Design methodology for the swirl separator

Aquacultural Engineering 33 (2005) 21–45 www.elsevier.com/locate/aqua-online

Design methodology for the swirl separator Jayen P. Veerapen*, Brian J. Lowry, Michel F. Couturier Department of Chemical Engineering, University of New Brunswick, P.O. Box 4400, 15 Dineen Drive, Fredericton, NB, Canada E3B 5A3 Received 31 May 2004; accepted 1 November 2004

Abstract A methodology is proposed for designing the swirl separators that are commonly used for removing waste solids in recirculating aquaculture systems. The size of the swirl separator is calculated based on the desired solids removal efficiency and the water flow rate to be treated. The approach was validated by performing experiments on swirl separators with diameters of 0.6 and 1.5 m and by carrying out CFD simulations. Results show that tank height and the position of the inlet have a minor influence on separation performance compared to outlet geometry, inlet diameter and tank diameter. It is also shown that solids separation is mainly due to gravity rather than centrifugal forces. Separation follows closely the theory of sedimentation in well-mixed systems and can be predicted using a simple analytical model. The swirl flow generates relatively strong horizontal mixing but relatively weak axial mixing. As a result, particles are uniformly distributed across the tank, and separation is mainly by sedimentation. The settling velocity of the particles was accurately predicted by a new correlation that takes particle shape into account. # 2004 Elsevier B.V. All rights reserved. Keywords: Swirl separator; Aquaculture; Solids removal; Wastewater

1. Introduction As suspended solids adversely impact all aspects of a recirculating aquaculture system, the primary objective of any recirculating treatment scheme is the removal of solid wastes (Timmons et al., 2001). Various solids removal strategies are used in the aquaculture * Corresponding author. E-mail addresses: [email protected] (J.P. Veerapen), [email protected] (B.J. Lowry), [email protected] (M.F. Couturier). 0144-8609/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaeng.2004.11.001

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industry (Lawson, 1995; Ebeling, 2000). In this work, we focus on the operation and design of the swirl separator. Swirl separators are cylindrical vessels with a conical base. Water laden with particulate waste from the culture tank enters the separator tangentially and generates a swirling flow. A fraction of the flow exits through the bottom of the unit and is called the underflow (Lawson, 1995). Ideally, the underflow contains most of the solid waste. The remaining fraction, consisting mainly of clear water, exits at the top and is called the overflow (Lawson, 1995). The separator is generally operated with no continuous underflow. The bottom drain is instead opened intermittently to flush out solids. Fish faecal matter has a density of about 1050–1080 kg/m3 (Timmons et al., 2001; Brooks, 2001) and fish feed a density of about 1150–1200 kg/m3 (Patterson et al., 2002; Brooks, 2001). Chen et al., 1993 reported an average density of 1190 kg/m3 for particles present in fish culture water while Patterson et al. (2002) reported a range of 1050–1160 kg/ m3. The low density-difference with respect to water (about 1000 kg/m3 for freshwater), combined with the fact that aquacultural waste has a wide size distribution, make the separation of aquacultural solids more challenging. It is the purpose of this study to provide a better understanding of the underlying separation mechanisms in swirl separators, and to develop guidelines for designing and operating swirl separators. Experiments were performed on 0.6 and 1.5 m swirl separators, with plastic particles having properties similar to those of aquacultural waste. CFD simulations were employed to confirm experimental trends. The insight afforded by the experiments and the simulations allowed us to derive an analytical model for separation, based on sedimentation and turbulent dispersion.

2. Literature review Static separators, based on swirling flow, are simple and relatively inexpensive to manufacture and operate, which accounts for their widespread use, in a wide spectrum of industries. These include: stormwater treatment (U.S. E.P.A., 1999; Konı´e`ek et al., 1996; Villeneuve and Gaume, 1994; Sullivan et al., 1978, 1982), industrial dedusting (Hoffmann et al., 2001; Hoekstra et al., 1999), powder coating (Thorn, 1998) and pulp and paper (Sevilla and Branion, 1997). Much research has been done on the solid–liquid hydrocyclone. In the aquaculture industry, swirl separators are sometimes referred to as hydrocyclones. However, the swirl separator as operated in the aquaculture industry is significantly different from conventional hydrocyclones. Though both have a similar structure with a cono-cylindrical body, a tangential inlet and bottom and top outlets, they differ in dimension. Hydrocyclones tend to have a diameter of the order of a few centimetres (Chen et al., 2000; Svarovsky, 1984) while swirl separators generally have diameters on the order of a metre. The pressure drop across hydrocyclones is also much larger than across swirl separators. The high pressure drops in hydrocyclones are achieved by high inlet velocities which give rise to large shearing forces. These should be avoided in swirl separators because they break wastes into smaller particles that are more difficult to remove. Though the design of hydrocyclones has been the subject of several studies (including those by Castilho and Medronho, 2000; Chen et al., 2000 and Svarovsky, 1984), the differences between

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conventional hydrocyclones and swirl separators makes it impractical to apply these results to the swirl separator. In particular, swirl separators as considered here are dilute systems (<1% volume fraction solids) with more moderate flows than conventional hydrocyclones. The research performed on the swirl-based separators used in the treatment of municipal wastewater is more relevant to the swirl separator used in the aquaculture industry. The equipment is an analogue of the swirl separator: a cylinder-like body with a tangential inlet and top and bottom outlets. The US Environmental Protection Agency (EPA) carried out an investigation (Sullivan et al., 1978) on what was termed the swirl primary separator, to determine the viability of using the ‘swirl concentrator’ principle for primary treatment of municipal wastewater. Villeneuve and Gaume, 1994 studied the Quebec swirl regulator to assess its performance with respect to treatment of storm water. Konı´e`ek et al. (1996) investigated vortex flow separators in the Czech Republic, again as regards storm water. These designs seem appropriate for aquaculture. However, as Konı´e`ek et al. (1996) state, though there are several swirl-based separators in the world, operation data and performance are rarely available. Moreover, when such data are reported, generally there is a lack of agreement between the definition of the reported parameters so that comparison is challenging. Also, due to the presence of grit which has a specific gravity of 2.65, these systems typically handle suspended solids with a mean specific gravity much greater than that of the solids encountered in recirculating aquaculture. Swirl separators have been given various names in aquaculture literature, including hydrocyclone (Timmons et al., 2001; Ebeling, 2000), tea-cup settler (Timmons et al., 2001), hydroclone (Lawson, 1995; Wheaton, 1977), cyclone (Lawson, 1995), sludge collector or settling cone (Losordo et al., 2000, Twarowska, 1997). Though the swirl separator is mentioned in several aquaculture publications, no study has been found in the aquaculture literature specifically geared towards design guidelines. Wheaton (1977), Lawson (1995) and Timmons et al. (2001) do have sections of their respective books devoted to the swirl separator. However, these are a summary of previous work on conventional hydrocyclones and of empirical knowledge of the swirl separator. Other authors (Twarowska et al., 1997; Ebeling, 2000, Losordo et al., 2000) mention the use of swirl separators as components of recirculating aquaculture systems though this is not their primary focus.

3. Materials and methods 3.1. Experiments The flow loop used for the experiments is shown schematically in Fig. 1. It consisted of a swirl separator, a 0.8 m3 water storage tank, a 0.75 kW centrifugal pump and a particle injection system. Water was pumped from the reservoir to the swirl separator and returned by gravity to the storage tank via the underflow and overflow outlets of the separator. The flow split between the two outlets was adjusted using the valve on the underflow line. The flow out of each outlet was measured by placing a bucket at the end and letting a known volume of water accumulate over a known period of time of at least 10 s. Two measurements were made and the average calculated. The volume was determined by

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Fig. 1. Experimental set-up.

weight measurement. The total inlet flow was checked against the reading of the flowmeter (rotameter) as shown in Fig. 1. Experiments were carried out with the underflow set at either 0, 10, 20 or 40% of the total flow. The total flow was controlled using the regulating valve located downstream of the centrifugal pump. Flow rate values tested ranged from 40 to 170 l/min (LPM). Acrylic particles with densities similar to those of faeces and feed were injected as a dilute mixture into the inlet stream using a peristaltic pump. Five-micron bag filters placed on each outlet, trapped the particles. The experimental trap efficiency was determined by weighing the (dried) filters before and after each experiment. Trap efficiency was calculated as: h¼

Mu Mi

(1)

where Mu is the amount of particles in the underflow and Mi is the amount of particles in the inlet stream. Three classes of acrylic particles (Table 1) were used. The particles were Table 1 Properties of plastic particles (spheres) No.

1 2 3

Type

Poly(methylmethacrylate) Copolymer of methylmethacrylate and n-butylmethacrylate Copolymer of methylmethacrylate and n-butylmethacrylate

Size (mm)

Mean size (mm)

Density (kg/m3)

Settling velocity, us (mm/s) Experiment

Using Eqs. (29), (30), (34)

200 300–350

200 325

1180 1070

4.0  0.1 3.4  0.4

3.6 3.6

350–420

385

1060

4.1  0.4

4.2

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Table 2 Swirl separator dimensions Description

Symbol

Dimensions (cm) Small swirl separator

Large swirl separator

Tank diameter Tank height Cone height Inlet diameter Inlet height Outlet diameter

Dt Ht Hc Di Hi Do

62a 28, 56a 25a 3.8, 7.6a 5a, 28, 48 3.8a

150 75 0 3.8 35 3.8

a

Denotes the base swirl separator dimensions.

chosen so that their density (1060–1180 kg/m3) is close to reported densities for particulate wastes in fish culture water. Only one type of particles was used in a given experiment. Each experiment required about 400 g of particles. The particles were mixed in about 2 L of water prior to injection and were kept in suspension by a mixer while the mixture was pumped at a constant rate into the inlet stream. Particles collected at the base of the separator were flushed into the filter at the end of each experiment by fully opening the valve on the underflow outlet. The total mass of particles recovered in the two filters was always very close to the mass injected, indicating negligible loss within the system. The base swirl separator configuration consisted of a 0.6 m swirl separator with the base dimensions given in Table 2 and operated at a base flow rate of 100 LPM, with no continuous underflow. During the series of experiments, the dimensions of the swirl separator, the inlet flow rate and the underflow rate were varied from the base case to study their respective influence on the separation performance. The dimensions of the swirl separator that were believed to have an influence on separator performance are indicated in Fig. 2. The effect of tank diameter Dt was determined by repeating some experiments on a 1.5 m swirl separator, whereas the effects

Fig. 2. Schematic of swirl separator with disc outlet.

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Fig. 3. 1/2-pipe and 3/4-pipe outlets, respectively. The arrows represent flow direction.

of tank height Ht, inlet diameter Di and inlet height Hi were determined by modifying the dimensions of the 0.6 m separator. A summary of the dimensions tested is given in Table 2. Various structures were also used as overflow outlet:    

Central-pipe outlet: vertical pipe along the swirl separator axis open at top (Fig. 1). Disc outlet: a circular (diameter = 47 cm) spill plate atop the axial pipe (Fig. 2). 1/2-pipe and 3/4-pipe outlets (Fig. 3). Side and center–side outlets (Fig. 4).

4. CFD modeling CFD modeling of the swirl separator was also performed. The first step of the modeling work consisted in generating a mesh of tetrahedral elements for the swirl separator (Fig. 5). The mesh consisted approximately of 200,000 elements. It was chosen such that the grid is finest where velocity gradients are largest. While the overall number of elements is constrained by computer memory and processor speed, tests were conducted with various distributions of elements (e.g. finer grid at the inlet versus the outlets). These tests demonstrated that grid refinement at the outlets was most crucial. This can be explained by considering that modeling the flow along the inlet pipe is modeling flow along a straight horizontal pipe which is more straightforward than modeling the complex swirling flow in TM TM the cylindrical section. Fluid flow was simulated using FLUENT . FLUENT applies the finite volume method to solve the steady–state continuity and Navier–Stokes equations for incompressible flow (Versteeg and Malalasekera, 1995; Fluent Inc., 2001). The Reynolds Stress Model (Pope, 2001) was used to account for turbulence. The Reynolds Stress Model is more appropriate for modeling anisotropic dispersion than the k-e model and its variants

Fig. 4. Side and center–side outlets.

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Fig. 5. Swirl separator mesh.

(Pope, 2001). In the modeled swirl separator, the Reynolds Stress Model simulates the transition between the inlet jet and swirling flow better than the alternatives. The flow simulation required about 15 h on a 1.8 GHz Pentium 4 processor-512 MB RAM computer. Once the flow field throughout the domain was computed, computational particles whose density and size could be assigned at will, were released from the inlet and tracked. As the volume fraction of particles is very small, particles are tracked based on an uncoupled approach whereby their presence does not impact the fluid flow. Tracks are computed by integrating the drag, gravitational and inertial forces acting on spherical particles in a Lagrangian frame of reference. The particles reaching the bottom outlet were deemed TM trapped and the rest considered escaped. Particle tracking is fast with FLUENT and 1000 particles could be tracked in less than 5 min once the flow field had been computed. A final step of the modeling was the post-processing which consisted in displaying fluid velocity vectors (Fig. 6) and particle tracks (Fig. 7) among other quantities to check whether the results were realistic. It should be noted that all the simulations reported herein pertain to swirl separators with a disc outlet. Because of the difficulty to model a free surface, the horizontal, annular surface between the vertical swirl separator wall and the horizontal disc was defined as an outlet plane for the water and as an escape surface for the particles.

5. Theoretical analysis 5.1. Trap efficiency of swirl separators The experiments and simulations allowed us to identify two fundamental processes affecting separation in the swirl separator: sedimentation (settling) and turbulent dispersion. Based on this finding, a simple analytical model can be derived to describe the separation. We first proceed by considering a simplified one dimensional view of the fate of

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Fig. 6. Simulated fluid velocity vectors.

Fig. 7. Simulated particle tracks (six displayed).

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Fig. 8. Analytical model description.

particles entering the swirl separator at a point located at a distance Hi above the base of the cylindrical section (Fig. 8). The flux, n of particles of diameter dp at a particular point in the unit is given by n ¼ j þ Cup

(2)

where j is the flux due to turbulent dispersion, C is the particle concentration, and up is the axial (vertical) velocity of the particles. While the first term on the right hand side of Eq. (2) represents the flux contribution due to turbulence, the second term represents the bulk particle flow. As the concentration of particles inside the swirl separator is low enough to neglect particle–particle interactions, the velocity, up is given by
uu þ us for 0  z < Hi up ¼ (3) uo  us for Hi < z  Ht where us is the terminal settling velocity of the particles, uu is the mean downward water velocity and uo is the mean upward water velocity. The water velocities are given by uu ¼ RQ=A

and

uo ¼ ð1  RÞQ=A

(4)

where Q/A is the surface loading and R is the split R¼

Qu Q

(5)

In the above equations, Q is the inlet flow rate, Qu is the underflow rate and A is the tank cross-sectional area. Therefore,
us  RQ=A for 0  z < Hi up ¼ (6) us þ ð1  RÞQ=A for Hi < z  Ht

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The dispersion flux is dC (7) dz where E is the turbulence dispersion coefficient. Therefore, the particle fluxes below and above the inlet are given, respectively, by dC nu ¼ E Cðus þ RQ=AÞ for 0  z < Hi (8) dz dC þC½us þ ð1  RÞQ=A for Hi < z  Ht no ¼ E (9) dz Based on the definition of trap efficiency Eq. (1), hmi ð1  hÞmi nu ¼  and no ¼ (10) A A where mi is the inlet particle mass flow rate. Substituting in Eqs. (8) and (9), j ¼ E

dC Cðus þ RQ=AÞ hmi =A þ ¼ for 0  z < Ht dz E E dC C½us þ ð1  RÞQ=A ð1  hÞmi =A þ ¼ for dz E E The boundary conditions are  dC  ¼0 dz z¼0

(11) Hi  z < Ht

(12)

(13)

and dC j  CðHt Þus ¼ 0 (14) dz z¼Ht Eq. (13) was determined by assuming that the flux at the base (z = 0) is due to sedimentation and bulk flow only. Eq. (14) results from the requirement that there be no step change in concentration at the outlet, that is  dC  no ¼ CðHt Þuo ¼ E  þCðHt Þðus þ uo Þ (15) dz E

z¼Ht

When E is independent of position, the solution of the above ordinary differential equations is CðzÞ ¼ h and

mi =Q fþR

for

0  z  Hi


 mi =Q f ðf þ R  1ÞðHt  zÞQ=A CðzÞ ¼ ð1  hÞ 1 exp ð1  R  fÞ 1R E for

(16)

(17)

Hi  z  Ht

where us (18) Q=A For the case of no underflow f is the ratio of settling velocity to the mean upward velocity in the tank, Q/A. In the absence of any vertical mixing, particles would settle for f > 1 and f¼

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rise for f < 1. As settling velocity is a function of particle size, particle shape, particle density, fluid viscosity and fluid density, f accounts for these factors. The concentrations predicted by Eqs. (16) and (17) must be the same at z = Hi. This condition leads to the following expression for the trap efficiency: h¼

1  R  f exp½aðf þ R  1Þ

1R f exp½aðf þ R  1Þ

fþR

(19)

where ðHt  Hi ÞQ=A (20) E Eq. (19) predicts that the trap efficiency is a function of three dimensionless parameters: f, R and a. Since the inlet region was assumed to be a perfect flow divider, the trap efficiency increases as R increases and tends to 100% as R approaches unity. The parameter a characterizes the extent of mixing due to turbulence. Two limits are of interest. When a = 0, turbulent dispersion is high and the system is well-mixed. Under this condition, Eq. (19) reduces to f hr ¼ ða ¼ 0Þ (21) fþ1 where hr is the reduced trap efficiency (Svarovsky, 1984) defined as hR (22) hr ¼ 1R When a!1, separation is governed by settling only and Eq. (19) reduces to h¼fþR (23) a¼

Eq. (23) is identical to the upper limit derived by Sullivan et al. (1978) using a different approach. Like Eq. (19), Eq. (23) is only valid for values of h less than unity. Particle size and density and fluid properties affect trap efficiency through their effect on the settling velocity, contained in f. A simple equation for calculating the settling velocity of spherical particles is presented in the next section. 5.2. Determination of us When a particle of diameter, dp and density, rp reaches its terminal settling velocity, us the weight of the particle must equal the drag force exerted by the fluid of density rf, on the particle. The terminal settling velocity is then given by (Rhodes, 1999):  1=2 4 dp gðrp  rf Þ (24) us ¼ 3 rf CD where CD is the drag coefficient and g is acceleration due to gravity. The drag coefficient for particles has been determined as a function of the particle Reynolds number by Levenspiel, 1984. Levenspiel’s graphical correlation has two asymptotes, at low Reynolds numbers (Re < 0.3) 24 CD ¼ ðStokes0 lawÞ (25) Re

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whereas at large Reynolds numbers (1000 < Re < 100,000) CD ffi CDN ðCÞ ðNewton0 s lawÞ

(26)

where C is the sphericity. As indicated by Eqs. (25) and (26), shape affects drag coefficient far more at large Reynolds numbers than in the region where Stokes’ law is valid. The Reynolds number, Re is defined as Re ¼

dp r f us m

(27)

with m being the dynamic viscosity of the fluid. The sphericity, C of a particle is defined as the ratio of the surface area of a sphere of volume equal to that of the particle, to the surface area of the particle. For non-spherical particles, dp is the equal-volume sphere diameter, i.e. the diameter of the sphere having the same volume as that of the particle. The value of CDN reached by the drag coefficient within the Newton’s range is nearly independent of Reynolds number but a strong function of sphericity. As shown in Fig. 9, the CDN values reported by Levenspiel, 1984 are well correlated by CDN ¼ 34:8 exp ð4:26cÞ

(28)

The determination of us as a function of dp must be by trial and error if Eq. (24) is solved using the graphical correlation (CD = f(Re, C)) of Levenspiel, 1984. A direct solution can, however, be obtained if the dimensionless group us (29) Nu ¼ ðRe=CD Þ1=3 ¼ ½4mgðrp  rf Þ=3r2f 1=3

Fig. 9. Correlation between CDN and C.

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Fig. 10. Nu vs. Nd.

is plotted versus the dimensionless group Nd ¼ ðRe2 CD Þ1=3 ¼

½3m2 =4r

dp f gðrp  rf Þ

(30)

as shown in Fig. 10. Fig. 10 covers the range of Reynolds numbers from 102 to 105 and each of its coordinates contains only one of the two variables us and dp. The two asymptotes (Eqs. (25), (26)) when expressed in terms of Nu and Nd become, respectively, Nu ¼

Nd2 24

at low Nd



1=2

(31)

and Nu ¼

Nd CDN

at large Nd

(32)

Churchill and Usagi, 1972 have proposed a simple equation for correlating the rates of transfer of processes which vary uniformly between two asymptotic solutions. Applying their correlation to the asymptotes (Eqs. (31), (32)) the following equation is obtained: (  n "   #n )1=n Nd2 Nd 1=2 Nu ¼ þ (33) 24 CDN Eq. (33) was fitted to the data of Levenspiel, 1984 and n = 1 gave a good fit for all particle sphericities. For n = 1, Eq. (28) and (33) yield Nu ¼

Nd2 3=2 24 þ 5:9Nd exp ð2:13CÞ

(34)

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The predictions of Eq. (34) are compared to the data reported by Levenspiel, 1984 in Fig. 10. 6. Results and discussion 6.1. Effect of flow rate, Q A set of experiments was performed with the swirl separator in the base configuration except for the inlet diameter which was reduced from 7.6 to 3.8 cm so as to prevent particle settling in the horizontal section of the inlet pipe at low flow rates. As well inlet flow rates of 45, 67 and 90 LPM were used instead of the base 100 LPM. Trap efficiencies were measured TM for 200 mm particles. FLUENT was also used to simulate these cases. Fig. 11 summarizes the results of the three experiments. Both the experiments and the simulations show that better trap efficiency is achieved on decreasing the flow rate. This is in agreement with our analytical model Eq. (19) which predicts that h is an increasing function of f. Decreasing the flow rate implies increasing f, so that h is expected to rise. Decreasing the inlet flow also implies reducing centrifugal force. Since trap efficiency rises on decreasing inlet flow, therefore, it can be concluded that centrifugal force is not the major force involved in achieving separation in a swirl separator unlike in conventional hydrocyclones (Svarovsky, 1984; Castilho and Medronho, 2000). The separation mechanism is mainly gravity-driven. 6.2. Effect of tank height, Ht To investigate the influence of the height of the cylindrical section of the swirl separator on its separation performance, two experiments were performed at the base flow rate of

Fig. 11. Effect of flow rate on trap efficiency. Base dimensions (cf. Table 2) except Di = 3.8 cm, disc outlet, R = 0, dp = 200 mm.

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Table 3 Effect of tank height on trap efficiency f

Ht (cm)

0.73 0.73 0.73 0.73

28 42 56 84

h (%) Experiment

Simulation

51 – 47 –

45 46 42 42

Base dimensions (cf. Table 2) disc outlet, flow rate = 100 LPM, R = 0, dp = 200 mm.

100 LPM with no underflow. In both cases, 200 mm particles and the disc outlet were used. The swirl separator in the strict base configuration was used on the one hand (Ht = 56 cm) and with Ht = 28 cm on the other. These cases were also simulated. The results (Table 3) show that the tank height has a small influence on the trap efficiency. These results were verified by performing additional simulations for Ht = 42 and 84 cm. However, the fact that the tank height has a negligible effect on the separation performance of the separator does not mean tank height can be minimized indefinitely. An overflow outlet too close to the inlet would result in significant short-circuiting of the flow, thereby drastically reducing trap efficiency. Our analytical model predicts that trap efficiency is a function of f. Tank height affects neither us nor Q/A and hence not f, so that h should not be affected, which is in accordance with the findings above. Nevertheless, the model does include a parameter a which is proportional to the ratio of Ht  Hi to E for constant Q/A. The results suggest that a is approximately constant which means that E is proportional to Ht  Hi, roughly in line with turbulent eddy theory. 6.3. Effect of inlet height, Hi Experiments were performed to investigate the effect of the height of the inlet pipe (Hi) on the trap efficiency of the swirl separator. The base swirl separator configuration was used, with only the inlet height, Hi varying. The base swirl separator was modified to accommodate two additional inlets so that three configurations were possible: Hi/ Ht = 0.09, 0.50 and 0.82. Each inlet could be used separately, with the other two plugged. Experiments were performed with the 200 mm particles (Table 1) at 100 LPM. The experimental results are shown in Fig. 12 together with the corresponding simulation results. The experimental results show some variation of trap efficiency with inlet height, with efficiency highest for the central inlet (Hi/Ht = 0.5). This result is counter-intuitive since as the inlet is raised and thus brought closer to the overflow outlet one would expect the trap efficiency to drop due to incoming water short-circuiting directly to the outlet. TM The trend can be explained by analyzing the velocity profiles computed by FLUENT . This analysis was only feasible by relying on simulated velocity profiles. Indeed, direct velocity measurements done by inserting a velocity probe inside the swirl separator and tracking measurements were hampered by the presence of the disc outlet preventing access to most of the swirl separator volume. Also, usually such techniques are intrusive in nature, in the sense that they modify the phenomena (velocity profile) they are meant to capture. For each of the three inlet heights, the simulated axial water velocity profiles are shown

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Fig. 12. Effect of inlet height on trap efficiency. Base dimensions (cf. Table 2), disc outlet, flow rate = 100 LPM, R = 0, dp = 200 mm.

over a cross-section immediately (0.2 cm) below the inlet pipe, in Fig. 13. The region bounded by the dashed line represents the critical region where the incoming water laden with particles enters and can start losing its large initial horizontal momentum, moving vertically towards the outlets. In this region, rising water promotes escape of particles via the overflow outlet, while downward flowing water assists particle trapping. For Hi/ Ht = 0.50, this critical region has the highest fraction of negative vertical velocity, thus the highest fraction of downward-moving water, thereby promoting particle trapping. As the inlet is moved nearer to the top outlet, the propensity for short-circuiting rises. This is why trap efficiency decreases as Hi/Ht nears unity. Though there is no major gain in efficiency, the best compromise between the two opposing phenomena seems to be achieved for Hi/Ht around 0.5.

Fig. 13. Contours of axial water velocity in a horizontal plane, immediately below the inlet pipe; black regions stand for downward-moving water and grey regions for rising water. Base dimensions (cf. Table 2), disc outlet, flow rate = 100 LPM, R = 0.

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Table 4 Effect of inlet diameter on trap efficiency f

Di (cm)

h (%) Experiment

Simulation

0.73 0.82

7.6 3.8

47 32

42 25

Base dimensions (cf. Table 2), disc outlet, flow rate = 100 LPM, R = 0, dp =200 mm.

6.4. Effect of inlet diameter, Di The influence of the inlet diameter of the swirl separator on its separation performance was also investigated. The results of experiments performed with inlets of 7.6 and 3.8 cm (Table 4) show that the larger diameter favours separation. Simulations confirm the trend but also show that further increasing the inlet diameter gives no additional benefit (Fig. 14). This can be interpreted by considering the inlet velocity, Vin. Halving the inlet diameter increases inlet velocity four-fold Eq. (35): Vin /

1 D2i

(35)

The lower the diameter, the higher the momentum of the inlet jet, and the higher the tendency to short-circuiting. The incoming water, laden with particles, bypasses the body of the swirl separator instead of being distributed across the tank’s cross-section. As the

Fig. 14. Effect of inlet diameter on trap efficiency. Base dimensions (cf. Table 2), disc outlet, flow rate  100 LPM, R = 0, dp = 200 mm.

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diameter increases, the momentum of the inlet jet decreases, the dispersion of particles improves and eventually the resulting gain in trap efficiency plateaus. This points to a distinction that needs to be made between axial and cross-sectional dispersion. According to the analytical model Eq. (19), the higher the level of axial dispersion (higher E), the lower the trap efficiency. High axial dispersion precludes segregation between the upward-moving water and the downward-moving particles, thus reducing separation performance. However, cross-sectional dispersion is needed to distribute the particles laterally, thus permitting gravity to separate the particles which, otherwise, might remain caught in an upward-moving inlet stream. The practical significance of this phenomenon is the justification of the use of a tangential inlet. The tangential injection of water causes mixing in a horizontal plane which, in turn, promotes separation. 6.5. Overflow outlet structure To optimize the trap efficiency, various overflow outlet structures were tested experimentally. Experiments were performed with 3/4-pipe and 1/2-pipe outlets (Fig. 3) and the results compared to those carried out with the disc outlet. The three types of acrylic particles were used in these experiments (Table 1). The base swirl separator configuration was applied, at the base flow rate of 100 LPM (no underflow). The results (Table 5) show that under these conditions the 3/4-pipe outlet outranks the disc outlet and the 1/2-pipe outlet is the least efficient. The effect of having solely a central pipe as overflow outlet (central-pipe outlet) was also studied by performing experiments at 45, 67 and 90 LPM with the base swirl separator configuration except for the inlet diameter which was halved (3.8 cm). The results were compared to those of experiments undertaken under exactly the same conditions with the disc outlet. These results are grouped in Table 6. Having no particular structure atop the central pipe severely reduces the trap efficiency. The performance of the side and center–side outlets (Fig. 4) is compared to that of the other outlets in Table 7. The results clearly show that simply removing water at the center as in the case of the central-pipe and the center–side outlets, leads to poor efficiency. As before, the 3/4-pipe outlet provides the highest trap efficiency. The 3/4-pipe performs best because it offers the largest resistance to water rotation. The other extreme is the central-pipe outlet with the least resistance to rotating flow. The rotating water generates a radial pressure gradient which forces water along the base of

Table 5 Comparison of the efficiency of the 3-4-pipe, 1/2-pipe and disc outlets f

0.73 0.61 0.74

Experimental trap efficiency (%) 3/4-pipe

Disc

1/2-pipe

50 40 45

47 34 39

45 24 31

Base dimensions (cf. Table 2), flow rate = 100 LPM, R = 0, dp = 200, 325, 385 mm.

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Table 6 Comparison of the efficiency of the central-pipe and disc outlets Outlet type

Experimental trap efficiency (%) f = 1.63

f = 1.09

f = 0.82

Disc Central-pipe

64 4

52 1

32 1

Base dimensions (cf. Table 2) except Di = 3.8 cm, flow rate = 45, 67 and 90 LPM, R = 0, dp = 200 mm.

the separator to flow radially inward (Schlichting, 1979). This secondary flow is useful because it helps carry particles towards the bottom outlet. However, if the secondary flow is larger than the flow out of the bottom outlet, the excess must flow axially upward within the core region of the separator. This upward flow resuspends particles accumulated at the base of the separator and entrains them towards the overflow. A central-pipe outlet is undesirable for two reasons. First, it promotes the formation of a strong vortex and thus a strong secondary flow. Second, by reducing the core upflow area, it yields higher upflow core velocities. Without the pipe, the core upflow is weaker and less able to resuspend settled particles. This is the reason why the center–side outlet performs slightly better than the central-pipe outlet. Entrainment of resuspended particles into the overflow can be minimized by moving the overflow outlet away from the center of the swirl separator and by increasing the overflow outlet area so as to reduce outlet flow velocities. The side outlet achieves high efficiencies by using the first strategy, whereas the disc, 1/2-pipe and 3/4-pipe outlets use both strategies. The side, 1/2- and 3/4-pipe outlets further reduce entrainment by slowing down the rotational motion that induces resuspension. The disc outlet, on the other hand, offers little resistance to water rotation and has the added disadvantage that a ‘‘dead’’ zone forms underneath the disc as observed in our simulations and as stated by Sullivan et al. (1978). This zone is undesirable because it represents wasted volume since little flow enters or leaves this region. Furthermore, by reducing the effective upflow area, it results in a high upflow velocity along the outer wall which entrains particles in the overflow. Comparison of Tables 5 and 7 indicates that the performance of the 1/2-pipe outlet approaches that of the 3/4-pipe outlet as f increases. Since these experiments were performed with particles of essentially the same size, high f values were obtained at low flow rates and thus low tangential velocities. The 3/4-pipe outlet, which achieves superior performance by resisting rotating flow, offers no significant advantage over the 1/2-pipe outlet when rotational velocities are low. Since separation is driven by gravity in a swirl Table 7 Effect of the center–side and side outlets on trap efficiency Type of outlet

Experimental trap efficiency (%)(f = 3.1)

Central-pipe Center–side Side 1/2-pipe 3/4-pipe

1 10 74 89 90

Dt = 1.5 m, flow rate = 100 LPM, R = 0, dp = 325 mm.

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separator, high rotational velocities are not advantageous. The rotation is necessary to distribute the incoming particles uniformly over the cross-section of the swirl separator but should be kept low to prevent resuspension of the particles. This can be achieved by keeping the inlet velocity marginally above what is required to prevent sedimentation within the inlet pipe (see ‘‘Design of swirl separators’’ section). 6.6. Effect of surface loading, Q/A From the above study of the various parameters influencing trap efficiency, the optimum configuration for the 0.6 m swirl separator is: Di = 7.6 cm, Hi/Ht = 0.5, and type of outlet: 3/4-pipe. The trap efficiencies obtained at 100 LPM with the 0.6 m swirl separator in this configuration are shown in Fig. 15. Also, included in Fig. 15 are results obtained with the 1.5 m swirl separator at 50, 70 and 100 LPM and data obtained by Sullivan et al. (1978) with a 0.92 m swirl separator. In their experiments, Sullivan et al. used resin particles (dp = 75–150 mm, us = 0.02–0.04 cm/s) and three types of overflow outlets (‘‘radial gutters’’) that resemble our 1/2-pipe outlet. As can be seen in Fig. 15, all the data fall between the lower and upper limits of the analytical model (Eqs. (21) and (23) when R = 0). In agreement with the predictions of the model, trap efficiency increases with f. For particles of constant settling velocity, the value of f can be increased by increasing tank diameter or by decreasing inlet flow rate. TM The efficiencies predicted using FLUENT for the 0.6 m swirl separator with the optimized dimensions, are included in Fig. 15 and appear to provide a more realistic upper

Fig. 15. Effect of surface loading on trap efficiency. R = 0. Experiments on 1.5 m separator: flow rates= 100, 70 and 50 LPM, dp = 325 mm. Experiments on 0.6 m separator: flow rate = 100 LPM, dp = 200, 325 and 385 mm. Experiments/simulations reported for the 0.6 m separator pertain to the base dimensions (cf. Table 2) except Hi/ Ht = 0.5.

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bound than Eq. (23). As shown in Fig. 15, the analytical model with a = 1.5 provides a TM good representation of the FLUENT prediction. According to Eq. (20), for a = 1.5, Q = 100 LPM, Dt = 0.6 m and (Ht  Hi) = 0.28 m, the corresponding value of E, the turbulent dispersion coefficient, is 1.03  103 m2/s. Intuitively, we expect the dispersion coefficient to increase with increasing tangential velocity. Furthermore, since the Peclet number, Pe, for turbulent dispersion is often constant (Cussler, 1997), we might expect that Pe ¼

Lvu ¼ constant E

(36)

where vu is the tangential velocity of the water at the tank’s periphery and L is a characteristic dimension. Both (Ht  Hi) and Dt are logical characteristic dimensions. Since the scale of turbulence cannot be larger than the smaller of these two dimensions, (Ht  Hi) will be substituted for L. Using (Ht  Hi) = 0.28 m, E = 1.03  103 m2/s and the measured value of 0.2 m/s for vu, the following is obtained: Pe ¼

Vu ðHt  Hi Þ ¼ 54 E

(37)

This estimate of the Peclet number is of the order observed for turbulent dispersion in other systems (Cussler, 1997). It can be used to determine E given vu. 6.7. Effect of split, R Results presented in Fig. 15 for the side outlet suggest that this configuration yields a well-mixed particle/water system since its trap efficiency follows closely the infinite mixing (a = 0) limit of the analytical model. When the system is well-mixed, the reduced trap efficiency, hr in Eq. (22) should be a unique function of f according to Eq. (21). To verify this prediction, experiments were performed on the 1.5 m swirl separator with the side outlet, at flow rates between 50 and 150 LPM and flow splits of 0, 10, 20 and 40%. The experimental results (Fig. 16) confirm that the reduced trap efficiency of the side outlet configuration is well represented by Eq. (21). In agreement with model predictions, the results show that an increase in flow split at constant f increases trap efficiency but not reduced trap efficiency. This suggests that rather than improving particle–fluid separation, the underflow simply partitions the outflow. 6.8. Design of swirl separators A design methodology for the swirl separator can be developed based on the above findings. It is assumed a priori that the flow rate, Q and flow split R are known. Normally, Q is fixed by upstream equipment and R is zero. The primary parameter to be determined in sizing a swirl separator is the tank diameter, Dt. It is the physical dimension that has the most influence over trap efficiency. The tank diameter is determined by first setting a target trap efficiency, h for a particular particle size, dp. Knowing h, f can be read from Fig. 15. Since the well-mixed curve (a = 0) is the lower limit for the separation efficiency it is recommended that this curve (or Eqs. (21) and

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Fig. 16. Effect of split on reduced trap efficiency. Dt = 1.5 m, side outlet, flow rate = 150, 100, 70 and 50, dp = 325 mm.

(22)) be used as a worst case scenario. The tank diameter required to achieve the desired efficiency can then be calculated from the value of f if us is known: f¼

pD2t us 4Q

(38)

The settling velocity, us of particles of size, dp can be determined experimentally or estimated using Eqs. (29), (30) and (34). The settling velocities predicted by the semiempirical Eq. (34) are in good agreement with the data reported by Levenspiel (Fig. 10) and are within 10% of the experimental values for the particles used in this study (Table 1). With Dt known, it is possible to predict the total trap efficiency, hT of the swirl separator if the size distribution of particles in the feed is known. The fractional trap efficiency, h(dp) for the separator must first be generated. This is done by calculating f for different dp values and then determining the corresponding efficiencies using Eqs. (21) and (22). The total trap efficiency is given by (Svarovsky, 1984): hT ¼

Z1

hðdp ÞdFðdp Þ

(39)

0

where F(dp) is the cumulative size distribution based on mass of the particles in the feed. The integral can be evaluated numerically by plotting h(dp) versus F(dp) and determining the area under the curve. If this efficiency is found to be too low, a larger value of Dt should be chosen and the calculation procedure repeated until the desired total trap efficiency is obtained. Our findings indicate that the tank height, Ht does not significantly affect trap efficiency. This means that no benefit is achieved by using tall swirl separators. However, it does not

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mean that Ht can be reduced to zero. A top outlet too close to the inlet will lead to shortcircuiting. We recommend that Ht/Dt be between 0.5 and 1 and that Hi/Ht be about 0.5. Our study also shows that the larger the inlet diameter the better the separation, up to a point. Too large a diameter leads to such a low fluid velocity in the horizontal inlet pipe that particles start to deposit on the lower section of the pipe. These form a stationary bed of sediments which can affect water quality. Therefore, a maximum pipe diameter should be used such that the fluid velocity in the pipe is above the critical deposition velocity, i.e. the velocity below which sedimentation occurs. Various correlations for critical deposition velocity can be found in the literature (Perry et al., 1997; Wasp et al., 1977). Though the presence of the cone does not directly impact the separation, it is important to have a conical section as sludge collector to prevent scouring before the wastes are flushed out. Its depth will govern how often the solids will have to be flushed out. The 3/4-pipe outlet was shown to perform best; therefore, its use is recommended. A 1/2-pipe should perform equally well at flows with low rotation. Each of these two outlets can be easily implemented without much piping or structural support. Indeed, a horizontal structure running along the whole tank diameter, wall to wall with no central drain pipe along the axis of the swirl separator, should be fine. If the flow rate that needs to be treated is too large and leads to unrealistic swirl separator dimensions, the designer should consider splitting the flow and use separators in parallel.

7. Conclusions This paper summarizes experimental and modeling work performed to identify and assess the various parameters affecting the separation performance of swirl separators. The parameters studied included the flow rate, the split, the physical dimensions of the separator and the structure of the overflow outlet. Separation is shown to follow closely the theory of sedimentation in well-mixed systems and can be predicted using a simple analytical model. Settling velocity, a key input parameter of the model, is shown to be accurately predicted by a new correlation that takes particle shape into account. The findings were used to develop a methodology for designing swirl separators. In the swirl separator, separation is mainly gravity-driven so that low inlet velocities achieve higher trap efficiencies. The swirl flow generates relatively strong horizontal mixing but relatively weak axial mixing. As a result, particles are uniformly distributed across the tank, and centrifugal separation is negligible. Tank height barely affects efficiency so that there is no benefit from building tall separators. The vertical position of the inlet does not significantly affect efficiency though an inlet midway between the top and bottom of the cylindrical section results in slightly better efficiency. The larger the tank diameter the higher the trap efficiency, the tank diameter being the most important parameter in sizing a swirl separator. Increasing the underflow rate increases trap efficiency but not reduced trap efficiency when using the side outlet. This means that, with increased split, little additional benefit is achieved beyond the expected gain due to the increased diversion of feed towards the bottom drain. Finally, novel structures for the overflow outlet were investigated. One such outlet called the 3/4-pipe outlet was found to perform best, especially with highly rotating flows.

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Acknowledgments This research has been supported in part by funds from AquaNet, the Network of Centres of Excellence for Aquaculture and the New Brunswick Department of Agriculture, Fisheries and Aquaculture. The authors are grateful to Waterline Ltd. for providing some of the equipment used during this work. Finally, they are indebted to Julie Emond for performing some of the experiments.

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