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CFD analysis of inlet chamber body profile effects on de-oiling hydrocyclone efficiency
chemical engineering research and design 8 9 ( 2 0 1 1 ) 968–977
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CFD analysis of inlet chamber body profile effects on de-oiling hydrocyclone efficiency S. Noroozi, S.H. Hashemabadi ∗ Computational Fluid Dynamics (CFD) Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, 16846 Tehran, Iran
a b s t r a c t In this study the effect of inlet chamber design on de-oiling hydrocyclone efficiency has been investigated numerically with the aim of minimizing the energy loss. To this aim, effects of four different inlet chamber designs (exponential, conical, quadratic polynomial body profile and standard design) on efficiency have been considered. Algebraic slip mixture model and Reynolds Stress Model (RSM) have been employed for prediction of multiphase flow behavior and simulation of turbulent flow through the cyclone respectively. The simulation results for efficiency of standard design demonstrate a proper agreement with reported experimental data. The results show that the separation efficiency can be improved approximately 8% using exponential body shape. The recirculation eddies that exists in the upper section prevents inward radial flow, consequently the efficiency reduces; the simulations illustrate that inlet chamber shape affects on the size of these eddies. More recirculation in hydrocyclone inlet chamber with quadratic polynomial body profile causes minimum separation efficiency. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Hydrocyclone; De-oiling; Computational fluid dynamics; Simulation; Separation efficiency
1.
Introduction
In the recent years applications of long hydrocyclone as a liquid–liquid separator especially in offshore platforms according to recover of oil from oily wastewater (Devorak, 1989; Gomez et al., 2002) and crude oil dewatering (Belaidi et al., 2003) have been extended. The specific features of hydrocyclones such as low maintenance cost due to the lack of moving parts, simple operation, and installation make them suitable and useful devices for separation processes. Investigation of new designs is time consuming and expensive to do by experimentation and very difficult or impossible by analytical methods. On account of this fact, many attempts have been performed numerically for analysis of solid–liquid flow through the cyclones and appropriate results have been compared with the experimental works (Pericleous and Rhodes, 1986; Hsieh and Rajamani, 1988; Monredon et al., 1992; Dyakowski et al., 1994; Malhotra et al., 1994; Stovin and Saul, 1998; Nowakowski et al., 2000; Slack et al., 2003; Nowakowski and Dyakowski, 2003; Schuetz et al., 2004; Yang et al., 2004; Cullivan et al., 2003, 2004; Bhaskar et al.,
∗
2007). Some differences exist between the liquid–liquid (LLHC) and solid–liquid hydrocyclones (SLHC) in terms of operational and geometrical parameters due to low density differences between two liquids in LLHC. The pressure drop between two outlet orifices in SLHC is almost zero, but in LLHC the pressure gradient is not equal in order to create more back flow toward the overflow. Moreover, the liquid–liquid hydrocyclone is made long because of increasing the droplet residence time for better separation (Devorak, 1989). Despite these differences, Delgadillo and Rajamani (2006) applied the same numerical techniques for flow field simulation and separation efficiency estimation for long hydrocyclone in solid–liquid separation. A few CFD simulations of de-oiling hydrocyclones have been reported previously. Hargreaves and Silvester (1990) studied numerically the velocity field and separation efficiency through the long de-oiling hydrocyclone; they applied the ASM (Algebraic Stress Model) and k-ε turbulence models in that order. Grady et al. (2003) employed the RSM turbulence closure and algebraic slip mixture multiphase model for prediction of velocity field and separation efficiency in 10 mm de-oiling hydrocyclone; they compared the results with experimental
Corresponding author. Tel.: +98 21 7724 0376; fax: +98 21 7724 0495. E-mail address: [email protected] (S.H. Hashemabadi). Received 13 December 2009; Received in revised form 5 September 2010; Accepted 29 November 2010 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.11.017
chemical engineering research and design 8 9 ( 2 0 1 1 ) 968–977
Nomenclature CD d D E F g k L n p Q Re Rf t u x
drag coefficient [–] diameter [mm] hydrocyclone diameter [mm] de-oiling efficiency [%] interphase momentum transfer term [N m−3 ] gravity acceleration [m/s] viscosity ratio of dispersed phase to continuous phase [–] length [mm] number of phases [–] static pressure [N m−2 ] volume flow rate [l/min] Reynolds number (defined by Eq. (8)) [–] overflow split ratio (Qo /Qin ) [%] time [s] velocity [m/s] coordinates [–]
Greek symbols ˛ volume fraction [%] viscosity [kg/m/s] density [Kg/m3 ] stress tensor [pa] Subscripts c continuous phase d droplet D drift i, j, k coordinate directions in inlet orifice m mixture phase o overflow orifice p dispersed phase S slip u underflow orifice Superscripts l laminar t turbulence
efficiency. Paladino et al. (2005) also applied the same methods for simulation of multiphase flow behavior for low concentration of oil in two inlets hydrocyclone; moreover, they also considered the distribution of droplet diameter in hydrocyclone feed. Huang (2005) used the RSM model for modeling the turbulence flow and Eulerian–Eulerian approach for prediction of two-phase flow behavior for high concentration of oil in feed through the Colman–Thew hydrocyclone type; in addition, Huang (2005) verified his results using the Colman–Thew experimental results in terms of separation efficiency. Noroozi and Hashemabadi (2009) studied numerically the influence of different inlet designs on the de-oiling hydrocyclone efficiency. Their simulations show that the separation efficiency can be improved approximately 10% by a suitable inlet design. Schutz et al. (2009) studied the coalescence and breakage effects in de-watering hydrocyclone utilizing a CFD method. Furthermore, in this study they considered the effect of the structure and two inlets design on the droplets size distribution at outlets.
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For the hydrocyclone flow analysis, there are several variables that have been classified in two groups: (a) dimensional variables, (b) operational and feed stream variables (Young et al., 1994). Due to low spinning flow in cylindrical inlet chamber compared to the other flow regions into the hydrocyclone and higher energy lost for fluid flow because of wall drag (Young et al., 1994), optimization of inlet chamber design can play a crucial role in improving the clarification process. There exist some attempts for optimization of separation efficiency in liquid–liquid hydrocyclone with the aid of geometrical body changes. Thew and Colman (1989) studied experimentally the exponential and cubic profile for whole de-oiling hydrocyclone body. Young et al. (1994) investigated empirically two cylindrical entrance chambers with different length. Chu et al. (2000) took account of the effect of body and inlet chamber design of hydrocyclone on separation efficiency. They studied the energy loss in different sections of SLHC experimentally. Belaidi and Thew (2003) reported the new design for inlet chamber in air sparged de-oiling hydrocyclone. In this new design a conical inlet chamber has been placed instead of the entrance cylindrical part. Delgadillo and Rajamani (2006) employed the numerical simulation for prediction of new designs efficiency with different inlet chamber designs for SLHC and their results were compared with the standard form. In addition, Andrade et al. (2006) considered the separation efficiency of two new inlet chamber designs for Rietema and Bradley hydrocyclone type. They used the small conical part on top of hydrocyclone rather than vortex finder section; they, also, considered the effect of using a static screw with eleven threads rather than the cylindrical part on hydrocyclone efficiency. Due to this fact that the body design of hydrocyclone has great effects on separation efficiency (Chu et al., 2000), this investigation tries to search by CFD simulation the influences of non-standard inlet chamber designs on de-oiling hydrocyclone efficiency that has not reported before. To this goal, influences of three non-standard inlet chamber body designs as well as standard one on dissipation rate of kinetic energy and velocity profile have been discussed in this study.
2.
Problem statements
2.1.
Phase’s interaction modeling
For modeling of multiphase flow behavior and consideration of multiphase interaction, algebraic slip mixture model is employed in this work. Algebraic slip mixture approach for multiphase flow allows one to consider the problem at low computational cost as opposed to Eulerian–Eulerian approach especially when the entrance volume fraction of dispersed phase is very low (lower than 10%) (Paladino et al., 2005). In this model the transport equations are solved for the mixture of phases. The slip velocity (the velocity relative to the continuous phase) and drift velocity (the velocity relative to the mixture average velocity) for each phase are obtained from the fluid properties and local flow conditions. The continuity and momentum equation for the mixture phase can be represented as follow respectively (Paladino et al., 2005; Bai and Wang, 2006):
∂ (m ) + ∇(m um ) = 0 ∂t
(1)
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∂ l t + m ) + m g (m um ) + ∇(m um um ) = −∇p − ∇(m ∂t +F + ∇
n
˛p p uDp uDp
(2)
p=1
where ˛p and uDp are the volume fraction and drift velocity for phase p respectively. The volume fraction equation can be gained from solving the following continuity equation for phase p: ∂ (˛p p ) + ∇(˛p p um ) = −∇(˛p p uDp ) ∂t
(3)
All of the flow properties for mixture flow such as m , m , um can be calculated as follows: n
m =
n
m =
˛p p ,
p=1
n
˛p p ,
p=1
um =
˛p p up
p=1
m
(4)
The drift velocity (uDp ) and slip velocity (uSp ) for each dispersed phase (such as phase p) are represented by the following expression:
uDp = uSp −
n ˛p p p=1
m
uSp
(5)
where uDp = up − um and uSp = up − uc and uc is the velocity for continuous phase. The term of F in Eq. (2) includes all the related phase interaction forces such as lift, virtual mass and drag force. In this work due to the assumptions of spherical shape and small diameter for the droplets the shear-lift force and the lift force caused by slanted wakes can be discounted (Ishii and Hibiki, 2006). Also because of low concentration of oil in feed and therefore very low concentration of dispersed phase in the vicinity of the walls, the wall-lift (wall-lubrication) force has been eliminated (Antal et al., 1991; Ishii and Hibiki, 2006). Moreover, due to low density differences between two liquids virtual mass force is negligible. So the simplified interphase momentum exchange term can be obtained via the following equation (Ranade, 2002):
F=
3˛p ˛c c CD up − uc (up − uc ) 4dd
droplet which can decrease the droplets drag force. Due to this assumption, Hadamard–Rybcynski’s correlation (Saboni and Alexandrova, 2002) is used in this work to estimate the drag coefficient for the creeping flow (Red < 1) that has been recommended in previous literatures in the case of hydrocyclone (Rovinsky, 1995). For estimation of drag coefficient in the Reynolds number range of 1–500 two theoretical based correlations have been examined (Saboni and Alexandrova, 2002; Rivkind and Ryskin, 1976). In this range of Reynolds, two correlations have almost the same prediction, but the Rivikind and Ryskin correlation due to the simpler mathematical form, less computational divergence, and fewer computational costs has been found as better correlation. For high Reynolds numbers (Red > 500), the drag coefficient is constant (set to 0.44). Therefore, the drag coefficient used for calculation of drag force in this work is represented as follows:
CD =
⎧ 8 3k + 2 ⎪ ⎪ ⎨ Red k + 1 1
⎪ ⎪ ⎩ 1+k 0.44
k
Red ≤ 1
24 + 4Red −1/3 Red
+ 14.9Red −0.78
1 < Red ≤ 500
(7)
Red > 500
where the Red is the droplet Reynolds number that can be produced as: Red =
c |uc − up |dd c
(8)
The deformation of droplets due to the small diameter of droplets is ignored (Loth, 2008).
2.2.
Turbulence flow model
Although Reynolds Stress Model (RSM) compared to the other RANS (Reynolds Average Navier–stokes) models is more time consuming, the RSM model has great potential to predict behavior of complex flows such as swirling flow through the hydrocyclone and cyclone accurately (Launder, 1989; Grady et al., 2003; Huang, 2005; Schutz et al., 2009). The RSM model involves calculation of the individual component of turbulence stress tensor using the partial differential transport equation. In this work, the RSM model has been used for simulation of turbulence water–oil two phase flow behavior through the hydrocyclone.
(6)
where dd and CD are droplet diameter and drag coefficient respectively. The value of droplet drag coefficient in liquid–liquid emulsion flows (such as flow through the LLHC) depends on droplet Reynolds number and viscosity ratio k (dispersed phase-to-continuous phase viscosity ratio, k = p /c ) (Rovinsky, 1995; Delfos et al., 2004). For pure droplets with no contaminant, there is a slip flow along the interface which is driven by internal circulation that reduces the drag coefficient (Loth, 2008). On the other hand, if the droplet is contaminated or viscosity ratio approaches to infinity (k > 50) the drag coefficient can be calculated as solid particle due to effectively no-slip condition on particle surface; in this conditions the empirical correlations based on the solid particle assumption such as Schiller–Naumann correlation can be used (Loth, 2008). In this study, it is assumed that the droplets have no contaminant and there is slip flow between the oil drop and water phase that can result in the internal circulation in
3.
Design parameters
Fig. 1 illustrates four different feed chamber designs (A, B, C and D) for de-oiling hydrocyclones that used in this investigation. Table 1 presents geometrical details of these hydrocyclones. All the four hydrocyclones models are fed by two inlets that can be improved the symmetry of flow. Fig. 1A shows the standard de-oiling hydrocyclone with nominal diameter (Ds ) of 20 mm for large diameter of long conical tapered section. The exponential body configuration employed in design (B) instead of cylindrical and reduction conical section in standard design (Fig. 1B). In design (C) the conical section with angle of 20◦ is used instead of entrance cylindrical section in standard design (Fig. 1C); in design (D) the quadratic polynomial body configuration is employed rather than cylindrical and reducing conical section in standard design. All the geometrical parameters with the exception of feed chamber and reducing conical section are same in the four designs.
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Table 1 – Design parameters for three different designs as well as standard design (A). Design (B)
Design (C)
Design (D)
Standard design (A)
Ds (mm) Do /Ds Du /Ds D/Ds Ls /Ds Lu (mm) ˛◦ ˇ◦ ◦
20 0.2 0.5 – – 235 – – 1.5
20 0.2 0.5 2 – 235 15 20 1.5
20 0.2 0.5 – – 235 – – 1.5
20 0.2 0.5 2 2 235 15 – 1.5
Chamber body profile 0 < z < 13 mm
r = 9.083 + 19.43exp( − 2.26z1.15 )
–
r = − 5.43z2 − 78.5z + 29.5
–
Fig. 1 – Geometry details of four de-oiling hydrocyclones with different feed chamber.
4.
Boundary conditions and CFD simulation
The constant mass flow rate (20 l/min) at the inlet boundary surface as a plug flow is employed. By reason of complex flow and hydrocyclone geometry complexity, three tetrahedral mesh densities (250,000, 450,000, and 830,000) in order to take into account of mesh independency for standard typical de-oiling hydrocyclone have been used. Fig. 2 illustrates a graphical representation of the computational mesh. Because of higher phases and velocity gradient in central core, a grid refinement has been done locally. Moreover, for each simulation the mean oil droplet diameter is employed at the entrance boundary. The imposed mass flow rate boundary condition with respect to overflow split
ratio Rf (in this work 17%) as a percentage of inlet mass flow rate are used for outlets (17% exit from overflow and the rest leave the underflow). Furthermore, the overflow orifice of the hydrocyclone is assumed to be fully open to the atmosphere. The wall boundaries are subjected to no slip condition and the standard wall function is applied to near the wall. In this work, finite volume based (Patankar, 1980) in-house CFD code has been used for simulation of two phase flow through the hydrocyclone. The Semi-Implicit Pressure Linked Equations (SIMPLE) algorithm is used for combination of continuity and pressure driven flow equation for two phases to gain the pressure distribution inside the hydrocyclone (Versteeg and Malasekera, 1995). The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) schemes is applied for interpolation of variables from cell centers to faces of control volumes that recommended for higher accuracy in complex flow like in hydrocyclone (Ko et al., 2006; Bhaskar et al., 2007). The simulations are carried out for unsteady state conditions to 100,000 iterations while the variation of governing variable (pressure and velocity components) becomes negligible. The convergence criteria are set to 10−3 except continuity equation and volumetric ratio of oil phase, in which the criteria are 10−5 for continuity and volumetric ratio. All of the simulations in this work for three-dimensional two phase flow through the hydrocyclone were performed on 2 Intel® Xeon® E5335 Quad Core, 2 GHz 8 MB cash CPU with 8 GB RAM.
5.
Results and discussion
5.1.
Model validation
Prior to application the numerical analysis of flow through the different designs of hydrocyclone, it is necessary to validate the models and above mentioned code which are used for simulation. To this aim, the prediction of CFD simulation
Fig. 2 – Unstructured grid for hydrocyclone CFD simulation in two cross sections.
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Fig. 4 – Kinetic energy dissipation rate versus the radial position for different axial distance from the top wall of standard hydrocyclone (design A).
Fig. 3 – Comparison of experimental (Belaidi and Thew, 2003) and numerical simulation results for effect of oil droplet size on separation efficiency in design (A). for separation efficiency is compared to experimental data, reported by Belaidi and Thew (2003) for standard typical deoiling hydrocyclone. The separation efficiency is defined as the ratio of oil overflow flow rate to oil feed flow rate (Gomez et al., 2002): E=
˛o Qo ˛u Qu =1− ˛in Qin ˛in Qin
(9)
As it is shown, the separation efficiency is a factor that is dependent on the velocity profile and pressure field (Eq. (9)), so when the simulation results predict the proper efficiency compared to the experimental work, it almost confirms the CFD results. This criterion used by Grady et al. (2003) and Huang (2005) as a verification factor in case of CFD simulation of flow through the hydrocyclone. Fig. 3 shows the separation efficiency against the mean droplet diameter of oil in the feed entrance flow for the standard design of typical de-oiling hydrocyclone. In this study, three different mesh densities are used for considering the effect of mesh density on prediction of separation efficiency. Fig. 3 illustrates in higher mesh density, mean divergence of results from experimental data are about 8% for fine mesh (830,000 cells) and this deviation increases to about 19% while the mesh density decreases (to about 250,000 cells). Therefore the higher mesh density has better results but computation time is very higher in comparison with the lower mesh case (the computation time ratio for mentioned meshes is 252–72 h with same hardware). Moreover, the results for mesh density of 450,000 cells have good agreement with reported experimental data (approximately 10% deviation) and the computation time is very smaller than the higher mesh. Owing to these results the mesh density of 450,000 tetrahedral cells was found as optimum mesh density. Fig. 3, also, depicts that in very small oil droplets diameter, less than 10 m, overprediction compared to the reported empirical data is gained. It might be attributed to a phenomenon so-called fish hook effect (Majumder et al., 2007), which occurs in the centrifugal devices like hydrocyclones. Because of this phenomenon, the droplet with small diameter is affected by the wake of larger particles and the resulted force moves the smaller droplets
toward the wall. This promotes the drag force and breakage of the small droplets (Grady et al., 2003; Majumder et al., 2007). Consequently, the separation efficiency reduces just as it can be observed in the experimental work. For droplet size larger than 50 m the CFD simulations also show the over-prediction compared to the experimental results (more than 7%). This has been ascribed to the dominant effect of large droplet breakage that occurs in the experimental work (Meyer and Bohnet, 2003). More breakage can decrease the separation efficiency, which has been ignored in this simulation.
5.2. Influence of inlet chamber design on the LLHC efficiency In this work, two issues that play important roles on separation efficiency are considered with changing of the hydrocyclone body profile. The first one is dissipation rate of kinetic energy due to wall drag in different part of hydrocyclone body. Fig. 4 shows the kinetic energy dissipation rate for standard design (Fig. 1A) in radial direction in different axial
Fig. 5 – Radial distribution of kinetic energy dissipation rate for various feed chamber designs at 5 mm from the top.
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Fig. 6 – Schematic diagram of primary and secondary flow pattern in conical hydrocyclone. positions of the hydrocyclone. The results illustrate in all axial position the dissipation rate near the wall is higher than the regions where are closer to axis of hydrocyclone by reason of wall drag. Furthermore, the dissipation rate magnitudes are reduced from the top wall toward the underflow outlet. As it is shown, the flow kinetic energy dissipation rate through the inlet chamber is more than the other sections; therefore optimum design for that (with minimized energy lost) can lead to the higher separation efficiency. Fig. 5 shows the dissipation rate of kinetic energy in radial direction in 5 mm from the top wall of four different inlet
chamber designs. It shows that the dissipation rate is lower than the standard design in three modified designs. Moreover, the energy dissipation rate in design (D) is lower than the designs (B) and (C) that might be related to its special shape in inlet chamber body shape. The second factor is the effect of body shape on flow profile through the hydrocyclone. Fig. 6 shows schematically the different regions of flow which are created through the hydrocyclone. The flow field is divided into primary and secondary flows. The primary flow includes the inner vortex that is caused due to swirl back flow and outer vortex that is resulted
Fig. 7 – Radial distribution of axial velocity for various inlet chamber designs at four positions from the top wall of hydrocyclone.
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Fig. 8 – Velocity vector plot for different designs in longitudinal cross section of inlet chamber.
in swirl flow toward the underflow. Secondary flow consists of the side and end-wall circuit flow which bypasses the hydrocyclone without experiencing the primary flow, and also it contains the recirculation eddy that exists in the upper section and prevents inward radial flow across its boundaries (Devorak, 1989; Dai et al., 1998). The migration of droplets to central zone of the hydrocyclone can be avoided by recirculation eddies in inlet chamber, consequently with increasing the size of these vortex, the separation efficiency of hydrocyclone can be decreased. Fig. 7 presents the axial velocity profile at four different positions from the top wall in four different hydrocyclones. The positive axial velocities indicate backflow at the central zone of the hydrocyclones and the negative axial velocities present downward flow near the walls. The results clearly show that the backflow zone decreases from overflow (20 mm) to underflow (240 mm) for all designs. In addition, the results illustrate that in standard design and design (D) the axial velocity profile has two positive regions in upper sections, one in the central zone and the other one is located between wall and central core. This phenomenon is related to the presence of recirculation eddy in top regions in these two designs. Indeed, this eddy recirculation in standard design is created only in cylindrical section, and in design (D) is created in all inlet chamber body. On the other hand, this phenomenon is not seen in two other designs which reveal that the recirculation eddy is omitted in these two designs because of their special body designs. Fig. 8 presents the velocity vector plot in
Fig. 9 – Radial distribution of tangential velocity for various inlet chamber designs at four positions from the top wall of the hydrocyclone.
chemical engineering research and design 8 9 ( 2 0 1 1 ) 968–977
Fig. 10 – De-oiling hydrocyclone separation efficiency versus mean droplet diameter for various inlet chamber designs. longitudinal cross section of inlet chambers for four different designs. This figure shows vividly that the recirculation eddy in standard design is reduced in size for design (C) and almost is removed in design (B). In contrast, the recirculation eddy region is improved in design (D) compared to standard one. The swirling fluid flow through the hydrocyclone and separation efficiency can be affected directly by tangential velocity. Fig. 9 illustrates the radial distribution of tangential velocity at four different distances from the top wall of hydrocyclone for different inlet chamber designs (Fig. 1). It is shown the tangential velocity profile in designs (B) and (C) is higher than two other designs which results in the higher centrifugal forces. Consequently, the separation efficiency increases for oily water clarification process in these two designs. That might be attributed to the effect of body design in inlet chamber section and lower energy dissipation rate with reference to the standard design. Despite the minor kinetic energy dissipation rate in design (D), the tangential velocity is lower than the other designs that can be related to dominate effect of inlet chamber form on tangential velocity profile. Fig. 10 shows the separation efficiency versus various mean droplet diameter at the hydrocyclone’s feed for different
Fig. 11 – Distribution of dispersed phase (oil) volume fraction in four different designs.
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Fig. 12 – Radial distribution of dispersed phase (oil) volume fraction in four different designs at 5 mm from the top. designs (Fig. 1). For mean oil droplet size larger than 100 m in feed, the efficiency for whole hydrocyclones approaches to 100%. Furthermore, the results depict that designs (B) and (C) have higher efficiency due to the higher tangential velocity compared to the standard design (Fig. 9). These results demonstrate the improving effect of the proposed modifications to inlet chambers for the standard de-oiling hydrocyclone design. According to Fig. 10 the separation efficiency for standard design is higher than that for design (D) and this modification reduces the clarification performance. These results demonstrate that for enhancement of de-oiling efficiency, the hydrocyclone with design (D) is not a good option for experimentation. The accumulation and shift of oil to the axis of hydrocyclone and migration of water phase toward the wall in four different designs (Fig. 1) is visualized well in Fig. 11. Fig. 11 shows the contour of volume fraction for oil phase in a longitudinal cross section of hydrocyclone. The range of colors from red to blue represents oil and water volume fractions
Fig. 13 – Radial distribution of dispersed phase (oil) volume fraction in four different designs at 200 mm from the top.
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(for example red color shows oil concentrated regions), respectively. The results illustrate the maximum separation of oil from water phase in designs (B) and (C) occurs in entrance chamber, but in two other ones takes place in whole of hydrocyclone. Figs. 12 and 13 show the radial oil volume fraction distribution for four different designs in two axial positions, 5 and 200 mm from the top of hydrocyclone respectively. Fig. 12 depicts that the central oil concentration for designs (B) and (C) are higher than design (D) and standard ones; therefore, more separation is occurred in the inlet section of these hydrocyclones. In tapered section (13), the central oil phase fraction for two designs (B) and (C) have been reversed and the separation efficiency is reduced. The results show the hydrocyclone inlet section plays a key role in determination of separation performance.
6.
Conclusion
The influence of four different inlet chamber designs on de-oiling hydrocyclone efficiency was studied by CFD simulation in this work. Three nonstandard inlet chamber designs were simulated and the results have been compared to the simulation results for the standard configuration. Two phase liquid–liquid flow through the hydrocyclone is simulated in this work with algebraic slip mixture multiphase model and RSM turbulence closure in unsteady flow. Moreover, the combination of Hadamard–Rybcynski’s correlation and Rivkind–Ryskin drag correlation as a modified drag correlation for liquid–liquid interaction was employed to estimate the drag force on droplets based on Reynolds number and viscosity ratio of two phases. The simulation results for standard hydrocyclone efficiency demonstrate an acceptable agreement with reported empirical data. The results show that the exponential body form for inlet chamber improves the separation efficiency approximately 8% due to making the higher tangential velocity, lower kinetic energy dissipation, and eliminating the recirculation eddy in inlet chamber with reference to the standard design. Moreover, the modification for standard inlet design based on alternate the conical section instead of cylindrical entrance chamber has an improvement in the separation efficiency approximately 4.5% as a result of lower dissipation rate of kinetic energy due to the wall drag and eliminating the recirculation eddy at the inlet chamber body. Furthermore, the modified quadratic polynomial body shape for inlet chamber decreases the separation efficiency because of creation of lower tangential velocity in inlet chamber and formation the recirculation eddy through the inlet chamber body with regard to the standard design.
References Andrade, V.T.d., Santos, J.F.d., Alegre, R.M., Moreira, M.d.P., 2006. Numerical simulation of oil–water separation in hydrocyclones. In: XXII Interamerican Congress of Chemical Engineering, Interamerican Confederation of Chemical Engineering. Antal, S., Lahey, R., Flaherty, J., 1991. Analysis of phase distribution in fully-developed laminar bubbly two phase flow. Int. J. Multiphase Flow 7, 635–644. Bai, Z., Wang, H., 2006. Numerical simulation of the separating performance of hydrocyclones. Chem. Eng. Technol. 29 (10), 1161–1166.
Belaidi, A., Thew, M.T., 2003. The effect of oil and gas content on the controllability and separation in a de-oiling hydrocyclone. Chem. Eng. Res. Des. 81 (3), 305–314. Belaidi, A., Thew, M.T., Munaweera, S.J., 2003. Hydrocyclone performance with complex oil–water emulsions in the feed. Can. J. Chem. Eng. 81, 1159–1170. Bhaskar, K.U., Murthy, Y.R., Raju, M.R., Tiwari, S., Srivastava, J.K., Ramakrishnan, N., 2007. A study of the fluid dynamic behavior of filtering hydrocyclones. Miner. Eng. 20, 60–71. Cullivan, J.C., Williams, R.A., Cross, C.R., 2003. Understanding the hydrocyclone separator through computational fluid dynamics. Chem. Eng. Res. Des. 81 (4), 455–466. Cullivan, J.C., Williams, R.A., Dyakowski, T., Cross, C.R., 2004. New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics. Miner. Eng. 17, 651–660. Chu, L.Y., Chen, W.M., Lee, X.Z., 2000. Effect of structural modification on hydrocyclone performance. Sep. Purif. Technol. 21, 71–86. Dai, G.Q., Li, J.M., Chen, W.M., 1998. Numerical prediction of the liquid flow within a hydrocyclone. Chem. Eng. J. 74, 217–223. Delgadillo, J.A., Rajamani, R.K., 2006. Exploration of hydrocyclone designs using computational fluid dynamics. Int. J. Miner. Process. 84, 252–261. Delfos, R., Murphy, S., Stanbridge, D., Olujicˇı, Z., Jansens, P.J., 2004. A design tool for optimising axial liquid–liquid hydrocyclones. Miner. Eng. 17 (5), 721–731. Devorak, R.G., 1989. Separation of light dispersions in long hydrocyclones. Master of Science Thesis No. 1338609, Michigan State University. Dyakowski, T., Hornung, G., Williams, R.A., 1994. Simulation of non-Newtonian flow in a hydrocyclone. Chem. Eng. Res. Des. 72 (A4), 513–520. Grady, S.A., Wesson, G.D., Abdullah, M., Kalu, E.E., 2003. Prediction of 10-mm hydrocyclone separation efficiency using computational fluid dynamics. Filtr. Sep. 40 (9), 40–46. Gomez, C., Caldenty, J., Wang, S., 2002. Oil/water separation in liquid/liquid hydrocyclons: part 1—experimental investigation. SPE J. 7, 353–372. Hargreaves, J.H., Silvester, R.S., 1990. Computational fluid dynamics applied to the analysis of de-oiling hydrocyclone performance. Chem. Eng. Res. Des. 68 (4), 365–383. Hsieh, K.T., Rajamani, K., 1988. Phenomenological model of the hydrocyclone: Model development and verification for single-phase flow. Int. J. Miner. Process. 22 (1–4), 223–237. Huang, S., 2005. Numerical simulation of oil–water hydrocyclone using Reynolds-Stress Model for Eulerian multiphase flows. Can. J. Chem. Eng. 83, 829–834. Ishii, M., Hibiki, T., 2006. Thermo Fluid Dynamics of Two-Phase Flow, first ed. Springer Science, New York. Ko, J., Zahrai, S., Macchion, O., Vomhoff, H., 2006. Numerical modeling of highly swirling flows in a through-flow cylindrical hydrocyclone. AIChE J. 52 (10), 3334–3344. Launder, B.E., 1989. Second-moment closure and its use in modeling turbulent industrial flows. Int. J. Numer. Methods Fluids 9 (8), 963–985. Loth, E., 2008. Quasi-steady shape and drag of deformable bubbles and drops. Int. J. Multiphase Flow 34 (6), 523–546. Majumder, A.K., Shah, H., Shukla, P., Barnwal, J.P., 2007. Effect of operating variables on shape of “fish-hook” curves in cyclones. Miner. Eng. 20 (2), 204–206. Malhotra, A., Branion, R.M.R., Hauptman, E.G., 1994. Modelling the flow in a hydrocyclone. Can. J. Chem. Eng. 72, 953–960. Meyer, M., Bohnet, M., 2003. Influence of entrance droplet size distribution and feed concentration on separation of immiscible liquids using hydrocyclones. Chem. Eng. Technol. 26 (6), 660–665. Monredon, T.C., Hsieh, K.T., Rajamani, R.K., 1992. Fluid flow model of the hydrocyclone: an investigation of device dimensions. Int. J. Miner. Process. 35 (1–2), 65–83. Noroozi, S., Hashemabadi, S.H., 2009. CFD simulation of inlet design effect on de-oiling hydrocyclone separation efficiency. Chem. Eng. Technol. 32 (12), 1885–1893.
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Nowakowski, A.F., Kraipech, W., Williams, R.A., Dyakowski, T., 2000. The hydrodynamics of a hydrocyclone based on a three-dimensional multi-continuum model. Chem. Eng. J. 80 (1–3), 275–282. Nowakowski, A.F., Dyakowski, T., 2003. Investigation of swirling flow structure in hydrocyclones. Chem. Eng. Res. Des. 81 (8), 862–873. Paladino, E.E., Nunes, G.C., Schwenk, L., 2005. CFD analysis of the transient flow in a low-oil concentration hydrocyclone. Proc. of the Annual Meeting. AIChE 646–657. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC. Pericleous, K.A., Rhodes, N., 1986. The hydrocyclone classifier—a numerical approach. Int. J. Miner. Process. 17 (1–2), 23–43. Ranade, V.V., 2002. Computational Flow Modeling for Chemical Reactor Engineering, third ed. Academic Press, New York. Rovinsky, L.A., 1995. Application of separation theory design to hydrocyclone. J. Food Eng. 26 (2), 131–146. Rivkind, V.Y., Ryskin, G.M., 1976. Flow structure in motion of spherical drop in fluid medium at intermediate Reynolds numbers. Fluid Dyn. 11 (1), 5–12. Saboni, A., Alexandrova, S., 2002. Numerical study of the drag on a fluid sphere. AIChE J. 48 (12), 2992–2994. Schuetz, S., Mayor, G., Bierdel, M., Piesche, M., 2004. Investigations on the flow and separation behavior of
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hydrocyclones using computational fluid dynamics. Int. J. Miner. Process. 73 (2–4), 229–237. Schutz, S., Gorbach, G., Piesche, M., 2009. Modeling fluid behavior and droplet interactions during liquid–liquid separation in hydrocyclones. Chem. Eng. Sci. 64, 3935–3952. Slack, M.D., Del Porte, S., Engelman, M.S., 2003. Designing automated computational fluid dynamics modeling tools for hydrocyclone design. Miner. Eng. 17, 705–711. Stovin, V.R., Saul, A.J., 1998. A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction. Water Sci. Technol. 37 (1), 285–293. Thew, M.T., Colman, D.A., 1989. Cyclone separator, U.S. Patent 4849107. Versteeg, H.K., Malasekera, W., 1995. An Introduction to Computational Fluid Dynamics, first ed. Prentice Hall Publishing, New York. Yang, I.H., Shin, C.B., Kim, T.H., Kim, S., 2004. A three-dimensional simulation of a hydrocyclone for the sludge separation in water purifying plants and comparison with experimental data. Miner. Eng. 17 (5), 637–641. Young, G.A.B., Wakly, W.D., Taggart, D.L., Andrews, S.L., Worrell, J.R., 1994. Oil–water separation using hydrocyclones: An experimental search for optimum dimensions. J. Pet. Sci. Eng. 11, 37–50.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
CFD analysis of inlet chamber body profile effects on de-oiling hydrocyclone efficiency S. Noroozi, S.H. Hashemabadi ∗ Computational Fluid Dynamics (CFD) Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, 16846 Tehran, Iran
a b s t r a c t In this study the effect of inlet chamber design on de-oiling hydrocyclone efficiency has been investigated numerically with the aim of minimizing the energy loss. To this aim, effects of four different inlet chamber designs (exponential, conical, quadratic polynomial body profile and standard design) on efficiency have been considered. Algebraic slip mixture model and Reynolds Stress Model (RSM) have been employed for prediction of multiphase flow behavior and simulation of turbulent flow through the cyclone respectively. The simulation results for efficiency of standard design demonstrate a proper agreement with reported experimental data. The results show that the separation efficiency can be improved approximately 8% using exponential body shape. The recirculation eddies that exists in the upper section prevents inward radial flow, consequently the efficiency reduces; the simulations illustrate that inlet chamber shape affects on the size of these eddies. More recirculation in hydrocyclone inlet chamber with quadratic polynomial body profile causes minimum separation efficiency. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Hydrocyclone; De-oiling; Computational fluid dynamics; Simulation; Separation efficiency
1.
Introduction
In the recent years applications of long hydrocyclone as a liquid–liquid separator especially in offshore platforms according to recover of oil from oily wastewater (Devorak, 1989; Gomez et al., 2002) and crude oil dewatering (Belaidi et al., 2003) have been extended. The specific features of hydrocyclones such as low maintenance cost due to the lack of moving parts, simple operation, and installation make them suitable and useful devices for separation processes. Investigation of new designs is time consuming and expensive to do by experimentation and very difficult or impossible by analytical methods. On account of this fact, many attempts have been performed numerically for analysis of solid–liquid flow through the cyclones and appropriate results have been compared with the experimental works (Pericleous and Rhodes, 1986; Hsieh and Rajamani, 1988; Monredon et al., 1992; Dyakowski et al., 1994; Malhotra et al., 1994; Stovin and Saul, 1998; Nowakowski et al., 2000; Slack et al., 2003; Nowakowski and Dyakowski, 2003; Schuetz et al., 2004; Yang et al., 2004; Cullivan et al., 2003, 2004; Bhaskar et al.,
∗
2007). Some differences exist between the liquid–liquid (LLHC) and solid–liquid hydrocyclones (SLHC) in terms of operational and geometrical parameters due to low density differences between two liquids in LLHC. The pressure drop between two outlet orifices in SLHC is almost zero, but in LLHC the pressure gradient is not equal in order to create more back flow toward the overflow. Moreover, the liquid–liquid hydrocyclone is made long because of increasing the droplet residence time for better separation (Devorak, 1989). Despite these differences, Delgadillo and Rajamani (2006) applied the same numerical techniques for flow field simulation and separation efficiency estimation for long hydrocyclone in solid–liquid separation. A few CFD simulations of de-oiling hydrocyclones have been reported previously. Hargreaves and Silvester (1990) studied numerically the velocity field and separation efficiency through the long de-oiling hydrocyclone; they applied the ASM (Algebraic Stress Model) and k-ε turbulence models in that order. Grady et al. (2003) employed the RSM turbulence closure and algebraic slip mixture multiphase model for prediction of velocity field and separation efficiency in 10 mm de-oiling hydrocyclone; they compared the results with experimental
Corresponding author. Tel.: +98 21 7724 0376; fax: +98 21 7724 0495. E-mail address: [email protected] (S.H. Hashemabadi). Received 13 December 2009; Received in revised form 5 September 2010; Accepted 29 November 2010 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.11.017
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Nomenclature CD d D E F g k L n p Q Re Rf t u x
drag coefficient [–] diameter [mm] hydrocyclone diameter [mm] de-oiling efficiency [%] interphase momentum transfer term [N m−3 ] gravity acceleration [m/s] viscosity ratio of dispersed phase to continuous phase [–] length [mm] number of phases [–] static pressure [N m−2 ] volume flow rate [l/min] Reynolds number (defined by Eq. (8)) [–] overflow split ratio (Qo /Qin ) [%] time [s] velocity [m/s] coordinates [–]
Greek symbols ˛ volume fraction [%] viscosity [kg/m/s] density [Kg/m3 ] stress tensor [pa] Subscripts c continuous phase d droplet D drift i, j, k coordinate directions in inlet orifice m mixture phase o overflow orifice p dispersed phase S slip u underflow orifice Superscripts l laminar t turbulence
efficiency. Paladino et al. (2005) also applied the same methods for simulation of multiphase flow behavior for low concentration of oil in two inlets hydrocyclone; moreover, they also considered the distribution of droplet diameter in hydrocyclone feed. Huang (2005) used the RSM model for modeling the turbulence flow and Eulerian–Eulerian approach for prediction of two-phase flow behavior for high concentration of oil in feed through the Colman–Thew hydrocyclone type; in addition, Huang (2005) verified his results using the Colman–Thew experimental results in terms of separation efficiency. Noroozi and Hashemabadi (2009) studied numerically the influence of different inlet designs on the de-oiling hydrocyclone efficiency. Their simulations show that the separation efficiency can be improved approximately 10% by a suitable inlet design. Schutz et al. (2009) studied the coalescence and breakage effects in de-watering hydrocyclone utilizing a CFD method. Furthermore, in this study they considered the effect of the structure and two inlets design on the droplets size distribution at outlets.
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For the hydrocyclone flow analysis, there are several variables that have been classified in two groups: (a) dimensional variables, (b) operational and feed stream variables (Young et al., 1994). Due to low spinning flow in cylindrical inlet chamber compared to the other flow regions into the hydrocyclone and higher energy lost for fluid flow because of wall drag (Young et al., 1994), optimization of inlet chamber design can play a crucial role in improving the clarification process. There exist some attempts for optimization of separation efficiency in liquid–liquid hydrocyclone with the aid of geometrical body changes. Thew and Colman (1989) studied experimentally the exponential and cubic profile for whole de-oiling hydrocyclone body. Young et al. (1994) investigated empirically two cylindrical entrance chambers with different length. Chu et al. (2000) took account of the effect of body and inlet chamber design of hydrocyclone on separation efficiency. They studied the energy loss in different sections of SLHC experimentally. Belaidi and Thew (2003) reported the new design for inlet chamber in air sparged de-oiling hydrocyclone. In this new design a conical inlet chamber has been placed instead of the entrance cylindrical part. Delgadillo and Rajamani (2006) employed the numerical simulation for prediction of new designs efficiency with different inlet chamber designs for SLHC and their results were compared with the standard form. In addition, Andrade et al. (2006) considered the separation efficiency of two new inlet chamber designs for Rietema and Bradley hydrocyclone type. They used the small conical part on top of hydrocyclone rather than vortex finder section; they, also, considered the effect of using a static screw with eleven threads rather than the cylindrical part on hydrocyclone efficiency. Due to this fact that the body design of hydrocyclone has great effects on separation efficiency (Chu et al., 2000), this investigation tries to search by CFD simulation the influences of non-standard inlet chamber designs on de-oiling hydrocyclone efficiency that has not reported before. To this goal, influences of three non-standard inlet chamber body designs as well as standard one on dissipation rate of kinetic energy and velocity profile have been discussed in this study.
2.
Problem statements
2.1.
Phase’s interaction modeling
For modeling of multiphase flow behavior and consideration of multiphase interaction, algebraic slip mixture model is employed in this work. Algebraic slip mixture approach for multiphase flow allows one to consider the problem at low computational cost as opposed to Eulerian–Eulerian approach especially when the entrance volume fraction of dispersed phase is very low (lower than 10%) (Paladino et al., 2005). In this model the transport equations are solved for the mixture of phases. The slip velocity (the velocity relative to the continuous phase) and drift velocity (the velocity relative to the mixture average velocity) for each phase are obtained from the fluid properties and local flow conditions. The continuity and momentum equation for the mixture phase can be represented as follow respectively (Paladino et al., 2005; Bai and Wang, 2006):
∂ (m ) + ∇(m um ) = 0 ∂t
(1)
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∂ l t + m ) + m g (m um ) + ∇(m um um ) = −∇p − ∇(m ∂t +F + ∇
n
˛p p uDp uDp
(2)
p=1
where ˛p and uDp are the volume fraction and drift velocity for phase p respectively. The volume fraction equation can be gained from solving the following continuity equation for phase p: ∂ (˛p p ) + ∇(˛p p um ) = −∇(˛p p uDp ) ∂t
(3)
All of the flow properties for mixture flow such as m , m , um can be calculated as follows: n
m =
n
m =
˛p p ,
p=1
n
˛p p ,
p=1
um =
˛p p up
p=1
m
(4)
The drift velocity (uDp ) and slip velocity (uSp ) for each dispersed phase (such as phase p) are represented by the following expression:
uDp = uSp −
n ˛p p p=1
m
uSp
(5)
where uDp = up − um and uSp = up − uc and uc is the velocity for continuous phase. The term of F in Eq. (2) includes all the related phase interaction forces such as lift, virtual mass and drag force. In this work due to the assumptions of spherical shape and small diameter for the droplets the shear-lift force and the lift force caused by slanted wakes can be discounted (Ishii and Hibiki, 2006). Also because of low concentration of oil in feed and therefore very low concentration of dispersed phase in the vicinity of the walls, the wall-lift (wall-lubrication) force has been eliminated (Antal et al., 1991; Ishii and Hibiki, 2006). Moreover, due to low density differences between two liquids virtual mass force is negligible. So the simplified interphase momentum exchange term can be obtained via the following equation (Ranade, 2002):
F=
3˛p ˛c c CD up − uc (up − uc ) 4dd
droplet which can decrease the droplets drag force. Due to this assumption, Hadamard–Rybcynski’s correlation (Saboni and Alexandrova, 2002) is used in this work to estimate the drag coefficient for the creeping flow (Red < 1) that has been recommended in previous literatures in the case of hydrocyclone (Rovinsky, 1995). For estimation of drag coefficient in the Reynolds number range of 1–500 two theoretical based correlations have been examined (Saboni and Alexandrova, 2002; Rivkind and Ryskin, 1976). In this range of Reynolds, two correlations have almost the same prediction, but the Rivikind and Ryskin correlation due to the simpler mathematical form, less computational divergence, and fewer computational costs has been found as better correlation. For high Reynolds numbers (Red > 500), the drag coefficient is constant (set to 0.44). Therefore, the drag coefficient used for calculation of drag force in this work is represented as follows:
CD =
⎧ 8 3k + 2 ⎪ ⎪ ⎨ Red k + 1 1
⎪ ⎪ ⎩ 1+k 0.44
k
Red ≤ 1
24 + 4Red −1/3 Red
+ 14.9Red −0.78
1 < Red ≤ 500
(7)
Red > 500
where the Red is the droplet Reynolds number that can be produced as: Red =
c |uc − up |dd c
(8)
The deformation of droplets due to the small diameter of droplets is ignored (Loth, 2008).
2.2.
Turbulence flow model
Although Reynolds Stress Model (RSM) compared to the other RANS (Reynolds Average Navier–stokes) models is more time consuming, the RSM model has great potential to predict behavior of complex flows such as swirling flow through the hydrocyclone and cyclone accurately (Launder, 1989; Grady et al., 2003; Huang, 2005; Schutz et al., 2009). The RSM model involves calculation of the individual component of turbulence stress tensor using the partial differential transport equation. In this work, the RSM model has been used for simulation of turbulence water–oil two phase flow behavior through the hydrocyclone.
(6)
where dd and CD are droplet diameter and drag coefficient respectively. The value of droplet drag coefficient in liquid–liquid emulsion flows (such as flow through the LLHC) depends on droplet Reynolds number and viscosity ratio k (dispersed phase-to-continuous phase viscosity ratio, k = p /c ) (Rovinsky, 1995; Delfos et al., 2004). For pure droplets with no contaminant, there is a slip flow along the interface which is driven by internal circulation that reduces the drag coefficient (Loth, 2008). On the other hand, if the droplet is contaminated or viscosity ratio approaches to infinity (k > 50) the drag coefficient can be calculated as solid particle due to effectively no-slip condition on particle surface; in this conditions the empirical correlations based on the solid particle assumption such as Schiller–Naumann correlation can be used (Loth, 2008). In this study, it is assumed that the droplets have no contaminant and there is slip flow between the oil drop and water phase that can result in the internal circulation in
3.
Design parameters
Fig. 1 illustrates four different feed chamber designs (A, B, C and D) for de-oiling hydrocyclones that used in this investigation. Table 1 presents geometrical details of these hydrocyclones. All the four hydrocyclones models are fed by two inlets that can be improved the symmetry of flow. Fig. 1A shows the standard de-oiling hydrocyclone with nominal diameter (Ds ) of 20 mm for large diameter of long conical tapered section. The exponential body configuration employed in design (B) instead of cylindrical and reduction conical section in standard design (Fig. 1B). In design (C) the conical section with angle of 20◦ is used instead of entrance cylindrical section in standard design (Fig. 1C); in design (D) the quadratic polynomial body configuration is employed rather than cylindrical and reducing conical section in standard design. All the geometrical parameters with the exception of feed chamber and reducing conical section are same in the four designs.
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Table 1 – Design parameters for three different designs as well as standard design (A). Design (B)
Design (C)
Design (D)
Standard design (A)
Ds (mm) Do /Ds Du /Ds D/Ds Ls /Ds Lu (mm) ˛◦ ˇ◦ ◦
20 0.2 0.5 – – 235 – – 1.5
20 0.2 0.5 2 – 235 15 20 1.5
20 0.2 0.5 – – 235 – – 1.5
20 0.2 0.5 2 2 235 15 – 1.5
Chamber body profile 0 < z < 13 mm
r = 9.083 + 19.43exp( − 2.26z1.15 )
–
r = − 5.43z2 − 78.5z + 29.5
–
Fig. 1 – Geometry details of four de-oiling hydrocyclones with different feed chamber.
4.
Boundary conditions and CFD simulation
The constant mass flow rate (20 l/min) at the inlet boundary surface as a plug flow is employed. By reason of complex flow and hydrocyclone geometry complexity, three tetrahedral mesh densities (250,000, 450,000, and 830,000) in order to take into account of mesh independency for standard typical de-oiling hydrocyclone have been used. Fig. 2 illustrates a graphical representation of the computational mesh. Because of higher phases and velocity gradient in central core, a grid refinement has been done locally. Moreover, for each simulation the mean oil droplet diameter is employed at the entrance boundary. The imposed mass flow rate boundary condition with respect to overflow split
ratio Rf (in this work 17%) as a percentage of inlet mass flow rate are used for outlets (17% exit from overflow and the rest leave the underflow). Furthermore, the overflow orifice of the hydrocyclone is assumed to be fully open to the atmosphere. The wall boundaries are subjected to no slip condition and the standard wall function is applied to near the wall. In this work, finite volume based (Patankar, 1980) in-house CFD code has been used for simulation of two phase flow through the hydrocyclone. The Semi-Implicit Pressure Linked Equations (SIMPLE) algorithm is used for combination of continuity and pressure driven flow equation for two phases to gain the pressure distribution inside the hydrocyclone (Versteeg and Malasekera, 1995). The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) schemes is applied for interpolation of variables from cell centers to faces of control volumes that recommended for higher accuracy in complex flow like in hydrocyclone (Ko et al., 2006; Bhaskar et al., 2007). The simulations are carried out for unsteady state conditions to 100,000 iterations while the variation of governing variable (pressure and velocity components) becomes negligible. The convergence criteria are set to 10−3 except continuity equation and volumetric ratio of oil phase, in which the criteria are 10−5 for continuity and volumetric ratio. All of the simulations in this work for three-dimensional two phase flow through the hydrocyclone were performed on 2 Intel® Xeon® E5335 Quad Core, 2 GHz 8 MB cash CPU with 8 GB RAM.
5.
Results and discussion
5.1.
Model validation
Prior to application the numerical analysis of flow through the different designs of hydrocyclone, it is necessary to validate the models and above mentioned code which are used for simulation. To this aim, the prediction of CFD simulation
Fig. 2 – Unstructured grid for hydrocyclone CFD simulation in two cross sections.
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Fig. 4 – Kinetic energy dissipation rate versus the radial position for different axial distance from the top wall of standard hydrocyclone (design A).
Fig. 3 – Comparison of experimental (Belaidi and Thew, 2003) and numerical simulation results for effect of oil droplet size on separation efficiency in design (A). for separation efficiency is compared to experimental data, reported by Belaidi and Thew (2003) for standard typical deoiling hydrocyclone. The separation efficiency is defined as the ratio of oil overflow flow rate to oil feed flow rate (Gomez et al., 2002): E=
˛o Qo ˛u Qu =1− ˛in Qin ˛in Qin
(9)
As it is shown, the separation efficiency is a factor that is dependent on the velocity profile and pressure field (Eq. (9)), so when the simulation results predict the proper efficiency compared to the experimental work, it almost confirms the CFD results. This criterion used by Grady et al. (2003) and Huang (2005) as a verification factor in case of CFD simulation of flow through the hydrocyclone. Fig. 3 shows the separation efficiency against the mean droplet diameter of oil in the feed entrance flow for the standard design of typical de-oiling hydrocyclone. In this study, three different mesh densities are used for considering the effect of mesh density on prediction of separation efficiency. Fig. 3 illustrates in higher mesh density, mean divergence of results from experimental data are about 8% for fine mesh (830,000 cells) and this deviation increases to about 19% while the mesh density decreases (to about 250,000 cells). Therefore the higher mesh density has better results but computation time is very higher in comparison with the lower mesh case (the computation time ratio for mentioned meshes is 252–72 h with same hardware). Moreover, the results for mesh density of 450,000 cells have good agreement with reported experimental data (approximately 10% deviation) and the computation time is very smaller than the higher mesh. Owing to these results the mesh density of 450,000 tetrahedral cells was found as optimum mesh density. Fig. 3, also, depicts that in very small oil droplets diameter, less than 10 m, overprediction compared to the reported empirical data is gained. It might be attributed to a phenomenon so-called fish hook effect (Majumder et al., 2007), which occurs in the centrifugal devices like hydrocyclones. Because of this phenomenon, the droplet with small diameter is affected by the wake of larger particles and the resulted force moves the smaller droplets
toward the wall. This promotes the drag force and breakage of the small droplets (Grady et al., 2003; Majumder et al., 2007). Consequently, the separation efficiency reduces just as it can be observed in the experimental work. For droplet size larger than 50 m the CFD simulations also show the over-prediction compared to the experimental results (more than 7%). This has been ascribed to the dominant effect of large droplet breakage that occurs in the experimental work (Meyer and Bohnet, 2003). More breakage can decrease the separation efficiency, which has been ignored in this simulation.
5.2. Influence of inlet chamber design on the LLHC efficiency In this work, two issues that play important roles on separation efficiency are considered with changing of the hydrocyclone body profile. The first one is dissipation rate of kinetic energy due to wall drag in different part of hydrocyclone body. Fig. 4 shows the kinetic energy dissipation rate for standard design (Fig. 1A) in radial direction in different axial
Fig. 5 – Radial distribution of kinetic energy dissipation rate for various feed chamber designs at 5 mm from the top.
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Fig. 6 – Schematic diagram of primary and secondary flow pattern in conical hydrocyclone. positions of the hydrocyclone. The results illustrate in all axial position the dissipation rate near the wall is higher than the regions where are closer to axis of hydrocyclone by reason of wall drag. Furthermore, the dissipation rate magnitudes are reduced from the top wall toward the underflow outlet. As it is shown, the flow kinetic energy dissipation rate through the inlet chamber is more than the other sections; therefore optimum design for that (with minimized energy lost) can lead to the higher separation efficiency. Fig. 5 shows the dissipation rate of kinetic energy in radial direction in 5 mm from the top wall of four different inlet
chamber designs. It shows that the dissipation rate is lower than the standard design in three modified designs. Moreover, the energy dissipation rate in design (D) is lower than the designs (B) and (C) that might be related to its special shape in inlet chamber body shape. The second factor is the effect of body shape on flow profile through the hydrocyclone. Fig. 6 shows schematically the different regions of flow which are created through the hydrocyclone. The flow field is divided into primary and secondary flows. The primary flow includes the inner vortex that is caused due to swirl back flow and outer vortex that is resulted
Fig. 7 – Radial distribution of axial velocity for various inlet chamber designs at four positions from the top wall of hydrocyclone.
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Fig. 8 – Velocity vector plot for different designs in longitudinal cross section of inlet chamber.
in swirl flow toward the underflow. Secondary flow consists of the side and end-wall circuit flow which bypasses the hydrocyclone without experiencing the primary flow, and also it contains the recirculation eddy that exists in the upper section and prevents inward radial flow across its boundaries (Devorak, 1989; Dai et al., 1998). The migration of droplets to central zone of the hydrocyclone can be avoided by recirculation eddies in inlet chamber, consequently with increasing the size of these vortex, the separation efficiency of hydrocyclone can be decreased. Fig. 7 presents the axial velocity profile at four different positions from the top wall in four different hydrocyclones. The positive axial velocities indicate backflow at the central zone of the hydrocyclones and the negative axial velocities present downward flow near the walls. The results clearly show that the backflow zone decreases from overflow (20 mm) to underflow (240 mm) for all designs. In addition, the results illustrate that in standard design and design (D) the axial velocity profile has two positive regions in upper sections, one in the central zone and the other one is located between wall and central core. This phenomenon is related to the presence of recirculation eddy in top regions in these two designs. Indeed, this eddy recirculation in standard design is created only in cylindrical section, and in design (D) is created in all inlet chamber body. On the other hand, this phenomenon is not seen in two other designs which reveal that the recirculation eddy is omitted in these two designs because of their special body designs. Fig. 8 presents the velocity vector plot in
Fig. 9 – Radial distribution of tangential velocity for various inlet chamber designs at four positions from the top wall of the hydrocyclone.
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Fig. 10 – De-oiling hydrocyclone separation efficiency versus mean droplet diameter for various inlet chamber designs. longitudinal cross section of inlet chambers for four different designs. This figure shows vividly that the recirculation eddy in standard design is reduced in size for design (C) and almost is removed in design (B). In contrast, the recirculation eddy region is improved in design (D) compared to standard one. The swirling fluid flow through the hydrocyclone and separation efficiency can be affected directly by tangential velocity. Fig. 9 illustrates the radial distribution of tangential velocity at four different distances from the top wall of hydrocyclone for different inlet chamber designs (Fig. 1). It is shown the tangential velocity profile in designs (B) and (C) is higher than two other designs which results in the higher centrifugal forces. Consequently, the separation efficiency increases for oily water clarification process in these two designs. That might be attributed to the effect of body design in inlet chamber section and lower energy dissipation rate with reference to the standard design. Despite the minor kinetic energy dissipation rate in design (D), the tangential velocity is lower than the other designs that can be related to dominate effect of inlet chamber form on tangential velocity profile. Fig. 10 shows the separation efficiency versus various mean droplet diameter at the hydrocyclone’s feed for different
Fig. 11 – Distribution of dispersed phase (oil) volume fraction in four different designs.
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Fig. 12 – Radial distribution of dispersed phase (oil) volume fraction in four different designs at 5 mm from the top. designs (Fig. 1). For mean oil droplet size larger than 100 m in feed, the efficiency for whole hydrocyclones approaches to 100%. Furthermore, the results depict that designs (B) and (C) have higher efficiency due to the higher tangential velocity compared to the standard design (Fig. 9). These results demonstrate the improving effect of the proposed modifications to inlet chambers for the standard de-oiling hydrocyclone design. According to Fig. 10 the separation efficiency for standard design is higher than that for design (D) and this modification reduces the clarification performance. These results demonstrate that for enhancement of de-oiling efficiency, the hydrocyclone with design (D) is not a good option for experimentation. The accumulation and shift of oil to the axis of hydrocyclone and migration of water phase toward the wall in four different designs (Fig. 1) is visualized well in Fig. 11. Fig. 11 shows the contour of volume fraction for oil phase in a longitudinal cross section of hydrocyclone. The range of colors from red to blue represents oil and water volume fractions
Fig. 13 – Radial distribution of dispersed phase (oil) volume fraction in four different designs at 200 mm from the top.
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(for example red color shows oil concentrated regions), respectively. The results illustrate the maximum separation of oil from water phase in designs (B) and (C) occurs in entrance chamber, but in two other ones takes place in whole of hydrocyclone. Figs. 12 and 13 show the radial oil volume fraction distribution for four different designs in two axial positions, 5 and 200 mm from the top of hydrocyclone respectively. Fig. 12 depicts that the central oil concentration for designs (B) and (C) are higher than design (D) and standard ones; therefore, more separation is occurred in the inlet section of these hydrocyclones. In tapered section (13), the central oil phase fraction for two designs (B) and (C) have been reversed and the separation efficiency is reduced. The results show the hydrocyclone inlet section plays a key role in determination of separation performance.
6.
Conclusion
The influence of four different inlet chamber designs on de-oiling hydrocyclone efficiency was studied by CFD simulation in this work. Three nonstandard inlet chamber designs were simulated and the results have been compared to the simulation results for the standard configuration. Two phase liquid–liquid flow through the hydrocyclone is simulated in this work with algebraic slip mixture multiphase model and RSM turbulence closure in unsteady flow. Moreover, the combination of Hadamard–Rybcynski’s correlation and Rivkind–Ryskin drag correlation as a modified drag correlation for liquid–liquid interaction was employed to estimate the drag force on droplets based on Reynolds number and viscosity ratio of two phases. The simulation results for standard hydrocyclone efficiency demonstrate an acceptable agreement with reported empirical data. The results show that the exponential body form for inlet chamber improves the separation efficiency approximately 8% due to making the higher tangential velocity, lower kinetic energy dissipation, and eliminating the recirculation eddy in inlet chamber with reference to the standard design. Moreover, the modification for standard inlet design based on alternate the conical section instead of cylindrical entrance chamber has an improvement in the separation efficiency approximately 4.5% as a result of lower dissipation rate of kinetic energy due to the wall drag and eliminating the recirculation eddy at the inlet chamber body. Furthermore, the modified quadratic polynomial body shape for inlet chamber decreases the separation efficiency because of creation of lower tangential velocity in inlet chamber and formation the recirculation eddy through the inlet chamber body with regard to the standard design.
References Andrade, V.T.d., Santos, J.F.d., Alegre, R.M., Moreira, M.d.P., 2006. Numerical simulation of oil–water separation in hydrocyclones. In: XXII Interamerican Congress of Chemical Engineering, Interamerican Confederation of Chemical Engineering. Antal, S., Lahey, R., Flaherty, J., 1991. Analysis of phase distribution in fully-developed laminar bubbly two phase flow. Int. J. Multiphase Flow 7, 635–644. Bai, Z., Wang, H., 2006. Numerical simulation of the separating performance of hydrocyclones. Chem. Eng. Technol. 29 (10), 1161–1166.
Belaidi, A., Thew, M.T., 2003. The effect of oil and gas content on the controllability and separation in a de-oiling hydrocyclone. Chem. Eng. Res. Des. 81 (3), 305–314. Belaidi, A., Thew, M.T., Munaweera, S.J., 2003. Hydrocyclone performance with complex oil–water emulsions in the feed. Can. J. Chem. Eng. 81, 1159–1170. Bhaskar, K.U., Murthy, Y.R., Raju, M.R., Tiwari, S., Srivastava, J.K., Ramakrishnan, N., 2007. A study of the fluid dynamic behavior of filtering hydrocyclones. Miner. Eng. 20, 60–71. Cullivan, J.C., Williams, R.A., Cross, C.R., 2003. Understanding the hydrocyclone separator through computational fluid dynamics. Chem. Eng. Res. Des. 81 (4), 455–466. Cullivan, J.C., Williams, R.A., Dyakowski, T., Cross, C.R., 2004. New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics. Miner. Eng. 17, 651–660. Chu, L.Y., Chen, W.M., Lee, X.Z., 2000. Effect of structural modification on hydrocyclone performance. Sep. Purif. Technol. 21, 71–86. Dai, G.Q., Li, J.M., Chen, W.M., 1998. Numerical prediction of the liquid flow within a hydrocyclone. Chem. Eng. J. 74, 217–223. Delgadillo, J.A., Rajamani, R.K., 2006. Exploration of hydrocyclone designs using computational fluid dynamics. Int. J. Miner. Process. 84, 252–261. Delfos, R., Murphy, S., Stanbridge, D., Olujicˇı, Z., Jansens, P.J., 2004. A design tool for optimising axial liquid–liquid hydrocyclones. Miner. Eng. 17 (5), 721–731. Devorak, R.G., 1989. Separation of light dispersions in long hydrocyclones. Master of Science Thesis No. 1338609, Michigan State University. Dyakowski, T., Hornung, G., Williams, R.A., 1994. Simulation of non-Newtonian flow in a hydrocyclone. Chem. Eng. Res. Des. 72 (A4), 513–520. Grady, S.A., Wesson, G.D., Abdullah, M., Kalu, E.E., 2003. Prediction of 10-mm hydrocyclone separation efficiency using computational fluid dynamics. Filtr. Sep. 40 (9), 40–46. Gomez, C., Caldenty, J., Wang, S., 2002. Oil/water separation in liquid/liquid hydrocyclons: part 1—experimental investigation. SPE J. 7, 353–372. Hargreaves, J.H., Silvester, R.S., 1990. Computational fluid dynamics applied to the analysis of de-oiling hydrocyclone performance. Chem. Eng. Res. Des. 68 (4), 365–383. Hsieh, K.T., Rajamani, K., 1988. Phenomenological model of the hydrocyclone: Model development and verification for single-phase flow. Int. J. Miner. Process. 22 (1–4), 223–237. Huang, S., 2005. Numerical simulation of oil–water hydrocyclone using Reynolds-Stress Model for Eulerian multiphase flows. Can. J. Chem. Eng. 83, 829–834. Ishii, M., Hibiki, T., 2006. Thermo Fluid Dynamics of Two-Phase Flow, first ed. Springer Science, New York. Ko, J., Zahrai, S., Macchion, O., Vomhoff, H., 2006. Numerical modeling of highly swirling flows in a through-flow cylindrical hydrocyclone. AIChE J. 52 (10), 3334–3344. Launder, B.E., 1989. Second-moment closure and its use in modeling turbulent industrial flows. Int. J. Numer. Methods Fluids 9 (8), 963–985. Loth, E., 2008. Quasi-steady shape and drag of deformable bubbles and drops. Int. J. Multiphase Flow 34 (6), 523–546. Majumder, A.K., Shah, H., Shukla, P., Barnwal, J.P., 2007. Effect of operating variables on shape of “fish-hook” curves in cyclones. Miner. Eng. 20 (2), 204–206. Malhotra, A., Branion, R.M.R., Hauptman, E.G., 1994. Modelling the flow in a hydrocyclone. Can. J. Chem. Eng. 72, 953–960. Meyer, M., Bohnet, M., 2003. Influence of entrance droplet size distribution and feed concentration on separation of immiscible liquids using hydrocyclones. Chem. Eng. Technol. 26 (6), 660–665. Monredon, T.C., Hsieh, K.T., Rajamani, R.K., 1992. Fluid flow model of the hydrocyclone: an investigation of device dimensions. Int. J. Miner. Process. 35 (1–2), 65–83. Noroozi, S., Hashemabadi, S.H., 2009. CFD simulation of inlet design effect on de-oiling hydrocyclone separation efficiency. Chem. Eng. Technol. 32 (12), 1885–1893.
chemical engineering research and design 8 9 ( 2 0 1 1 ) 968–977
Nowakowski, A.F., Kraipech, W., Williams, R.A., Dyakowski, T., 2000. The hydrodynamics of a hydrocyclone based on a three-dimensional multi-continuum model. Chem. Eng. J. 80 (1–3), 275–282. Nowakowski, A.F., Dyakowski, T., 2003. Investigation of swirling flow structure in hydrocyclones. Chem. Eng. Res. Des. 81 (8), 862–873. Paladino, E.E., Nunes, G.C., Schwenk, L., 2005. CFD analysis of the transient flow in a low-oil concentration hydrocyclone. Proc. of the Annual Meeting. AIChE 646–657. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC. Pericleous, K.A., Rhodes, N., 1986. The hydrocyclone classifier—a numerical approach. Int. J. Miner. Process. 17 (1–2), 23–43. Ranade, V.V., 2002. Computational Flow Modeling for Chemical Reactor Engineering, third ed. Academic Press, New York. Rovinsky, L.A., 1995. Application of separation theory design to hydrocyclone. J. Food Eng. 26 (2), 131–146. Rivkind, V.Y., Ryskin, G.M., 1976. Flow structure in motion of spherical drop in fluid medium at intermediate Reynolds numbers. Fluid Dyn. 11 (1), 5–12. Saboni, A., Alexandrova, S., 2002. Numerical study of the drag on a fluid sphere. AIChE J. 48 (12), 2992–2994. Schuetz, S., Mayor, G., Bierdel, M., Piesche, M., 2004. Investigations on the flow and separation behavior of
977
hydrocyclones using computational fluid dynamics. Int. J. Miner. Process. 73 (2–4), 229–237. Schutz, S., Gorbach, G., Piesche, M., 2009. Modeling fluid behavior and droplet interactions during liquid–liquid separation in hydrocyclones. Chem. Eng. Sci. 64, 3935–3952. Slack, M.D., Del Porte, S., Engelman, M.S., 2003. Designing automated computational fluid dynamics modeling tools for hydrocyclone design. Miner. Eng. 17, 705–711. Stovin, V.R., Saul, A.J., 1998. A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction. Water Sci. Technol. 37 (1), 285–293. Thew, M.T., Colman, D.A., 1989. Cyclone separator, U.S. Patent 4849107. Versteeg, H.K., Malasekera, W., 1995. An Introduction to Computational Fluid Dynamics, first ed. Prentice Hall Publishing, New York. Yang, I.H., Shin, C.B., Kim, T.H., Kim, S., 2004. A three-dimensional simulation of a hydrocyclone for the sludge separation in water purifying plants and comparison with experimental data. Miner. Eng. 17 (5), 637–641. Young, G.A.B., Wakly, W.D., Taggart, D.L., Andrews, S.L., Worrell, J.R., 1994. Oil–water separation using hydrocyclones: An experimental search for optimum dimensions. J. Pet. Sci. Eng. 11, 37–50.