Available on line at Association of the Chemical Engineers of Serbia AChE Chemical Industry & Chemical Engineering Quarterly www.ache.org.rs/CICEQ Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) CI&CEQ ALI SAKIN1 NUMERICAL PREDICTION OF SHORT-CUT IRFAN KARAGOZ2 FLOWS IN GAS-SOLID REVERSE FLOW 1TOFAS-FIAT R&D Department, CYCLONE SEPARATORS Istanbul Caddesi, Osmangazi, Bursa, Turkey 2 Article Highlights Department of Mechanical • Short-cut flows are mainly affected by vortex finder diameter and insertion length Engineering, Uludag University, • Insertion length has an optimum value for minimum short-cut flow Nilufer, Bursa, Turkey • Decrease in vortex finder diameter increases short-cut flow and pressure drop • Short-cut flow increases with the cone tip diameter SCIENTIFIC PAPER Abstract UDC 519.876.5:66:66.07 The effect of operational and geometrical parameters on the short-cut flow in cyclone separators has been investigated computationally using the Reynolds stress model (RSM). The motion of solid particles in the flow field was simulated using the Eulerian-Lagrangian approach with one way discrete phase method (DPM). Eleven cyclones with different cone tip diameters, vortex finder lengths and diameters were studied and the simulation results were analyzed in terms of velocity fields, pressure drops, cut-off diameters and short-cut flows. The num- erical simulation was verified with the published experimental results. The results obtained demonstrate that all three parameters, particularly, vortex finder dia- meter, have significant effects on the cut-off diameter (collection efficiency), the short-cut flow and the pressure drop. Keywords: CFD, cut-off diameter, pressure drop, separation efficiency, swirl flow. A cyclone separator is a simple tool that leads comprehensive [5,6] for the prediction of a cyclone the incoming solid-gas flow into a spiral motion and performance. separates the solid particles from the main stream Several studies of small scale reverse flow cyc- under the influence of centrifugal and gravity forces. lones have been undertaken by examining the effects Robust in structure, relatively inexpensive to construct of cyclone design and air flow rate on collection effi- and operate with little maintenance, cyclones are ciency and pressure drop [7-10]. used for removal of harmful or nuisance air-borne Optimization of cyclone performance by increas- particulates or liquid droplets. There are many ver- ing cyclone separator collection efficiency and red- sions of cyclone separators with various geometries ucing the pressure drop was mainly derived from exp- and designs. eriments rather than theoretical studies because the The major performance parameters of a cyclone fluid motion in cyclones are complicated, including separator are pressure drop and cut-off diameter highly swirling turbulent characteristics and restrict- values. Numerous theoretical and experimental stu- ions in the usage of empirical models [8,9,11-16]. dies carried out on this tough subject provide semi- Advances in computer capabilities, software and empirical models varying from basic [1-4] to more numerical methods provide more opportunities to com- putational calculation of cyclone separators [17-34]. Elsayed and Lacor performed numerical cyclone Correspondence: A. Sakin, TOFAS-FIAT R&D Department, Istanbul Caddesi, No:574 16369 Osmangazi, Bursa, Turkey. studies for the effect of cone tip diameter, dust bin geo- E-mail: ali.sakin@tofas.com.tr metry, vortex finder and inlet dimensions [28,31,35,36]. Paper received: 9 October, 2016 They reported that for the inlet dimensions effect of Paper revised: 4 January, 2017 Paper accepted: 13 January, 2017 changing the inlet width on the cut-off diameter is https://doi.org/10.2298/CICEQ161009002S more considerable than inlet height and optimum ratio 483 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) of the inlet width to the inlet height is from 0.5 to 0.7 540 L/min. They stated that the capability of CFD [36]. Regarding the cone tip diameter change, they accurately predicts performance indicators of pres- reported that there is no significant effect on flow sure drop and collection efficiency. pattern and performance, and that decreasing the Taking advantage of the increased availability of cone tip diameter increases the pressure drop [28]. adjoint solvers in many commercial CFD codes, Els- Another study based on vortex finder dimensions, ayed [42] performed CFD analysis to find optimum reported that reducing the vortex finder diameter by shape of vortex finder. Resultant optimum vortex finder 40% leads to 175% increase in the dimensionless geometry provided reduction of 34% pressure drop pressure drop (Euler number) and 50% reduction in and 83% cutoff diameter. the Stokes number [35]. In contrast with previous stu- Song et al. [43] performed CFD analysis for D = dies, they performed numerical cyclone analysis with = 290 mm and they investigated the influence of par- Reynolds stress model (RSM) for investigation of dust ticle forces on separation efficiency. They analyzed outlet shape and reported that lack of dust outlet pro- effect of drag force, pressure gradient force, added vides saving of large computational cost and it can mass force and Saffmann lift force. They stated that affect the calculations in an error margin about 10% for pressure gradient and added mass forces are at least the Euler number and 35% for the cut-off diameter [31]. 3 orders of magnitude smaller than the drag force and Kaya and Karagoz [37] performed numerical the Saffmann lift force is at least 15 orders of magni- studies to investigate performance characteristics of a tude smaller. Therefore these forces can be neg- cyclone prolonged with a dipleg and they reported lected and the main driver of separation forces are that particle collection efficiency can be enhanced by drag and centrifugal forces. applying a dipleg, which results in a variation in flow The present study aims to investigate the effect pattern for tangential inlet short cyclones. Increasing of short-cut flow on the pressure drop and collection the dipleg length surface of the wall friction is inc- efficiency of reverse flow cyclone by changing cyc- reased which should lead to moderately lower tan- lone tip diameter and vortex finder dimensions. gential velocity. Kaya et al. [38] investigated effects of surface MATHEMATICAL MODEL AND NUMERICAL roughness parameters on the performance of tan- SIMULATION gential inlet cyclones. Body diameter of 31 mm cyc- lone was utilized for numerical simulations by assign- Calculations were carried out on three cyclones ing different roughness values for inlet velocities 8 with different cone tip diameters (fixed S and Dx and 16 m/s, respectively. They concluded that the values), four cyclones with different vortex finder tangential velocity in the cyclone is decreased by inc- lengths (fixed Bc and Dx values) and four cyclones reasing wall roughness, due to an increase in flow with different vortex finder diameters (fixed S and Bc resistance and weakening of swirl so particle col- values). The dimensional layout and cyclone config- lection efficiency is deteriorated by greater surface urations are given in Figure 1 and Table 1. roughness values. El-Batsh [39] performed CFD stu- Numerical method dies to improve performance of cyclone separator by appropriate selection of vortex finder dimensions. It The Eulerian-Lagrangian approach was used for was found that pressure drop is decreased with inc- numerical calculations of gas-solid flow in this study reasing vortex finder diameter and length of exit pipe and flow is assumed as unsteady, incompressible and is not a significant parameter on the cyclone perform- turbulent. Continuity and momentum equations are ance. solved in order to obtain velocity field. The turbulent Houben et al. [40] performed CFD simulations of flow was represented by the Reynolds stress model cyclone separator with central vortex stabilization rod (RSM) and particle trajectories and collection effi- to suppress the vortex core precession and results ciencies were calculated by Lagrangian approach. were compared with the experimental data. They Numerous particles that are injected from the inlet stated that the vortex is kept in position by using a surface were followed through the flow field by solving stabilizer and maximum tangential velocity is found to the particle force balance equation of motion. be larger which has a positive effect on collection effi- The flow field was defined as three-dimensional, ciency of small particles. the particle phase was assumed as dilute, and the Haig et al. [41] performed CFD analysis on small particle loading level is low so interaction between the scale cyclones with the body diameter of ranging from particles are insignificant and particles have no 29 to 52 mm and inlet flow rates ranging from 60 to influence on the main stream flow. Therefore, the problem was assumed as one-way coupling [44]. By 484 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) this assumption, the source terms in Navier-Stokes ∂     (ρv )+∇(ρvv ) = −∇p +∇(τ )+ ρg +F (2) equations due to two-way coupling strategy are not ∂t considered. where ρ is the fluid density, v is the fluid velocity, p is the static pressure, τ is the stress tensor 2 ( = μ[(∇v +∇v T )− ∇vI ] ), μ is the molecular visco- sity, I is the unit te3nsor, ρg is the gravitational body force, and F is the external body force. The RSM was used to modify the viscous turb- ulent flow in reverse flow cyclone. The turbulent trans- port equation for RSM is [45]: ∂ (ρui′u ′j )+ ∂ (ρuk ui′u ′j ) =∂t ∂xk = − ∂ ρui′u ′juk′ + p(δkjui′ + δiku ′j )  ∂x  + k ∂  ∂   ∂u + μ (ui′u ′ j ∂u) ∂x ∂x j  − ρ u ii′u ′j +u ′u ′ − (3) k  k   ∂x j k k ∂x  k  −ρβ g u ′θ + g u ′θ + p ∂u ′ ∂u ′ ( i j  i j j i )  + u ′j − Figure 1. Schematic diagram of cyclone geometry and  ∂x ∂x  j i  coordinate system definition. ∂u −2μ i ′u ′j +S Transport equations ∂xk ∂xk The three-dimensional flow field in reverse flow where t is the time, ui′ is the fluctuating velocity to cyclone was simulated using CFD. The conservation direction i (= ui −um ) , ui is the velocity direction i, um equations for mass and momentum in an incompres- is the mean velocity to direction i, ui′u ′j is the sible Newtonian flow are as follows [45]: Reynolds stress tensor, β is the thermal expansion, ∂ρ  p is the pressure, μ is the eddy viscosity, and S is the +∇(ρv ) =S (1) source term. ∂t The two terms on the left-hand side of Eq. (3) indicate local time derivative and convection, res- Table 1. Geometrical dimensions of cyclones; body diameter, D = 31 mm. Inlet length, Li = 1.5D from the cyclone center, outlet length above cylindrical surface of cyclone is Le = D Dimension Cyclonea Dimension, D Inlet height, a – 0.4 Inlet width, b – 0.16 Cylinder height, h – 1.0 Total cyclone height, Ht – 2.5 Cone tip diameter, Bc S = 0.5D CY1 0.625 Dx = 0.5D CY2 0.5 CY3 0.375 Vortex finder length, S Bc = 0.375D CY4 0.4 Dx = 0.5D CY5 0.5 CY6 0.875 CY7 1.0 Vortex finder diameter, Dx Bc = 0.375D CY8 0.3 S = 0.5D CY9 0.4 CY10 0.5 CY11 0.645 aCyclone CY3, CY5 and CY10 are identical 485 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) pectively from left to right. The terms on the right- Numerical scheme -hand side of Eq. (3) indicate turbulent diffusion, mol- The selection of spatial and temporal discret- ecular diffusion, stress production, buoyancy product- ization schemes has an important effect on the CFD ion, pressure strain and dissipation respectively from results and fluent provides various solution strategies left to right. The terms for turbulent diffusion, buoy- for pressure velocity coupling, pressure, momentum, ancy production, pressure strain and dissipation are kinetic energy, rate of kinetic energy dissipation dis- needed for modeling [46]. cretization. Both Kaya and Karagoz [25] and Shukla Discrete phase modeling et al. [30] analyzed various solution strategies in steady and unsteady simulations of cyclone separ- The motion of solid particles in a flow field was ators. Based on the study of Kaya and Karagoz [25], simulated using the Eulerian-Lagrangian approach governing equations of the three-dimensional, incom- with a discrete phase method (DPM). Gas phase was pressible flow inside the cyclone, Eqs. (1) and (2), treated as continuum by Navier-Stokes equations and and the RSM turbulence equations were discretized the solid phase is calculated. After flow field variables over the computational cells and iteratively solved by are obtained, particle tracking calculations are per- using ANSYS Fluent commercial CFD software. formed using Lagrangian approach. The volume fract- SIMPLEC algorithm was used for pressure velocity ion of the dispersed phase did not exceed 10%, so coupling in this study and pressure staggering option particle-particle interaction can be neglected and par- (PRESTO) scheme was chosen for the pressure inter- ticle phase did not affect flow field (one-way coup- polation as it was shown to be well suited for steep ling). A stochastic tracking method was used for pressure gradient involved in complex swirling flows. modeling turbulent dispersion of particles. The traject- QUICK scheme was chosen for discretization of ory of a particle can be calculated by integrating the momentum, second order upwind scheme was chosen force balance in a Lagrangian reference frame. This for turbulent kinetic energy and turbulent dissipation force balance equates the particle inertia with the forces rate and first order upwind scheme was used for turb- acting on the particle, and can be written as [45]:   ulence stresses. dup   g(ρ − ρ) = F (u −u )+ p +F (4) Simulations started with steady solution, when dt D p ρp convergence plot becomes nearly horizontal and  there was no significant change, temporal discretizat- where F is an additional acceleration (force/unit par- ion was switched to unsteady solution with the time ticle mass) term, FD (u −up ) is the drag force per unit step of 0.0001 s. Residence time values of cyclone particle mass and: configurations depending on inlet velocity are given in 18μC Re F = D p Table 2. Residence time exceeded for all simulations D 2 (5) 24ρpd p to prevent inconsistent results of flow field. where u is the air velocity in a separator, u is the Boundary conditions and other settings p particle velocity, μ is the viscosity of air, ρ is the air Velocity inlet boundary condition is employed at density, ρp is the particle density, d p is the particle inlet, outflow at gas exit and wall (no-slip condition) at diameter, Re is the relative Reynolds number, CD is all other boundaries. Volumetric flow rate equals to 30 the drag coefficient and C1 to C3 are the constants and 60 L/h, corresponding to air inlet velocity 8 and that depends on the range of Re [47]: 16 m/s, respectively, dynamic viscosity of 2.11×10-5 Pa⋅s and air density 1.0 kg/m3C C . The turbulence inten-CD =C1 + 2 + 3 (6) Re Re sity and the hydraulic diameter were defined as 5% and 0.007 m, respectively. For the near wall treat- ρd p u p −u ment, scalable wall function was selected. Re = (7) μ Table 2. Residence time and cell numbers Parameter CY1 CY2 CY3, CY4, CY5, CY6, CY7, CY10 CY8 CY9 CY11 Cyclone volume×103, m3 0.0552 0.0521 0.0493 0.0456 0.0472 0.0532 tres / s (Uin = 8 m/s) 0.1122 0.1059 0.1003 0.0927 0.0960 0.1082 tres / s (Uin = 16 m/s) 0.0561 0.0529 0.0501 0.0463 0.0480 0.0541 Cell number 98582 95631 93756 92138 92556 96806 486 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) 104 particles were released from the inlet sur- RESULTS face with the air inlet velocity and a mass flow rate m Model validation p of 0.001 kg/s and particle diameter varies from 0.5 to 10 μm. The density of released particles is 860 Stairmand cyclones are widely used for indus- kg/m3 and the maximum time steps number was 105 trial purposes so they became a significant research steps for each injection. The restitution coefficient area from past to today. Hoekstra [48] studied barrel was set as 0.8 for both normal and tangential dir- diameter of 290 mm and measured velocity profiles ection. Trap DPM boundary condition was applied by LDA. This study is the newest one that can be bottom surface of cyclone to calculate particle collect- taken as a reference for model validation. Xiang et al. ion efficiency, escape was applied both inlet and out- [9] studied barrel diameter of 31 mm for various pur- let. The solution was assumed to be converged at poses and most of the studies, especially based on each time step when preset scaled residuals reached CFD, used this geometry due to small geometric 10-5 as convergence criteria for all variables. The cal- domain and lower computational effort. It is also used culations were carried out on an Intel® Core i7- for comprehensive optimization studies. 2630QM 2.0 GHZ with 8 GB of RAM. Calculated results were compared with the LDA Solution of grid dependency velocity measurements of Hoekstra [48], measured by using laser Doppler anemometry (LDA) system. Fig- The flow volume was divided into a number of ure 2 shows the comparison between RSM solution blocks by using Icem CFD 15.0 software to generate and the measured axial and tangential velocity pro- unstructured topology among the domain. However, files at axial station z = 2.5D (Plane 3). As can be fine mesh structure was used in the core region seen from Figure 2b, very good agreement was where strong gradients in the flow parameters were obtained for tangential velocity profiles at all planes. present. Grid independency was examined for CY3 The axial velocity profiles do not agree well with the cyclone. Three different grid domains containing experimental values (Figure 2a). Considering comp- 25.330, 93.756 and 349.222 cells were compared. lexity of the flow in cyclones, the agreement between The calculated grade efficiency curve with mesh the calculations and measurements is considered design 349.222 cells is very close to mesh design highly sufficient. with 93.756 cells and there is no appreciable differ- ence in the prediction and mesh design with 93.756 Calculation of short-cut flow rate cells is provided for computational solution. Grid inde- A small rate of mass flow directly moves toward pendent cell numbers of other cyclone configurations the vortex finder by entering upward the vortex were given in Table 2. region. The short-cut flow rate strongly depends on cyclone separator parameters. To predict the short- Figure 2. Comparison of axial (a) and tangential (b) velocity profiles between CFD results and LDA measurements (cyclone barrel diameter for validation study, D = 290 mm). 487 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) -cut flow rate, the downward flow rate at an axial Present CFD results of 8 m/s inlet velocity are in station should be calculated instantly [49]. If the good agreement with LES [28] and for 16 m/s results downward axial velocity is integrated between cyc- are close to experimental data (Figure 4). Calculated lone wall and the locus of zero at the axial station, the cut off diameter differs from experimental data 41, 33 total downward flow rate is obtained. Since we create and 31% for CY1, CY2 and CY3, respectively. Els- a new surface 1 mm below bottom of the vortex finder ayed and Lacor [31] observed that cyclone para- and clip axial velocity by locus of the zero and dif- meters are predicted without dust bin, an error margin ference between downward and total flow rate in the around 10% in the calculations of Euler number and cyclone will give the short-cut flow rate. 35% in the calculation of cut-off diameter should be In this study, short-cut flow effect on cyclone considered for CFD calculations. performance is explained with tangential velocity pro- Maximum collection efficiency is obtained for files and short-cut flow rate. Tangential and axial vel- smaller cone tip diameter of 11.625 mm (CY3). Total ocity components have more significant effect on vel- friction surface area rates based on CY3 are 9.15% ocity field rather than radial velocity component. Tan- and 13.52% larger for CY2 and CY1 respectively, so gential velocity component is more significant because maximum tangential velocity profiles of CY3 for both it leads to centrifugal force for particle separation inlet velocities are higher than CY1 and CY2. This mechanism [49]. The axial flow has effect on down- results stronger swirl intense and more centrifugal ward and upward flows. To represent all velocity pro- force for particle separation. files for both inlet velocities and all five sections will The short-cut flow increases with increasing create more pages so to prevent exceeding page cone tip diameter and this results in decreasing swirl number, velocity profiles at 1.75D section is pre- intensity. While short-cut flow rate is increased, dec- sented for comparison of axial and tangential velo- reasing separation efficiency is expected but down- cities for both inlet values. ward flow migration increases with increasing cone tip diameter so there is no significant change in the sep- Effect of cone tip diameter aration efficiency due to the change in cone tip dia- Velocity profiles are given in Figure 3 represent meter. In this case, maximum particle collection effi- the tangential and axial velocity distribution at ciency is obtained for maximum tangential velocity z = 1.75D distance. The tangential velocity profiles and minimum short-cut flow percentage. show axis-symmetrical distribution for both inlet vel- The pressure drop values are in good agree- ocity values and inner region profiles are identical. ment with experimental data and LES [28] calcul- The axial flows indicate existing of two flow streams: ations. Pressure drop increases with decreasing cone downward (positive axial velocity) and upward (neg- tip diameter as expected. Contrary to cut-off diameter, ative axial velocity) directed to vortex finder exit. Figure 3. Comparison of axial (a) and tangential (b) velocity of CY1, CY2 and CY3 for Uin = 8 and 16 m/s at z = 1.75D section. 488 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) Figure 4. Cone tip diameter effects on cut off diameter, shortcut flow (a), pressure drop and downward flow (b). The results are compared to “Xiang and Lee [49]” literature [9]. pressure drop decreases with increasing short-cut increased short-cut flow so swirl intensity and pres- flow due to weaker swirl in the flow field. sure drop decrease concurrently. For this case, the inlet height ( Effect of vortex finder length a) and vortex finder length (s) are equal and portion of inlet flow joins upward inner flow easily In Figure 5, the tangential velocity profiles are and short-cut flow rate is greater than CY5. quite similar. Maximum tangential velocity occurs at Only for small vortex finder length (CY4), axial CY5 configuration (s = 0.5D) and maximum collection velocity and downward flow through the cone is inc- efficiency for both inlet velocities (Figure 6) is obtained reased but at the same time separation efficiency is for this configuration due to domination of tangential decreased due to increasing short-cut flow rate. CY5 velocity on centrifugal force. has the optimum vortex finder length and results mini- Shortest vortex finder (CY4, s = 0.4D) results mum short-cut flow and maximum efficiency. Figure 5. Comparison of axial (a) and tangential (b) velocity of CY4, CY5, CY6 and CY7 for Uin = 8 and 16 m/s at z = 1.75D section. 489 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) Figure 6. Vortex finder length effects on cut off diameter, shortcut flow (a), pressure drop and downward flow (b). From the viewpoint of velocity profiles, CY5 has ration is decreased by increasing vortex finder length. the maximum tangential velocity and pressure drop. Sharp decrease between CY4 and CY5 occurs and Vortex finder of CY6 and CY7, extended into the cone this can be explained by axial velocity profiles. For section of cyclone, where the wall was contracting CY6 and CY7 both axial velocity profiles and down- and flow coming from the cylindrical section, will be ward flow rates are quite similar however swirl int- influenced by the contracting wall and easily join into ensity is decreased with increasing friction surface. the upward flow. The trend of short-cut flow rate is in Effect of vortex finder diameter good agreement with the explanation of Xiang and Lee [49]. The separation efficiency is decreased with It can be clearly seen that maximum tangential decreasing tangential velocity and increasing short- velocity is decreased with increasing vortex finder cut flow rate for CY6 and CY7. diameter (Figure 7). From the viewpoint of tangential The pressure drop is increases with increasing velocity profiles, cut off diameter is increased and tangential velocity and CY5 has the maximum pres- pressure drop is decreased with increasing vortex sure drop for both inlet values. Downward flow mig- finder diameter. Increased vortex finder diameter Figure 7. Comparison of axial (a) and tangential (b) velocity of CY8, CY9, CY10 and CY11 for Uin = 8 and 16 m/s at z = 1.75D section. 490 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) causes larger friction surface inside cyclone body so CONCLUSIONS vortex strength (also tangential velocity which is the most dominant component for particle collection Cyclones of different cone tip diameters, vortex efficiency) is decreased. finder lengths and diameters were numerically ana- Smaller vortex finder diameter (D ) results the lyzed using Reynold stress model (RSM). The follow-x maximum separation efficiency although maximum ing conclusions were obtained. short-cut flow rate occurs at the same time. The axial • Short-cut flow curve trend of cone tip diameter velocity profile demonstrates reversed W profile configurations at both inlet velocities are similar. Mini- everywhere, but for small vortex finder diameter pro- mum short-cut flow rate is obtained for minimum cone file initially exhibits reversed V and becoming W at tip diameter on contrary to maximum tangential velo- downward sections. Similar behavior was also rep- city and pressure drop obtained with this cyclone con- orted by Elsayed and Lacor [35] and Hoekstra et al. figuration. Decreasing cone tip diameter increases [18]. Elsayed and Lacor [35] reported that this change separation efficiency, pressure drop, short-cut and results 73% increase in the maximum axial velocity. downward flow concurrently. Hoekstra et al. [18] explained this situation; adverse • Vortex finder length has no significant effect on pressure gradient leads to decay of swirl due to frict- tangential velocity profile but shortest length causes ion losses in the vortex finder. Swirl intensity inc- increasing short-cut flow. S = 0.5D is the optimum reases for narrow vortex finder diameters, so that the value for minimum short-cut flow and greater values adverse pressure gradient can be overcome. result increasing short-cut flow due to contraction of Pressure drop is monotonically decreased for conic cyclone walls. Downward flow migration is dec- both inlet velocities as shown Figure 8. For smaller reased with increasing vortex finder length due to inc- vortex finder diameters, pressure drop is increased reasing friction surface area. due to increase in velocity and swirl intensity as exp- • Vortex finder diameter has an important effect lained previously and for larger vortex finder dia- on cut-off diameter and tangential velocity. Increased meters pressure drop decreases with weaker swirl vortex finder diameter results larger friction surface in intensity. For CY8, downward flow rate is small in cyclone body, weaker swirl intense and decreased comparison with the others and this can be explained pressure drop. Dx = 0.3D is the smallest vortex dia- by the shape change of velocity profile. Downward meter configuration and maximum short-cut flow and flow rate is decreasing monotonically for CY9, CY10 pressure drop is obtained due to velocity profile shape and CY11 due to increased friction surface and change from inverted “W” to inverted “V” shape. weaker swirl intensity. From the viewpoint of short-cut flow rate, vortex finder dimensions (diameter and length) have more significant effect than cone tip diameter. Vortex finder Figure 8. Vortex finder diameter effects on cut off diameter, shortcut flow (a), pressure drop and downward flow (b). 491 A. SAKIN, I. KARAGOZ: NUMERICAL PREDICTION OF SHORT-CUT FLOWS… Chem. Ind. Chem. Eng. Q. 23 (4) 483−493 (2017) length of 0.5D is an optimum point for short-cut flow Subscript rate and for greater values of vortex finder length i Cartesian coordinate downward flow is joining upward flow due to con- j Cartesian coordinate traction wall between cylindrical and conical section. z Cartesian coordinate Smaller vortex finder diameter causes change of vel- ax Axial ocity profile from “W” to “V” and short-cut flow per- in Inlet centage is increased. tan Tangential As a recommendation of future work, numerical calculations can be carried out by modifying the cyl- Abbreviations inder and total height of the cyclone in order to inv- CFD Computational Fluid Dynamics estigate the effect of short-cut flow on pressure drop DPM Discrete Phase Method and particle collection efficiency. LDA Laser Doppler Anemometry Nomenclature LES Large Eddy Simulation PRESTO Pressure Staggering Option a Inlet height of the cyclone RSM Reynolds Stress Model b Inlet width of the cyclone SIMPLEC Semi-Implicit Method for Pressure Linked BC Cone tip diameter Equations-Consistent C1 Constant in Equation (6) QUICK Quadratic Upwind Interpolation C2 Constant in Equation (6) C3 Constant in Equation (6) REFERENCES CD Particle drag coefficient D Cyclone body diameter [1] G.B. Shepherd, C.E. Lapple, J. Ind. Eng. Chem. 31 d Particle diameter (1939) 972-984 p DX Vortex finder diameter [2] R.M. Alexander, Proc. - Australas. Inst. Min. Metall. 203 F External body force in Equation (2) (1949) NS 152–153:203-228 F Additional acceleration term in Equation (4) [3] W. Barth, Brennst.-Waerme-Kraft 8 (1956) 1–9 F Drag force [4] W. Barth, L. Leineweber, Staub - Reinhalt. Luft 24 (1964) D g Acceleration due to gravity 41–55 h Cylinder height [5] A. Avci, I. Karagoz, J. 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Shukla, P. Ghosh, Eng. Appl. Comput. [49] R.B. Xiang, K.W. Lee, Chem. Eng. Process. 44 (2005) Fluid Mech. 5 (2011) 235–246 877–883. ALI SAKIN1 NUMERIČKA PREDVIĐANJE STRUJNIH PREČICA IRFAN KARAGOZ2 U CIKLONSKIM SEPARATORIMA GASNO-ČVRSTO SA REVERSNIM TOKOM NAUČNI RAD Efekat operativnih i geometrijskih parametara na strujne prečice u ciklonskim separa- torima istražen je pomoću modela Rejnoldsovih napona (RSM). Kretanje čvrstih čestica u strujnom polju simulirano je korišćenjem Ojler-Lagranžovog pristupa metodom dis- kretne faze u jednom smeru (DPM). Ispitivana su jedanaest ciklona sa različitim prečni- cima konusa, dužinama i prečnicima vorteksa, a rezultati simulacije su analizirani u pogledu polja brzine, pada pritiska, kritičnog prečnika i strujnih prečica. Numerička simulacija je potvrđena već publikovanim eksperimentalnim rezultatima. Dobijeni rezul- tati pokazuju da sva tri parametra, a pre svega prečnik vorteksa, imaju značajne efekte na kritični prečnik (efikasnost sakupljanja), strujne prečice i pad pritiska. Ključne reči: CFD, kritični prečnik, pad pritiska, efikasnost razdvajanja, kružni tok. 493