyclone Dimension
Length (m )
Dimension ratio ( Dimension/D)
Body diameter, D
0.205
1
Inlet height, a
0.105
0.5
Inlet width, b
0.041
0.2
Gas outlet diameter, Dx
0.105
0.5
Gas outlet duct length, S
0.105
0.5
0.076875
0.375
Cylinder height, h
0.3075
1.5
Cyclone height, Ht
0.82
4
Duct length, Li
0.15375
0.75
Outlet trube length, Le
0.1025
0.5
Cone-tip diameter, Bc
Table 2. Numerical schemes for the current simulation Numerical setting
Scheme
Pressure discretization
Body force weighted
Pressure velocity coupling SIMPLE Momentum discretization
QUICK
Turbulent kinetic energy
Second-order upwind
Turbulent dissipation rate
Second-order upwind
Reynolds stress
First-order upwind
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Table 3. Position of the plotting sections. section
S1
S2
S3
S4
S5
S6
S7
S8
S9
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
a: measured from the top inlet section
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Graphical abstract The vortex finder eccentricity impact on the flow pattern of an aero-cyclone was studied by CFD and the results were presented.
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Highlights ○ Study of vortex finder eccentricity impact on some hydrodynamics parameters by CFD ○ Study of collection efficiency for cyclones with and without vortex finder eccentricity ○ Vortex finder eccentricity affect the pressure drop and instability of forced vortex ○ Impact of boundary conditions of wall-film and rebound on the collection efficiency
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