Strongly swirling flows in a cylindrical separator

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1 Available online at Minerals Engineering 21 (2008) This article is also available online at: Strongly swirling flows in a cylindrical separator Ali M. Jawarneh *, Hitham Tlilan, Ahmad Al-Shyyab, Amer Ababneh Department of Mechanical Engineering, The Hashemite University, Zarqa 13115, Jordan Received 12 June 2007; accepted 9 October 2007 Available online 3 December 2007 Abstract This paper describes a numerical study of two-phase, strongly swirling flow in a cylindrical separator with double vortex generators to predict the separation efficiency of a mixture consisting of oil as the primary phase and sand, with a specific diameter, as the secondary phase. The mixture-granular multiphase and RNG k e turbulence models are implemented in this study. The analytical predictions are compared against experimental data; i.e., the mean tangential velocity and the mean radial pressure profiles. The overall agreement between the experimental data and the predictions obtained with the RNG k e model are reasonably good. The numerical procedure has the ability to capture a narrow localized residence zone for the solid particles at a periphery location near the mid-separator where the two vortices merge and the suspension process occurs. Moreover, the analysis has proven to be useful in predicting the internal flow structure of the primary phase, thereby, the separation of the particulate phase. The separated particles are forced to remain near the periphery of the cylindrical separator and being concentrated at the mid-separator as a result of the strong centrifugal force. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Two vortices; Separator; Centrifugal force; Two-phase flow; Turbulence 1. Introduction Separation technology has a dominant role in many process industries; e.g., is that of a crude and shale oil industry. The cylindrical separator is a newly technology for solid liquid separation and is increasingly attracting attention in the oil and sand industry. There are many reasons for the importance of quality separation; e.g., the increasing demand on product purity, the gradual reduction in the quality of raw materials and the growing environmental constraints for the acceptability of waste materials. Separation of oil and sand is therefore vital in the oil sand production and processing. Solids may be separated in settling tanks/basins or by mechanical devices. A wide variety of commercial separators are used. Some of the more commonly used types are static inclined screens, vibrating screens, rotary screens, belt presses, perforated roll presses and screw presses. Each of these separator types has one or * Corresponding author. address: jawarneh@hu.edu.jo (A.M. Jawarneh). more disadvantages, such as high initial cost, high operating cost, high maintenance cost and/or inadequate degree of separation. Swirl and vortex technologies have been developed during the last three decades with their major applications have been found in the vortex combustor, liquid atomizer, vortex flow meter, Hilsch vortex tube and many others. A variety of opinions have been developed regarding their effectiveness in the applications of these technologies, which vary from overwhelming support to conservative. Design and performance of swirl/vortex devices depend on the understanding of their characteristics, such as the velocity and the pressure distributions, the strength of the centrifugal forces, the vortex tube geometry and the size of the solid particles. The separation action of the cylinder separator is based on the effects of the centrifugal forces where the necessary vortex action is produced by directing the fluid tangentially into the vortex generators. The vortex action distributes the solid particles over the radius of the separator. The larger particles are forced near the periphery of the /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.mineng

2 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) Nomenclature A inlet area C p radial pressure d o diameter of the separator d p diameter of the particle f drag function L separator length p static pressure Q in volumetric flow rate q velocity vector r* normalized radius, r/r e r normalized radius, r/r o R e radius of exit port Re o Reynolds number R o radius of the separator S swirl number u i, u j, u k velocity components in Cartesian coordinates V u V z, V r mean tangential, axial and radial velocity components v velocity Greek symbols a volume fraction e turbulence dissipation rate l dynamic viscosity k turbulent kinetic energy q density t kinematics viscosity u inlet angle Subscripts f fluid in swirler inlet p particle r, u, z radial, tangential and axial coordinate, respectively t turbulent separator, while the smaller ones remain closer to the central-axis. Investigation was conducted on the performance of a vortex-separation system, regarding the particle size and its ability to retain the solid particles, through the work of Roberts (1968) and Barnhart and Laurendeau (1979). An experimental work in a cylindrical double vortex chamber was conducted by Georgantas et al. (1987) in order to predict the flow pattern of the inserted solid particles. The minimum particle size retained in a vortex chamber was established in relation to different operating parameters. Studies of the turbulent flow field in cyclones are needed for improving the cyclone performance. Experimentally, Deotte (1990) studied the velocity field in a small-size cylindrical cyclone; Hoekstra et al. (1999) measured flow field parameters in a cyclone of industrial dimensions. Derksen and van den Akker (2000), utilizing the Reynolds stress model, found that velocities fluctuations near the center are much higher than those close to the wall; Lu et al. (1999) measured the Reynolds stresses in a liquid liquid hydrocyclone and reported that the turbulence is anisotropic. Boysan et al. (1982) simulated the two dimensional turbulent flow in a cyclone using an algebraic stress model. Zhou and Soo (1990) predicted the time-averaged axial and tangential velocities and the pressure distributions using the k e model and compared them with Laser Doppler Velocimetry (LDV) measurements. Lu et al. (2001) simulated the turbulent flow in hydrocyclones using the k e, renormalization group of k e, and the Reynolds stress model and compared them with LDV. Hu et al. (2005) studied the 3D strongly swirling turbulent flows in a cyclone separator using a Reynolds stress model and measured the velocities using LDV. Erdal et al. (1997) presented CFD simulation utilizing a commercial code CFX, whereby they used axis-symmetric assumption for the two-phase flow, and for the inlets, which are tangentially inclined, were simulated via specifying the rotational velocity along with the axial and radial components. In addition, an expression was developed for the equivalent inlet tangential velocity for the axis-symmetric model, and the effects of the inlet swirl velocity to the axial velocity on the flow behavior was also carried out. Motta et al. (1997) presented a CFD model in the case of an axis-symmetric flow for rotational two-phase flow in a gas liquid cylindrical separator. Jawarneh et al. (2005) have generated a swirling flow by using a single vortex generator and utilizing an expression that was developed for the pressure drop. An understanding of the mechanism of the double vortex separator to concentrate the dispersed phase using two strong vortices is still insufficient. Therefore, this paper is concerned with the ability of the double vortex cylinder to separate the oil from sand and to create a localized residence zone for the solid particles at some distance from the end walls of the vortex cylinder using a numerical technique based on the k e turbulent and the two-phase flow models. The mixture-granular multiphase and the RNGbased k e turbulence models are implemented in the CFD code Fluent 6.1 (Fluent Inc., 2003). 2. Numerical method Since the flow simulation involved the combined effects of turbulence and the two-phase flow, the mixture-granular multiphase model and the RNG-based k e turbulence model are implemented in this study.

3 368 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) Geometry and materials Fig. 2 schematically shows the geometry for the present simulation, which was described in a previous study by Jawarneh and Vatistas (2005). The double vortex separator has a cylindrical configuration with constant cross-sectional area (R o = 7 cm), circumferential inlets and a central-axis outlet. A swirl is imparted to the fluid via the two vortex generators shown in Fig. 1. Each of the vortex generators has four perpendicular inlets through which the compressed fluid enters. A number of passages with a circular cross-section (d in ) are drilled at a specified angle u =30. As the flow passes through the swirlers, it is guided to enter the vortex chamber in a tangential direction so that a vortex is formed inside the cylindrical chamber. The two vortex generators are placed at the opposite ends of the vortex chamber. Each generator has eight passages with a diameter d in = cm and an inlet area A 1,2 =10cm 2. The chamber length L is set to 42 cm and the radius of the exit opening R e is set to 1.75 cm. The mixture flow rate Q in through each generator is m 3 /s. The density of the engine-oil q f, was used for the primary or the continuous phase 889 kg/m 3 while the density of sand particles q p, defined as the secondary phase or the dispersed phase, was set at 2500 kg/m 3. The particle size d p was chosen 250 lm according to a recommendation outlined by Georgantas et al. (1987). The feed volume fraction a p at the two inlets is Governing equations Mixture model The swirling flow was considered to be turbulent, incompressible, steady and axis-symmetric The mixture model uses a single-fluid approach and allows the phases to be interpenetrating. The continuity and the momentum equations are solved for the mixture while the volume fraction equation is used for the secondary phase, in addition to algebraic expressions for the relative velocities if the phases are moving at different velocities. The continuity equation for the mixture is rðqvþ ¼0:0 where v is the velocity of the mixture, v ¼ a fq f v f þ a p q p v p ð2þ q and q is the mixture density, q ¼ a f q f þ a p q p ð3þ The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases. It can be expressed as rðqvvþ ¼ rpþr½lðrv þrv T ÞŠ þ qg þr ða f q f v df v df þ a p q p v dp v dp Þ ð4þ where l is the viscosity of the mixture as defined by Batchelor (2000), l ¼ l f 1 þ 5 2 a p ð5þ v dp is the drift velocity for the solid phase, v dp ¼ v p v ð6þ The relative velocity or the slip velocity v pf is defined as the velocity of the solid phase p relative to the velocity of the fluid phase f, v pf ¼ v p v f ð7þ The drift velocity and the slip velocity are related through, v dp ¼ v pf a fq f q þ a pq p v fp ð8þ q Manninen et al. (1996) suggested the form of the relative velocity as, v pf ¼ ðq p qþd 2 p a ð9þ 18l f f where d p is the diameter of the particles of the secondary phase and a is the acceleration of the secondary phase. ð1þ Fig. 1. Schematic of the vortex chamber (Jawarneh and Vatistas, 2005).

4 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) Fig. 2. Schematic diagram for the geometry used for the simulation. The drag function f is taken from Schiller and Naumann (1935), f ¼ 0:0183Re o ð10þ The Reynolds number Re o is defined based on the average axial velocity as, Re o ¼ 4Q in ð11þ mpd o and the acceleration a is of the form, a ¼ g ðvrþv ð12þ From the continuity equation for the secondary phase p, the volume fraction equation for secondary phase can be obtained, rða p q p vþ ¼ rða p q p v dp Þ ð13þ RNG k e model The RNG-based k e turbulence model is derived from the instantaneous Navier Stokes equations using a mathematical technique called renormalization group (RNG) methods. The analytical derivation results in a model with constants different from those in the standard k e model, and additional terms and functions appear in the transport equations for k and e, see Choudhury (1993). The RNG k e model is similar in form to the standard k e model, but it has shown substantial improvements over the standard k e model where the flow features of strong streamline curvature, vortices, and rotation are included. So, the effect of swirl on turbulence is included in the RNG model, enhancing the solution accuracy for swirling flows. Transport equations for the RNG k e model, oðqku i Þ oðx i Þ oðqeu i Þ oðx i Þ ¼ o ok a k l oðx j Þ eff ox j ¼ o oe a e l oðx j Þ eff ox j ou qu 0 iu 0 j j þ C 1 e k qe ð14þ ox i ou qu 0 iu 0 j j C 2 q e2 ox i k þ R e ð15þ The quantities a k and a e are the inverse effective Prandtl numbers for k and e and for high Reynolds number their values are a k = a e The effective viscosity l eff is the sum of the laminar l and turbulent viscosities l t of the mixture, k 2 l t ¼ qc l ð16þ e The model constants; C 1, C 2 and C l are 1.42, 1.68 and , respectively. The main difference between the RNG and standard k e model lies in the additional term in the e equation given by R e ¼ C lqg 3 ð1 g=g 0 Þ e 2 ð17þ 1 þ bg 3 k where g = Sk/e, g 0 = 4.38, b = The swirl number S is defined as the ratio of the axial flux of angular momentum to the axial flux of axial momentum: R Ro qv 0 z V u r 2 dr S ¼ R Ro ð18þ R o qv 0 z r 2 dr where R o is the separator radius, V u and V z are the tangential and axial velocities components. Turbulence is affected by the swirl in the mean flow. The RNG model provides an option to account for the effects of swirl by modifying the turbulent viscosity appropriately. The modification takes the following functional form, l t ¼ l to f W; S; k ð19þ e where l to is the value of the turbulent viscosity calculated without the swirl modification using Eq. (16), andw is a swirl constant that takes on different values depending on whether the flow is swirl-dominated or only mildly swirling. For strongly swirling flows as in the present work a value of 0.08 was used Boundary conditions and numerical schemes At the two inlets to the vortex chamber uniform velocity components are used. The same velocity is specified for both the fluid and particulate phases. The total inlet velocity vector q in at both inlets has two components V r in and V uin and they are related to each other by,

5 370 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) V u in ¼ q in cos u V r in ¼ q in sin u ð20þ ð21þ where q in = Q in /A in. It should be noted that the vortex at the right end acts clockwise while the left one acts in the counter clockwise. At the outlet boundary there is no information about the variables and some assumptions have to be made. The diffusion fluxes in the direction normal to the exit plane are assumed to be zero. At the solid walls, the no-slip condition was applied where the velocities at the walls were specified to be zero. The centerline boundary was considered axis of symmetry. A phase-coupled SIMPLE algorithm for the pressure velocity coupling is adopted. The second order upwind schemes were used for the momentum and the swirl velocity while first order upwind schemes were used for the turbulence kinetic energy, turbulence dissipation rate, and volume fraction. Convergence was assumed when the residual of the equations dropped more than three orders of magnitude. Triangular mesh elements and an unstructured grid were used for the separator. The mesh is sufficiently refined in order to resolve the expected large flow parameter gradients. The under-relaxation parameters for the velocities were selected for the radial and axial, and 0.9 for the swirl velocity components. The segregated implicit solver, which is well suited for the sharp pressure and velocity gradients, has been applied for the solution of the separator. When using the present models it is necessary to run the simulation for a significant number of iterations beyond normal convergence criteria. Experience has shown that typically 6000 iterations are needed before the peak tangential velocity in the simulation stabilizes. An independent grid sensitivity study was conducted by performing simulations for three different grids consisting of 33,000, 37,000 and 48,000 nodes. It was observed that there was no significant variation in the solutions utilizing the later two grid sizes; therefore a grid size of 37,000 was adopted. 3. Results and discussion In order to gain confidence of the modeling methodology, that is required to adequately simulate the separator flow, the experimental work of Georgantas et al. (1986) was used for comparison purposes of the modeling results presented in this paper. Fig. 3 compares the tangential velocity and the radial pressure distributions. The results presented in Fig. 3a where obtained using the renormalization group of k e model. The tangential velocity increases sharply with the radius in the central core region then it decreases. This is a typical radial transition between a free and a forced vortex regions. The two vortex modes are clearly captured and compares well with the measured values. The mean pressure coefficient C p is defined as, C p ¼ 2 ð pðrþ pðr ¼ 1Þ qv 2 in Þ ; where r ¼ r R o ð22þ It is obvious from Fig. 3b that the renormalization group of k e model can capture the experimental points. It is evident that the maximum pressure occurs at the longitudinal wall of the separator due to the action of the centrifugal forces. The pressure decreases at a progressively higher rate as the center of the separator is approached. The most important feature of the double vortex system is its ability to create a localized residence zone for the solid particles, as shown in Figs. 4 and 5, at some distance from the end walls of the vortex chamber, whereby in that region the suspension process can take place. Upon the introduction of the mixture through the two swirlers, the particles a Experiment Georgantas et al (1986) Vt, Present x=35 cm, Prediction Re=2.8 cm fluent b 2 0 Experiment georgantas et al (1986) Presenrt Prediction Mean Swirl Velocity Vϕ (m/s) C p r r Fig. 3. Comparison of the flow field at a plane of z = 300 mm obtained from the measurements and the CFD simulation: (a) mean swirl velocity and (b) mean pressure coefficient.

6 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) Fig. 4. Contours of the volume fraction of the liquid phase. Fig. 5. Contours of the volume fraction of the particulate phase. are suspended by the action of the axial drag force produced by the right swirl generator meanwhile they are prevented from leaving the exit opening by the action of the left swirl generator. So, the two axial drag forces acting in opposite directions at the periphery of the chamber are high enough to confine the particles in a narrow zone where the two vortices merge. The tangential drag forces accelerate the particles toward the periphery while the radial drag forces retard the particles toward the center of the chamber. For particle equilibrium in the horizontal plane the centrifugal forces must balance the radial drag forces. An additional feature of the double vortex flow system is that the residence zone of the solid particles can be shifted along the height of the chamber by altering the flow rates from the two inlet ports. The best performance is obtained when the bottom to top mixture flow ratio is equal to unity where the strength of both vortices are the same, and the residence zone is formed at the middle level of the separator. From the numerical simulation the volume fraction contours for the two-phases are shown in Figs. 4 and 5. The distributions of the volume fractions are evaluated over the cross-sectional (r z) plane of the cylindrical separator using the contour maps. The portion shown in warm colors such as red and orange indicate high concentrations compared with those shown in cold colors such as blue and sky blue. Fig. 4 shows the liquid volume fraction distribution whereby it is seen that the flow field in the separator consist of strong swirling flow of high velocity around the center (forced vortex region) and weak swirling flow of low velocity near the wall (free vortex region). The strong swirling flow in the center results in centrifugal forces that propel the solid particles to the outer free-vortex region, where particles are collected and reside in the weak swirling intensity region. Thus pure liquid-phase will flow through the exit port; meanwhile some solid particles will escape at the periphery of the exit port. Solid particles of 250 lm in size are shown in Fig. 5. The particles are more likely to be collected at the mid-separator because they exchange more momentum and energy during the collision and hence the majority of the particles do not trace the liquid flow, so the solid particles are trapped at the midseparator. 4. Conclusions The numerical methodology presented herein establishes that the double vortex separator technology is potentially of a significant value in the area of designing and utilizing separators. The mixture-granular multiphase model and RNG-based k e turbulence model are able to predict the flow features inside the separator such as the tangential velocity and the radial pressure profiles. The results of

7 372 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) the numerical simulation were compared with the experimental data and were found in reasonable agreement. The analyses reveal from the behavior of the mean tangential velocity distribution that the flow of the vortex separator is of a forced-vortex inside the core and a free-vortex outside the core. The maximum pressure was observed to occur along the longitudinal wall of the separator as a result of the strong action of the centrifugal forces and it decreases sharply as the center of the separator is approached. The collected solid particles at the mid-separator are predicted using the present models and the best performance is obtained when the bottom to top mixture flow ratio is equal to unity where the strength of both vortices are the same. As a result of the strong centrifugal force, two vortices are formed causing the solid particles and liquid to separate. The solid particles move toward the wall, while the liquid flows to the center and leaves from the exit opening. The majority of the particles are forced to remain near the periphery of the separator, while fewer ones escape from the outer exit annulus. References Barnhart, J.S., Laurendeau, N.M Gasification in pulverized coal flames, Fossil Energy Report, FE , Purdue University. Batchelor, G.K., An Introduction to Fluid Dynamics. Cambridge University Press. Boysan, F., Ayers, W., Swithenbank, J., Fundamental mathematical modeling approach to cyclone design. Trans. Inst. Chem. Eng. 60, Choudhury, D Introduction to the renormalization group method and turbulence modeling. Fluent Inc.Technical Memorandum TM Deotte, R.J., Characterization of the velocity field in a small cylindrical, low Reynolds number aerosol sampling cyclone. Aerosol. Sci. Technol. 12, Derksen, J.J., van den Akker, H.E.A., Simulation of vortex core precession in a reverse-flow cyclone. AICHE J. 46, Erdal, F.M., Shirazi, S.A., Shohan, O., Kouba, G., CFD simulation of single-phase and two-phase in gas liquid cylindrical cyclone separators. SPE J. 2, Georgantas, A.I., Krepec, T., Kwork, C.K., Vortex flow patterns in a cylindrical chamber, In: AIAA/ASME Fourth Fluid Mechanics, Plasma Dynamics and Laser Conference, AIAA , May 12 14, 1986/Atlanta, GA. Georgantas, A.I., krepec, T., Kwork, C.K., Flow pattern of solid particles in a double vortex chamber. Trans. CSME 11, Hoekstra, A., Derksen, J.J., van den Akker, An experimental and numerical study of turbulent swirling flow in gas cyclones. Chem. Eng. Sci. 54, Hu, L.Y., Zhou, L.X., Zhang, J., Shi, M.X., Studies on strongly swirling flows in the full space of a volute cyclone separator. Am. Inst. Chem. Eng. 51 (3), Jawarneh, A.M., Vatistas, G.H., Effect of inlet conditions on the pressure drop in a confined vortex chamber. AIAA J. Propul. Power 21 (6), Jawarneh, A.M., Vatistas, G.H., Hong, H., On the flow development in jet-driven vortex chambers. AIAA J. Propul. Power 21 (3), Lu, Y.-J., Shen, X., Zhou, L.-X., LDV diagnosis for the flow field in a liquid liquid hydrocyclone with double cones and cylinders. J. Exp. Mech. (China) 14, Lu, Y.J., Shen, X., Zhou, L.X., Application and comparison of different turbulence models in simulating liquid liquid hydrocyclones. J. Tsingha Univ. (China) 41, Manninen, M., Taivassalo, M., Kallio, V., On the mixture model for multiphase flow, VTT Publications 288, Technical Research Centre of Finland. Motta, B.R., Erdal, F.M., Shirazi, S.A., Shohan, O., Rhyne, L.D., Simulation of single-phase and two-phase flow in gas liquid cylindrical cyclone separators. In: Proceeding of the ASME summer meeting, Fluid Eng. Division, Vancouver, Canada, June Roberts, A The combustion of pulverized fuel in a vortex chamber, Doctoral Thesis, University of Sheffield. Schiller, L., Naumann, Z., Ver. Deutsch. Ing. 77, 318. Zhou, L.X., Soo, S.L., Gas solid flow and collection of solids in a cyclone separator. Powder Technol. 63,