# Performance of Single and Double Shaft Disk Separators

Authors: Yazan Taamneh; Siegfried Ripperger
Journal: Physical Separation in Science and Engineering
 (2008)

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## Abstract

Rotating disks separators, mounted on single and double hollow shafts, are investigated experimentally. The shaft and disks were enclosed in stainless steel housing. Many parameters were measured to study their influence on the performance of single and double shaft disk filters at various rotation speeds. These parameters are pressure inside the housing, permeate flux, and electrical power consumption. The average velocity coefficientk˜  for single and double shaft disk separators was estimated and was found to be a good criterion of module performance as well. The comparison of measured and calculated filtration flow rate at various rotation speeds was in a good agreement. The estimated average shear stress is found to be about twice in double shaft filter disk. The feasibility of double shaft disk separator in treating filtration without filter cake is highly appreciated.


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## Body

## 1. Introduction

Shear-enhanced or dynamic filtration consisting of
rotating disks relies on the presence of a shear stress at the filter media
surface to reduce the accumulation of the particles.  The reason for its good performance is that very high shear rates are
produced with a low inlet flow, thereby resulting in low pressure drop in the
module. In the classical cross flow filtration with membrane modules, the
shear stress is linked to the feed flow rate which leads to the pressure drop.
High shear stress is produced by increasing the tangential flow along the
membrane surface and continuous circulation of the feed flow. In rotating
filters, the shear stress and flow rate are unlinked because the shear stress
is a function of the rotating filter disk. Dynamic filters which create
relative motion between the filter media and the suspension producing high
shear rate are compared with conventional cross flow filtration [1]. In this
study, the average shear stress is estimated based on the power consumed by the
rotating disk filter. Rotating disk within an enclosed housing has been investigated
extensively in the past decades [2]. It was found that the hydrodynamics of the
system is governed by the Reynolds number Re=ω⋅r2/υ and the axial clearance sc where ω is the rotational speed, r is the disk radius, υ is the fluid kinematics viscosity, and sc is the axial clearance between the disk and a
stationary wall.With relatively large axial gap between the disk and a
stationary wall, the boundary layers are separated by a  core of fluid moving at
an angular velocity of (kωd), where k=ωf/ωd is a velocity coefficient and has a value  of almost
less than one. In recent papers [3–7], the coef-ficient k for various disks is determined by regression
from peripheral pressure measurements taken on the housing rim at various
angular velocities using Bernoulli’s equation. The velocity coefficient is found
to be in the range 0.4-0.5 for a smooth
disk. Many disks with different modification on the surface types are recently
developed to increase the velocity coefficient, thereby enhancing the dynamic fil-tration performance. With eight radial vanes on the rotating disc, Schiele
got k = 0.9, resulting in a dramatic
in-crease of the shear stress and, of course, the power input  [8].The main objective of this study is to estimate andvalidate the average velocity coefficient, both for single and double shaft
disk separators and the dynamic filtrationperformance, respectively. Additionally,
we want to assess the contribution of filter overlapping by estimating the
average shear stress based on electrical powerconsumption. Lastly, we would
like to compare the single and double shaft disk separators based on filtration
experiments.


## 2. Experimental Setup

Two different
geometries have been used as shown in Figure1. The first consists of five filter
disks (dp = 40 μm, ro=45 mm, ri=15 mm) mounted on a single hollow shaft
with axial gap between two successive filter disks sg=14 mm, see Figure 1(a). The second
geometry consists also of five filter disks but mounted on two hollow shafts
rotating with the same speed direction. The axial shear gap between two
overlapped disks is ss = 4 mm and sg = 14 mm between nonoverlapping disks; see
Figure 1(b). The whole system is placed in stainless steel housing. Permeate is
collected inside each disk by a hollow shaft. The filtration unit is provided
with two pressure sensors, one of which is installed inside the housing close
to disk periphery while the second is mounted on the shaft where the filtrate
exits. Permeate and concentrate flow rates are measured by magnetic-inductive
flow meters. The filtration pressure difference can be estimated by the
pressure sensors.Single shaft disk separator (a) double shaft disk separator (b).
(a)(b)The filtration
experiments are carried out using asuspension of sphere glass (mean particle size
10μm), which is easy to prepare. The suspensions behave as a Newtonian fluid
at low concentration (13.4 g/l).


## 3. Results and Discussion

### 3.1. Determination of Velocity Factork with Water

The clearance inside
the filter disk where the filtrate collects is small and divided in radial flow
channel (about 2 mm). Therefore, the filtrate rotates as a solid body at
the same rotation speed of the filter, that is,k = 1 and its pressure pf varies as the square of angular velocity due to
centrifugal force according to
(1)pf(r)=pf0+12ρ⋅ω2⋅r2.
Here, pf0 denotes its pressure when it enters the hollow
shaft. Its average value over the membrane area is given by integrating (1)
over the
membrane area as
(2)p¯f(r)=pf0+14ρ⋅ω2(ro4−ri4)(ro2−ri2).
In the single
shaft configuration, the axial gap between two rotating filter disks is relatively
large. The concentrate flow is assumed to present an inviscid core rotating at
a velocity kω, where ω is the disk angular velocity and k is the average velocity coefficient.
The parameter k=ωf/ωd is always less than 1. The concentrate radial
pressure in the boundary layer is equal to the inviscid core and is given by
(3)pc(r)=pc0+12ρ⋅r2⋅k˜2⋅ω2withk˜=averagevalue.
Here, pc0 is the concentrate pressure inside the housing
at the center, which is also equal to the pressure when the disk is at rest. By
averaging the concentrate pressure over the filter surface to eliminate the radial
dependence of the pressure, we can get
(4)p¯c(r)=pc0+14ρ⋅k˜2⋅ω2(ro4−ri4)(ro2−ri2).
Since the
permeate is collected at atmospheric pressure, the mean pressure difference along
the filter surface is obtained by
(5)Δp=p¯c−p¯f=pc0−14ρ⋅(1−k˜2)⋅ω2(ro4−ri4)(ro2−ri2).
Filtrate flow
rate was measured using filter disks with average pore size 40 μm and clean
water as a test fluid at various rotation speeds. The pressure pc0 was measured when the filter disk at rest was
6 kPa (see Figure 2). In general, by increasing the rotation speeds permeate flux
decreases due to the centrifugal forces acting on permeate side. We can
determine the rotations speeds via extrapolation at which permeate flux vanish, V˙=0,
that is, the pressure difference is zero. By using (5)
we will be able to
estimate the average velocity coefficient k˜ for the two configurations. The average
velocity coefficient was found to be 0.898 and 0.875 for single and double
shafts disk separator, respectively.Figure 2
Comparison of measured permeate flux rate for single and double shaft disk separator.In order to
check the consistency of the filtration data with the averaged pressure
difference (5), we calculate
the water filtration rate from
(6)V˙(ro,ri)=2πRM⋅μ∫riroΔprdr=πRM.μ[pc0(ro2−ri2)−ρ⋅ω2⋅(1−k˜2)4(ro4−ri4)].
The comparison between
calculated and measured filtration flow rates at various rotation speeds is
plotted in Figure 3, with k˜ = 0.898 and 0.875 for single and double shaft
disk separators. The agreement was excellent and confirms the validity of (5) for
the estimated average velocity coefficient k˜ which must be independent of radial.Figure 3
Comparison of measured and calculated permeate flux rate for single and double shaft
disk separator.The variation of
the measured filtrate flux rate with rotation speed is represented in Figure2 for
single and double shaft disk separators. The filtrate flux rate is seen to be
larger using single shaft disk separator. In fact, the difference in permeate
flux rate using single and double shaft disk separators refers to the average velocity
coefficient k˜.
Thus, the coefficient k˜ may also be good criteria for configuration
performance with absence filter cake, since higher value of k˜ will produce higher permeate flux rate
according to (6). Moreover, we can expect that the torque is necessary to
rotate the disk and thus the shear stress over the disks will be varied in
terms of the average velocity coefficient k˜.


### 3.2. Energetic Consideration

It is important
to estimate the energy that is necessary to drive the disk especially in an industrial
sized system.Therefore, we have measured the electrical power consumed by the
single and double shaft disk separators under consideration. In our small scale
device, a large part of the electrical power supplied is consumed by friction
of the rotating shaft. Thus, to eliminate the shaft friction, we have
subtracted the electrical power necessary to drive the system without disks from
the power at the same speed in the filtration test (with filters).  The power
difference corresponds to the friction forces (shear stress) exerted by the
fluid on the disks, which, in a large scale system, will be the most dominating
forces. This power difference is shown in Figure4 for clean water. It increases
nonlinearly with speed and is larger for double shaft disk separators due to
filter disks overlapping. The electrical efficiency for 0.75 kW motor sizes is
assumed 60% at average rate (independent on the load rate). To estimate the
mechanical power Pm developed by friction forces on the two sides of
the disk, we use
(7)Pm=2⋅π∫rrroτ⋅r2⋅ω⋅dr=η⋅Pe,
where Pe is the electrical power, η the output efficiency without discs, ω the
angular velocity of the motor, τ the shear stress over disk surface.Figure 4
Electrical power consumed for variable rotation speed by single and double shaft
disk separator (0.057 m2 filter media area, 5 disks).The power difference consumed by single and
double shaft disk separators is converted into shear forces exerted on the
disks. Thus, we were able to estimate the average shear stress over the filter
surface for single and double shaft disk separators
according to (7). Figure 5
shows the average shear stress for different rotation speeds using single and
double shaft disk separators. It is clear that the estimated average shear
stress for the double shaft filter disk is about twice as much as shear stress
for the single shaft filter disk. This is due to the filter disk overlapping.Figure 5
Average shear stress at different rotation speed using single and double shaft disk
separator (0.057 m2 filter media area, 5 disks).


### 3.3. Filtration Experiments

We have shown that
the average shear stress for the filter disk overlapping is almost twice as
large as compared to the single shaft disk separator. Thus, it is legitimate to
investigate its ability in avoiding cake formation under filtration process.
Therefore, filtration experiments were carried out using single and double
shaft disk separators atN=750 rpm, C=13.4 g/l, and TMP = 7 kPa. The time
dependency of the permeate flux rate were recorded for single and double shafts
disk separator (Figure 6). It was found that permeate flux remains constant (steady
state filtration) over time for the double shaft disk separator and decays
sharply using the single shaft disk separator. The higher shear stress produced
by using double shaft disk filter as shown before is mainly the reason for the free
cake filter disk. The single shaft showed unsteady state filtration under the
same filtration conditions. The shapes of the filter cakes, for single and
double shaft disk separators, are depicted in Figure 7. The filter cake in the single
shaft disk was observed to be denser and homogenously distributed over the
filter surface as compared to the double shaft disk filter.Figure 6
Variation of filtrate flux rate with time for single and double shaft disk separator using
sphere glass at TMP = 7 kPa,C=13.4 g/l.Filter cake shape after using double shafts (a) single shaft (b).
(a)(b)


## 3.1. Determination of Velocity Factork with Water

The clearance inside
the filter disk where the filtrate collects is small and divided in radial flow
channel (about 2 mm). Therefore, the filtrate rotates as a solid body at
the same rotation speed of the filter, that is,k = 1 and its pressure pf varies as the square of angular velocity due to
centrifugal force according to
(1)pf(r)=pf0+12ρ⋅ω2⋅r2.
Here, pf0 denotes its pressure when it enters the hollow
shaft. Its average value over the membrane area is given by integrating (1)
over the
membrane area as
(2)p¯f(r)=pf0+14ρ⋅ω2(ro4−ri4)(ro2−ri2).
In the single
shaft configuration, the axial gap between two rotating filter disks is relatively
large. The concentrate flow is assumed to present an inviscid core rotating at
a velocity kω, where ω is the disk angular velocity and k is the average velocity coefficient.
The parameter k=ωf/ωd is always less than 1. The concentrate radial
pressure in the boundary layer is equal to the inviscid core and is given by
(3)pc(r)=pc0+12ρ⋅r2⋅k˜2⋅ω2withk˜=averagevalue.
Here, pc0 is the concentrate pressure inside the housing
at the center, which is also equal to the pressure when the disk is at rest. By
averaging the concentrate pressure over the filter surface to eliminate the radial
dependence of the pressure, we can get
(4)p¯c(r)=pc0+14ρ⋅k˜2⋅ω2(ro4−ri4)(ro2−ri2).
Since the
permeate is collected at atmospheric pressure, the mean pressure difference along
the filter surface is obtained by
(5)Δp=p¯c−p¯f=pc0−14ρ⋅(1−k˜2)⋅ω2(ro4−ri4)(ro2−ri2).
Filtrate flow
rate was measured using filter disks with average pore size 40 μm and clean
water as a test fluid at various rotation speeds. The pressure pc0 was measured when the filter disk at rest was
6 kPa (see Figure 2). In general, by increasing the rotation speeds permeate flux
decreases due to the centrifugal forces acting on permeate side. We can
determine the rotations speeds via extrapolation at which permeate flux vanish, V˙=0,
that is, the pressure difference is zero. By using (5)
we will be able to
estimate the average velocity coefficient k˜ for the two configurations. The average
velocity coefficient was found to be 0.898 and 0.875 for single and double
shafts disk separator, respectively.Figure 2
Comparison of measured permeate flux rate for single and double shaft disk separator.In order to
check the consistency of the filtration data with the averaged pressure
difference (5), we calculate
the water filtration rate from
(6)V˙(ro,ri)=2πRM⋅μ∫riroΔprdr=πRM.μ[pc0(ro2−ri2)−ρ⋅ω2⋅(1−k˜2)4(ro4−ri4)].
The comparison between
calculated and measured filtration flow rates at various rotation speeds is
plotted in Figure 3, with k˜ = 0.898 and 0.875 for single and double shaft
disk separators. The agreement was excellent and confirms the validity of (5) for
the estimated average velocity coefficient k˜ which must be independent of radial.Figure 3
Comparison of measured and calculated permeate flux rate for single and double shaft
disk separator.The variation of
the measured filtrate flux rate with rotation speed is represented in Figure2 for
single and double shaft disk separators. The filtrate flux rate is seen to be
larger using single shaft disk separator. In fact, the difference in permeate
flux rate using single and double shaft disk separators refers to the average velocity
coefficient k˜.
Thus, the coefficient k˜ may also be good criteria for configuration
performance with absence filter cake, since higher value of k˜ will produce higher permeate flux rate
according to (6). Moreover, we can expect that the torque is necessary to
rotate the disk and thus the shear stress over the disks will be varied in
terms of the average velocity coefficient k˜.


## 3.2. Energetic Consideration

It is important
to estimate the energy that is necessary to drive the disk especially in an industrial
sized system.Therefore, we have measured the electrical power consumed by the
single and double shaft disk separators under consideration. In our small scale
device, a large part of the electrical power supplied is consumed by friction
of the rotating shaft. Thus, to eliminate the shaft friction, we have
subtracted the electrical power necessary to drive the system without disks from
the power at the same speed in the filtration test (with filters).  The power
difference corresponds to the friction forces (shear stress) exerted by the
fluid on the disks, which, in a large scale system, will be the most dominating
forces. This power difference is shown in Figure4 for clean water. It increases
nonlinearly with speed and is larger for double shaft disk separators due to
filter disks overlapping. The electrical efficiency for 0.75 kW motor sizes is
assumed 60% at average rate (independent on the load rate). To estimate the
mechanical power Pm developed by friction forces on the two sides of
the disk, we use
(7)Pm=2⋅π∫rrroτ⋅r2⋅ω⋅dr=η⋅Pe,
where Pe is the electrical power, η the output efficiency without discs, ω the
angular velocity of the motor, τ the shear stress over disk surface.Figure 4
Electrical power consumed for variable rotation speed by single and double shaft
disk separator (0.057 m2 filter media area, 5 disks).The power difference consumed by single and
double shaft disk separators is converted into shear forces exerted on the
disks. Thus, we were able to estimate the average shear stress over the filter
surface for single and double shaft disk separators
according to (7). Figure 5
shows the average shear stress for different rotation speeds using single and
double shaft disk separators. It is clear that the estimated average shear
stress for the double shaft filter disk is about twice as much as shear stress
for the single shaft filter disk. This is due to the filter disk overlapping.Figure 5
Average shear stress at different rotation speed using single and double shaft disk
separator (0.057 m2 filter media area, 5 disks).


## 3.3. Filtration Experiments

We have shown that
the average shear stress for the filter disk overlapping is almost twice as
large as compared to the single shaft disk separator. Thus, it is legitimate to
investigate its ability in avoiding cake formation under filtration process.
Therefore, filtration experiments were carried out using single and double
shaft disk separators atN=750 rpm, C=13.4 g/l, and TMP = 7 kPa. The time
dependency of the permeate flux rate were recorded for single and double shafts
disk separator (Figure 6). It was found that permeate flux remains constant (steady
state filtration) over time for the double shaft disk separator and decays
sharply using the single shaft disk separator. The higher shear stress produced
by using double shaft disk filter as shown before is mainly the reason for the free
cake filter disk. The single shaft showed unsteady state filtration under the
same filtration conditions. The shapes of the filter cakes, for single and
double shaft disk separators, are depicted in Figure 7. The filter cake in the single
shaft disk was observed to be denser and homogenously distributed over the
filter surface as compared to the double shaft disk filter.Figure 6
Variation of filtrate flux rate with time for single and double shaft disk separator using
sphere glass at TMP = 7 kPa,C=13.4 g/l.Filter cake shape after using double shafts (a) single shaft (b).
(a)(b)


## 4. Conclusion

The performance
of single and double shaft disk separators has been investigated. Permeate flux rate is found
to decrease as the rotation speed increases for both configurations. The
average velocity coefficientk˜ was estimated for both configurations and also
confirmed under the filtrationprocess. It  was found that the average velocity coefficient k˜ is thecriterion for configuration performance.
Shear stress is enhanced by decreasing the average velocity coefficient. The
power consumption is not only a function of rotation speed but is also affected
by the filter geometry. It is possible to obtain steady state filtration (without
cake formation) using double shaft disk separator.



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*Source: 508617-2008-06-02.xml*