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Instrumented flow-following sensor particles with magnetic position detection and buoyancy control

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A concept for buoyancy control and magnetic position detection has been developed for the improvement of instrumented flow-following sensor particles. The sensor particles are used for investigation of hydrodynamic and biochemical processes in large-scale vessels such as biogas fermenters, bioreactors and aerated sludge basins. Neutral buoyancy of the sensor particles is required for tracing of the fluid flows. Buoyancy control is performed by adjustment of the sensor particles' volume, which is altered by an integrated piston. A miniaturized linear actuator, namely a stepper motor with linear transmission, is operated by a microcontroller to drive the piston. The buoyancy control unit enables accurate automated taring of the sensor particles in the stagnant process fluid to achieve neutral buoyancy. Therefore, the measured vertical position of the sensor particle as a function of the hydrostatic pressure is used as feedback. It has an incremental density change of 0.0136 % as compared to water and a residual drift velocity of approximately 3.6 × 10−3 m s−1. Furthermore, a minimum density of 926 kg m−3 can be set by full extension of the piston, which allows floating of the sensor particles after a defined event, namely critical charge of battery, full data storage or the end of a fixed time cycle. Thus, recovery of the sensor particles can proceed easily from the fluid level. The sensor particles with a buoyancy control unit are tested for depths up to 15 m. Also, detection of a local magnetic position marker by the sensor particles has been implemented to enhance movement tracking. It was tested in a lab-scale biogas digester and was used for estimation of the liquid circulation time distribution and Peclét number to describe the macro-flow.
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J. Sens. Sens. Syst., 5, 213–220, 2016
www.j-sens-sens-syst.net/5/213/2016/
doi:10.5194/jsss-5-213-2016
© Author(s) 2016. CC Attribution 3.0 License.
Instrumented flow-following sensor particles with
magnetic position detection and buoyancy control
Sebastian Felix Reinecke1and Uwe Hampel1,2
1Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328 Dresden, Germany
2AREVA Endowed Chair of Imaging Techniques in Energy and Process Engineering, Technical University of
Dresden, 01062 Dresden, Germany
Correspondence to: Sebastian Felix Reinecke (s.reinecke@hzdr.de)
Received: 19 February 2016 – Revised: 31 May 2016 – Accepted: 31 May 2016 – Published: 17 June 2016
Abstract. A concept for buoyancy control and magnetic position detection has been developed for the im-
provement of instrumented flow-following sensor particles. The sensor particles are used for investigation of
hydrodynamic and biochemical processes in large-scale vessels such as biogas fermenters, bioreactors and aer-
ated sludge basins. Neutral buoyancy of the sensor particles is required for tracing of the fluid flows. Buoyancy
control is performed by adjustment of the sensor particles’ volume, which is altered by an integrated piston. A
miniaturized linear actuator, namely a stepper motor with linear transmission, is operated by a microcontroller to
drive the piston. The buoyancy control unit enables accurate automated taring of the sensor particles in the stag-
nant process fluid to achieve neutral buoyancy. Therefore, the measured vertical position of the sensor particle
as a function of the hydrostatic pressure is used as feedback. It has an incremental density change of 0.0136 %
as compared to water and a residual drift velocity of approximately 3.6 ×103m s1. Furthermore, a minimum
density of 926 kg m3can be set by full extension of the piston, which allows floating of the sensor particles
after a defined event, namely critical charge of battery, full data storage or the end of a fixed time cycle. Thus,
recovery of the sensor particles can proceed easily from the fluid level. The sensor particles with a buoyancy
control unit are tested for depths up to 15 m. Also, detection of a local magnetic position marker by the sensor
particles has been implemented to enhance movement tracking. It was tested in a lab-scale biogas digester and
was used for estimation of the liquid circulation time distribution and Peclét number to describe the macro-flow.
1 Introduction
Large-scale plants and vessels in the energy and process in-
dustry have limited accessibility for measurement instrumen-
tation. Installation of local sensors with cabled connections
is often not possible or avoided due to high costs. Further-
more, standard measurement techniques such as videometry,
thermography, particle imaging velocimetry (PIV) and pro-
cess tomography are not applicable to the process vessels
due to the large vessel dimensions, the harsh environmental
conditions and the opaque fluids. Thus, investigation, mod-
elling and control of the chemical, mechanical and thermal
processes are limited and often insufficient.
Temperature profiles, pH profiles, gas–liquid–solid distri-
bution in the substrate and local digestion rate are of main
interest for estimation of the process efficiency and for de-
velopment and design of plants in the field of stirred biore-
actors, fermenters and biological waste water treatment fa-
cilities. Moreover, hydrodynamic parameters – e.g. flow ve-
locity, distribution of dead zones and short-circuit flows, and
circulation times – are in focus for characterization of pro-
cesses.
Application of instrumented flow followers and au-
tonomous sensor technologies allows investigation of the aer-
ation, mixing and heating regimes by acquisition of a few
basic physical parameters, such as temperature and pressure.
This information is currently only available at a few local
measurement positions. Thus, design and operation of plants
and processes are mainly based on the experience of the op-
erator. Therefore, autonomous sensor technologies are get-
Published by Copernicus Publications on behalf of the AMA Association for Sensor Technology.
214 S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control
ting more relevant for the process industry (Antoniou et al.,
2009).
Autonomous sensor particles were developed by Thiele et
al. (2010) to be applied to large-scale vessels – such as biore-
actors, biogas digesters and activated sludge basins – as in-
strumented flow followers that continuously capture the spa-
tially distributed process parameters and provide the data to
an external computer system for further analysis. The sensor
particles have been tested under realistic flow conditions of
stirred tanks and biogas digesters, and characteristic process
parameters have been estimated, e.g. vertical flow velocity,
circulation time, circulation number, Peclét number and de-
gree of suspension (Reinecke et al., 2012; Reinecke, 2014).
The configuration of the sensor particles by Thiele et
al. (2010) comprises a set of sensors for basic parameters,
namely immersions depth as a function of ambient pres-
sure, 3-D acceleration and temperature. Therefore movement
tracking of the sensor particles was limited to the vertical
position and vertical velocity. An important feature of flow-
following sensor particles is sufficient tracing of the fluid
flows. Therefore, neutral buoyancy of the sensor particles is
required to avoid flow offsets from the sensor particles’ grav-
ity and buoyancy. In practice, neutral buoyancy of particles
for mixing process applications is related to a residual termi-
nal velocity of the particles below 1 ×102m s1measured
in stagnant fluids. The sensor particles’ mass used to be ad-
justed manually to tare the sensor particles for a low sinking
or rising velocity. Moreover, recovery was cumbersome due
to the undefined final position of the sensor particles.
This paper presents an enhanced concept of sensor parti-
cles with an integrated buoyancy control unit and detection
of external magnetic position markers. An autonomous taring
regime is implemented in the sensor particles to achieve neu-
tral buoyancy in a sample volume of the process substrate.
Moreover, an event-driven floating of the sensor particles is
possible with the buoyancy control unit, which allows recov-
ery from the liquid surface.
Movement-tracking capabilities of the sensor particles are
also extended to the horizontal direction by detection of ex-
ternal magnetic position markers. Transmitting coils are im-
mersed into to vessel at a fixed position and excited by a
modulated signal. The transmitted signal is captured by the
sensor particles during passage at the marker position.
The enhanced sensor particles were tested under real flow
conditions in a lab-scale biogas digester with an oval shape
where the position marker was used to deliver information
about the horizontal flow in the vessel.
2 Sensor particle design
The enhanced sensor particles are based on the original con-
cept by Thiele et al. (2010) and comprise a robust hous-
ing with an integrated electronic measuring and control unit
(Fig. 1). The integrated electronics include miniaturized sen-
Figure 1. Components of a sensor particle with internal electronics
and buoyancy control unit.
Figure 2. Open sensor particle with the electronics and the ex-
tended piston of the buoyancy control unit.
sors for temperature (0 ...50 C), vertical position as a func-
tion of hydrostatic pressure (0 ...300 kPa), 3-D acceleration
(6...+6 g) and magnetic field (4...+4 G), and a micro-
controller that performs the autonomous taring and measur-
ing regimes. A lithium polymer battery pack is connected to
a voltage converter and works as an onboard energy supply.
The robust housing is modular to carry the electronics and
the components of the buoyancy control unit. Figure 2 de-
picts the sensor particle housing with the extended piston
and the connected electronics. The mounted sensor particles
have a minimal volume of VSP =1.5×104m3, a mass
of mSP =0.145 kg and thus a density of ρSP =967 kg ×m3
without internal payload and retracted piston. The equivalent
spherical diameter is dSP =6.6 ×102m, and the sphericity
is ψ=0.9. Internally, a void of 1.7 ×105m3is reserved for
the payload which is set to 0.005 kg to achieve almost neu-
tral buoyancy with a minimally extended piston in water. A
maximal density of the sensor particles of 1873 kg ×m3is
achievable when the whole void is filled with the payload
made of stainless steel (density 8000 kg ×m3).
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S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control 215
Figure 3. Characterization of the required density offset of sensor
particles in a stirred vessel experiment in water for an improved
recovery at the liquid surface.
2.1 Buoyancy control concept
The purpose of the buoyancy control unit is (i) to enable au-
tomated taring of sensor particles to achieve neutral buoy-
ancy before the start of the autonomous measurement regime
and (ii) to ensure an event-driven floating of sensor parti-
cles for recovery from the liquid surface. Recovery of sen-
sor particles from the liquid surface is only possible if the
sensor particles have sufficient buoyancy offset to float and
remain at the liquid surface. A buoyancy offset of sensor
particles implies a reduction of the particles’ density. In in-
dustrial applications the fluids are in motion due to mixing
by impellers or gas dispersion, and thus turbulent flows are
present also at the liquid surface. This turbulence at the sur-
face support resuspension of the sensor particles into the
liquid body, and a higher buoyancy offset is necessary to
keep the sensor particles floating. An experimental study
was conducted under highly turbulent flow conditions in a
stirred tank to estimate the required density offset of sen-
sor particles to achieve sufficient buoyancy offset. Figure 3
depicts the stirred tank that was filled with water of den-
sity ρf=998 kg m3up to a filling level H0=0.8 m and
the suspended sensor particles. Strong axial forces that pull
down the sensor particles are present at the intake region
of the pitched-blade impeller in the circulation flow. There-
fore, different impeller speeds nwere used, namely 0.92,
1.23 and 1.53 s1. These correspond to Reynolds numbers of
2.3 ×105, 3.1 ×105and 3.8 ×105, respectively, which meet
the criterion Re > 0.2 ×105×5×105for a fully turbulent
flow in the stirred tank (Liepe et al., 1998; Schubert, 2003).
Three sensor particles with the configuration by Thiele et
al. (2010) were used with different taring, namely neutrally
buoyant (ρSP ρf), offset of 2% (ρSP 0.98×ρf) and offset
of 6 % (ρSP 0.94 ×ρf).
Vertical residence profiles were extracted from the mea-
sured data according to Reinecke et al. (2010) to describe
the residence of the sensor particles over the height of the
liquid column (Fig. 4). The neutrally buoyant sensor particle
(ρSP ρf) reflects the relevant residence profile to charac-
terize the hydrodynamics of the process. An upwards shift
of the profiles is recognized for the sensor particle with the
offset of 2 % (ρSP 0.98×ρf). However, the residence at the
liquid surface is still too low for improved recovery. A signif-
icant peak of the residence profile at the surface is achieved
with the density offset of 6 % (ρSP 0.94 ×ρf), and only
temporary resuspension was observed. In conclusion a den-
sity offset of 6 % compared to the neutrally buoyant setting
is required to ensure predominant floating of sensor particles
even under highly turbulent flow conditions.
Based on the results of the experimental study, a buoyancy
control concept for sensor particles has been developed. Fig-
ure 5 shows the main components. The housing has an in-
tegrated piston to adjust the volume and therefore also the
buoyancy of the sensor particle. A miniaturized linear ac-
tuator, namely a stepper motor with integrated linear trans-
mission and incremental step length of 0.0254 mm, drives
the piston and is powered by the onboard battery pack. The
motor driver is directly controlled by the microcontroller. A
feedback of the current vertical position of the sensor parti-
cle is provided by the pressure sensor which is required for
automated taring. Floating of the sensor particle is set by the
microcontroller after a defined event, namely critical charge
of battery, full data storage or the end of a fixed time cycle.
The piston is integrated in the upper front of the sensor
particle and is supported by an O-ring seal. The fitting of
the seal was adjusted to reduce the force for actuation of the
piston to below 10 N but still ensures tightness of the housing
for water columns of up to 15 m (test pressure of 250 kPa;
safety factor: 1.5). The linear transmission of the actuator is
situated inside the hollow part of the piston and is connected
to the upper end of it to use the full travel of the actuator of
15 mm for the piston. In this way, a volume change of 8 %
is possible as compared to the normal volume of the sensor
particle, which results in a minimum density of 926 kg m3,
and floating of the sensor particles is ensured at full travel
of the piston even under turbulent flow conditions in most
aqueous fluids.
Neutral buoyancy can only be achieved if the incremen-
tal density change is sufficiently small. Due to the small step
length of the linear actuator, the incremental density change
of the buoyancy unit is 0.0136 %. An estimate of the result-
ing maximal particle terminal velocity can be calculated by
Eq. (1):
vT=v ρ2
f
g×µf×(ρSP ρf)!1
3
(1)
with the liquid viscosity represented by µf, the dimen-
sionless terminal velocity by v=f (d,ψ) and the dimen-
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216 S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control
(a) (b) (c)
0 1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z/H
0
Relative frequency density
n
= 0.92 s
-1
n
= 1.23 s
-1
n
= 1.53 s
-1
0 1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z/H
0
Relative frequency density
n = 0.92 s
-1
n = 1.23 s
-1
n = 1.53 s
-1
0 5 10 15
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z/H
0
Relative frequency density
n
= 0.92 s
-1
n
= 1.23 s
-1
n
= 1.53 s
-1
Figure 4. Vertical residence profiles of the sensor particles from the experiments in the stirred vessel for characterization of the required
density offset at the impeller speeds of 0.92, 1.23 and 1.53 s1with different density ρSP of the sensor particles at the fluid density ρf:
(a) ρSP ρf,(b) ρSP 0.98 ×ρfand (c) ρSP 0.94 ×ρf.
Figure 5. Components of the buoyancy control unit of sensor par-
ticles.
sionless diameter by daccording to Haider and Leven-
spiel (1989). Assuming µf=1×103Pa ×s for water and
µf=1 Pa ×s as effective viscosity for typical liquid bio-
substrates, the expected maximal terminal velocity of sen-
sor particles is 1 ×102m s1and 3 ×104m s1, respec-
tively. This is below the acceptable limit of 1 ×102m s1
for neutral buoyancy in mixing processes and shows that the
incremental density change of the buoyancy unit is sufficient
for taring of sensor particles. An automated taring regime of
sensor particles has been implemented in the microcontroller
that uses the signal of the pressure sensor as feedback for the
current vertical position. This regime proceeds prior to the
application of sensor particles to the process vessel. At first
each sensor particle is inserted into a mobile container, i.e. a
column of ca. 1 m height, which is filled with a sample vol-
ume of process substrate, and the sensor particles detect the
immersion from the pressure signal (Fig. 6a). The piston of
the buoyancy control unit is initially retracted. That makes
the sensor particle sink slightly, which is recognized by the
sensor particle. The sensor particle remains at the bottom of
the container for a short duration for thermal adjustment of
the housing to the substrate temperature. Then the piston is
extended stepwise, and the hydrostatic pressure is measured
after a duration of 250 ms, which is the empirically estimated
relaxation time tmin of the sensor particle for incremental
extension of the piston in water. For tmin < 200 ms in wa-
ter the density change is faster than the sensor particle body
responds, and thus the maximal amplitudes of the vertical
sensor particle movement starts to reach the container height
during taring due to the low liquid viscosity. In the period
of tmin the incremental density change of 0.0136 % gives a
change of the vertical position of 3 ×103and 8 ×105m
with regard to the estimated maximal terminal velocity of
sensor particles in water and in biosubstrate, respectively.
The piston is further extended until the sensor particle
slowly starts to rise and the current pressure value gets lower
than the maximum pressure at the container bottom (Fig. 6b).
Then comes the control regime where the position of the
piston is adjusted with regard to tmin until the pressure dif-
ference of consecutive measurements remains zero; i.e. it
constantly falls below the resolution of the pressure sen-
sor of 9 Pa and 9 ×103m in vertical position. Thus, the
sensor particle is neutrally buoyant with a minimal toler-
ance after the automated taring regime. The resolution of
9×103m and the relaxation time tmin result in a residual
terminal velocity of approximately 3.6 ×103m s1, which
is a hypothetical estimate. Also this value is below the limit
of 1 ×102m s1for neutral buoyancy in mixing processes.
However, only a negligible terminal velocity of the sensor
particles has been observed during application of the auto-
mated taring regime under laboratory conditions. Achieve-
ment of such results is cumbersome with manual buoyancy
adjustment of sensor particles and takes a lot of effort.
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S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control 217
2.2 Magnetic position detection
Enhanced movement tracking of sensor particles includes
detection of a local position marker that is located at a
fixed position in the process vessel, by an onboard sensor.
Bryant (1969) and Day (1975) applied a similar concept for
estimation of fluid circulation times in bioreactors for the first
time. They used a flow-following radio pill, and the emitted
radio signal was detected inside the vessel by a locally in-
stalled antenna. Position marking for sensor particles is based
on an immersible coil that is mounted into the cross section
of the flow in the process vessel to extend the movement-
tracking abilities of the sensor particles. The coil is made of
a cable spool which is mounted in a watertight pipe frame.
It has a width of 0.53 m and a height of 0.78 m. This simple
construction allows scaling of the coil from laboratory up to
industrial applications. It emits a magnetic signal in a lim-
ited range, and this signal is detected by a magnetic sensor of
the sensor particle during passage of the coil. A magnetome-
ter is used in the current configuration to measure the am-
bient magnetic flux generated by the coil. Nevertheless, the
influence of the magnetic background – namely earth’s mag-
netic field, metallic vessel components and other surrounding
magnetic sources – is also measured. Thus, either sufficiently
high magnetic signal levels above the magnetic background
level or signal modulation/coding are required for confident
position detection at the coil. A simple frequency hop exci-
tation signal is used at the coil to achieve a clear discrimina-
tion of the position marker from the magnetic background.
The measured magnetic flux signal Bat the magnetometer in
the sensor particle is correlated with the reference signal Bref
according to Eq. (2):
ˆ
RXY(m)=
Nm1
X
n=0
B(n+m)B
ref(n),(2)
where nand mare the discrete time steps and N the length of
the time series Band Bref. Furthermore, the envelope of the
correlated sequence ˆ
RXY(m) is extracted to apply a robust
threshold binarization of the signal.
The signal frequency changes from 1 to 2 Hz in a period of
2 s. A low-frequency band was chosen to ensure correct ac-
quisition of the marker signal also at lower acquisition rates
of the autonomous measurement regime. However, due to the
small bandwidth of the excitation signal the signal correla-
tion may be too low in certain flow situations. Higher pro-
cessing gain of the signal detection may be achieved with
more advanced modulation techniques that require a higher
signal bandwidth, such as spread spectrum techniques in dig-
ital modulation. However, this in turn requires higher com-
putational performance and energy consumption of the elec-
tronics, which reduces the runtime of sensor particles.
Therefore the position marker was designed to generate a
higher magnetic flux than the magnitude of earth’s magnetic
field of 0.5 G even in the centre of the coil. In combination
(a) (b)
Figure 6. Sensor particles during the automated taring regime in a
fluid sample: (a) residence at the container bottom and (b) elevated
position during the automated taring regime.
with the simple signal modulation this allows clear detec-
tion of the passage of the sensor particles at the coil. Fur-
thermore, the magnetic position detection of sensor particles
extends the abilities of sensor particles to estimate individual
circulation times also in horizontal flow situations. That is a
characteristic process parameter for mixing in agitated tanks.
3 Experiment in a lab-scale biogas digester
3.1 Experimental set-up
Advanced sensor particles with a buoyancy control unit and
magnetic position marker were tested in a lab-scale biogas
digester. The digester has an oval geometry and is operated
as a circulation reactor to achieve homogeneous and mild
mixing of the substrates in the biogas digester (Fig. 7). Two
impellers are installed horizontally at the long sides of the di-
gester in the centre of the channel. The filling volume is 2 m3,
and the channel width is 0.55 m. Both impellers were driven
at the impeller tip speed of 5.5 and 6.7 m s1. An aqueous
xanthan solution with a concentration of 5 g L1was used to
simulate the rheology of real biogas substrates. The coil was
installed at the apex of the vessel (Fig. 7b). Four sensor par-
ticles performed the automated taring regime and were then
applied to the digester at an acquisition rate of 8 s1. They
remained in the process for 100 min before final floating and
recovery from the liquid surface. Afterwards the measured
digital values were downloaded from the data storage of the
sensor particles for further analysis on an external computer.
3.2 Floating and recovery of sensor particles
After the programmed measurement period of 100 min, full
extension of the piston was initiated by the buoyancy con-
trol unit on all sensor particles for final floating. The first
sensor particles already remained at the liquid surface before
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218 S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control
Figure 7. Lab-scale biogas digester with oval geometry and an in-
stalled coil as a position marker. The horizontal positions of the two
impellers and the main flow direction are marked in (a).
the piston was fully extended when they entered a stagnant
zone (see Fig. 8a). After full extension of the piston, the sen-
sor particles were clearly visible at the liquid surface (see
Fig. 8b) and were recovered manually by means of a dip net.
No resuspension of sensor particles was observed with a fully
extended piston even in turbulent flow regions (see Fig. 8c)
3.3 Detection of position marker
The time series of the measured magnetic signal contains
the received signal of the position marker and is influenced
by the movement of the sensor particles in earth’s magnetic
field. Figure 9a depicts a sequence of the measured mag-
netic signal of a sensor particle in the biogas digester. Pas-
sages at the position marker can already be seen from the
higher signal magnitudes above 0.5 G. A clear discrimination
of the passages is achieved by cross-correlation of the mea-
sured magnetic signal with the reference signal according to
Eq. (2), which can be seen from the extracted envelope of
the correlated signal sequence in Fig. 9b. Binarization of the
correlated signal provides further reduction of the received
signal (Fig. 9c). The threshold was adjusted to avoid false de-
tection of sensor particle movement in earth’s magnetic field.
Therefore, a separate test measurement was performed in the
(a)
(b)
(c)
Figure 8. Floating sensor particles at different positions on the liq-
uid surface in the biogas digester.
digester without position marker, and the threshold value was
minimized. Finally, the temporal differences in the binary
signal represent the horizontal circulation times of the sen-
sor particles in the digester.
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S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control 219
1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320
0
0.5
1
Flux density (Gauss)
1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320
0
2
4
6
Correlated signal
1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320
0
1
Binary signal
Time (s)
(a)
(b)
(c)
Figure 9. Sequence of the analysed magnetic field signal of a sen-
sor particle for detection of a position marker for the horizontal flow
in the biogas digester: (a) magnitude of the magnetic flux density,
(b) correlated signal with the threshold for binarization and (c) bi-
nary signal.
3.4 Estimation of circulation time distribution and
dispersion
The population of the individual circulation times tcyields
the circulation time distribution which is depicted in Fig. 10
for both impeller speeds. All four sensor particles show a
similar shape of the circulation time distribution which sup-
ports the reliability of the data. An even more significant
result is obtained by the analysis of the combined time se-
ries data of all four sensor particles which is also depicted in
Fig. 10.
The influence of the impeller speed can be observed sim-
ply from the shape of the circulation time distributions. A
rather flat distribution is obtained for the lower impeller
speed, where the average value is ¯
tc=56.0 s and the stan-
dard deviation is σc=66.1 s. In contrast, the distribution is
more distinct for the higher impeller speed with ¯
tc=25.7 s
and σc=23.5 s.
According to Luo and Al-Dahhan (2008) these statisti-
cal quantities of the circulation time distribution estimate the
Peclét number:
P e 2·tc
σc2
,(3)
which is the ratio of the advective flow to diffusion and thus
describes back mixing of mass transfer. An ideal stirred tank
reactor has Pe =0 (ideal mixing), and an ideal plug flow re-
actor has Pe = ∞ (convection and no back mixing). The val-
ues of the circulation time distribution yield Pe =1.4 for the
lower impeller speed and Pe =2.4 for the higher impeller
speed. This indicates a slight reduction of back mixing and
0 20 40 60 80 100 120 140 160 180 200
0
0.02
0.04
0.06
0.08
Relative frequency density
Circulation time (s)
SP 1
SP 2
SP 3
SP 4
Combined
0 20 40 60 80 100 120 140 160 180 200
0
0.02
0.04
0.06
0.08
Relative frequency density
Circulation time (s)
SP 1
SP 2
SP 3
SP 4
Combined
(a)
(b)
Figure 10. Circulation time distribution of all four sensor particles
(SP1 ...4) in the biogas digester at the impeller speeds (a) 5.5 and
(b) 6.7 m s1. The distribution of the combined time series of all
sensor particles is given in blue.
an increased convective flow after the increase of the impeller
speed. In conclusion, the extracted values from the sensor
particle measurements – namely the average circulation time,
the standard deviation and the Peclét number – describe the
macro-flow conditions in the biogas digester and indicate that
the sole increase of impeller speed in the biogas digester ex-
periment did not contribute to an improved mixing in this
vessel geometry.
4 Conclusions
Enhanced instrumented flow-following sensor particles have
been developed with an integrated buoyancy control unit and
magnetic position detection. The buoyancy control unit en-
ables automated taring by a sensor particle to achieve neutral
buoyancy in the process fluid without cumbersome manual
adjustments of payloads. Furthermore, the sensor particles
are capable of floating to the liquid surface after a certain
event, such as critical charge of battery, full data storage or
the end of a fixed time cycle, for easy recovery. This facil-
itates the handling during application of sensor particles to
processes in laboratory set-ups and especially in vessels of
real plants in the energy and process industry.
The movement-tracking ability of sensor particles is ex-
tended by detection of a magnetic position marker, namely
an immersible coil. The marker is placed at a fixed position
in the process vessel to cover horizontal movement of sensor
particles in addition to the vertical position as a function of
the ambient pressure.
Four sensor particles with a buoyancy control unit and
magnetic position detection were successfully tested in a lab-
scale biogas digester with horizontally circulation flow. The
www.j-sens-sens-syst.net/5/213/2016/ J. Sens. Sens. Syst., 5, 213–220, 2016
220 S. F. Reinecke and U. Hampel: Sensor particles with magnetic position detection and buoyancy control
measured data describe the macro-flow in the digester. Mag-
netic position detection of sensor particles was used to es-
timate the individual circulation times and the circulation
time distribution in the horizontal flow of the digester. More-
over, back mixing is characterized by estimation of the Peclét
number from the circulation time statistics of sensor parti-
cles.
Performance of the magnetic position detection can be im-
proved by implementation of advanced signal modulation
techniques, such as spread spectrum techniques. However,
this requires thorough design of the data acquisition unit
in the sensor particles. Furthermore, it will be investigated
whether the position marker concept can be combined with
an inertial measurement unit in the sensor particles to achieve
a position-tracking system with 3-D capabilities. However,
signal coding for detection of multiple position markers dis-
tributed across the vessel will be considered as well. Never-
theless, accuracy of the estimated position has to be investi-
gated for development of a reliable position-tracking system.
Acknowledgements. Results of this paper also originate from
the research project LEOBEL, which is funded by the German Fed-
eral Environmental Foundation (DBU – Deutsche Bundesstiftung
Umwelt) under the reference number AZ30799. The experiment
in the lab-scale biogas digester was conducted in cooperation with
the Fraunhofer Institute for Ceramic Technologies and Systems
Dresden (IKTS).
Edited by: S. Zimmermann
Reviewed by: two anonymous referees
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Mixing in stirred tanks, Dissertation
  • A Day
Day, A.: Mixing in stirred tanks, Dissertation, University of Exeter, Exeter, UK, 1975.
Mixing in Fermenters
  • J Bryant
Bryant, J.: Mixing in Fermenters, Dissertation, University of Cambridge, Camdridge, UK, 1969.
Instrumentierte Strömungsfolger zur Prozessdiagnose in gerührten Fermentern, Dissertation, Dresdner Beiträge zur Sensorik
  • S F Reinecke
Reinecke, S. F.: Instrumentierte Strömungsfolger zur Prozessdiagnose in gerührten Fermentern, Dissertation, Dresdner Beiträge zur Sensorik, Band 52, TUDpress, Dresden, Germany, 2014.