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Improved design of conical accelerators for decanter and pusher centrifuges
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Improved Design of Conical Accelerators for Decanter and Pusher Centrifuges Bird M a c h i n e C o m p a n y ,
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Wallace W.-F. Leung 100 N e p o n s e t S t r e e t , S o u t h W a l p o l e , M A 02071, U S A
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1> A s c h e r H, Shapiro Bird Machine Company, and Massachusetts Institute of Technology, 111 Perkins Street, Boston, MA 02130, USA
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This p a p e r was presented at the American Filtration & Separations (AFS) Society Annual Conference in Valley Forge, Pennsylvania, USA on 21-24 April 1996 • . 0:,.
The simple cone-type feed accelerator commonly used for solid-bowl and screen-bowl decanter and pusher centrifuges delivers to the surface of the decanter pool or the pusher basket a tangential speed far below the value of ~ R (the rim speed of the cone), with consequences adverse to performance. A novel, more effective cone accelerator is described. This has forward-curved vanes that produce overspeeding and a final unvaned section of cone - called a smoothener - which smears out the jets from the vanes into a nearly uniform conical sheet. Model tests in the laboratory were used for developing the new accelerator technology. Operation in the field has verified the expected Improvements in capacity performance. T
his paper on the cone-type accelerator, together with a companion paper [1] on the disc-type accelerator, deals with the application to centrifuges of XLoPLUS "~ technology,j2, 3] including the novel features of overspeeding and smoothening. It is well appreciated that the bowl and screw conveyor are important components in decanters. Likewise, for pusher centrifuges, much attention is given to the design of the baskets and the reciprocating drive. By contrast, the feed delivery system is often thought of only as a means of somehow getting the feed slurry into the machine• That it may have a significant effect on performance is often overlooked• THE 'IDEAL' FEED ACCELERATOR On entry to the decanter pool surface or to the pusher basket, the desirable features of feed behaviour include the following: [] The tangential speed should match the value of ~_/7, where is the angular velocity of the machine, and R is the radius at the pool or basket. This assures a full value of the centrifugal force, and avoids shearing forces that might lead to instability, turbulence and re-suspension• The performance of an actual feed accelerator system may be characterised by an accelerator efficiency, defined as
•
evaluated with the values of u and R at the exit of the accelerator• However, the performance of the machine is in practice determined by the value of the G-efficiency calculated with the values of u and R at the entry of the feed to the pool or basket. [ ] The radial speed of the feed should be relatively small• This avoids a 'plunging' of the feed into the pool or basket, with accompanying disturbances. [ ] The feed flow should be uniform in the circumferential direction in order to avoid penetration of concentrated jets•
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Figure 1 is a schematic representation of a conventional conetype accelerator. Appropriately adapted, it may be applied to either a decanter or a pusher centrifuge. The feed is directed to a distributor which lays down the liquid in a thin conical layer at the small end of the cone. We shall consider the mechanics of how it flows 'down' the cone and at the same time acquires a tangential velocity: [ ] As shown in Figure 2a (a cross-sectional view of a portion of the cone in a plane normal to the axis), frictional forces exerted by the cone wall in the tangential direction cause
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the efficacy of the accelerator for separation is proportional to the square of u. Thus, an additional index of accelerator performance is the G-efficiency. This is defined as the ratio of the actual G-field to that for acceleration to the local value of f~R:
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If, for instance, r/a iS 50%, then ~/c is only 25%. When referring to the accelerator alone, the efficiencies are
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where u is the average tangential velocity. Since separation is brought about by the centrifugal field
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Although the conventional cone accelerator often provides adequate circumferential uniformity, it typically has a poor value of r/a. The reason is simple: the tangential acceleration depends on viscous friction, which is not sufficiently strong. Figures 3a and b show a design in which multiple radial vanes achieve excellent tangential acceleration. As the flow is swept up into individual streams by the driving faces of the vanes, the streams acquire the tangential speed of the vanes at the same time that they flow and accelerate radially outwards• At the vane exit, the velocity relative to the vane, W, which is radial in direction, combines vectorially with the tangential velocity ~ R imparted to the liquid stream to yield the 'absolute' velocity V; that is, the velocity as seen in the reference frame of the laboratory. The tangential speed u at the vane exit is close to ~ / t at that location, hence the ~/,, is nearly 100% at the radius of the vane exit•
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The flow leaving the vanes is highly concentrated into individual streams. In order to eliminate this undesirable formation, a 'smoothener' section of the cone is left unvaned.
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the liquid layer to accelerate in the tangential direction. The acquired tangential speed decreases from ~tR (local value) at the wall to a smaller value at the surface of the layer. Figure 2b (a section of the cone wall in a plane passing through the axis) shows that the radially outward centrifugal field created by the tangential velocity distribution in the layer has a component acting along the wall. That component acts to accelerate the liquid layer x-wise, ' d o w n w a r d s ' along the wall. Consequently the layer thickness h decreases with x, as a result of both the increase of z-wise speed and of the increasing circumference of the cone. The acquired distribution of velocity along the wall has a shape indicated schematically in Figure 2b, with a maximum somewhere between the wall and the edge of the layer. This comes about because of the no-slip condition at the wall and the profile of tangential velocity shown in Figure 2a.
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The foregoing three events actually occur interactively and simultaneously, and it is evident that a steady condition can never be a t t a i n e d because the radius R is constantly increasing with distance x. Accordingly, the local tangential speed always lags behind the local value of ~R, and the values of ~l~ and rio cannot possibly reach 100%. Analysis of the foregoing fluid mechanical phenomena is beyond the scope of this paper, but the following results of analysis are significant:
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[] The accelerator efficiency is increased by larger values of the angular speed ~, the viscosity and the exit radius R~=,t. It is also increased by smaller values of the cone half-angle O and the flow rate Q. For values of the geometric and operating parameters pertinent to commercial machines, the value of r/,, at the cone exit is well below 100%, and sometimes as low as 25%; and tic is of course even smaller. Because of conservation of the angular momentum per unit mass uR, and as shown in more detail in Reference 1, there is a further reduction• The value of qc, for instance, decreases with the inverse square of the radius, as the feed moves from the radius at the cone exit to the larger radius at the entry to the pool or basket.
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Figure 4. Similar to Figure 3b, but with forward-curved vanes, and showing the velocity triangle at the exit of the vane.
The movement of the flow from the radius of the vane exit to the larger radius at the smoothener exit, in combination with tangential friction and the velocity profile in the liquid streams, acts to smear out the individual streams into a conical sheet that is approximately uniform in the circumferential direction. This distributing action is shown in Figure 3b by the schematic streamlines as seen in the laboratory frame. Overspeeding The smoothening action in Figure 3b is at the expense of accelerator efficiency. The reason is that, as described previously, tangential friction is not effective in increasing u from the value of f~R at the vane exit to the value at the exit of the smoothener. The resulting deficiency in u may, however, be compensated for by curving the vanes forwards (i.e. in the direction of rotation) at the vane exits, as shown in Figure 4. This 'overspeeding' strategy gives rise to a velocity triangle in which u is larger than f~R, whlch means that the accelerator efficiency is greater than 100% at the vane exit. The excess above 100% may be used to accommodate not only the loss in r/, that occurs in the smoothener, but, further, to compensate for the loss in q~ as the feed travels from the radius of the smoothener exit to the radius of the pool or basket. Practical considerations In applying the concepts of smoothening and overspeeding, it is important that the designer consider many other factors. Among these are: the number of vanes; the vane height normal to the cone surface; the location and geometry at the start and end points of the vanes; the speed and gravitational droop of the feed jet; the geometry of the feed distributor; splash; erosion; and plugging.
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Test apparatus As is shown schematically in Figure 5, the cone is driven by a motor through a section of shafting in which a torque-meter is installed. Measurements are made of the torques T with and without flow, the volume flow rate Q and the angular velocity fL If we already know 1~=i t and the density p of water, the values of u and r/~ at the exit of the cone may then be determined from the theorem of moment of momentum, which yields
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The development of an improved cone accelerator design incorporating the features of overspeeding and smoothening was carried out with the help of model tests in the laboratory, using water as the test liquid, in which the various parameters and geometric factors could be explored. The tests were performed at approximately full scale.
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Figure 6. Effect of vanes on accelerator efficiency. Open symbols: smooth cone without vanes, Solid symbols: smooth cone with 16 axIal vanes.
Typical rosulls Figure 6 shows some typical results, obtained in this case with 16 straight radial vanes, each 2 inches (5.08 cm) tall (no overspeeding) and with semi-angle 0 = 30 °,/~zit = 10 inches (25.4 cm) and speed = 1980 rev/min. [ ] S m o o t h c o n e : The accelerator efficiency is low, and decreases continuously as the flow rate increases. At 100 gal/min of flow, q~ = 60% and r/c = 36%. At double this flow, i.e. 200 gal/min, the p e r f o r m a n c e is seriously deficient:~la = 42% and r/c = 17%. [ ] Vanes, n o s m o o t h e n e r : At low flow rates, for a variety of reasons, the accelerator efficiency is poor. As the flow rate increases, however, the efficiency rises and levels off at about 100%, as expected. If a smoothener had been installed, the curve would be similar, except that the value of r/a would level off at less than 100%. With overspeeding, accelerator efficiencies of more than 100% can be attained at the smoothener exit, if desired. This type of performance is shown for a double-disc geometry in Reference 1.
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TABLE 2. PERFORMANCE DATAAT 3200 revlmln FOR DEWATEBING OF MUNICIPAL SLUDGE IN SOLID-BOWL DECANTER.
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Beforemodification
W _1 U,l
Aftermodification
Capacity,gal}0~s/min
45
60
Polymerpumpsetting
75%
85%
15- 16%
15- 16%
86%
96%
Cakepercentsolids Percentsolidsrecovery
W TABLE 1. AVERAGE RESULTS FROM 12 TESTS PRIOR TO, AND 6 TESTS FOLLOWING MODIFICATION.
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Beforemodification Z ~J
Aftermodification
Capacily,t0nnes/hr
2.07
520
Productpercentmoisture
1.43%
1.39%
Productpercentsulphates
2.3%
16%
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The i m p r o v e d design described a b o v e was investigated in two plants.
Dewalering/wa•hing of •odium chloride •lurry in t w o - • t a g e pusher The functions of the centrifuge w e r e (i) to reduce the water content, and (ii) to wash the cake on the second-stage basket so as to minimise the sulphate content in the sodium chloride crystals. Originally, the machine had an unvaned conical accelerator with ~) = 18° and R~xit = 5.1 inches (13.0 cm). It was modified by installing 16 straight longitudinal vanes, each 1.25 inches (3.2 cm) tall and 3.25 inches (8.3 cm) long. This left a s m o o t h e n e r section 1 inch (2.54 cm) long, Table 1 shows a v e r a g e results obtained from 12 tests prior to, and six tests following the modification. The capacity was increased by a factor of 2.5, with reduced levels of both moisture and sulphate in the product salt crystals. Visual o b s e r v a t i o n with a strobe also showed that, notwithstanding the accumulation of the feed at the driving faces of the vanes, the s m o o t h e n e r section effectively restored circumferential uniformity at the basket entry. The uniformity was confirmed by the absence of longitudinally running 'ridges' and 'valleys'
in the cake. The low level of sulphates in the salt crystals was further evidence of uniform washing associated with circumferential uniformity of the feed.
Dewatering of municipal •ludge in a solid-bowl decanter In this installation, the machine was tested in its original configuration with a conventional hub accelerator, and was then modified by installation of a vaned cone a s s e m b l y with the following geometry: ~ = 30°; ~texit = 6.91 inches (17.55 cm); eight longitudinal vanes, each 0.5 inches (1.27 cm) high; and no smoothener. Table 2 gives the performance data at 3200 rev/min. Although there was a 13% greater use of polymer, the capacity was increased by 3 0 - - 4 0 % . The c o m b i n a t i o n of these numbers therefore indicates a 15% reduction in the a m o u n t of p o l y m e r per gallon of sludge. These numbers show that the modification substantially i m p r o v e d the performance. With a larger v a l u e of C)and a cone smoothener, even better p e r f o r m a n c e would be expected. CONCLUSIONS The poor accelerating capability of a s m o o t h - w a l l e d feed accelerator of conical shape may be o v e r c o m e by installing accelerating vanes on the inner surface of the cone. The p e r f o r m a n c e is enhanced by f o r w a r d - c u r v e d vanes that produce overspeeding, and by a final unvaned section that acts as a smoothener in the interests of circumferential uniformity. Model tests have confirmed the effectiveness of the accelerating vanes o v e r a wide range of flow rates, and field e x p e r i e n c e has confirmed in both decanters and pushers that the XLePLUS ~ technology improves the performance. Because the feed can be introduced to the vanes at a relatively small radius, the XLePLUS t e c h n o l o g y is applicable to the separation and dewatering of fragile organic solids that would d e g r a d e from rough handling or s e v e r e shear straining.
REFERENCES 1 Leung, W.W.-F. and Shapiro, A.H.: 'Efficient double-disc accelerator for continuous-feed centrifuges', to be published in Fiffration & Separation, October 1996, 33(9). 2 Leung, W.F. and Shapiro, A.H.: 'Feed accelerator system including accelerator cone'. US Patent 5380266, 10 January 1995. 3 Leung, W.F. and Shapiro, A.H.: 'Feed accelerator system including accelerator disk'. US Patent 5401423, 28 March 1995.
Improved Design of Conical Accelerators for Decanter and Pusher Centrifuges Bird M a c h i n e C o m p a n y ,
i
V" m
z -4
c
Wallace W.-F. Leung 100 N e p o n s e t S t r e e t , S o u t h W a l p o l e , M A 02071, U S A
m
1> A s c h e r H, Shapiro Bird Machine Company, and Massachusetts Institute of Technology, 111 Perkins Street, Boston, MA 02130, USA
m ira
This p a p e r was presented at the American Filtration & Separations (AFS) Society Annual Conference in Valley Forge, Pennsylvania, USA on 21-24 April 1996 • . 0:,.
The simple cone-type feed accelerator commonly used for solid-bowl and screen-bowl decanter and pusher centrifuges delivers to the surface of the decanter pool or the pusher basket a tangential speed far below the value of ~ R (the rim speed of the cone), with consequences adverse to performance. A novel, more effective cone accelerator is described. This has forward-curved vanes that produce overspeeding and a final unvaned section of cone - called a smoothener - which smears out the jets from the vanes into a nearly uniform conical sheet. Model tests in the laboratory were used for developing the new accelerator technology. Operation in the field has verified the expected Improvements in capacity performance. T
his paper on the cone-type accelerator, together with a companion paper [1] on the disc-type accelerator, deals with the application to centrifuges of XLoPLUS "~ technology,j2, 3] including the novel features of overspeeding and smoothening. It is well appreciated that the bowl and screw conveyor are important components in decanters. Likewise, for pusher centrifuges, much attention is given to the design of the baskets and the reciprocating drive. By contrast, the feed delivery system is often thought of only as a means of somehow getting the feed slurry into the machine• That it may have a significant effect on performance is often overlooked• THE 'IDEAL' FEED ACCELERATOR On entry to the decanter pool surface or to the pusher basket, the desirable features of feed behaviour include the following: [] The tangential speed should match the value of ~_/7, where is the angular velocity of the machine, and R is the radius at the pool or basket. This assures a full value of the centrifugal force, and avoids shearing forces that might lead to instability, turbulence and re-suspension• The performance of an actual feed accelerator system may be characterised by an accelerator efficiency, defined as
•
evaluated with the values of u and R at the exit of the accelerator• However, the performance of the machine is in practice determined by the value of the G-efficiency calculated with the values of u and R at the entry of the feed to the pool or basket. [ ] The radial speed of the feed should be relatively small• This avoids a 'plunging' of the feed into the pool or basket, with accompanying disturbances. [ ] The feed flow should be uniform in the circumferential direction in order to avoid penetration of concentrated jets•
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Figure 1 is a schematic representation of a conventional conetype accelerator. Appropriately adapted, it may be applied to either a decanter or a pusher centrifuge. The feed is directed to a distributor which lays down the liquid in a thin conical layer at the small end of the cone. We shall consider the mechanics of how it flows 'down' the cone and at the same time acquires a tangential velocity: [ ] As shown in Figure 2a (a cross-sectional view of a portion of the cone in a plane normal to the axis), frictional forces exerted by the cone wall in the tangential direction cause
.........
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the efficacy of the accelerator for separation is proportional to the square of u. Thus, an additional index of accelerator performance is the G-efficiency. This is defined as the ratio of the actual G-field to that for acceleration to the local value of f~R:
u2/n ~]C-
~t2R
-
vo
(3)
If, for instance, r/a iS 50%, then ~/c is only 25%. When referring to the accelerator alone, the efficiencies are
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where u is the average tangential velocity. Since separation is brought about by the centrifugal field
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Although the conventional cone accelerator often provides adequate circumferential uniformity, it typically has a poor value of r/a. The reason is simple: the tangential acceleration depends on viscous friction, which is not sufficiently strong. Figures 3a and b show a design in which multiple radial vanes achieve excellent tangential acceleration. As the flow is swept up into individual streams by the driving faces of the vanes, the streams acquire the tangential speed of the vanes at the same time that they flow and accelerate radially outwards• At the vane exit, the velocity relative to the vane, W, which is radial in direction, combines vectorially with the tangential velocity ~ R imparted to the liquid stream to yield the 'absolute' velocity V; that is, the velocity as seen in the reference frame of the laboratory. The tangential speed u at the vane exit is close to ~ / t at that location, hence the ~/,, is nearly 100% at the radius of the vane exit•
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the liquid layer to accelerate in the tangential direction. The acquired tangential speed decreases from ~tR (local value) at the wall to a smaller value at the surface of the layer. Figure 2b (a section of the cone wall in a plane passing through the axis) shows that the radially outward centrifugal field created by the tangential velocity distribution in the layer has a component acting along the wall. That component acts to accelerate the liquid layer x-wise, ' d o w n w a r d s ' along the wall. Consequently the layer thickness h decreases with x, as a result of both the increase of z-wise speed and of the increasing circumference of the cone. The acquired distribution of velocity along the wall has a shape indicated schematically in Figure 2b, with a maximum somewhere between the wall and the edge of the layer. This comes about because of the no-slip condition at the wall and the profile of tangential velocity shown in Figure 2a.
i i¸!i!
The foregoing three events actually occur interactively and simultaneously, and it is evident that a steady condition can never be a t t a i n e d because the radius R is constantly increasing with distance x. Accordingly, the local tangential speed always lags behind the local value of ~R, and the values of ~l~ and rio cannot possibly reach 100%. Analysis of the foregoing fluid mechanical phenomena is beyond the scope of this paper, but the following results of analysis are significant:
cooof
R/ / 1
_ Radial ~1~vanes ~ ,
Smoothener Section
[] The accelerator efficiency is increased by larger values of the angular speed ~, the viscosity and the exit radius R~=,t. It is also increased by smaller values of the cone half-angle O and the flow rate Q. For values of the geometric and operating parameters pertinent to commercial machines, the value of r/,, at the cone exit is well below 100%, and sometimes as low as 25%; and tic is of course even smaller. Because of conservation of the angular momentum per unit mass uR, and as shown in more detail in Reference 1, there is a further reduction• The value of qc, for instance, decreases with the inverse square of the radius, as the feed moves from the radius at the cone exit to the larger radius at the entry to the pool or basket.
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MODEL TESTS
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Curved N Vanes '~
.
Figure 4. Similar to Figure 3b, but with forward-curved vanes, and showing the velocity triangle at the exit of the vane.
The movement of the flow from the radius of the vane exit to the larger radius at the smoothener exit, in combination with tangential friction and the velocity profile in the liquid streams, acts to smear out the individual streams into a conical sheet that is approximately uniform in the circumferential direction. This distributing action is shown in Figure 3b by the schematic streamlines as seen in the laboratory frame. Overspeeding The smoothening action in Figure 3b is at the expense of accelerator efficiency. The reason is that, as described previously, tangential friction is not effective in increasing u from the value of f~R at the vane exit to the value at the exit of the smoothener. The resulting deficiency in u may, however, be compensated for by curving the vanes forwards (i.e. in the direction of rotation) at the vane exits, as shown in Figure 4. This 'overspeeding' strategy gives rise to a velocity triangle in which u is larger than f~R, whlch means that the accelerator efficiency is greater than 100% at the vane exit. The excess above 100% may be used to accommodate not only the loss in r/, that occurs in the smoothener, but, further, to compensate for the loss in q~ as the feed travels from the radius of the smoothener exit to the radius of the pool or basket. Practical considerations In applying the concepts of smoothening and overspeeding, it is important that the designer consider many other factors. Among these are: the number of vanes; the vane height normal to the cone surface; the location and geometry at the start and end points of the vanes; the speed and gravitational droop of the feed jet; the geometry of the feed distributor; splash; erosion; and plugging.
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The development of an improved cone accelerator design incorporating the features of overspeeding and smoothening was carried out with the help of model tests in the laboratory, using water as the test liquid, in which the various parameters and geometric factors could be explored. The tests were performed at approximately full scale.
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Typical rosulls Figure 6 shows some typical results, obtained in this case with 16 straight radial vanes, each 2 inches (5.08 cm) tall (no overspeeding) and with semi-angle 0 = 30 °,/~zit = 10 inches (25.4 cm) and speed = 1980 rev/min. [ ] S m o o t h c o n e : The accelerator efficiency is low, and decreases continuously as the flow rate increases. At 100 gal/min of flow, q~ = 60% and r/c = 36%. At double this flow, i.e. 200 gal/min, the p e r f o r m a n c e is seriously deficient:~la = 42% and r/c = 17%. [ ] Vanes, n o s m o o t h e n e r : At low flow rates, for a variety of reasons, the accelerator efficiency is poor. As the flow rate increases, however, the efficiency rises and levels off at about 100%, as expected. If a smoothener had been installed, the curve would be similar, except that the value of r/a would level off at less than 100%. With overspeeding, accelerator efficiencies of more than 100% can be attained at the smoothener exit, if desired. This type of performance is shown for a double-disc geometry in Reference 1.
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60
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85%
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The i m p r o v e d design described a b o v e was investigated in two plants.
Dewalering/wa•hing of •odium chloride •lurry in t w o - • t a g e pusher The functions of the centrifuge w e r e (i) to reduce the water content, and (ii) to wash the cake on the second-stage basket so as to minimise the sulphate content in the sodium chloride crystals. Originally, the machine had an unvaned conical accelerator with ~) = 18° and R~xit = 5.1 inches (13.0 cm). It was modified by installing 16 straight longitudinal vanes, each 1.25 inches (3.2 cm) tall and 3.25 inches (8.3 cm) long. This left a s m o o t h e n e r section 1 inch (2.54 cm) long, Table 1 shows a v e r a g e results obtained from 12 tests prior to, and six tests following the modification. The capacity was increased by a factor of 2.5, with reduced levels of both moisture and sulphate in the product salt crystals. Visual o b s e r v a t i o n with a strobe also showed that, notwithstanding the accumulation of the feed at the driving faces of the vanes, the s m o o t h e n e r section effectively restored circumferential uniformity at the basket entry. The uniformity was confirmed by the absence of longitudinally running 'ridges' and 'valleys'
in the cake. The low level of sulphates in the salt crystals was further evidence of uniform washing associated with circumferential uniformity of the feed.
Dewatering of municipal •ludge in a solid-bowl decanter In this installation, the machine was tested in its original configuration with a conventional hub accelerator, and was then modified by installation of a vaned cone a s s e m b l y with the following geometry: ~ = 30°; ~texit = 6.91 inches (17.55 cm); eight longitudinal vanes, each 0.5 inches (1.27 cm) high; and no smoothener. Table 2 gives the performance data at 3200 rev/min. Although there was a 13% greater use of polymer, the capacity was increased by 3 0 - - 4 0 % . The c o m b i n a t i o n of these numbers therefore indicates a 15% reduction in the a m o u n t of p o l y m e r per gallon of sludge. These numbers show that the modification substantially i m p r o v e d the performance. With a larger v a l u e of C)and a cone smoothener, even better p e r f o r m a n c e would be expected. CONCLUSIONS The poor accelerating capability of a s m o o t h - w a l l e d feed accelerator of conical shape may be o v e r c o m e by installing accelerating vanes on the inner surface of the cone. The p e r f o r m a n c e is enhanced by f o r w a r d - c u r v e d vanes that produce overspeeding, and by a final unvaned section that acts as a smoothener in the interests of circumferential uniformity. Model tests have confirmed the effectiveness of the accelerating vanes o v e r a wide range of flow rates, and field e x p e r i e n c e has confirmed in both decanters and pushers that the XLePLUS ~ technology improves the performance. Because the feed can be introduced to the vanes at a relatively small radius, the XLePLUS t e c h n o l o g y is applicable to the separation and dewatering of fragile organic solids that would d e g r a d e from rough handling or s e v e r e shear straining.
REFERENCES 1 Leung, W.W.-F. and Shapiro, A.H.: 'Efficient double-disc accelerator for continuous-feed centrifuges', to be published in Fiffration & Separation, October 1996, 33(9). 2 Leung, W.F. and Shapiro, A.H.: 'Feed accelerator system including accelerator cone'. US Patent 5380266, 10 January 1995. 3 Leung, W.F. and Shapiro, A.H.: 'Feed accelerator system including accelerator disk'. US Patent 5401423, 28 March 1995.