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On-stream particle size, concentration and velocity measurements by auto-correlation of scattered laser light
Powder 0
Technology,
Elsewer
Sequoia
29 (1981) S-A.,
Lauanne
217 - 223 -Printed
31i in The
Netherlands
On-Stream Particle Size, Concentration Correlation of Scattered Laser Light? N. G_ STANLEY-WOOD*,
G_ J_ LLEWELLYN**
Poslgraduale Schoois of Studies in Powder Bradford. IV_ Yorks. 807 IDP (Gt Brrtain) (Received
November
and
and Velocity
by Auto-
Measurements
A. TAYLOR+*
Tcchnolog>
* and Control
Enginccrrng**
Unirersity
of
Bradford
26.1979)
long
SUMMARY
been
instrument
With the increase IR automatic control of powder processes there is now a need for onstream or real time instrumentation to treasure the size and solid concentration of partrcles in slurries_ On-stream ueloclty, particle size and concentration have been obtained by the interrogatlon of sand-water slurries by two 5 mW HeNe laser beams_ The scattered laser light, from concentrated slurries in the range 1.0 X IO-” - l-090 w/u) flourmg at uelocltles between 0.5 - 3.0 m set-’ in a 2.5 cm diam. uerticalpipe, is transduced byaphotodetector into random fluctuating electrical signals. The rrld:vrdual signak are auto-correlated and the power spectra computed to determine the particle size range and concentration of the suspended particles while the velocity of flow is determined from cross-correlation of the signals obtained from the axudly separated lasers The change in particle concentration and size jointly affect the shape of both the autocorrelogram and the power spectral density of the photodiode signnl. By improued methods of detection, instrumentation implementation and data analysis, the velocrty, particle size and concentration in a flowing suspension can be separately evaluated. INTROD’JCTION
The onstream measurement size and concentration in flowmg
of particle slurries has
*Presented at the 2nd European Symposium on Particle Characterisation, Part&cl Technologie, Nuremberg, September 1979_
reasons
recognised design
for these
as a ‘difficult’ and
area
development_
difficulties
are manifold
III
The but
some of the problems have been outlined by Asbj0msen [l] : (a) lack of understanding of the physical characteristics of slurries, their properties and classification; (b) lack of definition in measurement parameters; (c) the difficult and involved nature of onstream real time measurements; (d) the demanding conditions under which the instrument has to operate_ In most industrial slurries or liquid-solid mixtures, naturally occurring disturbances such as local spatial and temporal variations m composition, density or turbulence - the tagging element e_xist within a flowing suspension_ Detection of these spatial and temporal variations of solid phase by optical or electrical transducers together with subsequent interrogation and analysis of the transducer signals by cross- or auto-correlation can be used to measure the parameters of size, concentration and sohd or flow velocity in a flowing system 12, 3]_ The ‘tagging element’ used in the present system of two-phase flow is the scattered laser light from the solid phase. By designing an instrument that employs cross- and/or auto-correlation techniques as its measurement principle, an acceptable solution has been achieved to some of the problems encountered in on-stream and instream measurements(a) On-stream - the instrument works m real time_ It is also suitable for interfacing with micro-processor or other computer control ;
218
(b) In-stream - no sampling of the slurry stream is required, and the range of solid concentration and size of particles can be extended by suitable dilution; (c) Robustness and ease of maintenance the basic transducer system of laser light and photodetectors is suitable for development into a rugged modular construction suitable for industrial plants. The laser requires a reasonable power input and can be made to normal safety standards_ (d) Wide range of particle sizes - the system is adaptable to measure particle sizes in the range 100 pm - lOOO+ pm subdivided into three or four size ranges. In this work, laser light scattered by solid particles flowing m a vertical 2.5 cm diam. perspex pipe has been collected onto a photodetector positioned at 90” to the beam and the resultant electrical signals auto-correlated and the power spectra computed to determine the relationships between particle size, concentration and velocity of the flowmg solid phase_
PRINCIPLES Data analysis Prior to a description of the measurement system, a brief r&urn6 of the data analysis techniques of correlation and power spectral densities is necessary [4] _
lmn
Rx,(?-) =
T-+-
R,,(T)
= ECx(t)
where E(f) represents the ensemble average of the function (fi of sample values_ Similarly, for two jointly stationary processes, x(t) and y(t), their cross-correlation is defmed by R,,(r)
= EEx(t)
Y(C + 711
These ensemble autoand correlograms can be alternatively mathematically as
crossexpressed
y(t + T)dT
(2)
Power spectral density In the frequency band between f and f + Af, the mean square value (Gz) of a sample time history record, x(t), can be obtained through the computation of the average of the output when x(t) is applied to a sharp cut-off, band-pass filter. Expressed mathematically,
G,ZCf.f
x2 (t, f, NWt
+Afl=
where x(t, f, An is that portion of x(t) in the frequency range from f to f + Af_ When the band-pass filter is very narrow (r-e_ A f is small), the power spectral density function, G,(f), can be defined such that lull
G,(f)
G:(f,f
=
+Afl
Af
nr-0
is stationary,
an important
of G,(fl is that it is related to R,,(T) Fourier transform: G,(f)
= 2
-_
= 4
x(t + T)]
T
5 x(t) c-8
if the stationary, random processes are ergondic R,,(r) and R,,(r) are respectively termed the time auto-correlogram and time crosscorrelogram
As x(t) Correlation For a single process, x(t), which can be considered to be stationary in the wide sense, the secondorder moment or auto-correlogram (R,,(r), where 7 represents time displacement) can be defined by
1
jR,,(~)e-‘~‘~~
I
R,,(r)
cos 2afrdr
-_ as R,,(T)
property by the
is an even function
(3)
of T.
The practical computation of auto- and crosscorrelograms and power spectral density functions can be achieved by a HewlettPackard (3721A) Correlator and a HewlettPackard Spectrum Display (3720A) instrument.
119
General prmciples of measurement system Autoand cross-correlograms and the power spectral density function are the basis of the measurement system described in this paper. The relationships between crosscorrelation, auto-correlation and power spectral densities and the measured characteristics of the flowing solid phase are outlined in Table 1. Flow velocity From Table 1 column 1 it can be seen that slurry flow velocity is obtainable from the cross-correlogram of the time-varying signals obtained from upstream and down-stream locations in the flow_ If, in eqn. (2), x(t) is the ‘up-stream signal’ and y(t) is the ‘downstream signal’, then the cross-correlogram, R,,(r), will exhibit a peak value when r, the time displacement, is equal to the transit time of the slurry between the two locations from which the signals are derived_ Thus, flow velocity is equal to the disknce between the up-stream and downstream locations divided by the transit time_ Particle size Once the slurry flow velocity has been determined (see Table 1 column 2), esaminatton of the form of the power spectral density G, (fl may be used to determine a relationship between the changes in signal frequency content and the mean size of the particulate phase _
Concentration Table 1 column 3 shows that knowledge of particle size enables the auto-correlogram R, T then r = 0 to be related to the slurry concentration because R,,(O) is a measure of total signal power. This is shown by eqn (3) where, when T = 0, R,,(O)
=
-_
/
G,if)df
The derivation of signals from a flowing solid-liquid system and the subsequent analysis and application to particle size and concentration measurements are discussed under’E_sperimental:
EXPERIhIENTAL Hydrauirc rrg All experimental work was carried out on the circuit rig shown didgrammatically in Fig1. The vertical test line was a 2.5 cm id. perspes pipe mounted vertically_ The return line delivered the various sand-water concentra+xd slurries back to a main 182 litre capacity tank. The slurry was circulated by means of a monopump (Monopump Ltd., London, EClR OHE) which delivered a maximum flowrate of 210 1 mm-‘. The velocity of flow was controlled by a Saunders valve in the by-pass line. Flow velocity was initially calculated from the
TABLE 1 Inter-relationshlps analysis ROW
of slurry characteristics
Slurry -physical Velocity
and manifestations
characteristics
Particle size
Cbncentratlon
x
x
1
jiiJ
2
v
3
x
L/
Ckllumll
1
2
El
9
I4 3
0 Denotes parameter used for slurry characterisation. Y Dependent on measured parameter. x Independent of measured parameter_
in terms of data pre-
Parameters measured
Cros-correlntlon Changes in transit time Rx, (~1 Changes in signal frequency content 9=(f) Auto-correlation Changes in signal power R,(O)
330
Fig.
1
Schematic
dmgram
of experimental
rig.
mass of water flowing in a known period of time, but was subsequently calculated, after c-Jibration, fiorn the time delay obtained from cross-correlation of the down and up-stream electrical signals. Solids in the slurry were continuously agitated by the turbulent return of the slurry to the storage tank
Cs, 61Irzstrumerzt system A block diagram of the newly system is shown in Fig. 2_ Detection
HeNe lasers. These lasers were mounted on a circular optical bench and produce monochromatic, polarised coherent beams of approximately 100 pm diameter through the flowing system. Scattered light from the flowing solid particles was collected at rightangles to the beams and focused via two individual lens systems onto a single hybrid photodetector_ The hybrid photodetector was obtained from Centronic Ltd. The separation of the two laser beams normal to flow was either 2 or 5 mm. A simple lens system focuses the scattered light from particles passing through the central sensing zone onto the hybrid photodetector. The non-scattered laser light was collected by a blacken light trap. The dimensions of the central sensing zone are described by the focusing power of the lens - depth of field and the dimension of the coherent laser_ Figure 3 shows the e!ectrical srgnak obtained from a photodetector measuring scattered laser light when a particle of sand mean size 330 pm (Fig_ 3a) and 512 pm (Fig 3b) respectively passed along a vertical pipe. Measurements of the range of frequencies in these signals, if frequencies were solely dependent upon srze, can be used to evaluate the srze of particles The width of the auto-correlation function derived from a photodetector signal at R,,(T) equal to zero is also proportional to particle size_
developed I= v4
sub-system
The source elements of the detection subsystem consrsted of two Spectra Physics 5 mW
I‘1 V
Fig.
2_ Block
diagram
of measunzment
system_
I.4
L
L
l33ms,t7!
L
Fig 3(a)_ Sgnals from particle of size 268 - 393
photodetector pm.
for
szmd
Fig_ 3(b)_ Signals particle of size 452
photodetector pm_
for
sand
from - 572
Data analysis sub-system The random electrical output, o(t), from the hybrid photodetector is the additive signal comprising the scattered light from two laser beams: u(t) =x(t)
+ y(t)
On auto-correlation by a Hewlett-Packard Correlator 3721A this becomes R,,.(T)
= &x(r)
+ R,.(r)
+ R,,(r)
+ R,,(r)
where R,, (7) and Ryy(~) are the auto-correlograms of the signals from x(t) and y(t + 7) summed which measure both concentration and particle size. R,, is the cross-correlogram of x(t) and y(t + T) which evaluates the movement of particles between positions _x and y in an upward, X to Y, direction_ The function R,,(r) is the cross-correlogram due to particles moving in a downward, Y to X, direction which is taken to be negligible_ Figure 4 shows a typical auto-correlogram of the :t(t) output signal from the hybrid detector_ Section I is the auto-correlogram of R,,(T) and R=“(T) and section II the crosscorrelogram of R,, _ The autocorrelogram can be transformed in the manner of eqn_ (3) by a Hewlett-
Packard
Spectrum
Display
(3720A)
to give
the power spectral density of the flowing slurry_ The power spectrum by Fourier transformation of R,,,,(r) can be used to estimate from the frequencies bandwidth the mean particle size of the flowing solid. In addition, the breadth, W, of the auto-correlogram or the normalised auto-correlogram R,, (5) when R”“(T) is zero, can also be used to give an estimation of particle size.
Fig. 4. Typical auto-correlogrxn from the hybrid photodetector.
of the signed, u(l),
RESULTS
AND
DISCUSSION
Velocity measurement of slurry flow Combmed cross- and auto-correlograms of the additive electrical signals from the hybrid photodetector were obtained from the Hewlett-Packard Correlator (3721A) for various concentrations of 170 (160 - lS6 pm), 330 (268 - 393 pm) and 510 (452 - 572 pm) mean particle size sand in the range 1.0 X lo-“ to 1.0% wv/w over the velocity range The transit time, deter0.5 - 3.0 m set-l. mined from Section II of Fig_ -1, gives the cross-correlation R,, (7) of the signal u(t) which, together with the separation distance between the two laser beams, was used to calculate the velocity of slurry flow (see Fig_ 7, transit time r1 )_ The calculated crosscorrelation flow velocity is in good agreement with the independent mass method of velocity measurement and is independent of concentration and particle size (Table 1 row 1). Particle size from and barzdwidth
In a turbulent particles
can,
by
and small eddies
normalised
flow inertia,
auto-correlo,gram
system
small
solid
follow
both
large
in a turbulent flowing system_ Large solid particles, because of the increase in inertia, can, however, only follow large eddies. The range of frequencies in a turbulent flowing slurry is greater when the system contains small particles than when large particles are present_ High frequency lines of the power spectrum indicate the presence of small particles folIowing small eddies whilst low frequency lines represent small and large particles following large eddies_ The auto-correlogram computed by the Hewlett-Packard Correlator (3721X) from the additive electrical signals from the hybnd photodetector can be transformed by the Wiener-Khinchine algorithm. Figure 5 shows the power spectra display (PSD) of three different distributions of sand flowing at a velocity of 3 0 m 5-l _ From each individual spectrum an arbitrary value of the power spectra can be chosen - in this case 50% of the power - to give a unique bandwidth for each size distribution_ Thus, bandwidth B1, B2 and Ba represents the range of frequencies measured in the flowing
222
f\ 3
\
2-E
_313fl
=2
L3
-r‘;
+
Fig_ 5. Power spectra of three different butions
size distri-
of sand_
systems containing particle size distributions 111the range 600 - 1000 pm, 452 - 572 urn and 268 - 393 pm respectively. The frequency bandwidth determined by the wiener-Khinchine algorithm is not, however, solely dependent upon the size or size distribution of the flowing solid but is also dependent upon the velocity of flow. Figure 6 shows that the power spectra bandwidth, B. when sand of particle size distribution 268 393 pm at a concentration of 0.1% w/w flows at various velocities m the range 1-O 3-O m set, is a linear function of velocity_
Pig_ 6. Variation velocity_
of power
spectrum
width
Fig. 7_ Non-naked auto-correlation hybrid photodetector signal.
R,(r)
of the
ment of the width of the auto-correlogram at zero R,,(r) can also give an estimation of particle size. The magnitude of W is, however, also a function of velocity (Fig. 8). It is possible, however, horn the auto-correlogram of the additive photodetector signal, u(t) (Fig. 4), to determine the velocity of flow from the transit time and to evaluate the contribution velocity made to the power spectra of the flowing system and thus modify the total range of system frequencies to determine the magnitude of the particle size within the flowing system (Table 1 row 2)
with 0
Because the auto-correlograrn is also a Fourier transformation of the power spectra, part of the auto-correlogram R,,(O) section I may be used to give an alternative estimate of particle size. Figure 7 shows the normalised autocorrelogram of the hybrid signals from a different particle size distribution_ R”“(T) has been normalised so that comparison can be easily made, at one velocity, between the magnitude, W, of the auto-correlogram for different particle size distributions. This method of bandwidth measurement, although similar to, is not identical to the power spectra bandwidth measurement_ The bandwidth from the power spectra is related to the reciprocal time of the auto-correlogram when R”,(T) is equivalent to zero_ Thus, measure-
5
Kl
15 20
2s
30
35
UK&
Fig. 8. Variation of the width, R,(T) with velocity
WY,of the normalised
Concentration from R,,(O) amplitude The magnitude of the auto-correlogram R,,(r) at zero time shift R,,(O) derived from the hybrid photodetector signal is independent of the frequency content of the signaI Figure 9 shows the variation of R,,(O) with concentration at two different particle size distributions_ R,,(O) is independent of velocity and solely dependent on the mean particle size of the flowing slurry.
223
h
the amplitude of the auto-correlogram is affected by particle size_ Particle size of the flowing solid phase can be derived either from the width of the normal&d autocorrelogram at zero &(r) or from the of frequencies_ The power spectra frequency bandwidth either from the hybrid auto-correlogram or power spectra, although independent of concentration, is dependent on velocity_ Evaluation of the velocity from transit tune and subsequent modification of the bandwidth of the auto-correlogram can be used to give a measurement of the mean particle size of a solid in a flowing slurry _
ACKNOWLEDGEMENTS
The authors (N G.S.-W. and G-J-L.) wish to express their gratitude to the Science Research Council for fmancial support which rendered this investigation possible_ Fig
9. Variation
of RLII(0) with concentration.
CONCLUSION
Interrogation of the scattered laser hght from solids in a sand-water slurry collected at right-angles to the laser beam by a single photodetector has shown that auto-correlation of the hybrid signal produced a correlogram which contained information on the velocity of flow, and the concentration and particle size of the solid phase. Velocity measurement is independent of both particle size and concentration (Table 1). Solid concentration, although independent of velocity, is dependent on the size of the solids because
REFERENCES 1 0. A_ Asbjermen. Automatic Control nnd its Instrumentation in Particulate Solid Processes, Bergen, No-y, 23 - 23 August 197% 2 R. Davies, _4m. Lab.. Dee_ 1973 and JanJFeb. 1974, pp_ li - 33.73 - 86,4i - 55 3 N. G. Stanley-Wood, Control Instrum.. 6 (19i4) 42 - 47; 7 (1975) 30 - 35. 4 K_ T. Lee. Ph. D_ Thesis, Univ. of Bradford, 1972_ 5 M S Beck, K. T. Lee and N. G. Stanley-Wood. Powder l-echnol.. 6 (1973) 85 - 90. 6 G. LIeweIlyn and N. G. Stanley-Wood, In-Stream Monitoring of Concentration and Particle Characteristics. 8th IMEKO Congr., Moscow, 21 27 May 1979.
Technology,
Elsewer
Sequoia
29 (1981) S-A.,
Lauanne
217 - 223 -Printed
31i in The
Netherlands
On-Stream Particle Size, Concentration Correlation of Scattered Laser Light? N. G_ STANLEY-WOOD*,
G_ J_ LLEWELLYN**
Poslgraduale Schoois of Studies in Powder Bradford. IV_ Yorks. 807 IDP (Gt Brrtain) (Received
November
and
and Velocity
by Auto-
Measurements
A. TAYLOR+*
Tcchnolog>
* and Control
Enginccrrng**
Unirersity
of
Bradford
26.1979)
long
SUMMARY
been
instrument
With the increase IR automatic control of powder processes there is now a need for onstream or real time instrumentation to treasure the size and solid concentration of partrcles in slurries_ On-stream ueloclty, particle size and concentration have been obtained by the interrogatlon of sand-water slurries by two 5 mW HeNe laser beams_ The scattered laser light, from concentrated slurries in the range 1.0 X IO-” - l-090 w/u) flourmg at uelocltles between 0.5 - 3.0 m set-’ in a 2.5 cm diam. uerticalpipe, is transduced byaphotodetector into random fluctuating electrical signals. The rrld:vrdual signak are auto-correlated and the power spectra computed to determine the particle size range and concentration of the suspended particles while the velocity of flow is determined from cross-correlation of the signals obtained from the axudly separated lasers The change in particle concentration and size jointly affect the shape of both the autocorrelogram and the power spectral density of the photodiode signnl. By improued methods of detection, instrumentation implementation and data analysis, the velocrty, particle size and concentration in a flowing suspension can be separately evaluated. INTROD’JCTION
The onstream measurement size and concentration in flowmg
of particle slurries has
*Presented at the 2nd European Symposium on Particle Characterisation, Part&cl Technologie, Nuremberg, September 1979_
reasons
recognised design
for these
as a ‘difficult’ and
area
development_
difficulties
are manifold
III
The but
some of the problems have been outlined by Asbj0msen [l] : (a) lack of understanding of the physical characteristics of slurries, their properties and classification; (b) lack of definition in measurement parameters; (c) the difficult and involved nature of onstream real time measurements; (d) the demanding conditions under which the instrument has to operate_ In most industrial slurries or liquid-solid mixtures, naturally occurring disturbances such as local spatial and temporal variations m composition, density or turbulence - the tagging element e_xist within a flowing suspension_ Detection of these spatial and temporal variations of solid phase by optical or electrical transducers together with subsequent interrogation and analysis of the transducer signals by cross- or auto-correlation can be used to measure the parameters of size, concentration and sohd or flow velocity in a flowing system 12, 3]_ The ‘tagging element’ used in the present system of two-phase flow is the scattered laser light from the solid phase. By designing an instrument that employs cross- and/or auto-correlation techniques as its measurement principle, an acceptable solution has been achieved to some of the problems encountered in on-stream and instream measurements(a) On-stream - the instrument works m real time_ It is also suitable for interfacing with micro-processor or other computer control ;
218
(b) In-stream - no sampling of the slurry stream is required, and the range of solid concentration and size of particles can be extended by suitable dilution; (c) Robustness and ease of maintenance the basic transducer system of laser light and photodetectors is suitable for development into a rugged modular construction suitable for industrial plants. The laser requires a reasonable power input and can be made to normal safety standards_ (d) Wide range of particle sizes - the system is adaptable to measure particle sizes in the range 100 pm - lOOO+ pm subdivided into three or four size ranges. In this work, laser light scattered by solid particles flowing m a vertical 2.5 cm diam. perspex pipe has been collected onto a photodetector positioned at 90” to the beam and the resultant electrical signals auto-correlated and the power spectra computed to determine the relationships between particle size, concentration and velocity of the flowmg solid phase_
PRINCIPLES Data analysis Prior to a description of the measurement system, a brief r&urn6 of the data analysis techniques of correlation and power spectral densities is necessary [4] _
lmn
Rx,(?-) =
T-+-
R,,(T)
= ECx(t)
where E(f) represents the ensemble average of the function (fi of sample values_ Similarly, for two jointly stationary processes, x(t) and y(t), their cross-correlation is defmed by R,,(r)
= EEx(t)
Y(C + 711
These ensemble autoand correlograms can be alternatively mathematically as
crossexpressed
y(t + T)dT
(2)
Power spectral density In the frequency band between f and f + Af, the mean square value (Gz) of a sample time history record, x(t), can be obtained through the computation of the average of the output when x(t) is applied to a sharp cut-off, band-pass filter. Expressed mathematically,
G,ZCf.f
x2 (t, f, NWt
+Afl=
where x(t, f, An is that portion of x(t) in the frequency range from f to f + Af_ When the band-pass filter is very narrow (r-e_ A f is small), the power spectral density function, G,(f), can be defined such that lull
G,(f)
G:(f,f
=
+Afl
Af
nr-0
is stationary,
an important
of G,(fl is that it is related to R,,(T) Fourier transform: G,(f)
= 2
-_
= 4
x(t + T)]
T
5 x(t) c-8
if the stationary, random processes are ergondic R,,(r) and R,,(r) are respectively termed the time auto-correlogram and time crosscorrelogram
As x(t) Correlation For a single process, x(t), which can be considered to be stationary in the wide sense, the secondorder moment or auto-correlogram (R,,(r), where 7 represents time displacement) can be defined by
1
jR,,(~)e-‘~‘~~
I
R,,(r)
cos 2afrdr
-_ as R,,(T)
property by the
is an even function
(3)
of T.
The practical computation of auto- and crosscorrelograms and power spectral density functions can be achieved by a HewlettPackard (3721A) Correlator and a HewlettPackard Spectrum Display (3720A) instrument.
119
General prmciples of measurement system Autoand cross-correlograms and the power spectral density function are the basis of the measurement system described in this paper. The relationships between crosscorrelation, auto-correlation and power spectral densities and the measured characteristics of the flowing solid phase are outlined in Table 1. Flow velocity From Table 1 column 1 it can be seen that slurry flow velocity is obtainable from the cross-correlogram of the time-varying signals obtained from upstream and down-stream locations in the flow_ If, in eqn. (2), x(t) is the ‘up-stream signal’ and y(t) is the ‘downstream signal’, then the cross-correlogram, R,,(r), will exhibit a peak value when r, the time displacement, is equal to the transit time of the slurry between the two locations from which the signals are derived_ Thus, flow velocity is equal to the disknce between the up-stream and downstream locations divided by the transit time_ Particle size Once the slurry flow velocity has been determined (see Table 1 column 2), esaminatton of the form of the power spectral density G, (fl may be used to determine a relationship between the changes in signal frequency content and the mean size of the particulate phase _
Concentration Table 1 column 3 shows that knowledge of particle size enables the auto-correlogram R, T then r = 0 to be related to the slurry concentration because R,,(O) is a measure of total signal power. This is shown by eqn (3) where, when T = 0, R,,(O)
=
-_
/
G,if)df
The derivation of signals from a flowing solid-liquid system and the subsequent analysis and application to particle size and concentration measurements are discussed under’E_sperimental:
EXPERIhIENTAL Hydrauirc rrg All experimental work was carried out on the circuit rig shown didgrammatically in Fig1. The vertical test line was a 2.5 cm id. perspes pipe mounted vertically_ The return line delivered the various sand-water concentra+xd slurries back to a main 182 litre capacity tank. The slurry was circulated by means of a monopump (Monopump Ltd., London, EClR OHE) which delivered a maximum flowrate of 210 1 mm-‘. The velocity of flow was controlled by a Saunders valve in the by-pass line. Flow velocity was initially calculated from the
TABLE 1 Inter-relationshlps analysis ROW
of slurry characteristics
Slurry -physical Velocity
and manifestations
characteristics
Particle size
Cbncentratlon
x
x
1
jiiJ
2
v
3
x
L/
Ckllumll
1
2
El
9
I4 3
0 Denotes parameter used for slurry characterisation. Y Dependent on measured parameter. x Independent of measured parameter_
in terms of data pre-
Parameters measured
Cros-correlntlon Changes in transit time Rx, (~1 Changes in signal frequency content 9=(f) Auto-correlation Changes in signal power R,(O)
330
Fig.
1
Schematic
dmgram
of experimental
rig.
mass of water flowing in a known period of time, but was subsequently calculated, after c-Jibration, fiorn the time delay obtained from cross-correlation of the down and up-stream electrical signals. Solids in the slurry were continuously agitated by the turbulent return of the slurry to the storage tank
Cs, 61Irzstrumerzt system A block diagram of the newly system is shown in Fig. 2_ Detection
HeNe lasers. These lasers were mounted on a circular optical bench and produce monochromatic, polarised coherent beams of approximately 100 pm diameter through the flowing system. Scattered light from the flowing solid particles was collected at rightangles to the beams and focused via two individual lens systems onto a single hybrid photodetector_ The hybrid photodetector was obtained from Centronic Ltd. The separation of the two laser beams normal to flow was either 2 or 5 mm. A simple lens system focuses the scattered light from particles passing through the central sensing zone onto the hybrid photodetector. The non-scattered laser light was collected by a blacken light trap. The dimensions of the central sensing zone are described by the focusing power of the lens - depth of field and the dimension of the coherent laser_ Figure 3 shows the e!ectrical srgnak obtained from a photodetector measuring scattered laser light when a particle of sand mean size 330 pm (Fig_ 3a) and 512 pm (Fig 3b) respectively passed along a vertical pipe. Measurements of the range of frequencies in these signals, if frequencies were solely dependent upon srze, can be used to evaluate the srze of particles The width of the auto-correlation function derived from a photodetector signal at R,,(T) equal to zero is also proportional to particle size_
developed I= v4
sub-system
The source elements of the detection subsystem consrsted of two Spectra Physics 5 mW
I‘1 V
Fig.
2_ Block
diagram
of measunzment
system_
I.4
L
L
l33ms,t7!
L
Fig 3(a)_ Sgnals from particle of size 268 - 393
photodetector pm.
for
szmd
Fig_ 3(b)_ Signals particle of size 452
photodetector pm_
for
sand
from - 572
Data analysis sub-system The random electrical output, o(t), from the hybrid photodetector is the additive signal comprising the scattered light from two laser beams: u(t) =x(t)
+ y(t)
On auto-correlation by a Hewlett-Packard Correlator 3721A this becomes R,,.(T)
= &x(r)
+ R,.(r)
+ R,,(r)
+ R,,(r)
where R,, (7) and Ryy(~) are the auto-correlograms of the signals from x(t) and y(t + 7) summed which measure both concentration and particle size. R,, is the cross-correlogram of x(t) and y(t + T) which evaluates the movement of particles between positions _x and y in an upward, X to Y, direction_ The function R,,(r) is the cross-correlogram due to particles moving in a downward, Y to X, direction which is taken to be negligible_ Figure 4 shows a typical auto-correlogram of the :t(t) output signal from the hybrid detector_ Section I is the auto-correlogram of R,,(T) and R=“(T) and section II the crosscorrelogram of R,, _ The autocorrelogram can be transformed in the manner of eqn_ (3) by a Hewlett-
Packard
Spectrum
Display
(3720A)
to give
the power spectral density of the flowing slurry_ The power spectrum by Fourier transformation of R,,,,(r) can be used to estimate from the frequencies bandwidth the mean particle size of the flowing solid. In addition, the breadth, W, of the auto-correlogram or the normalised auto-correlogram R,, (5) when R”“(T) is zero, can also be used to give an estimation of particle size.
Fig. 4. Typical auto-correlogrxn from the hybrid photodetector.
of the signed, u(l),
RESULTS
AND
DISCUSSION
Velocity measurement of slurry flow Combmed cross- and auto-correlograms of the additive electrical signals from the hybrid photodetector were obtained from the Hewlett-Packard Correlator (3721A) for various concentrations of 170 (160 - lS6 pm), 330 (268 - 393 pm) and 510 (452 - 572 pm) mean particle size sand in the range 1.0 X lo-“ to 1.0% wv/w over the velocity range The transit time, deter0.5 - 3.0 m set-l. mined from Section II of Fig_ -1, gives the cross-correlation R,, (7) of the signal u(t) which, together with the separation distance between the two laser beams, was used to calculate the velocity of slurry flow (see Fig_ 7, transit time r1 )_ The calculated crosscorrelation flow velocity is in good agreement with the independent mass method of velocity measurement and is independent of concentration and particle size (Table 1 row 1). Particle size from and barzdwidth
In a turbulent particles
can,
by
and small eddies
normalised
flow inertia,
auto-correlo,gram
system
small
solid
follow
both
large
in a turbulent flowing system_ Large solid particles, because of the increase in inertia, can, however, only follow large eddies. The range of frequencies in a turbulent flowing slurry is greater when the system contains small particles than when large particles are present_ High frequency lines of the power spectrum indicate the presence of small particles folIowing small eddies whilst low frequency lines represent small and large particles following large eddies_ The auto-correlogram computed by the Hewlett-Packard Correlator (3721X) from the additive electrical signals from the hybnd photodetector can be transformed by the Wiener-Khinchine algorithm. Figure 5 shows the power spectra display (PSD) of three different distributions of sand flowing at a velocity of 3 0 m 5-l _ From each individual spectrum an arbitrary value of the power spectra can be chosen - in this case 50% of the power - to give a unique bandwidth for each size distribution_ Thus, bandwidth B1, B2 and Ba represents the range of frequencies measured in the flowing
222
f\ 3
\
2-E
_313fl
=2
L3
-r‘;
+
Fig_ 5. Power spectra of three different butions
size distri-
of sand_
systems containing particle size distributions 111the range 600 - 1000 pm, 452 - 572 urn and 268 - 393 pm respectively. The frequency bandwidth determined by the wiener-Khinchine algorithm is not, however, solely dependent upon the size or size distribution of the flowing solid but is also dependent upon the velocity of flow. Figure 6 shows that the power spectra bandwidth, B. when sand of particle size distribution 268 393 pm at a concentration of 0.1% w/w flows at various velocities m the range 1-O 3-O m set, is a linear function of velocity_
Pig_ 6. Variation velocity_
of power
spectrum
width
Fig. 7_ Non-naked auto-correlation hybrid photodetector signal.
R,(r)
of the
ment of the width of the auto-correlogram at zero R,,(r) can also give an estimation of particle size. The magnitude of W is, however, also a function of velocity (Fig. 8). It is possible, however, horn the auto-correlogram of the additive photodetector signal, u(t) (Fig. 4), to determine the velocity of flow from the transit time and to evaluate the contribution velocity made to the power spectra of the flowing system and thus modify the total range of system frequencies to determine the magnitude of the particle size within the flowing system (Table 1 row 2)
with 0
Because the auto-correlograrn is also a Fourier transformation of the power spectra, part of the auto-correlogram R,,(O) section I may be used to give an alternative estimate of particle size. Figure 7 shows the normalised autocorrelogram of the hybrid signals from a different particle size distribution_ R”“(T) has been normalised so that comparison can be easily made, at one velocity, between the magnitude, W, of the auto-correlogram for different particle size distributions. This method of bandwidth measurement, although similar to, is not identical to the power spectra bandwidth measurement_ The bandwidth from the power spectra is related to the reciprocal time of the auto-correlogram when R”,(T) is equivalent to zero_ Thus, measure-
5
Kl
15 20
2s
30
35
UK&
Fig. 8. Variation of the width, R,(T) with velocity
WY,of the normalised
Concentration from R,,(O) amplitude The magnitude of the auto-correlogram R,,(r) at zero time shift R,,(O) derived from the hybrid photodetector signal is independent of the frequency content of the signaI Figure 9 shows the variation of R,,(O) with concentration at two different particle size distributions_ R,,(O) is independent of velocity and solely dependent on the mean particle size of the flowing slurry.
223
h
the amplitude of the auto-correlogram is affected by particle size_ Particle size of the flowing solid phase can be derived either from the width of the normal&d autocorrelogram at zero &(r) or from the of frequencies_ The power spectra frequency bandwidth either from the hybrid auto-correlogram or power spectra, although independent of concentration, is dependent on velocity_ Evaluation of the velocity from transit tune and subsequent modification of the bandwidth of the auto-correlogram can be used to give a measurement of the mean particle size of a solid in a flowing slurry _
ACKNOWLEDGEMENTS
The authors (N G.S.-W. and G-J-L.) wish to express their gratitude to the Science Research Council for fmancial support which rendered this investigation possible_ Fig
9. Variation
of RLII(0) with concentration.
CONCLUSION
Interrogation of the scattered laser hght from solids in a sand-water slurry collected at right-angles to the laser beam by a single photodetector has shown that auto-correlation of the hybrid signal produced a correlogram which contained information on the velocity of flow, and the concentration and particle size of the solid phase. Velocity measurement is independent of both particle size and concentration (Table 1). Solid concentration, although independent of velocity, is dependent on the size of the solids because
REFERENCES 1 0. A_ Asbjermen. Automatic Control nnd its Instrumentation in Particulate Solid Processes, Bergen, No-y, 23 - 23 August 197% 2 R. Davies, _4m. Lab.. Dee_ 1973 and JanJFeb. 1974, pp_ li - 33.73 - 86,4i - 55 3 N. G. Stanley-Wood, Control Instrum.. 6 (19i4) 42 - 47; 7 (1975) 30 - 35. 4 K_ T. Lee. Ph. D_ Thesis, Univ. of Bradford, 1972_ 5 M S Beck, K. T. Lee and N. G. Stanley-Wood. Powder l-echnol.. 6 (1973) 85 - 90. 6 G. LIeweIlyn and N. G. Stanley-Wood, In-Stream Monitoring of Concentration and Particle Characteristics. 8th IMEKO Congr., Moscow, 21 27 May 1979.